id stringlengths 6 8 | alias stringlengths 24 50 | problem stringlengths 24 5.03k | answer int64 -16,384 80.2B | graph stringlengths 0 6.44k | domain stringclasses 4
values | secondary_domain stringclasses 4
values | goal stringclasses 4
values | evaluator_id stringclasses 1
value | root_lemma stringclasses 89
values | lemma_paths listlengths 0 5 | recipe_id stringlengths 0 6 | seed_template_id stringclasses 96
values | ending_id stringclasses 13
values | olympiad_level int64 2 9 | num_spawns int64 0 3 ⌀ | lemma_set listlengths 1 7 ⌀ | num_lemmas int64 1 7 ⌀ | generation_time float64 0 43.9 | created_at stringlengths 27 27 | verification dict | problem_hash stringlengths 6 6 | parent_id stringlengths 0 6 | variant stringclasses 3
values | license stringclasses 1
value | llm_solvers listlengths 1 13 ⌀ | solution_status int64 0 2 ⌀ | lemma_applicability listlengths 0 12 | irt_difficulty dict |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
ff049c | nt_num_divisors_compute_v1_397696148_85 | Let $ n $ be the largest prime number such that $ 2 \leq n \leq 8 $. Compute the number of positive divisors of $ n $. | 2 | graphs = [
Graph(
let={
"_n": Const(8),
"n": MaxOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(2)), Leq(Var("n"), Ref("_n")), IsPrime(Var("n"))))),
"result": NumDivisors(n=Ref("n")),
},
goal=Ref("result"),
)
] | NT | null | COMPUTE | sympy | MAX_PRIME_BELOW | [
"MAX_PRIME_BELOW"
] | dc3ad3 | nt_num_divisors_compute_v1 | null | 2 | 0 | [
"MAX_PRIME_BELOW"
] | 1 | 0.002 | 2026-02-08T11:17:04.266481Z | {
"verified": true,
"answer": 2,
"timestamp": "2026-02-08T11:17:04.268511Z"
} | 3cadc0 | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 88,
"completion_tokens": 206
},
"timestamp": "2026-02-15T21:10:40.130Z",
"answer": 2
},
{
"id": 11,
"m... | 2 | [
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
}
] | {
"lo": -10,
"mid": -7.71,
"hi": -5.43
} | ||
c55068 | comb_sum_binomial_row_v1_865884756_2722 | Let $n = 14$. Define $c = \sum_{k=1}^{95} k$. Let $a = 2^n$ and $b = c - a$. Compute the remainder when $b$ is divided by 99768. | 87,944 | graphs = [
Graph(
let={
"_n": Const(99768),
"n": Const(14),
"result": Pow(Const(2), Ref("n")),
"_c": Summation(var="k", start=Const(1), end=Const(95), expr=Var("k")),
"Q": Mod(value=Sub(Ref("_c"), Ref("result")), modulus=Ref("_n")),
},
... | NT | null | SUM | sympy | SUM_ARITHMETIC | [
"SUM_ARITHMETIC"
] | 5c63b0 | comb_sum_binomial_row_v1 | negation_mod | 2 | 0 | [
"SUM_ARITHMETIC"
] | 1 | 0.002 | 2026-02-08T16:53:49.370689Z | {
"verified": true,
"answer": 87944,
"timestamp": "2026-02-08T16:53:49.372457Z"
} | 98076a | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 113,
"completion_tokens": 366
},
"timestamp": "2026-02-16T07:57:57.151Z",
"answer": 4556
},
{
"id": 11,... | 1 | [
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "SUM_ARITHMETIC",
"status": "ok"
},
{
"lemma": "V3",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
}
] | {
"lo": -8.26,
"mid": -5.01,
"hi": -1.76
} | ||
869909 | comb_count_derangements_v1_153355830_1673 | Let $n$ be the number of nonnegative integers $j$ such that $0 \leq j \leq 20482$ and $\binom{20482}{j}$ is odd. Define $r$ to be the number of derangements of $n$ elements. Compute the remainder when $44121 \cdot r$ is divided by $66167$. | 55,163 | graphs = [
Graph(
let={
"_n": Const(2),
"n": CountOverSet(set=SolutionsSet(var=Var("j"), condition=And(Geq(Var("j"), Const(0)), Leq(Var("j"), Const(20482)), Eq(Mod(value=Binom(n=Const(20482), k=Var("j")), modulus=Ref("_n")), Const(1))), domain='nonnegative_integers')),
"r... | COMB | null | COUNT | sympy | V8 | [
"V8"
] | 86348e | comb_count_derangements_v1 | null | 5 | 0 | [
"V8"
] | 1 | 0.002 | 2026-02-08T06:33:13.933855Z | {
"verified": true,
"answer": 55163,
"timestamp": "2026-02-08T06:33:13.935547Z"
} | 96c6ae | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 188,
"completion_tokens": 3723
},
"timestamp": "2026-02-24T06:31:38.846Z",
"answer": 55163
},
{
"... | 1 | [
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "V8",
"status": "o... | {
"lo": -0.06,
"mid": 2.89,
"hi": 5.27
} | ||
73bbb9 | modular_min_linear_v1_124444284_1813 | Let $a$ be the sum of the roots of the equation $x^2 - 689x - 12002 = 0$. Let $m = 38398$ and $b = 20391$. Determine the value of $x$ such that $1 \leq x \leq m$ and $$a \cdot x \equiv b \pmod{m},$$ and $x$ is as small as possible. | 19,145 | graphs = [
Graph(
let={
"a": SumOverSet(set=SolutionsSet(var=Var("x"), condition=Eq(Sum(Pow(Var("x"), Const(2)), Mul(Const(-689), Var("x")), Const(-12002)), Const(0)))),
"b": Const(20391),
"m": Const(38398),
"result": MinOverSet(set=SolutionsSet(var=Var("x"), ... | NT | null | EXTREMUM | sympy | VIETA_SUM | [
"VIETA_SUM"
] | b33a7a | modular_min_linear_v1 | null | 5 | 0 | [
"VIETA_SUM"
] | 1 | 1.55 | 2026-02-08T04:09:38.986230Z | {
"verified": true,
"answer": 19145,
"timestamp": "2026-02-08T04:09:40.536644Z"
} | 62a9b3 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 203,
"completion_tokens": 2259
},
"timestamp": "2026-02-10T15:34:02.125Z",
"answer": 19145
},
{
... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "VIETA_SUM",
"status": "ok"
... | {
"lo": -3.42,
"mid": 1.86,
"hi": 7.55
} | ||
f6da79 | comb_sum_binomial_row_v1_1742523217_2904 | Let $c = 144$ and $m = 9$. Let $s$ be the minimum value of $x + y$ over all pairs of positive integers $(x, y)$ such that $xy = 144$. Define $\alpha$ to be the number of positive integers $n \le s$ such that $9$ divides the $n$-th Fibonacci number. Define $\beta$ to be the number of integers $t$ with $5 \le t \le 17$ t... | 2,048 | graphs = [
Graph(
let={
"_c": Const(144),
"_m": Const(9),
"_n": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(a... | NT | null | SUM | sympy | B3 | [
"B3/COUNT_FIB_DIVISIBLE/LIN_FORM"
] | 953448 | comb_sum_binomial_row_v1 | null | 6 | 0 | [
"B3",
"COUNT_FIB_DIVISIBLE",
"LIN_FORM"
] | 3 | 0.004 | 2026-02-08T05:27:16.143631Z | {
"verified": true,
"answer": 2048,
"timestamp": "2026-02-08T05:27:16.147199Z"
} | 308134 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 199,
"completion_tokens": 1217
},
"timestamp": "2026-02-12T09:01:09.175Z",
"answer": 2048
},
{... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "ok_later"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok_later"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status":... | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
a70739 | nt_sum_totient_over_divisors_v1_655260480_1495 | Let $n$ be the number of positive integers $n_1$ such that $1 \leq n_1 \leq 21895$ and $5$ divides the $n_1$-th Fibonacci number. Define $\text{result} = \sum_{d \mid n} \phi(d)$, where $\phi$ is Euler's totient function. Let $Q$ be the remainder when $25669 \cdot \text{result}$ is divided by $61536$. Compute $Q$. | 39,815 | graphs = [
Graph(
let={
"_n": Const(61536),
"n": CountOverSet(set=SolutionsSet(var=Var("n1"), condition=And(Geq(Var("n1"), Const(1)), Leq(Var("n1"), Const(21895)), Divides(divisor=Const(5), dividend=Fibonacci(arg=Var(name='n1')))))),
"result": SumOverDivisors(n=Ref(name='... | NT | null | COMPUTE | sympy | COUNT_FIB_DIVISIBLE | [
"COUNT_FIB_DIVISIBLE"
] | 66de3c | nt_sum_totient_over_divisors_v1 | null | 6 | 0 | [
"COUNT_FIB_DIVISIBLE"
] | 1 | 0.003 | 2026-02-08T16:10:02.512560Z | {
"verified": true,
"answer": 39815,
"timestamp": "2026-02-08T16:10:02.515791Z"
} | 9599d8 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 150,
"completion_tokens": 2359
},
"timestamp": "2026-02-16T22:45:32.427Z",
"answer": 39815
},
... | 1 | [
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "ok"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "V1",
"status": "no"
},
{
"lemma": "V3",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
739f71 | nt_sum_totient_over_divisors_v1_784195855_4970 | Let $x_1$ and $x_2$ be the roots of the equation $x^2 - 2095x + 197604 = 0$. Let $n$ be the sum of these roots. Compute the sum of $\phi(d)$ over all positive divisors $d$ of $n$, where $\phi$ denotes Euler's totient function. Find the remainder when $33262$ times this sum is divided by $56873$. | 14,465 | graphs = [
Graph(
let={
"_n": Const(2),
"n": SumOverSet(set=SolutionsSet(var=Var("x"), condition=Eq(Sum(Pow(Var("x"), Ref("_n")), Mul(Const(-2095), Var("x")), Const(197604)), Const(0)))),
"result": SumOverDivisors(n=Ref(name='n'), var='d', expr=EulerPhi(n=Var(name='d'))),... | NT | null | COMPUTE | sympy | VIETA_SUM | [
"VIETA_SUM"
] | b33a7a | nt_sum_totient_over_divisors_v1 | null | 5 | 0 | [
"VIETA_SUM"
] | 1 | 0.006 | 2026-02-08T07:32:32.539471Z | {
"verified": true,
"answer": 14465,
"timestamp": "2026-02-08T07:32:32.545913Z"
} | 8c029b | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 140,
"completion_tokens": 1221
},
"timestamp": "2026-02-13T11:13:47.167Z",
"answer": 14465
},
... | 1 | [
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "V3",
"status": "no"
},
{
"lemma": "VIETA_SUM",
"status": "ok"
}
] | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
86f78c | nt_num_divisors_compute_v1_2051736721_497 | Let $n$ be the maximum value of $xy$ over all pairs of positive integers $(x, y)$ such that $x + y = 30$. Let $d(n)$ denote the number of positive divisors of $n$. Compute the remainder when $12787 \cdot d(n)$ is divided by $56587$. | 1,909 | graphs = [
Graph(
let={
"_n": Const(30),
"n": MaxOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(Sum(Var("x"), Var("y")), Ref("_n")))), expr=Mul(Var("x"), Var("y")))),
... | NT | null | COMPUTE | sympy | B1 | [
"B1"
] | 5b950e | nt_num_divisors_compute_v1 | null | 5 | 0 | [
"B1"
] | 1 | 0.005 | 2026-02-08T15:28:16.538774Z | {
"verified": true,
"answer": 1909,
"timestamp": "2026-02-08T15:28:16.543677Z"
} | 72680a | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 114,
"completion_tokens": 388
},
"timestamp": "2026-02-16T06:41:48.569Z",
"answer": 1909
},
{
... | 1 | [
{
"lemma": "B1",
"status": "ok"
},
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
6d5c30 | sequence_fibonacci_compute_v1_2051736721_2078 | Let $N = 50488$ and $C = 55423$. Consider the set of all ordered pairs $(x, y)$ of positive integers such that $xy = 121$. Let $n$ be the minimum value of $x + y$ over all such pairs. Let $F_n$ denote the $n$th Fibonacci number, where $F_1 = F_2 = 1$ and $F_{k} = F_{k-1} + F_{k-2}$ for $k \geq 3$. Compute the remainder... | 9,057 | graphs = [
Graph(
let={
"_n": Const(50488),
"n": MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(Mul(Var("x"), Var("y")), Const(121)))), expr=Sum(Var("x"), Var("y")))),... | NT | null | COMPUTE | sympy | B3 | [
"B3"
] | 0cd20d | sequence_fibonacci_compute_v1 | null | 4 | 0 | [
"B3"
] | 1 | 0.002 | 2026-02-08T16:26:15.844944Z | {
"verified": true,
"answer": 9057,
"timestamp": "2026-02-08T16:26:15.847254Z"
} | d912b7 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 177,
"completion_tokens": 1187
},
"timestamp": "2026-02-17T04:16:25.164Z",
"answer": 9057
},
{... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
45e95c | antilemma_sum_equals_v1_677425708_4279 | Let $N$ be the number of ordered pairs $(a, b)$ such that $1 \le a \le 8$ and $1 \le b \le 8$. Compute the number of ordered pairs $(i, j)$ of positive integers with $1 \le i \le 64$ and $1 \le j \le 64$ such that $i + j = N$. | 63 | graphs = [
Graph(
let={
"_n": CountOverSet(set=CartesianProduct(left=IntegerRange(start=Const(1), end=Const(8)), right=IntegerRange(start=Const(1), end=Const(8)))),
"x": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("i"), Var("j")]), condition=Eq(Sum(Var("i"), Var("j")), Ref(... | COMB | GEOM | COMPUTE | sympy | COUNT_CARTESIAN | [
"COUNT_CARTESIAN/COUNT_SUM_EQUALS",
"COUNT_SUM_EQUALS"
] | 8bee9e | antilemma_sum_equals_v1 | null | 3 | 0 | [
"COUNT_CARTESIAN",
"COUNT_SUM_EQUALS"
] | 2 | 0.146 | 2026-02-08T06:31:39.879086Z | {
"verified": true,
"answer": 63,
"timestamp": "2026-02-08T06:31:40.024732Z"
} | ff9bab | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 193,
"completion_tokens": 517
},
"timestamp": "2026-02-24T06:27:55.282Z",
"answer": 63
},
{
"id":... | 2 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "ok"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "ok"
},
{
"lemma": "V8",
... | {
"lo": -9.23,
"mid": -6.18,
"hi": -4.06
} | ||
198e49 | comb_count_surjections_v1_1439011603_1244 | Let $n$ be the number of integers $t$ with $18 \le t \le 25$ such that there exist positive integers $a$ and $b$ satisfying $1 \le a \le 3$, $1 \le b \le 2$, and $t = 2a + 3b + 13$. Let $k = 6$. Compute $k!$ multiplied by the Stirling number of the second kind $S(n, k)$. | 720 | graphs = [
Graph(
let={
"n": CountOverSet(set=SolutionsSet(var=Var("t"), condition=Exists(var=Var(name='a'), condition=Exists(var=Var(name='b'), condition=And(Geq(left=Var(name='a'), right=Const(value=1)), Leq(left=Var(name='a'), right=Const(value=3)), Geq(left=Var(name='b'), right=Const(value=1... | COMB | null | COUNT | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | comb_count_surjections_v1 | null | 4 | 0 | [
"LIN_FORM"
] | 1 | 0.004 | 2026-02-08T15:59:35.173947Z | {
"verified": true,
"answer": 720,
"timestamp": "2026-02-08T15:59:35.177876Z"
} | dd2c3c | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 211,
"completion_tokens": 721
},
"timestamp": "2026-02-24T19:26:43.072Z",
"answer": 720
},
{
"id... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "V8",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
... | {
"lo": -5.65,
"mid": -3.17,
"hi": -0.81
} | ||
264728 | geo_visible_lattice_v1_124444284_7408 | Let $n = 120$. A visible lattice point $(x, y)$ is a point with integer coordinates such that $1 \leq x, y \leq n$ and $\gcd(x, y) = 1$. Let $V$ be the number of visible lattice points for this $n$. Find the remainder when $29 - V$ is divided by $76020$. | 67,278 | graphs = [
Graph(
let={
"n": Const(120),
"result": VisibleLatticePoints(n=Ref(name='n')),
"_c": Const(29),
"Q": Mod(value=Sub(Ref("_c"), Ref("result")), modulus=Const(76020)),
},
goal=Ref("Q"),
)
] | GEOM | null | COUNT | sympy | [] | geo_visible_lattice_v1 | null | 4 | 0 | null | null | 0.309 | 2026-02-08T09:06:39.734616Z | {
"verified": true,
"answer": 67278,
"timestamp": "2026-02-08T09:06:40.043128Z"
} | 11f18a | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 191,
"completion_tokens": 3627
},
"timestamp": "2026-02-24T10:30:55.970Z",
"answer": 67278
},
{
"... | 1 | [] | {
"lo": 1.15,
"mid": 4.18,
"hi": 6.61
} | ||||
ac1307_n | modular_sum_quadratic_residues_v1_601307018_4217 | A security system uses a code based on the largest divisor $p$ of $313591$ that does not exceed $\sqrt{313591}$. Once $p$ is found, the access key is generated as $\frac{p(p - 1)}{4}$. What is the access key? | 77,423 | NT | null | SUM | sympy | B3_CLOSEST | [
"B3_CLOSEST"
] | 25e610 | modular_sum_quadratic_residues_v1 | null | 3 | null | [
"B3_CLOSEST"
] | 1 | 0.004 | 2026-03-10T04:50:38.076706Z | null | fdab5d | ac1307 | narrative | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 172,
"completion_tokens": 6010
},
"timestamp": "2026-03-29T18:27:13.727Z",
"answer": 77423
},
{
"... | 1 | [
{
"lemma": "B3_CLOSEST",
"status": "ok"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "VAL_SUM_EQ",
"status": "no"
}
] | {
"lo": -5.36,
"mid": 0.27,
"hi": 5.45
} | |
ab3fbb | comb_factorial_compute_v1_1218484723_1216 | Find the number of ordered pairs $(a, b)$ of positive integers with $1 \leq a \leq b \leq 30$ such that $2a^2 - 4ab + 2b^2 = 1058$. Let $n$ be this number, and compute $n!$. | 5,040 | graphs = [
Graph(
let={
"_n": Const(2),
"n": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("a"), Var("b")]), condition=And(Geq(Var("a"), Const(1)), Leq(Var("a"), Const(30)), Geq(Var("b"), Const(1)), Leq(Var("b"), Const(30)), Leq(Var("a"), Var("b")), Eq(Sum(Mul(Const(-4), Var(... | COMB | null | COMPUTE | sympy | QF_PSD_ORBIT | [
"QF_PSD_ORBIT"
] | 1d37f3 | comb_factorial_compute_v1 | null | 4 | 0 | [
"QF_PSD_ORBIT"
] | 1 | 0.002 | 2026-02-25T02:59:38.290300Z | {
"verified": true,
"answer": 5040,
"timestamp": "2026-02-25T02:59:38.292446Z"
} | 65bb37 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 177,
"completion_tokens": 585
},
"timestamp": "2026-03-10T06:03:26.668Z",
"answer": 5040
},
{
"id... | 2 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "QF_PSD_ORBIT",
"status": "ok"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
}
] | {
"lo": -10,
"mid": -6.41,
"hi": -2.82
} | ||
902182 | diophantine_fbi2_count_v1_809748730_1084 | Let $k = 420$. Determine the number of positive integers $d$ such that $3 \leq d \leq 101$, $d$ divides $k$, and the quotient $\frac{k}{d}$ is between $6$ and $104$, inclusive. Multiply this count by $16339$, and find the remainder when the result is divided by $56145$. | 20,505 | graphs = [
Graph(
let={
"_n": Const(104),
"k": Const(420),
"result": CountOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Const(3)), Leq(Var("d"), Const(101)), Divides(divisor=Var("d"), dividend=Ref("k")), Geq(Div(Ref("k"), Var("d")), Const(6)), Leq(Div... | NT | null | COUNT | sympy | MIN_PRIME_FACTOR | [
"MIN_PRIME_FACTOR"
] | bc3776 | diophantine_fbi2_count_v1 | null | 4 | 0 | [
"MIN_PRIME_FACTOR"
] | 1 | 0.008 | 2026-02-08T12:02:26.667516Z | {
"verified": true,
"answer": 20505,
"timestamp": "2026-02-08T12:02:26.675507Z"
} | d51de3 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 124,
"completion_tokens": 1415
},
"timestamp": "2026-02-14T22:46:46.468Z",
"answer": 20505
},
... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "MIN_PRIME_FACTOR",
"status": "ok"
... | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
23846d | nt_count_divisors_in_range_v1_48377204_492 | Let $s$ be the minimum value of $x + y$ over all pairs of positive integers $(x, y)$ such that $xy = 12100$. Let $a$ be the number of ordered pairs of positive odd integers $(x_1, x_2)$ such that $x_1 + x_2 = s$. Let $n = 332640$ and $b = 7401$. Find the number of positive divisors $d$ of $n$ such that $a \le d \le b$. | 113 | graphs = [
Graph(
let={
"_n": Const(12100),
"n": Const(332640),
"a": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x1"), Var("x2")]), condition=And(IsPositive(arg=Var(name='x1')), IsPositive(arg=Var(name='x2')), IsOdd(arg=Var(name='x1')), IsOdd(arg=Var(name='x2')... | NT | null | COUNT | sympy | L3C | [
"B3/COMB1"
] | e26f7e | nt_count_divisors_in_range_v1 | null | 6 | 0 | [
"B3",
"COMB1",
"L3C"
] | 3 | 1.227 | 2026-02-08T15:30:54.826743Z | {
"verified": true,
"answer": 113,
"timestamp": "2026-02-08T15:30:56.054189Z"
} | 361cfb | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 157,
"completion_tokens": 2842
},
"timestamp": "2026-02-16T07:34:20.895Z",
"answer": 113
},
{
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "COMB1",
"status": "ok_later"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
be9561 | nt_count_intersection_v1_784195855_7672 | Let $N = 100000$. Define $a = 3$. Let $b$ be the number of positive integers $n$ such that $1 \leq n \leq 59$ and $\gcd(n, 6) = 1$. Determine the number of positive integers $n$ such that $1 \leq n \leq N$, $a$ divides $n$, and $\gcd(n, b) = 1$. | 13,334 | graphs = [
Graph(
let={
"_n": Const(59),
"N": Const(100000),
"a": Const(3),
"b": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Ref("_n")), Eq(GCD(a=Var("n"), b=Const(6)), Const(1))))),
"result": Co... | NT | null | COUNT | sympy | C4 | [
"C4"
] | 08d162 | nt_count_intersection_v1 | null | 5 | 0 | [
"C4"
] | 1 | 5.714 | 2026-02-08T09:26:32.776683Z | {
"verified": true,
"answer": 13334,
"timestamp": "2026-02-08T09:26:38.491143Z"
} | 1e3558 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 137,
"completion_tokens": 1234
},
"timestamp": "2026-02-14T04:18:14.817Z",
"answer": 13334
},
... | 1 | [
{
"lemma": "C4",
"status": "ok"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
}
] | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
418100 | antilemma_sum_equals_v1_1125832087_2088 | Let $m = 196$. Let $n$ be the number of ordered pairs $(x_1, x_2)$ of positive odd integers such that $x_1 + x_2 = m$. Let $x$ be the number of ordered pairs $(i, j)$ of integers with $1 \leq i \leq 98$ and $1 \leq j \leq 98$ such that $i + j = n$. Determine the value of $k$, the smallest positive integer such that the... | 60 | graphs = [
Graph(
let={
"_m": Const(196),
"_n": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x1"), Var("x2")]), condition=And(IsPositive(arg=Var(name='x1')), IsPositive(arg=Var(name='x2')), IsOdd(arg=Var(name='x1')), IsOdd(arg=Var(name='x2')), Eq(Sum(Var("x1"), Var("x2")), ... | COMB | GEOM | COMPUTE | sympy | LIN_FORM | [
"COMB1/COUNT_SUM_EQUALS",
"COUNT_SUM_EQUALS"
] | 3e1adf | antilemma_sum_equals_v1 | null | 6 | 0 | [
"COMB1",
"COUNT_SUM_EQUALS",
"LIN_FORM"
] | 3 | 0.04 | 2026-02-08T04:19:58.492838Z | {
"verified": true,
"answer": 60,
"timestamp": "2026-02-08T04:19:58.533172Z"
} | 6dd0b0 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 237,
"completion_tokens": 4190
},
"timestamp": "2026-02-24T00:05:09.566Z",
"answer": 60
},
{
"id"... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COMB1",
"status": "ok"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "ok"
},
{
"lemma": "V8",
"statu... | {
"lo": -2.46,
"mid": 0.47,
"hi": 3.59
} | ||
cfd22a | comb_sum_binomial_row_v1_458359167_1508 | Let $n = 11$ and $r = 2^n$. Let $p$ be the largest prime number less than or equal to $12$. Compute the Bell number $B_{r \bmod p}$. | 2 | graphs = [
Graph(
let={
"n": Const(11),
"result": Pow(Const(2), Ref("n")),
"Q": Bell(Mod(value=Abs(arg=Ref(name='result')), modulus=MaxOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(2)), Leq(Var("n"), Const(12)), IsPrime(Var("n"))))))),
}... | NT | COMB | SUM | sympy | MIN_PRIME_FACTOR | [
"MAX_PRIME_BELOW"
] | 88ea9c | comb_sum_binomial_row_v1 | bell_mod | 5 | 0 | [
"MAX_PRIME_BELOW",
"MIN_PRIME_FACTOR"
] | 2 | 0.018 | 2026-02-08T04:40:45.372834Z | {
"verified": true,
"answer": 2,
"timestamp": "2026-02-08T04:40:45.391113Z"
} | dc3d74 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 157,
"completion_tokens": 268
},
"timestamp": "2026-02-11T21:51:10.290Z",
"answer": 2
},
{
"id":... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no... | {
"lo": -9.14,
"mid": -6.05,
"hi": -3.73
} | ||
178fdc | antilemma_sum_equals_v1_168721529_448 | Let $c=170$. Let $m$ be the number of ordered pairs $(x_1,x_2)$ of positive odd integers such that
$$x_1+x_2=c.$$
Let $n$ be the number of ordered pairs $(i,j)$ of integers with $1\le i\le83$ and $1\le j\le83$ such that
$$i+j=m.$$
Let $x$ be the number of ordered pairs $(i,j)$ of integers with $1\le i\le80$ and $1\le... | 25 | graphs = [
Graph(
let={
"_c": Const(170),
"_m": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x1"), Var("x2")]), condition=And(IsPositive(arg=Var(name='x1')), IsPositive(arg=Var(name='x2')), IsOdd(arg=Var(name='x1')), IsOdd(arg=Var(name='x2')), Eq(Sum(Var("x1"), Var("x2")), ... | COMB | GEOM | COMPUTE | sympy | COUNT_SUM_EQUALS | [
"COUNT_SUM_EQUALS/LIN_FORM/COUNT_SUM_EQUALS",
"COMB1/LIN_FORM/COUNT_SUM_EQUALS",
"LIN_FORM",
"COUNT_SUM_EQUALS"
] | 29778c | antilemma_sum_equals_v1 | negation_mod | 6 | 0 | [
"COMB1",
"COUNT_SUM_EQUALS",
"LIN_FORM"
] | 3 | 0.014 | 2026-02-08T13:03:39.330394Z | {
"verified": true,
"answer": 25,
"timestamp": "2026-02-08T13:03:39.344022Z"
} | b086d9 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 323,
"completion_tokens": 6343
},
"timestamp": "2026-02-24T17:08:11.824Z",
"answer": 25
},
{
"id"... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COMB1",
"status": "ok"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "ok"
},
{
"lemma": "LIN_FORM",
"sta... | {
"lo": 1.36,
"mid": 4.2,
"hi": 6.62
} | ||
1bac01 | antilemma_sum_equals_v1_1978505735_3499 | Let $m = 31$. Define $a$ to be the number of ordered pairs $(i, j)$ of positive integers such that $i + j = m$, $1 \le i \le 29$, and $1 \le j \le 30$. Define $b$ to be the number of ordered pairs $(i_1, j_1)$ of positive integers such that $i_1 + j_1 = a$, $1 \le i_1 \le 28$, and $1 \le j_1 \le 29$. Let $C$ be the tot... | 7,972 | graphs = [
Graph(
let={
"_m": Const(31),
"_n": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("i"), Var("j")]), condition=Eq(Sum(Var("i"), Var("j")), Ref("_m")), domain=CartesianProduct(left=IntegerRange(start=Const(1), end=Const(29)), right=IntegerRange(start=Const(1), end=Co... | COMB | GEOM | COMPUTE | sympy | COUNT_SUM_EQUALS | [
"COUNT_SUM_EQUALS/COUNT_CARTESIAN/COUNT_SUM_EQUALS",
"COUNT_CARTESIAN",
"COUNT_SUM_EQUALS"
] | c49753 | antilemma_sum_equals_v1 | negation_mod | 3 | 0 | [
"COUNT_CARTESIAN",
"COUNT_SUM_EQUALS"
] | 2 | 0.025 | 2026-02-08T17:41:36.631241Z | {
"verified": true,
"answer": 7972,
"timestamp": "2026-02-08T17:41:36.656330Z"
} | e20cf0 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 209,
"completion_tokens": 1286
},
"timestamp": "2026-02-18T06:13:13.468Z",
"answer": 7972
},
{... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "ok"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "ok"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8",
"status": "n... | {
"lo": -8,
"mid": -4.75,
"hi": -2.28
} | ||
8c4c5b | antilemma_k3_v1_1915831931_1685 | Let $x$ be the sum of $\phi(d)$ over all positive divisors $d$ of $91149$. Compute the remainder when $$x + \phi(|x| + 1) + \tau(|x| + 1)$$ is divided by $72828$. | 54,773 | graphs = [
Graph(
let={
"x": SumOverDivisors(n=Const(value=91149), var='d', expr=EulerPhi(n=Var(name='d'))),
"Q": Mod(value=Sum(Ref("x"), EulerPhi(n=Sum(Abs(arg=Ref(name='x')), Pow(Const(44), Const(0)))), NumDivisors(n=Sum(Abs(arg=Ref(name='x')), Const(1)))), modulus=Const(72828)),
... | NT | COMB | COMPUTE | sympy | IDENTITY_POW_ZERO | [
"IDENTITY_POW_ZERO",
"K3"
] | feee28 | antilemma_k3_v1 | null | 4 | 0 | [
"IDENTITY_POW_ZERO",
"K3"
] | 2 | 0.002 | 2026-02-08T16:22:13.923862Z | {
"verified": true,
"answer": 54773,
"timestamp": "2026-02-08T16:22:13.925837Z"
} | c226e2 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 105,
"completion_tokens": 1313
},
"timestamp": "2026-02-17T02:09:16.484Z",
"answer": 54773
},
... | 1 | [
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "IDENTITY_POW_ZERO",
"status": "ok"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K3",
"status": "ok"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "V5",
"status": "no"... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
b657b4 | nt_count_intersection_v1_798873815_534 | Let $N$ be the minimum value of $x + y$ over all pairs of positive integers $(x, y)$ such that $xy = 25000000$. Let $a$ be the largest prime number at most 12. Compute the number of positive integers $n \leq N$ that are divisible by $a$ and relatively prime to 10. | 364 | graphs = [
Graph(
let={
"_n": Const(12),
"N": MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(Mul(Var("x"), Var("y")), Const(25000000)))), expr=Sum(Var("x"), Var("y")))... | NT | null | COUNT | sympy | MAX_PRIME_BELOW | [
"MAX_PRIME_BELOW",
"B3"
] | 78ed98 | nt_count_intersection_v1 | null | 7 | 0 | [
"B3",
"MAX_PRIME_BELOW"
] | 2 | 2.437 | 2026-02-08T02:40:39.326194Z | {
"verified": true,
"answer": 364,
"timestamp": "2026-02-08T02:40:41.762932Z"
} | 0be8a7 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 190,
"completion_tokens": 2051
},
"timestamp": "2026-02-08T19:42:40.717Z",
"answer": 364
},
{
"id... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
},
{
"lemma":... | {
"lo": -2.81,
"mid": -0.78,
"hi": 1.23
} | ||
403eb0 | modular_sum_quadratic_residues_v1_865884756_4858 | Let $p$ be the largest prime number less than or equal to $349$. Define $r = \frac{p(p-1)}{4}$. Compute the remainder when $91872 \cdot r$ is divided by $79697$. | 34,839 | graphs = [
Graph(
let={
"_n": Const(79697),
"p": MaxOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(2)), Leq(Var("n"), Const(349)), IsPrime(Var("n"))))),
"result": Div(Mul(Ref("p"), Sub(Ref("p"), Const(1))), Const(4)),
"Q": Mod(value=M... | NT | null | SUM | sympy | MAX_PRIME_BELOW | [
"MAX_PRIME_BELOW"
] | dc3ad3 | modular_sum_quadratic_residues_v1 | null | 3 | 0 | [
"MAX_PRIME_BELOW"
] | 1 | 0.003 | 2026-02-08T18:13:07.946198Z | {
"verified": true,
"answer": 34839,
"timestamp": "2026-02-08T18:13:07.948773Z"
} | 52bfe1 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 95,
"completion_tokens": 2823
},
"timestamp": "2026-02-18T14:54:06.394Z",
"answer": 34839
},
{... | 1 | [
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
2ddc87 | algebra_poly_eval_v1_1439011603_712 | Let $y = 8$. Let $T$ be the set of all integers $t$ such that $36 \leq t \leq 1821$ and there exist positive integers $a$ and $b$ with $1 \leq a \leq 6$, $1 \leq b \leq 113$, and $t = 21a + 15b$. Compute the value of
$$
\frac{36y^6 - 84y^5 - 248y^4 + 516y^3 - 1092y^2 + 760y - 528}{|T|}.
$$ | 10,260 | graphs = [
Graph(
let={
"_n": Const(3),
"y": Const(8),
"result": Div(Sum(Mul(Const(36), Pow(Ref("y"), Const(6))), Mul(Const(-84), Pow(Ref("y"), Const(5))), Mul(Const(-248), Pow(Ref("y"), Const(4))), Mul(Const(516), Pow(Ref("y"), Ref("_n"))), Mul(Const(-1092), Pow(Ref("y")... | NT | null | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | algebra_poly_eval_v1 | null | 5 | 0 | [
"LIN_FORM"
] | 1 | 0.005 | 2026-02-08T15:41:00.356239Z | {
"verified": true,
"answer": 10260,
"timestamp": "2026-02-08T15:41:00.361049Z"
} | 87f029 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 174,
"completion_tokens": 7511
},
"timestamp": "2026-02-16T11:08:56.504Z",
"answer": 10260
},
... | 1 | [
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "V1",
"status": "no"... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
8a716a | geo_count_lattice_rect_v1_1915831931_1140 | Let $a = 128$ and $b = 253$. Define $R$ to be the set of all lattice points $(x, y)$ such that $0 \le x \le a$ and $0 \le y \le b$. Let $N$ be the number of points in $R$. Compute the remainder when $44121 \cdot N$ is divided by $53360$. | 39,566 | graphs = [
Graph(
let={
"a": Const(128),
"b": Const(253),
"result": LatticePointsRect(a=Ref(name='a'), b=Ref(name='b')),
"Q": Mod(value=Mul(Const(44121), Ref("result")), modulus=Const(53360)),
},
goal=Ref("Q"),
)
] | GEOM | null | COUNT | sympy | [] | geo_count_lattice_rect_v1 | null | 4 | 0 | null | null | 0.003 | 2026-02-08T15:54:40.471028Z | {
"verified": true,
"answer": 39566,
"timestamp": "2026-02-08T15:54:40.473576Z"
} | 61f254 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 194,
"completion_tokens": 2406
},
"timestamp": "2026-02-24T19:02:15.269Z",
"answer": 39566
},
{
... | 1 | [] | {
"lo": -2.4,
"mid": 1.57,
"hi": 5.75
} | ||||
e1ae85 | nt_max_prime_below_v1_458359167_4072 | Let $p$ be the largest prime number such that $2 \leq p \leq 41209$. Let $q$ be the largest prime number such that $2 \leq q \leq 208$. Compute the remainder when
$$
\left(p \bmod q\right) + 5003 \cdot \left(p \bmod 499\right)
$$
is divided by $94135$. | 13,840 | graphs = [
Graph(
let={
"_n": Const(2),
"upper": Const(41209),
"result": MaxOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Ref("_n")), Leq(Var("n"), Ref("upper")), IsPrime(Var("n"))))),
"_c": Const(5003),
"Q": Mod(value=Sum(Mod(... | NT | null | EXTREMUM | sympy | MAX_PRIME_BELOW | [
"MAX_PRIME_BELOW"
] | 08a653 | nt_max_prime_below_v1 | two_moduli | 4 | 0 | [
"MAX_PRIME_BELOW"
] | 1 | 0.951 | 2026-02-08T11:30:02.949096Z | {
"verified": true,
"answer": 13840,
"timestamp": "2026-02-08T11:30:03.900204Z"
} | 724b72 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 128,
"completion_tokens": 3235
},
"timestamp": "2026-02-14T15:27:24.334Z",
"answer": 13840
},
... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok"
... | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
599c0e | comb_sum_binomial_row_v1_1742523217_4980 | Let $s$ be the largest prime number between $2$ and $5$, inclusive. Define $n = \sum_{k=1}^{s} k$. Compute $2^n$. | 32,768 | graphs = [
Graph(
let={
"_n": Const(2),
"n": Summation(var="k", start=Const(1), end=MaxOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(2)), Leq(Var("n"), Const(5)), IsPrime(Var("n"))))), expr=Var("k")),
"result": Pow(Ref("_n"), Ref("n")),
... | NT | null | SUM | sympy | MAX_PRIME_BELOW | [
"MAX_PRIME_BELOW/SUM_ARITHMETIC"
] | 592103 | comb_sum_binomial_row_v1 | null | 3 | 0 | [
"MAX_PRIME_BELOW",
"SUM_ARITHMETIC"
] | 2 | 0.003 | 2026-02-08T10:41:59.527512Z | {
"verified": true,
"answer": 32768,
"timestamp": "2026-02-08T10:41:59.530229Z"
} | d275a4 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 86,
"completion_tokens": 318
},
"timestamp": "2026-02-14T08:23:35.821Z",
"answer": 32768
},
{
... | 1 | [
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
... | {
"lo": -6.96,
"mid": -4.56,
"hi": -1.46
} | ||
adb376 | nt_num_divisors_compute_v1_1742523217_748 | Let $n = 16$. Compute the number of positive divisors of $n$. Let $c$ be the number of integers $n$ with $1 \leq n \leq 4905$ such that $n \equiv \left\lfloor \frac{n}{2} \right\rfloor \pmod{11}$. Compute $c$ multiplied by the number of positive divisors of $16$. | 2,225 | graphs = [
Graph(
let={
"n": Const(16),
"result": NumDivisors(n=Ref("n")),
"_c": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Const(4905)), Congruent(a=Var(name='n'), b=Floor(arg=Div(left=Var(name='n'), right=Const(value... | NT | null | COMPUTE | sympy | L3C | [
"L3C"
] | 141fd9 | nt_num_divisors_compute_v1 | affine_mod | 5 | 0 | [
"L3C"
] | 1 | 0.002 | 2026-02-08T03:11:56.247433Z | {
"verified": true,
"answer": 2225,
"timestamp": "2026-02-08T03:11:56.249060Z"
} | e6bd42 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 201,
"completion_tokens": 1489
},
"timestamp": "2026-02-09T22:07:38.363Z",
"answer": 2225
},
{
"i... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "L3C",
"status": "ok"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "VAL_SUM_EQ",
"status": "no"
}
] | {
"lo": -3.46,
"mid": 1.03,
"hi": 5.49
} | ||
b3d026 | nt_min_phi_inverse_v1_717093673_725 | Let $S$ be the set of all ordered pairs $(i, j)$ of integers such that $1 \leq i \leq 50$, $1 \leq j \leq 51$, and $i + j = 51$. Let $k = 12$. Determine the value of the smallest positive integer $n$ such that $1 \leq n \leq |S|$ and $\phi(n) = k$. | 13 | graphs = [
Graph(
let={
"upper": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("i"), Var("j")]), condition=Eq(Sum(Var("i"), Var("j")), Const(51)), domain=CartesianProduct(left=IntegerRange(start=Const(1), end=Const(50)), right=IntegerRange(start=Const(1), end=Const(51))))),
"... | NT | null | EXTREMUM | sympy | EULER_TOTIENT_SUM | [
"COUNT_SUM_EQUALS"
] | 75ab0f | nt_min_phi_inverse_v1 | null | 5 | 0 | [
"COUNT_SUM_EQUALS",
"EULER_TOTIENT_SUM"
] | 2 | 0.117 | 2026-02-08T15:37:01.401619Z | {
"verified": true,
"answer": 13,
"timestamp": "2026-02-08T15:37:01.518983Z"
} | 0c282a | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 135,
"completion_tokens": 2560
},
"timestamp": "2026-02-16T10:39:10.352Z",
"answer": 13
},
{
... | 1 | [
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "ok"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL"... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
68b298 | nt_min_crt_v1_1520064083_9227 | Let $M=5$ and let $k$ be the number of integers $t$ such that $5\le t\le 15$ and there exist integers $a$ and $b$ with $1\le a\le 3$, $1\le b\le 3$, and
$$t=2a+3b.$$
Let $N=16512$ and let $m_0=2$.
Let $A$ be the number of nonnegative integers $j$ with $0\le j\le N$ such that
$$\binom{N}{j}\equiv 1\pmod{m_0}.$$
Let $... | 84 | graphs = [
Graph(
let={
"_m": Const(2),
"_n": Const(16512),
"m": Const(5),
"k": CountOverSet(set=SolutionsSet(var=Var("t"), condition=Exists(var=Var(name='a'), condition=Exists(var=Var(name='b'), condition=And(Geq(left=Var(name='a'), right=Const(value=1)), Leq... | NT | null | EXTREMUM | sympy | COUNT_COPRIME_GRID | [
"COUNT_COPRIME_GRID",
"LIN_FORM",
"V8"
] | ad8180 | nt_min_crt_v1 | null | 8 | 0 | [
"COUNT_COPRIME_GRID",
"LIN_FORM",
"V8"
] | 3 | 0.013 | 2026-02-08T10:38:00.525380Z | {
"verified": true,
"answer": 84,
"timestamp": "2026-02-08T10:38:00.538531Z"
} | 42725d | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 327,
"completion_tokens": 2240
},
"timestamp": "2026-02-14T07:57:13.946Z",
"answer": 84
},
{
... | 1 | [
{
"lemma": "COUNT_COPRIME_GRID",
"status": "ok"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
... | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
13a9b8 | comb_bell_compute_v1_1918700295_1683 | Let $P$ be the set of all pairs of positive integers $(x, y)$ such that $x + y = 6$. Let $n$ be the maximum value of $xy$ over all such pairs. Let $B_n$ denote the $n$th Bell number, which counts the number of partitions of a set of $n$ elements. Compute the remainder when $28901 \cdot B_n$ is divided by $61560$. | 1,767 | graphs = [
Graph(
let={
"_n": Const(28901),
"n": MaxOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(Sum(Var("x"), Var("y")), Const(6)))), expr=Mul(Var("x"), Var("y")))),
... | COMB | null | COMPUTE | sympy | B1 | [
"B1"
] | 5b950e | comb_bell_compute_v1 | null | 4 | 0 | [
"B1"
] | 1 | 0.001 | 2026-02-08T05:57:42.674020Z | {
"verified": true,
"answer": 1767,
"timestamp": "2026-02-08T05:57:42.674922Z"
} | 3418ec | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 204,
"completion_tokens": 2514
},
"timestamp": "2026-02-24T04:59:16.350Z",
"answer": 1767
},
{
"i... | 1 | [
{
"lemma": "B1",
"status": "ok"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
},
{
"lemma": "V8_SUM",
"stat... | {
"lo": -2.46,
"mid": 0.47,
"hi": 3.59
} | ||
cc37b8 | sequence_fibonacci_compute_v1_1742523217_4357 | Let $p$ and $q$ be positive integers such that $pq = 108$, $\gcd(p, q) = 1$, and $p < q$. Let $S$ be the set of all such integers $p$. Define $n = \sum_{k=|S|}^{6} k$. Compute the $n$-th Fibonacci number, where $F_1 = 1$, $F_2 = 1$, and $F_k = F_{k-1} + F_{k-2}$ for $k \geq 3$. | 10,946 | graphs = [
Graph(
let={
"_n": Const(6),
"n": Summation(var="k", start=EulerPhi(n=CountOverSet(set=SolutionsSet(var=Var("p"), condition=And(IsPositive(arg=Var(name='p')), Exists(var=Var(name='q'), condition=And(Eq(left=Mul(Var(name='p'), Var(name='q')), right=Const(value=108)), Eq(lef... | NT | null | COMPUTE | sympy | COPRIME_PAIRS | [
"COPRIME_PAIRS/ONE_PHI_2/SUM_ARITHMETIC"
] | 80113d | sequence_fibonacci_compute_v1 | null | 6 | 0 | [
"COPRIME_PAIRS",
"ONE_PHI_2",
"SUM_ARITHMETIC"
] | 3 | 0.002 | 2026-02-08T07:13:37.485322Z | {
"verified": true,
"answer": 10946,
"timestamp": "2026-02-08T07:13:37.487285Z"
} | 19ab21 | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 221,
"completion_tokens": 462
},
"timestamp": "2026-02-20T01:15:50.818Z",
"answer": 10946
}
] | 2 | [
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "ONE_PHI_2",
"status": "ok_later"
},
{
"lemma": "SUM_ARITHMETIC",
"status":... | {
"lo": -10,
"mid": -6.47,
"hi": -2.95
} | ||
7f0a0e | geo_count_lattice_rect_v1_2051736721_5040 | Let $a = 196$ and $b = 326$. Define $\text{result}$ to be the number of lattice points $(x, y)$ such that $0 \le x \le a$ and $0 \le y \le b$. Compute the remainder when $44121 \cdot \text{result}$ is divided by 71674. Answer with this remainder. | 69,903 | graphs = [
Graph(
let={
"a": Const(196),
"b": Const(326),
"result": LatticePointsRect(a=Ref(name='a'), b=Ref(name='b')),
"Q": Mod(value=Mul(Const(44121), Ref("result")), modulus=Const(71674)),
},
goal=Ref("Q"),
)
] | GEOM | null | COUNT | sympy | [] | geo_count_lattice_rect_v1 | null | 3 | 0 | null | null | 0.001 | 2026-02-08T18:21:06.675529Z | {
"verified": true,
"answer": 69903,
"timestamp": "2026-02-08T18:21:06.676499Z"
} | becdba | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 126,
"completion_tokens": 1979
},
"timestamp": "2026-02-18T16:19:13.752Z",
"answer": 69903
},
... | 1 | [] | {
"lo": -3.12,
"mid": 1.47,
"hi": 6.57
} | ||||
77971a | nt_sum_totient_over_divisors_v1_168721529_849 | Let $S$ be the set of all ordered pairs of positive integers $(x, y)$ such that $xy = 8191044$. Define $m$ to be the minimum value of $x + y$ as $(x, y)$ ranges over $S$. Let $d_1 = 1$ and define $s = \sum_{k \mid d_1} \mu(k)$, where $\mu$ denotes the M\"obius function. Let $n = m \cdot s \cdot s$. Compute $\sum_{d \mi... | 5,724 | graphs = [
Graph(
let={
"n2": Const(1),
"t": SumOverDivisors(n=Ref(name='n2'), var='d', expr=MoebiusMu(n=Var(name='d'))),
"n1": Const(1),
"s": SumOverDivisors(n=Ref(name='n1'), var='d', expr=MoebiusMu(n=Var(name='d'))),
"n": Mul(MinOverSet(set=MapO... | NT | null | COMPUTE | sympy | B3 | [
"B3/MOBIUS_SUM"
] | 6a6e01 | nt_sum_totient_over_divisors_v1 | null | 7 | 2 | [
"B3",
"MOBIUS_SUM"
] | 2 | 0.006 | 2026-02-08T13:19:16.456908Z | {
"verified": true,
"answer": 5724,
"timestamp": "2026-02-08T13:19:16.462665Z"
} | 96a7fd | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 249,
"completion_tokens": 1027
},
"timestamp": "2026-02-09T09:54:13.676Z",
"answer": 5724
},
{
"i... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "MOBIUS_SUM",
"status": "ok_later"
}... | {
"lo": -6.69,
"mid": -2.39,
"hi": 1.83
} | ||
3a573d | comb_catalan_compute_v1_971394319_1260 | Let $n$ be the number of elements in the Cartesian product of the sets $\{1, 2\}$ and $\{1, 2, 3, 4, 5\}$. Define the value of the $n$-th Catalan number as $\text{result}$. Let $c = 33489$. Compute $c - \text{result}$. | 16,693 | graphs = [
Graph(
let={
"n": CountOverSet(set=CartesianProduct(left=IntegerRange(start=Const(1), end=Const(2)), right=IntegerRange(start=Const(1), end=Const(5)))),
"result": Catalan(Ref("n")),
"_c": Const(33489),
"Q": Sub(Ref("_c"), Ref("result")),
},
... | COMB | null | COMPUTE | sympy | COUNT_CARTESIAN | [
"COUNT_CARTESIAN"
] | 409d7d | comb_catalan_compute_v1 | null | 2 | 0 | [
"COUNT_CARTESIAN"
] | 1 | 0.003 | 2026-02-08T13:34:03.138097Z | {
"verified": true,
"answer": 16693,
"timestamp": "2026-02-08T13:34:03.140623Z"
} | 08ad1b | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 191,
"completion_tokens": 471
},
"timestamp": "2026-02-24T18:39:06.368Z",
"answer": 16693
},
{
"i... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "ok"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
},
{
"lemma": "V8_SUM",
"statu... | {
"lo": -4.92,
"mid": -2.91,
"hi": -0.68
} | ||
5f4797 | antilemma_k2_v1_865884756_1815 | Let $c = 135$. Define $m$ to be the sum of $\phi(d)$ over all positive divisors $d$ of $c$. Let $n = 135$. Compute
$$
\sum_{k=1}^{n} \phi(k) \left\lfloor \frac{1}{k} \sum_{d_1 \mid m} \phi(d_1) \right\rfloor.
$$ | 9,180 | graphs = [
Graph(
let={
"_c": Const(135),
"_m": SumOverDivisors(n=Ref(name='_c'), var='d', expr=EulerPhi(n=Var(name='d'))),
"_n": Const(135),
"x": Summation(var="k", start=Const(1), end=Ref("_n"), expr=Mul(EulerPhi(n=Var("k")), Floor(Div(SumOverDivisors(n=Ref(... | NT | COMB | COMPUTE | sympy | K3 | [
"K3/K3/K2",
"K2"
] | d92398 | antilemma_k2_v1 | null | 7 | 0 | [
"K2",
"K3"
] | 2 | 0.002 | 2026-02-08T16:18:22.871564Z | {
"verified": true,
"answer": 9180,
"timestamp": "2026-02-08T16:18:22.873535Z"
} | 2b2c51 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 133,
"completion_tokens": 4235
},
"timestamp": "2026-02-17T01:49:02.806Z",
"answer": 9180
},
{... | 1 | [
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "K2",
"status": "ok"
},
{
"lemma": "K3",
"status": "ok"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
4569eb | antilemma_k3_v1_1874849503_558 | Let $x = \sum_{d \mid 39297} \phi(d)$, where the sum is over all positive divisors $d$ of $39297$, and $\phi$ denotes Euler's totient function. Let $N = |x| + 1$. Define $Q$ to be the sum of $x$, the number of positive divisors of $N$, and Euler's totient function evaluated at $N$. Find the value of $Q$. | 56,109 | graphs = [
Graph(
let={
"x": SumOverDivisors(n=Const(value=39297), var='d', expr=EulerPhi(n=Var(name='d'))),
"Q": Sum(Ref("x"), EulerPhi(n=Sum(Abs(arg=Ref(name='x')), Const(1))), NumDivisors(n=Sum(Abs(arg=Ref(name='x')), Const(1)))),
},
goal=Ref("Q"),
)
] | NT | COMB | COMPUTE | sympy | K13 | [
"IDENTITY_POW_ZERO",
"K3"
] | feee28 | antilemma_k3_v1 | null | 4 | 0 | [
"IDENTITY_POW_ZERO",
"K13",
"K3"
] | 3 | 0.005 | 2026-02-08T13:11:05.616378Z | {
"verified": true,
"answer": 56109,
"timestamp": "2026-02-08T13:11:05.621218Z"
} | b0cad2 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 208,
"completion_tokens": 4018
},
"timestamp": "2026-02-09T18:31:43.384Z",
"answer": 56109
},
{
"... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "IDENTITY_POW_ZERO",
"status": "ok"
},
{
"lemma": "K3",
"status": "ok"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "V8",
"status": "no"... | {
"lo": -5.15,
"mid": 0.12,
"hi": 6.12
} | ||
e0b091 | alg_poly4_min_v1_1419126231_467 | Let $T$ be the set of ordered pairs $(a_1, b_1)$ of positive integers with $1 \leq a_1, b_1 \leq 35$ such that $13a_1^2 - 2a_1b_1 + 2b_1^2 \leq 1377$. Let $m = |T|$. Find the minimum value of $$1887804a^4 - 7459128a^3b + 11188692a^2b^2 - 7459128ab^3 + 1864782b^4$$ over all positive integers $a, b$ with $1 \leq a \leq 2... | 23,022 | graphs = [
Graph(
let={
"_n": Const(3),
"result": MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("a"), Var("b")]), condition=And(Geq(Var("a"), Const(1)), Leq(Var("a"), Const(226)), Geq(Var("b"), Const(1)), Leq(Var("b"), CountOverSet(set=SolutionsSet(var=Tuple(elem... | ALG | null | COMPUTE | sympy | QF_PSD_COUNT_LEQ | [
"QF_PSD_COUNT_LEQ"
] | 009d0f | alg_poly4_min_v1 | null | 6 | 0 | [
"QF_PSD_COUNT_LEQ"
] | 1 | 0.129 | 2026-02-25T09:59:32.205528Z | {
"verified": true,
"answer": 23022,
"timestamp": "2026-02-25T09:59:32.334932Z"
} | 020950 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 275,
"completion_tokens": 16661
},
"timestamp": "2026-03-30T08:39:05.780Z",
"answer": 23022
},
{
... | 1 | [
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "QF_PSD_COUNT_LEQ",
"status": "ok"
}
] | {
"lo": -5.37,
"mid": 0.23,
"hi": 5.22
} | ||
3efbac | alg_poly_preperiod_count_v1_1218484723_7627 | Let $f(x) = 2x^5 - 2x^4 - 5x^2 + 4x - 5 \bmod 59$. For a non-negative integer $a$ with $0 \le a \le 72333$, define the sequence $N = f(a)$, $M = f(N)$, $R = f(M)$, $S = f(R)$, $T = f(S)$, $K = f(T)$. Find the number of such integers $a$ for which $K = M$, $R \ne M$, $S \ne M$, and $T \ne M$. | 6,130 | graphs = [
Graph(
let={
"p1": Mod(value=Sum(Mul(Const(2), Pow(Var("a"), Const(5))), Mul(Const(-2), Pow(Var("a"), Const(4))), Mul(Const(-5), Pow(Var("a"), Const(2))), Mul(Const(4), Var("a")), Const(-5)), modulus=Const(59)),
"p2": Mod(value=Sum(Mul(Const(2), Pow(Ref("p1"), Const(5))), ... | ALG | null | COUNT | sympy | POLY_ORBIT_COUNT | [
"POLY_ORBIT_COUNT"
] | 4ad965 | alg_poly_preperiod_count_v1 | null | 6 | null | [
"POLY_ORBIT_COUNT"
] | 1 | 0.443 | 2026-02-25T09:03:28.669902Z | {
"verified": true,
"answer": 6130,
"timestamp": "2026-02-25T09:03:29.113382Z"
} | 6d15da | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 246,
"completion_tokens": 27359
},
"timestamp": "2026-03-30T05:37:23.354Z",
"answer": 6130
},
{
"... | 1 | [
{
"lemma": "POLY_ORBIT_COUNT",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
}
] | {
"lo": 3.81,
"mid": 6.33,
"hi": 9.49
} | ||
10e99a | nt_count_divisible_v1_1978505735_5506 | Compute the number of positive integers $n$ such that $1 \leq n \leq 68121$ and $$n \equiv \sum_{k=0}^{8} (-1)^k \binom{8}{k} \pmod{11}.$$ Find the value of this count. | 6,192 | graphs = [
Graph(
let={
"upper": Const(68121),
"divisor": Const(11),
"result": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Ref("upper")), Eq(Mod(value=Var("n"), modulus=Ref("divisor")), Summation(var="k", start=Const(0)... | COMB | null | COUNT | sympy | BINOMIAL_ALTERNATING | [
"BINOMIAL_ALTERNATING"
] | c21569 | nt_count_divisible_v1 | null | 4 | 0 | [
"BINOMIAL_ALTERNATING"
] | 1 | 2.046 | 2026-02-08T19:02:19.196933Z | {
"verified": true,
"answer": 6192,
"timestamp": "2026-02-08T19:02:21.242724Z"
} | 93a499 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 108,
"completion_tokens": 3433
},
"timestamp": "2026-02-18T21:10:27.762Z",
"answer": 6192
},
{... | 1 | [
{
"lemma": "BINOMIAL_ALTERNATING",
"status": "ok"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
},
{
"lemma": "V8_SUM",
"stat... | {
"lo": -5.39,
"mid": -2.64,
"hi": 0.63
} | ||
b7514a | antilemma_sum_equals_v1_784195855_1176 | Let $x$ be the number of ordered pairs $(i, j)$ of integers such that $1 \leq i \leq 32$, $1 \leq j \leq 32$, and $i + j = 33$. Compute the remainder when $44121 \cdot x$ is divided by $76289$. | 38,670 | graphs = [
Graph(
let={
"_n": Const(33),
"x": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("i"), Var("j")]), condition=Eq(Sum(Var("i"), Var("j")), Ref("_n")), domain=CartesianProduct(left=IntegerRange(start=Const(1), end=Const(32)), right=IntegerRange(start=Const(1), end=Con... | COMB | GEOM | COMPUTE | sympy | COMB1 | [
"COUNT_SUM_EQUALS"
] | 75ab0f | antilemma_sum_equals_v1 | null | 2 | 0 | [
"COMB1",
"COUNT_SUM_EQUALS"
] | 2 | 0.02 | 2026-02-08T04:53:41.824433Z | {
"verified": true,
"answer": 38670,
"timestamp": "2026-02-08T04:53:41.844050Z"
} | 0f2b8b | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 181,
"completion_tokens": 880
},
"timestamp": "2026-02-11T22:28:03.380Z",
"answer": 38670
},
{
"i... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "ok"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
}
] | {
"lo": -4.92,
"mid": -2.9,
"hi": -0.7
} | ||
9a49cc | nt_count_intersection_v1_809748730_56 | Let $N = 100000$. Define $b$ to be the number of positive integers $p$ for which there exists a positive integer $q$ such that $p < q$, $\gcd(p, q) = 1$, and $pq = 16008300$. Compute the number of positive integers $n \leq N$ such that $3$ divides $n$ and $\gcd(n, b) = 1$. Find the remainder when this number is divided... | 16,667 | graphs = [
Graph(
let={
"N": Const(100000),
"a": Const(3),
"b": CountOverSet(set=SolutionsSet(var=Var("p"), condition=And(IsPositive(arg=Var(name='p')), Exists(var=Var(name='q'), condition=And(Eq(left=Mul(Var(name='p'), Var(name='q')), right=Const(value=16008300)), Eq(lef... | NT | null | COUNT | sympy | COPRIME_PAIRS | [
"COPRIME_PAIRS"
] | 2bb3aa | nt_count_intersection_v1 | null | 5 | 0 | [
"COPRIME_PAIRS"
] | 1 | 5.202 | 2026-02-08T11:18:34.122555Z | {
"verified": true,
"answer": 16667,
"timestamp": "2026-02-08T11:18:39.324823Z"
} | 3e602d | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 150,
"completion_tokens": 1783
},
"timestamp": "2026-02-14T11:40:30.908Z",
"answer": 16667
},
... | 1 | [
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
}
] | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
6a083a | nt_count_divisible_v1_655260480_5469 | Let $S$ be the set of all positive integers $n$ such that $1 \leq n \leq 88804$ and $n$ is divisible by $6$. Compute the number of elements in $S$. | 14,800 | graphs = [
Graph(
let={
"upper": Const(88804),
"divisor": Summation(var="k", start=Const(1), end=Const(3), expr=Var("k")),
"result": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Ref("upper")), Eq(Mod(value=Var("n"), modu... | NT | null | COUNT | sympy | SUM_ARITHMETIC | [
"SUM_ARITHMETIC"
] | eb34f0 | nt_count_divisible_v1 | null | 2 | 0 | [
"SUM_ARITHMETIC"
] | 1 | 2.75 | 2026-02-08T18:29:31.221235Z | {
"verified": true,
"answer": 14800,
"timestamp": "2026-02-08T18:29:33.971321Z"
} | 12cf1a | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 106,
"completion_tokens": 368
},
"timestamp": "2026-02-16T12:23:57.567Z",
"answer": 14800
},
{
"id": 11,
... | 2 | [
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "SUM_ARITHMETIC",
"status": "ok"
},
{
"lemma": "V8",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
}
] | {
"lo": -10,
"mid": -7.27,
"hi": -4.54
} | ||
6b3384 | algebra_quadratic_discriminant_v1_124444284_6181 | Let $a = 1$, $b = -1$, and $n = 2$. Let $S$ be the set of all positive integers $p$ for which there exists a positive integer $q$ such that $pq = 1800$, $\gcd(p, q) = 1$, and $p < q$. Compute $b^n - a \cdot |S| \cdot (-72)$. | 289 | graphs = [
Graph(
let={
"_n": Const(2),
"a": Const(1),
"b": Const(-1),
"c": Const(-72),
"result": Sub(Pow(Ref("b"), Ref("_n")), Mul(CountOverSet(set=SolutionsSet(var=Var("p"), condition=And(IsPositive(arg=Var(name='p')), Exists(var=Var(name='q'), c... | NT | null | COMPUTE | sympy | COPRIME_PAIRS | [
"COPRIME_PAIRS"
] | 2bb3aa | algebra_quadratic_discriminant_v1 | null | 4 | 0 | [
"COPRIME_PAIRS"
] | 1 | 0.003 | 2026-02-08T08:10:58.021871Z | {
"verified": true,
"answer": 289,
"timestamp": "2026-02-08T08:10:58.024614Z"
} | 460319 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 132,
"completion_tokens": 1602
},
"timestamp": "2026-02-13T15:33:09.259Z",
"answer": 289
},
{
... | 1 | [
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "V3",
"status": "no"
}
] | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
ba16a3 | antilemma_k3_v1_124444284_7585 | Compute the sum of $\phi(d)$ over all positive divisors $d$ of $74654$, where $\phi$ denotes Euler's totient function. | 74,654 | graphs = [
Graph(
let={
"x": SumOverDivisors(n=Const(value=74654), var='d', expr=EulerPhi(n=Var(name='d'))),
},
goal=Ref("x"),
)
] | NT | COMB | COMPUTE | sympy | K3 | [
"K3"
] | 54c41e | antilemma_k3_v1 | null | 3 | 0 | [
"K3"
] | 1 | 0.001 | 2026-02-08T09:11:48.144137Z | {
"verified": true,
"answer": 74654,
"timestamp": "2026-02-08T09:11:48.144733Z"
} | f80b85 | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 1,
"correct": {
"strict": false,
"boxed": false,
"relaxed": true
},
"usage": {
"prompt_tokens": 93,
"completion_tokens": 527
},
"timestamp": "2026-02-15T20:36:11.094Z",
"answer": 7201
},
{
"id": 11,
... | 1 | [
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K3",
"status": "ok"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
}
] | {
"lo": -6.96,
"mid": -4.56,
"hi": -1.46
} | ||
12c63f | modular_mod_compute_v1_153355830_790 | Let $a = 20$. Let $m$ be the largest prime number less than or equal to 2023. Compute the remainder when $a$ is divided by $m$. | 20 | graphs = [
Graph(
let={
"a": Const(20),
"m": MaxOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(2)), Leq(Var("n"), Const(2023)), IsPrime(Var("n"))))),
"result": Mod(value=Ref("a"), modulus=Ref("m")),
},
goal=Ref("result"),
)
] | NT | null | COMPUTE | sympy | MAX_PRIME_BELOW | [
"MAX_PRIME_BELOW"
] | dc3ad3 | modular_mod_compute_v1 | null | 2 | 0 | [
"MAX_PRIME_BELOW"
] | 1 | 0.001 | 2026-02-08T04:10:43.678615Z | {
"verified": true,
"answer": 20,
"timestamp": "2026-02-08T04:10:43.680066Z"
} | 70fb2a | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 148,
"completion_tokens": 663
},
"timestamp": "2026-02-10T15:39:46.304Z",
"answer": 20
},
{
"id"... | 1 | [
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
}
] | {
"lo": -9.14,
"mid": -6.05,
"hi": -3.73
} | ||
57aabf | alg_poly_orbit_hensel_v1_1419126231_1208 | Let $N = (a^2 + a + 590) \bmod 1849$ and $M = (N^2 + N + 590) \bmod 1849$. Find the number of non-negative integers $a$ with $0 \le a \le 525115$ such that $M = a$ and $N \ne a$. | 568 | graphs = [
Graph(
let={
"p1": Mod(value=Sum(Pow(Var("a"), Const(2)), Var("a"), Const(590)), modulus=Const(1849)),
"p2": Mod(value=Sum(Pow(Ref("p1"), Const(2)), Ref("p1"), Const(590)), modulus=Const(1849)),
"result": CountOverSet(set=SolutionsSet(var=Var("a"), condition=An... | ALG | null | COUNT | sympy | POLY_ORBIT_COUNT | [
"POLY_ORBIT_COUNT"
] | 4ad965 | alg_poly_orbit_hensel_v1 | null | 5 | null | [
"POLY_ORBIT_COUNT"
] | 1 | 0.02 | 2026-02-25T10:40:35.313466Z | {
"verified": true,
"answer": 568,
"timestamp": "2026-02-25T10:40:35.333027Z"
} | 1a085c | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 1,
"correct": {
"strict": false,
"boxed": false,
"relaxed": true
},
"usage": {
"prompt_tokens": 188,
"completion_tokens": 14208
},
"timestamp": "2026-03-30T11:45:36.795Z",
"answer": 2
},
{
"i... | 1 | [
{
"lemma": "POLY_ORBIT_COUNT",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
}
] | {
"lo": 3.8,
"mid": 6.33,
"hi": 9.49
} | ||
875b5b | nt_sum_totient_over_divisors_v1_124444284_6141 | Let $n$ be the number of ordered pairs $(a,b)$ such that $1 \leq a \leq 12$ and $1 \leq b \leq 263$. Compute the sum of $\phi(d)$ over all positive divisors $d$ of $n$, where $\phi$ denotes Euler's totient function. | 3,156 | graphs = [
Graph(
let={
"n": CountOverSet(set=CartesianProduct(left=IntegerRange(start=Const(1), end=Const(12)), right=IntegerRange(start=Const(1), end=Const(263)))),
"result": SumOverDivisors(n=Ref(name='n'), var='d', expr=EulerPhi(n=Var(name='d'))),
},
goal=Ref("res... | NT | null | COMPUTE | sympy | COUNT_CARTESIAN | [
"COUNT_CARTESIAN"
] | 409d7d | nt_sum_totient_over_divisors_v1 | null | 4 | 0 | [
"COUNT_CARTESIAN"
] | 1 | 0.004 | 2026-02-08T08:09:16.560985Z | {
"verified": true,
"answer": 3156,
"timestamp": "2026-02-08T08:09:16.565243Z"
} | 128c71 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 113,
"completion_tokens": 1590
},
"timestamp": "2026-02-13T15:32:00.893Z",
"answer": 3156
},
{... | 1 | [
{
"lemma": "COUNT_CARTESIAN",
"status": "ok"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no... | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
ae9e89 | nt_count_intersection_v1_124444284_4117 | Let $N = 20000$. Let $b$ be the number of integers $t$ such that $23 \leq t \leq 42$ and there exist integers $a$ and $b$ with $1 \leq a \leq 7$, $1 \leq b \leq 2$, and $t = 2a + 7b + 14$. Let $a = 3$. Compute the number of positive integers $n \leq N$ such that $3$ divides $n$ and $\gcd(n, b) = 1$. | 2,857 | graphs = [
Graph(
let={
"N": Const(20000),
"a": Const(3),
"b": CountOverSet(set=SolutionsSet(var=Var("t"), condition=Exists(var=Var(name='a'), condition=Exists(var=Var(name='b'), condition=And(Geq(left=Var(name='a'), right=Const(value=1)), Leq(left=Var(name='a'), right=Co... | NT | null | COUNT | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | nt_count_intersection_v1 | null | 5 | 0 | [
"LIN_FORM"
] | 1 | 0.967 | 2026-02-08T05:46:44.686793Z | {
"verified": true,
"answer": 2857,
"timestamp": "2026-02-08T05:46:45.653778Z"
} | 77d038 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 165,
"completion_tokens": 1713
},
"timestamp": "2026-02-12T14:26:17.537Z",
"answer": 2857
},
{... | 1 | [
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"statu... | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
01b5b8 | alg_sum_powers_v1_601307018_2245 | Let $M = \left( \sum_{k=1}^{1900} k^2 \right) \bmod 8953$. Find the remainder when $\min\{ |x - y| : x, y > 0,\, xy = 86721 \} - M$ is divided by $85620$. | 83,286 | graphs = [
Graph(
let={
"_n": Const(2),
"result": Mod(value=Summation(var="k", start=Const(1), end=Const(1900), expr=Pow(Var("k"), Ref("_n"))), modulus=Const(8953)),
"Q": Mod(value=Sub(MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), co... | ALG | null | COMPUTE | sympy | B3_DIFF | [
"B3_DIFF"
] | 01f407 | alg_sum_powers_v1 | negation_mod | 4 | 0 | [
"B3_DIFF"
] | 1 | 0.099 | 2026-03-10T02:54:27.408537Z | {
"verified": true,
"answer": 83286,
"timestamp": "2026-03-10T02:54:27.507134Z"
} | f33e1a | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 179,
"completion_tokens": 8875
},
"timestamp": "2026-03-29T04:49:54.776Z",
"answer": 26370
},
{
... | 1 | [
{
"lemma": "B3_DIFF",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
}
] | {
"lo": 1.23,
"mid": 4.27,
"hi": 6.7
} | ||
a463fd | geo_count_lattice_triangle_v1_601307018_4151 | Let $M = \left|144 \cdot 144 + 32 \cdot (0 - 99)\right|$ and let $$R = \gcd(144, 99) + \gcd(|32 - 144|, |144 - 99|) + \gcd(|0 - 32|, |0 - 144|).$$ Compute $\frac{M + 2 - R}{2}$. | 8,772 | graphs = [
Graph(
let={
"_n": Const(144),
"area_2x": Abs(arg=Sum(Mul(Ref(name='_n'), Const(value=144)), Mul(Const(value=32), Sub(left=Const(value=0), right=Const(value=99))))),
"boundary": Sum(GCD(a=Abs(arg=Const(value=144)), b=Abs(arg=Const(value=99))), GCD(a=Abs(arg=Sub... | GEOM | NT | COUNT | sympy | B1 | [
"B1"
] | 5b950e | geo_count_lattice_triangle_v1 | null | 4 | 0 | [
"B1"
] | 1 | 0.012 | 2026-03-10T04:44:21.592843Z | {
"verified": true,
"answer": 8772,
"timestamp": "2026-03-10T04:44:21.604722Z"
} | 6a247e | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 203,
"completion_tokens": 561
},
"timestamp": "2026-03-29T11:13:01.026Z",
"answer": 8772
},
{
"id... | 1 | [
{
"lemma": "B1",
"status": "ok"
}
] | {
"lo": -6.2,
"mid": -2.87,
"hi": 0.44
} | ||
37a909 | nt_count_phi_equals_v1_2051736721_2764 | Let $N = 49$. Define
$$
t = \sum_{k=1}^{N} \varphi(k) \left\lfloor \frac{49}{k} \right\rfloor,
$$
where $\varphi$ denotes Euler's totient function. Let $k = 471$. Determine the number of positive integers $n$ such that $1 \le n \le t$ and $\varphi(n) = k$. | 0 | graphs = [
Graph(
let={
"_n": Const(49),
"upper": Summation(var="k1", start=Const(1), end=Ref("_n"), expr=Mul(EulerPhi(n=Var("k1")), Floor(Div(Const(49), Var("k1"))))),
"k": Const(471),
"result": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Va... | NT | null | COUNT | sympy | K2 | [
"K2"
] | 6897ab | nt_count_phi_equals_v1 | null | 6 | 0 | [
"K2"
] | 1 | 0.637 | 2026-02-08T16:54:22.471498Z | {
"verified": true,
"answer": 0,
"timestamp": "2026-02-08T16:54:23.108424Z"
} | 7f4665 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 134,
"completion_tokens": 5174
},
"timestamp": "2026-02-17T14:51:29.641Z",
"answer": 0
},
{
... | 1 | [
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K2",
"status": "ok"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "V3",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
c62f5a | modular_inverse_v1_151522320_2573 | Let $a$ be the number of ordered pairs $(i, j)$ where $i$ is an integer from 1 to 3 and $j$ is an integer from 1 to 67. Let $m = 523$ and define $R$ to be the set of all integers $x$ such that $1 \leq x \leq 522$ and $a \cdot x \equiv 1 \pmod{m}$. Compute the smallest element of $R$. | 255 | graphs = [
Graph(
let={
"a": CountOverSet(set=CartesianProduct(left=IntegerRange(start=Const(1), end=Const(3)), right=IntegerRange(start=Const(1), end=Const(67)))),
"m": Const(523),
"upper": Const(522),
"result": MinOverSet(set=SolutionsSet(var=Var("x"), condi... | NT | null | EXTREMUM | sympy | COUNT_CARTESIAN | [
"COUNT_CARTESIAN"
] | 409d7d | modular_inverse_v1 | null | 6 | 0 | [
"COUNT_CARTESIAN"
] | 1 | 0.024 | 2026-02-08T04:52:56.036152Z | {
"verified": true,
"answer": 255,
"timestamp": "2026-02-08T04:52:56.059762Z"
} | 202024 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 215,
"completion_tokens": 1388
},
"timestamp": "2026-02-11T22:22:12.757Z",
"answer": 255
},
{
"i... | 1 | [
{
"lemma": "COUNT_CARTESIAN",
"status": "ok"
},
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "POLY_P... | {
"lo": -3.42,
"mid": 1.86,
"hi": 7.55
} | ||
314b9c_l | comb_factorial_compute_v1_1470522791_1246 | Let $n$ be the number of positive integers less than or equal to 8 that are divisible by 8. Compute $n!$. | 1 | ALG | COMB | COMPUTE | sympy | SUM_DIVISIBLE | [
"SUM_DIVISIBLE"
] | 02dbe3 | comb_factorial_compute_v1 | null | 2 | 0 | [
"SUM_DIVISIBLE"
] | 1 | 0.001 | 2026-02-08T13:32:14.602893Z | {
"verified": false,
"answer": 40320,
"timestamp": "2026-02-08T13:32:14.603909Z"
} | 65d1e2 | 314b9c | legacy_text | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 139,
"completion_tokens": 194
},
"timestamp": "2026-02-24T18:31:52.719Z",
"answer": 1
},
{
"id... | 1 | [
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "SUM_DIVISIBLE",
"status": "ok"
}
] | {
"lo": 3.25,
"mid": 5.68,
"hi": 8.81
} | |
6c207e | lin_form_endings_v1_1520064083_8790 | Let $a = 35$, $b = 10$, $A = 25$, and $B = 51$. Let $g = \gcd(a, b)$, $a' = \left\lfloor \frac{a}{g} \right\rfloor$, and $b' = \left\lfloor \frac{b}{g} \right\rfloor$. Define $\text{size}_T = a' \cdot A + b' \cdot B - a' \cdot b'$. Let $\text{total} = a \cdot A + b \cdot B - a - b + 1$. Compute $\text{total} - \text{si... | 1,078 | graphs = [
Graph(
let={
"a_coeff": Const(35),
"b_coeff": Const(10),
"A_val": Const(25),
"B_val": Const(51),
"g_step": GCD(a=Ref("a_coeff"), b=Ref("b_coeff")),
"ap_node": Floor(Div(Ref("a_coeff"), Ref("g_step"))),
"bp_node": ... | COMB | NT | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | lin_form_endings_v1 | null | 6 | null | [
"LIN_FORM"
] | 1 | 0.001 | 2026-02-08T10:23:33.287376Z | {
"verified": true,
"answer": 1078,
"timestamp": "2026-02-08T10:23:33.288543Z"
} | a41baf | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 207,
"completion_tokens": 568
},
"timestamp": "2026-02-15T20:59:04.839Z",
"answer": 1077
},
{
"id": 11,... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "V8",
"sta... | {
"lo": -6.96,
"mid": -4.56,
"hi": -1.46
} | ||
4968ab | alg_telescope_v1_601307018_3214 | Let $M = \left( \sum_{k=0}^{1596} (4k^3 + 6k^2 + 4k + 1) \right) \bmod \min\{x + y \mid x > 0, y > 0, xy = 21418384\}$. Find the remainder when $21449M$ is divided by $96730$. | 60,399 | graphs = [
Graph(
let={
"_n": Const(3),
"result": Mod(value=Summation(var="k", start=Const(0), end=Const(1596), expr=Sum(Mul(Const(4), Pow(Var("k"), Ref("_n"))), Mul(Const(6), Pow(Var("k"), Const(2))), Mul(Const(4), Var("k")), Const(1))), modulus=MinOverSet(set=MapOverSet(set=Solutio... | ALG | null | COMPUTE | sympy | B3 | [
"B3"
] | 0cd20d | alg_telescope_v1 | null | 4 | 0 | [
"B3"
] | 1 | 0.157 | 2026-03-10T03:46:10.626308Z | {
"verified": true,
"answer": 60399,
"timestamp": "2026-03-10T03:46:10.783595Z"
} | c8b1dd | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 196,
"completion_tokens": 32768
},
"timestamp": "2026-03-29T07:53:08.047Z",
"answer": null
},
{
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
}
] | {
"lo": 1.23,
"mid": 4.27,
"hi": 6.7
} | ||
c197e6 | comb_count_derangements_v1_1526740231_503 | Let $n$ be the number of ordered pairs $(i, j)$ of positive integers such that $1 \le i \le 3$, $1 \le j \le 3$, and $\gcd(i, j) = 1$. Let $r = !n$ denote the subfactorial of $n$. Compute the remainder when $53826 \cdot r$ is divided by $71425$. Find the value of this remainder. | 12,679 | graphs = [
Graph(
let={
"_n": Const(53826),
"n": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("i"), Var("j")]), condition=Eq(GCD(a=Var("i"), b=Var("j")), Const(1)), domain=CartesianProduct(left=IntegerRange(start=Const(1), end=Const(3)), right=IntegerRange(start=Const(1), en... | NT | COMB | COUNT | sympy | COUNT_COPRIME_GRID | [
"COUNT_COPRIME_GRID"
] | 20ec03 | comb_count_derangements_v1 | null | 3 | 0 | [
"COUNT_COPRIME_GRID"
] | 1 | 0.002 | 2026-02-08T11:34:30.931761Z | {
"verified": true,
"answer": 12679,
"timestamp": "2026-02-08T11:34:30.933601Z"
} | 0537e2 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 139,
"completion_tokens": 1901
},
"timestamp": "2026-02-14T16:20:09.105Z",
"answer": 12679
},
... | 1 | [
{
"lemma": "COUNT_COPRIME_GRID",
"status": "ok"
},
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "MOD_FACTORIA... | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
fb776c | sequence_count_fib_divisible_v1_238844314_217 | Determine the number of positive integers $n \leq 995$ such that the $n$th Fibonacci number is divisible by $7$. | 124 | graphs = [
Graph(
let={
"upper": Const(995),
"d": Const(7),
"result": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Ref("upper")), Divides(divisor=Ref("d"), dividend=Fibonacci(arg=Var(name='n')))))),
},
go... | NT | null | COUNT | sympy | ONE_PHI_2 | [
"LIN_FORM"
] | 7b2633 | sequence_count_fib_divisible_v1 | null | 5 | 0 | [
"LIN_FORM",
"ONE_PHI_2"
] | 2 | 0.409 | 2026-02-08T13:10:57.178646Z | {
"verified": true,
"answer": 124,
"timestamp": "2026-02-08T13:10:57.587362Z"
} | aeaea8 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 75,
"completion_tokens": 1949
},
"timestamp": "2026-02-15T11:10:15.690Z",
"answer": 124
},
{
... | 1 | [
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
}
] | {
"lo": -5.49,
"mid": 0.22,
"hi": 6.51
} | ||
f3ba17 | nt_count_divisible_v1_655260480_3425 | Let $T$ be the set of all integers $t$ such that $27 \leq t \leq 55$ and there exist positive integers $a$ and $b$ with $1 \leq a \leq 5$, $1 \leq b \leq 3$, and $t = 4a + 6b + 17$. Let $\text{divisor}$ be the number of elements in $T$. Let $\text{upper} = 77284$. Let $\text{result}$ be the number of positive integers ... | 5,944 | graphs = [
Graph(
let={
"upper": Const(77284),
"divisor": CountOverSet(set=SolutionsSet(var=Var("t"), condition=Exists(var=Var(name='a'), condition=Exists(var=Var(name='b'), condition=And(Geq(left=Var(name='a'), right=Const(value=1)), Leq(left=Var(name='a'), right=Const(value=5)), Ge... | NT | null | COUNT | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | nt_count_divisible_v1 | null | 4 | 0 | [
"LIN_FORM"
] | 1 | 2.426 | 2026-02-08T17:22:32.232719Z | {
"verified": true,
"answer": 5944,
"timestamp": "2026-02-08T17:22:34.659055Z"
} | 098137 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 195,
"completion_tokens": 1640
},
"timestamp": "2026-02-18T00:56:36.877Z",
"answer": 5944
},
{... | 1 | [
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
}... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
ea21ad | modular_modexp_compute_v1_601307018_3534 | Let $s = \min\{ x_1 + y_1 : x_1, y_1 > 0,\ x_1 y_1 = 8281,\ x_1 \le y_1 \}$. Let $e$ be the maximum value of $xy$ over all ordered pairs $(x, y)$ of positive integers such that $x + y = s$. Compute $31^e \bmod 29584$. | 12,175 | graphs = [
Graph(
let={
"a": Const(31),
"e": MaxOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(Sum(Var("x"), Var("y")), MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tup... | NT | null | COMPUTE | sympy | B3 | [
"B3/B1"
] | 7f76f7 | modular_modexp_compute_v1 | null | 5 | 0 | [
"B1",
"B3"
] | 2 | 0.004 | 2026-03-10T04:07:48.850933Z | {
"verified": true,
"answer": 12175,
"timestamp": "2026-03-10T04:07:48.855169Z"
} | 80ab4a | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 204,
"completion_tokens": 10422
},
"timestamp": "2026-03-29T09:01:28.443Z",
"answer": 12175
},
{
... | 1 | [
{
"lemma": "B1",
"status": "ok_later"
},
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "... | {
"lo": -2.46,
"mid": 1.23,
"hi": 4.93
} | ||
a92767 | nt_sum_divisors_mod_v1_784195855_1441 | Let $S$ be the set of all ordered pairs $(x, y)$ of positive integers such that $xy = 8100$. For each such pair, compute $x + y$, and let $n$ be the minimum value of $x + y$ over all such pairs. Let $\sigma$ be the sum of all positive divisors of $n$. Find the remainder when $\sigma$ is divided by $10607$. | 546 | graphs = [
Graph(
let={
"_n": Const(8100),
"n": MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(Mul(Var("x"), Var("y")), Ref("_n")))), expr=Sum(Var("x"), Var("y")))),
... | NT | null | COMPUTE | sympy | B3 | [
"B3"
] | 0cd20d | nt_sum_divisors_mod_v1 | null | 5 | 0 | [
"B3"
] | 1 | 0.006 | 2026-02-08T05:01:39.980168Z | {
"verified": true,
"answer": 546,
"timestamp": "2026-02-08T05:01:39.986361Z"
} | 6a5ebd | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 199,
"completion_tokens": 564
},
"timestamp": "2026-02-11T22:41:17.366Z",
"answer": 546
},
{
"id... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "V1",
"status": "no"
}
] | {
"lo": -5.55,
"mid": -3.01,
"hi": 0.33
} | ||
d37ae3 | nt_min_with_divisor_count_v1_784195855_1331 | Let $T$ be the set of all positive integers $t$ such that $10 \leq t \leq 8121$ and there exist positive integers $a$, $b$ with $1 \leq a \leq 726$, $1 \leq b \leq 849$, satisfying $t = 3a + 7b$. Let $u$ be the number of elements in $T$. Let $p$ be the largest prime number less than or equal to 3. Determine the smalles... | 4 | graphs = [
Graph(
let={
"_n": Const(3),
"upper": CountOverSet(set=SolutionsSet(var=Var("t"), condition=Exists(var=Var(name='a'), condition=Exists(var=Var(name='b'), condition=And(Geq(left=Var(name='a'), right=Const(value=1)), Leq(left=Var(name='a'), right=Const(value=726)), Geq(left=... | NT | null | EXTREMUM | sympy | MAX_PRIME_BELOW | [
"MAX_PRIME_BELOW",
"LIN_FORM"
] | d530e2 | nt_min_with_divisor_count_v1 | null | 5 | 0 | [
"LIN_FORM",
"MAX_PRIME_BELOW"
] | 2 | 0.316 | 2026-02-08T04:58:07.747333Z | {
"verified": true,
"answer": 4,
"timestamp": "2026-02-08T04:58:08.063652Z"
} | eeaf71 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 264,
"completion_tokens": 3285
},
"timestamp": "2026-02-11T22:34:44.790Z",
"answer": 4
},
{
"id"... | 1 | [
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
... | {
"lo": -3.42,
"mid": 1.86,
"hi": 7.55
} | ||
0a0262 | geo_count_lattice_rect_v1_677425708_752 | Let $a = 47$ and $b = 82$. Define a lattice point as a point in the plane with integer coordinates. Consider the rectangle consisting of all points $(x, y)$ such that $0 \leq x \leq a$ and $0 \leq y \leq b$. Compute the number of lattice points contained in this rectangle. | 3,984 | graphs = [
Graph(
let={
"a": Const(47),
"b": Const(82),
"result": LatticePointsRect(a=Ref(name='a'), b=Ref(name='b')),
},
goal=Ref("result"),
)
] | GEOM | null | COUNT | sympy | [] | geo_count_lattice_rect_v1 | null | 3 | 0 | null | null | 0.001 | 2026-02-08T03:42:50.245686Z | {
"verified": true,
"answer": 3984,
"timestamp": "2026-02-08T03:42:50.247064Z"
} | 671aff | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 190,
"completion_tokens": 218
},
"timestamp": "2026-02-08T21:01:36.561Z",
"answer": 3984
},
{
"id... | 1 | [] | {
"lo": -5.97,
"mid": -3.96,
"hi": -1.93
} | ||||
f13f43 | algebra_quadratic_discriminant_v1_1520064083_79 | Let $n = 66561$. Define $c$ to be the number of nonnegative integers $j$ such that $0 \leq j \leq n$ and $\binom{n}{j}$ is odd. Let $a = 2$ and $b = 4$. Define $\text{result} = b^2 - 4ac$. Let $Q = B_k$, where $B_k$ denotes the $k$-th Bell number and $k = |\text{result}| \bmod 11$. Compute $Q$. | 15 | graphs = [
Graph(
let={
"_n": Const(66561),
"a": Const(2),
"b": Const(4),
"c": CountOverSet(set=SolutionsSet(var=Var("j"), condition=And(Geq(Var("j"), Const(0)), Leq(Var("j"), Ref("_n")), Eq(Mod(value=Binom(n=Const(66561), k=Var("j")), modulus=Const(2)), Const... | COMB | null | COMPUTE | sympy | V8 | [
"V8"
] | 86348e | algebra_quadratic_discriminant_v1 | null | 7 | 0 | [
"V8"
] | 1 | 0.001 | 2026-02-08T02:58:50.817030Z | {
"verified": true,
"answer": 15,
"timestamp": "2026-02-08T02:58:50.818319Z"
} | 47bb72 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 227,
"completion_tokens": 1196
},
"timestamp": "2026-02-10T12:07:24.409Z",
"answer": 15
},
{
"id"... | 1 | [
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8",
"status": "ok"
},
{
"lemma": "VAL_SUM_EQ",
"status": "no"
}
] | {
"lo": -2.87,
"mid": -0.89,
"hi": 0.97
} | ||
2dccec | comb_bell_compute_v1_1125832087_1071 | Let $n$ be the number of prime numbers $p$ such that $2 \leq p \leq 23$.
The Bell number $B_n$ is the number of ways to partition a set of $n$ distinct elements.
Compute $B_n$. | 21,147 | graphs = [
Graph(
let={
"_n": Const(23),
"n": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(2)), Leq(Var("n"), Ref("_n")), IsPrime(Var("n"))))),
"result": Bell(Ref("n")),
},
goal=Ref("result"),
)
] | NT | COMB | COMPUTE | sympy | LTE_SUM | [
"COUNT_PRIMES"
] | 07c874 | comb_bell_compute_v1 | null | 4 | 0 | [
"COUNT_PRIMES",
"LTE_SUM"
] | 2 | 0.007 | 2026-02-08T03:29:55.923939Z | {
"verified": true,
"answer": 21147,
"timestamp": "2026-02-08T03:29:55.931346Z"
} | 8db23a | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 166,
"completion_tokens": 509
},
"timestamp": "2026-02-10T14:50:39.034Z",
"answer": 21147
},
{
"i... | 1 | [
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_PRIMES",
"status": "ok"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no... | {
"lo": -5.55,
"mid": -3.02,
"hi": 0.31
} | ||
091b6d | sequence_fibonacci_compute_v1_1248542787_325 | Let $S$ be the set of all positive integers $p$ for which there exists a positive integer $q$ such that $pq = 54$, $\gcd(p, q) = 1$, and $p < q$. Compute the number of elements in $S$. Let $n$ be the smallest divisor of $10938133$ that is at least this number. Find the $n$th Fibonacci number. | 28,657 | graphs = [
Graph(
let={
"_n": CountOverSet(set=SolutionsSet(var=Var("p"), condition=And(IsPositive(arg=Var(name='p')), Exists(var=Var(name='q'), condition=And(Eq(left=Mul(Var(name='p'), Var(name='q')), right=Const(value=54)), Eq(left=GCD(a=Var(name='p'), b=Var(name='q')), right=Const(value=1)), ... | NT | null | COMPUTE | sympy | COPRIME_PAIRS | [
"COPRIME_PAIRS/MIN_PRIME_FACTOR"
] | 52cee2 | sequence_fibonacci_compute_v1 | null | 5 | 0 | [
"COPRIME_PAIRS",
"MIN_PRIME_FACTOR"
] | 2 | 0.003 | 2026-02-08T03:03:40.114356Z | {
"verified": true,
"answer": 28657,
"timestamp": "2026-02-08T03:03:40.117486Z"
} | 9313cd | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 202,
"completion_tokens": 3925
},
"timestamp": "2026-02-09T02:56:47.264Z",
"answer": 28657
},
{
"... | 1 | [
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "MIN_PRIME_FACTOR",
"status": "ok_later"
},
{
"lemma": "V3",
"status": "no"
}... | {
"lo": 1.1,
"mid": 4.17,
"hi": 6.61
} | ||
7aca64 | modular_sum_quadratic_residues_v1_1520064083_1576 | Let $n$ be a positive integer. Define $S$ as the set of all ordered pairs $(x, y)$ of positive integers such that $xy = 19881$. Let $T$ be the set of all sums $x + y$ where $(x, y) \in S$. Let $m$ be the minimum value in $T$. Let $p$ be the largest prime number such that $2 \leq p \leq m$. Compute $\frac{p(p-1)}{4}$. | 19,670 | graphs = [
Graph(
let={
"_n": Const(2),
"p": MaxOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Ref("_n")), Leq(Var("n"), MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(ar... | NT | null | SUM | sympy | B3 | [
"B3/MAX_PRIME_BELOW"
] | f253c0 | modular_sum_quadratic_residues_v1 | null | 5 | 0 | [
"B3",
"MAX_PRIME_BELOW"
] | 2 | 0.002 | 2026-02-08T04:07:43.447559Z | {
"verified": true,
"answer": 19670,
"timestamp": "2026-02-08T04:07:43.449458Z"
} | bb5856 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 219,
"completion_tokens": 579
},
"timestamp": "2026-02-10T15:25:46.043Z",
"answer": 19670
},
{
"... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok_later"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
},
{
... | {
"lo": -3.49,
"mid": 1.84,
"hi": 7.55
} | ||
8a2cb6 | comb_binomial_compute_v1_124444284_7881 | Let $n = 15$. Define $k$ to be the number of positive integers $p$ for which there exists a positive integer $q$ such that $pq = 264600$, $\gcd(p, q) = 1$, and $p < q$. Compute $\binom{n}{k}$. | 6,435 | graphs = [
Graph(
let={
"n": Const(15),
"k": CountOverSet(set=SolutionsSet(var=Var("p"), condition=And(IsPositive(arg=Var(name='p')), Exists(var=Var(name='q'), condition=And(Eq(left=Mul(Var(name='p'), Var(name='q')), right=Const(value=264600)), Eq(left=GCD(a=Var(name='p'), b=Var(name... | NT | null | COMPUTE | sympy | COPRIME_PAIRS | [
"COPRIME_PAIRS"
] | 2bb3aa | comb_binomial_compute_v1 | null | 6 | 0 | [
"COPRIME_PAIRS"
] | 1 | 0.001 | 2026-02-08T09:24:40.340291Z | {
"verified": true,
"answer": 6435,
"timestamp": "2026-02-08T09:24:40.341146Z"
} | db6d5f | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 110,
"completion_tokens": 2024
},
"timestamp": "2026-02-14T04:12:41.251Z",
"answer": 6435
},
{... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "V1",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
},
{
"lemma": "VAL_SUM_EQ",
"status": "no"
}
] | {
"lo": -5.49,
"mid": 0.22,
"hi": 6.51
} | ||
16f2a5 | nt_sum_gcd_range_mod_v1_151522320_1042 | Let $N = 1156$ and $M = 11903$. Let $k$ be the minimum value of $x + y$ over all ordered pairs $(x, y)$ of positive integers such that $x \cdot y = 15876$.
Compute the remainder when
$$
\sum_{n=1}^{N} \gcd(n, k)
$$
is divided by $M$. | 9,916 | graphs = [
Graph(
let={
"_n": Const(15876),
"N": Const(1156),
"k": MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(Mul(Var("x"), Var("y")), Ref("_n")))), ex... | NT | null | COMPUTE | sympy | B3 | [
"B3"
] | 0cd20d | nt_sum_gcd_range_mod_v1 | null | 6 | 0 | [
"B3"
] | 1 | 0.055 | 2026-02-08T03:43:38.003448Z | {
"verified": true,
"answer": 9916,
"timestamp": "2026-02-08T03:43:38.058040Z"
} | 2b354f | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 197,
"completion_tokens": 4397
},
"timestamp": "2026-02-10T15:33:21.670Z",
"answer": 9916
},
{
"i... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
}
] | {
"lo": -3.52,
"mid": 1.14,
"hi": 6.18
} | ||
0ed26b | antilemma_k2_v1_1080341949_112 | Let $x = \sum_{k=1}^{267} \phi(k) \left\lfloor \frac{267}{k} \right\rfloor$, where $\phi(n)$ denotes Euler's totient function. Compute $x + \phi(|x|+1) + \tau(|x|+1)$, where $\tau(n)$ denotes the number of positive divisors of $n$. | 70,558 | graphs = [
Graph(
let={
"_n": Const(267),
"x": Summation(var="k", start=Const(1), end=Ref("_n"), expr=Mul(EulerPhi(n=Var("k")), Floor(Div(Const(267), Var("k"))))),
"Q": Sum(Ref("x"), EulerPhi(n=Sum(Abs(arg=Ref(name='x')), Const(1))), NumDivisors(n=Sum(Abs(arg=Ref(name='x'... | NT | COMB | COMPUTE | sympy | K2 | [
"K2"
] | 6897ab | antilemma_k2_v1 | null | 5 | 0 | [
"K2"
] | 1 | 0.001 | 2026-02-08T13:13:26.792638Z | {
"verified": true,
"answer": 70558,
"timestamp": "2026-02-08T13:13:26.794047Z"
} | d6eb37 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 127,
"completion_tokens": 1319
},
"timestamp": "2026-02-15T12:07:25.667Z",
"answer": 70558
},
... | 1 | [
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K2",
"status": "ok"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
}
] | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
e0f1a9 | sequence_count_fib_divisible_v1_1125832087_2426 | Let $p$ be the number of prime numbers $n$ such that $2 \leq n \leq 6547$. Determine the number of positive integers $n$ such that $1 \leq n \leq p$ and $8$ divides the $n$th Fibonacci number. | 140 | graphs = [
Graph(
let={
"upper": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(2)), Leq(Var("n"), Const(6547)), IsPrime(Var("n"))))),
"d": Const(8),
"result": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1))... | NT | null | COUNT | sympy | COUNT_PRIMES | [
"COUNT_PRIMES"
] | 07c874 | sequence_count_fib_divisible_v1 | null | 6 | 0 | [
"COUNT_PRIMES"
] | 1 | 0.034 | 2026-02-08T04:36:44.314167Z | {
"verified": true,
"answer": 140,
"timestamp": "2026-02-08T04:36:44.348105Z"
} | 932214 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 106,
"completion_tokens": 1882
},
"timestamp": "2026-02-12T01:50:36.998Z",
"answer": 140
},
{
... | 1 | [
{
"lemma": "COUNT_PRIMES",
"status": "ok"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
}
] | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
27f95a | antilemma_sum_factor_cartesian_v1_153355830_151 | For each pair of integers $(i, j)$ with $1 \le i \le 11$ and $1 \le j \le 17$, compute the product $i \cdot j$. Let $x$ be the sum of all such products. Compute the remainder when
$$
(x \bmod 199) + 5003 \cdot (x \bmod 499)
$$
is divided by $71469$. | 18,750 | graphs = [
Graph(
let={
"x": SumOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("i"), Var("j")]), condition=Const(1), domain=CartesianProduct(left=IntegerRange(start=Const(1), end=Const(11)), right=IntegerRange(start=Const(1), end=Const(17)))), expr=Mul(Var("i"), Var("j")))),
... | NT | null | COMPUTE | sympy | SUM_FACTOR_CARTESIAN | [
"SUM_FACTOR_CARTESIAN"
] | d9e436 | antilemma_sum_factor_cartesian_v1 | null | 3 | 0 | [
"SUM_FACTOR_CARTESIAN"
] | 1 | 0.001 | 2026-02-08T02:55:04.800019Z | {
"verified": true,
"answer": 18750,
"timestamp": "2026-02-08T02:55:04.800648Z"
} | 0bc5eb | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 196,
"completion_tokens": 568
},
"timestamp": "2026-02-17T15:59:41.643Z",
"answer": 3266
}
] | 0 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "SUM_FACTOR_CARTESIAN",
"status": "ok"
},
{
"lemma": "V5",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
}
] | {
"lo": -6.48,
"mid": 1.54,
"hi": 9.56
} | ||
b0724f | nt_max_prime_below_v1_1440796553_254 | Let $S$ be the set of all positive integers $p$ for which there exists a positive integer $q$ such that $p \cdot q = 12$, $\gcd(p, q) = 1$, and $p < q$. Let $n$ be the largest prime number that is at least $|S|$ and at most 55555. Find the value of $n$. | 55,547 | graphs = [
Graph(
let={
"upper": Const(55555),
"result": MaxOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), CountOverSet(set=SolutionsSet(var=Var("p"), condition=And(IsPositive(arg=Var(name='p')), Exists(var=Var(name='q'), condition=And(Eq(left=Mul(Var(name='p'), V... | NT | null | EXTREMUM | sympy | COPRIME_PAIRS | [
"COPRIME_PAIRS"
] | 2bb3aa | nt_max_prime_below_v1 | null | 4 | 0 | [
"COPRIME_PAIRS"
] | 1 | 3.536 | 2026-02-08T11:40:48.800345Z | {
"verified": true,
"answer": 55547,
"timestamp": "2026-02-08T11:40:52.335905Z"
} | 953a73 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 130,
"completion_tokens": 2929
},
"timestamp": "2026-02-14T17:40:40.491Z",
"answer": 55547
},
... | 1 | [
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "MOD_ADD",
"statu... | {
"lo": -6.96,
"mid": -4.56,
"hi": -1.46
} | ||
aab8dd | diophantine_fbi2_min_v1_1918700295_3243 | Let $S_1$ be the set of all ordered pairs $(x, y)$ of positive integers such that $xy = 419904$. Let $T_1$ be the set of all values $x + y$ where $(x, y) \in S_1$. Let $s_1$ be the minimum value in $T_1$. Let $S_2$ be the set of all ordered pairs $(x, y)$ of positive integers such that $xy = s_1$. Let $T_2$ be the set ... | 6 | graphs = [
Graph(
let={
"_n": MinOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Const(2)), Divides(divisor=Var("d"), dividend=Const(9625))))),
"k": MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Va... | NT | null | EXTREMUM | sympy | B1 | [
"MIN_PRIME_FACTOR/B3",
"B3/B3"
] | f2f7b2 | diophantine_fbi2_min_v1 | null | 7 | 0 | [
"B1",
"B3",
"MIN_PRIME_FACTOR"
] | 3 | 0.2 | 2026-02-08T08:28:15.967926Z | {
"verified": true,
"answer": 6,
"timestamp": "2026-02-08T08:28:16.167599Z"
} | 4c6039 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 271,
"completion_tokens": 1322
},
"timestamp": "2026-02-13T19:09:38.823Z",
"answer": 6
},
{
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "M... | {
"lo": -5.55,
"mid": -3.01,
"hi": 0.32
} | ||
0e1900 | algebra_quadratic_discriminant_v1_1431428450_1049 | Let $a = -10$, $b = 7$, and $c = 5$. Compute the discriminant $b^2 - 4ac$. Let $T$ be the set of integers $t$ with $7 \leq t \leq 24$ such that there exist integers $a'$ and $b'$ with $1 \leq a' \leq 4$, $1 \leq b' \leq 3$, and $t = 3a' + 4b'$. Let $N = 66535$. Compute the remainder when $|T| - (b^2 - 4ac)$ is divided ... | 66,298 | graphs = [
Graph(
let={
"_n": Const(66535),
"a": Const(-10),
"b": Const(7),
"c": Const(5),
"result": Sub(Pow(Ref("b"), Const(2)), Mul(Const(4), Ref("a"), Ref("c"))),
"Q": Mod(value=Sub(CountOverSet(set=SolutionsSet(var=Var("t"), conditi... | NT | null | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM"
] | 324ba4 | algebra_quadratic_discriminant_v1 | negation_mod | 3 | 0 | [
"LIN_FORM"
] | 1 | 0.002 | 2026-02-08T13:52:35.305696Z | {
"verified": true,
"answer": 66298,
"timestamp": "2026-02-08T13:52:35.308015Z"
} | d8fd07 | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 200,
"completion_tokens": 536
},
"timestamp": "2026-02-16T05:08:26.592Z",
"answer": 66296
},
{
"id": 11... | 1 | [
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "V3",
"status": "no"
}
] | {
"lo": -8.26,
"mid": -5.01,
"hi": -1.76
} | ||
16988e | antilemma_sum_equals_v1_1915831931_4153 | Let $x$ be the number of ordered pairs $(i,j)$ of positive integers such that $i + j = 19$, $1 \leq i \leq 17$, and $1 \leq j \leq 17$. Compute the remainder when $66725x$ is divided by $73353$. | 40,658 | graphs = [
Graph(
let={
"x": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("i"), Var("j")]), condition=Eq(Sum(Var("i"), Var("j")), Const(19)), domain=CartesianProduct(left=IntegerRange(start=Const(1), end=Const(17)), right=IntegerRange(start=Const(1), end=Const(17))))),
"Q": ... | COMB | GEOM | COMPUTE | sympy | COUNT_SUM_EQUALS | [
"COUNT_SUM_EQUALS"
] | 75ab0f | antilemma_sum_equals_v1 | null | 2 | 0 | [
"COUNT_SUM_EQUALS"
] | 1 | 0.011 | 2026-02-08T18:08:01.618281Z | {
"verified": true,
"answer": 40658,
"timestamp": "2026-02-08T18:08:01.628847Z"
} | cd55fe | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 111,
"completion_tokens": 32768
},
"timestamp": "2026-02-24T23:37:54.247Z",
"answer": null
},... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "ok"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8_SUM",
"status"... | {
"lo": -2.99,
"mid": 1.5,
"hi": 6.57
} | ||
62dc5e | nt_count_with_divisor_count_v1_1918700295_3629 | Let $ d $ be the number of positive integers $ n $ with $ 1 \leq n \leq 69 $ such that $ n \equiv \left\lfloor \frac{n}{2} \right\rfloor \pmod{7} $. Let $ S $ be the set of positive integers $ n $ with $ 1 \leq n \leq 10609 $ such that the number of positive divisors of $ n $ is equal to $ d $. Compute the number of el... | 32 | graphs = [
Graph(
let={
"upper": Const(10609),
"div_count": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Const(69)), Congruent(a=Var(name='n'), b=Floor(arg=Div(left=Var(name='n'), right=Const(value=2))), modulus=Const(value=7))))),
... | NT | null | COUNT | sympy | COPRIME_PAIRS | [
"L3C"
] | 73f8b0 | nt_count_with_divisor_count_v1 | null | 6 | 0 | [
"COPRIME_PAIRS",
"L3C"
] | 2 | 2.358 | 2026-02-08T08:47:02.843708Z | {
"verified": true,
"answer": 32,
"timestamp": "2026-02-08T08:47:05.201817Z"
} | 7fba4d | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 151,
"completion_tokens": 1623
},
"timestamp": "2026-02-13T21:39:42.891Z",
"answer": 32
},
{
... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "L3C",
"status": "ok"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
... | {
"lo": -3.51,
"mid": 1.33,
"hi": 6.56
} | ||
2282c0 | alg_telescope_v1_601307018_4443 | Let $B_n$ denote the $n$-th Bell number. Let $T$ be the set of integers $t$ such that $t = 7a + 2b$ for some integers $a, b$ with $1 \leq a \leq 164$, $1 \leq b \leq 217$, and $9 \leq t \leq 1582$. Let $M = \left( \sum_{k=0}^{|T|} (3k^2 + 3k + 1) \right) \bmod 3474$ and $Q = B_{|M| \bmod 11}$. Compute $Q$. | 5 | graphs = [
Graph(
let={
"_n": Const(3),
"result": Mod(value=Summation(var="k", start=Const(0), end=CountOverSet(set=SolutionsSet(var=Var("t"), condition=Exists(var=Var(name='a'), condition=Exists(var=Var(name='b'), condition=And(Geq(left=Var(name='a'), right=Const(value=1)), Leq(left... | COMB | COMB | COMPUTE | sympy | COUNT_CARTESIAN | [
"LIN_FORM"
] | 7b2633 | alg_telescope_v1 | null | 6 | 0 | [
"COUNT_CARTESIAN",
"LIN_FORM"
] | 2 | 0.221 | 2026-03-10T05:00:00.505289Z | {
"verified": true,
"answer": 5,
"timestamp": "2026-03-10T05:00:00.726730Z"
} | da3660 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 258,
"completion_tokens": 32768
},
"timestamp": "2026-03-29T12:17:21.832Z",
"answer": 5
},
{
"id"... | 1 | [
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": ... | {
"lo": 1.19,
"mid": 4.27,
"hi": 6.7
} | ||
cce9c0 | nt_max_prime_below_v1_458359167_3291 | Let $r$ be the largest prime number not exceeding $15876$. Let $a = r \bmod 317$. Let $b$ be the largest prime number not exceeding $3009$. Let $c$ be the number of positive integers $n$ such that $1 \leq n \leq 3453$ and $n \equiv \left\lfloor \frac{n}{2} \right\rfloor \pmod{11}$. Compute the remainder when $a + b \cd... | 35,600 | graphs = [
Graph(
let={
"_m": Const(317),
"_n": Const(3453),
"upper": Const(15876),
"result": MaxOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(2)), Leq(Var("n"), Ref("upper")), IsPrime(Var("n"))))),
"Q": Mod(value=Sum(Mod... | NT | null | EXTREMUM | sympy | MAX_PRIME_BELOW | [
"MAX_PRIME_BELOW",
"L3C"
] | acce41 | nt_max_prime_below_v1 | two_moduli | 6 | 0 | [
"L3C",
"MAX_PRIME_BELOW"
] | 2 | 0.371 | 2026-02-08T08:15:37.404128Z | {
"verified": true,
"answer": 35600,
"timestamp": "2026-02-08T08:15:37.775446Z"
} | e60dcc | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 163,
"completion_tokens": 3233
},
"timestamp": "2026-02-13T16:27:50.150Z",
"answer": 35600
},
... | 1 | [
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "L3C",
"status": "ok"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
},... | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
3234cc | nt_count_digit_sum_v1_1526740231_386 | Let $n$ be a positive integer. Define $\alpha$ to be the number of positive integers $n$ not exceeding 37493 such that $\gcd(n, 30) = 1$. Let $\beta$ be the number of positive integers $n$ not exceeding $\alpha$ such that the sum of the decimal digits of $n$ equals 20. Compute $\beta$. | 633 | graphs = [
Graph(
let={
"_n": Const(37493),
"upper": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Ref("_n")), Eq(GCD(a=Var("n"), b=Const(30)), Const(1))))),
"target_sum": Const(20),
"result": CountOverSet(set... | NT | null | COUNT | sympy | C4 | [
"C4"
] | 08d162 | nt_count_digit_sum_v1 | null | 4 | 0 | [
"C4"
] | 1 | 0.721 | 2026-02-08T11:30:26.175930Z | {
"verified": true,
"answer": 633,
"timestamp": "2026-02-08T11:30:26.897388Z"
} | 20a67a | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 126,
"completion_tokens": 1699
},
"timestamp": "2026-02-14T15:06:45.084Z",
"answer": 633
},
{
... | 1 | [
{
"lemma": "C4",
"status": "ok"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "V3",
"status": "no"
}
] | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
f61c86 | antilemma_k2_v1_124444284_7482 | Compute
$$
\sum_{k=1}^{443} \phi(k) \left\lfloor \frac{443}{k} \right\rfloor,
$$
where $\phi(k)$ denotes Euler's totient function. Determine the value of this sum. | 98,346 | graphs = [
Graph(
let={
"x": Summation(var="k", start=Const(1), end=Const(443), expr=Mul(EulerPhi(n=Var("k")), Floor(Div(Const(443), Var("k"))))),
},
goal=Ref("x"),
)
] | NT | COMB | COMPUTE | sympy | K2 | [
"K2"
] | 6897ab | antilemma_k2_v1 | null | 5 | 0 | [
"K2"
] | 1 | 0 | 2026-02-08T09:09:29.992212Z | {
"verified": true,
"answer": 98346,
"timestamp": "2026-02-08T09:09:29.992491Z"
} | dbe5ba | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 97,
"completion_tokens": 601
},
"timestamp": "2026-02-14T01:09:08.767Z",
"answer": 98346
},
{
... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K2",
"status": "ok"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "V1",
"status": "no"
}
] | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
51c7c2 | sequence_count_fib_divisible_v1_1440796553_1193 | Let $n = 71289$. Define $s$ to be the minimum value of $x + y$ over all pairs of positive integers $(x, y)$ such that $xy = n$. Let $d$ be the smallest divisor of $385$ that is at least $2$. Find the number of positive integers $n$ such that $1 \leq n \leq s$ and $d$ divides the $n$-th Fibonacci number. | 106 | graphs = [
Graph(
let={
"_n": Const(71289),
"upper": MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(Mul(Var("x"), Var("y")), Ref("_n")))), expr=Sum(Var("x"), Var("y"))... | NT | null | COUNT | sympy | MIN_PRIME_FACTOR | [
"MIN_PRIME_FACTOR",
"B3"
] | 6c6c26 | sequence_count_fib_divisible_v1 | null | 6 | 0 | [
"B3",
"MIN_PRIME_FACTOR"
] | 2 | 0.025 | 2026-02-08T12:13:46.320180Z | {
"verified": true,
"answer": 106,
"timestamp": "2026-02-08T12:13:46.344687Z"
} | e43cd9 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 140,
"completion_tokens": 1127
},
"timestamp": "2026-02-15T18:22:52.917Z",
"answer": 106
},
{
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "MIN_PRIME_FACTOR",
"status": "ok"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"s... | {
"lo": -8.26,
"mid": -5.01,
"hi": -1.76
} | ||
21697f | comb_binomial_compute_v1_1915831931_4008 | Let $S$ be the set of integers $t$ in the range $5 \leq t \leq 55$ for which there exist positive integers $a$ and $b$ with $1 \leq a \leq 23$, $1 \leq b \leq 3$, and $t = 2a + 3b$. Let $n$ be the smallest possible value of $x + y$ where $x$ and $y$ are positive integers such that $xy = |S|$. Compute the remainder when... | 62,332 | graphs = [
Graph(
let={
"n": MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(Mul(Var("x"), Var("y")), CountOverSet(set=SolutionsSet(var=Var("t"), condition=Exists(var=Var(name='a')... | ALG | COMB | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM/B3"
] | 05313e | comb_binomial_compute_v1 | null | 6 | 0 | [
"B3",
"LIN_FORM"
] | 2 | 0.003 | 2026-02-08T18:02:56.582152Z | {
"verified": true,
"answer": 62332,
"timestamp": "2026-02-08T18:02:56.584951Z"
} | 558d34 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 175,
"completion_tokens": 2971
},
"timestamp": "2026-02-24T23:26:27.346Z",
"answer": 62332
},
... | 1 | [
{
"lemma": "B3",
"status": "ok_later"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
}
] | {
"lo": -2.38,
"mid": 1.74,
"hi": 6.59
} | ||
87333b | antilemma_k3_v1_151522320_807 | Let $m = \sum_{d\mid 29} \phi(d)$, where $\phi$ denotes Euler's totient function. Let $n = 27021$ and let $x = \sum_{d\mid n} \phi(d)$. Let $S$ be the set of all integers $x$ such that $x^2 - 12x - 9964 = 0$. Compute the remainder when $x^2 + m \cdot x + \sum S$ is divided by $75154$. | 45,412 | graphs = [
Graph(
let={
"_c": Const(2),
"_m": SumOverDivisors(n=Const(value=29), var='d', expr=EulerPhi(n=Var(name='d'))),
"_n": Const(27021),
"x": SumOverDivisors(n=Ref(name='_n'), var='d', expr=EulerPhi(n=Var(name='d'))),
"Q": Mod(value=Sum(Pow(R... | NT | COMB | COMPUTE | sympy | K3 | [
"K3/VIETA_SUM",
"K3"
] | dfc3e0 | antilemma_k3_v1 | quadratic_mod | 5 | 0 | [
"K3",
"VIETA_SUM"
] | 2 | 0.003 | 2026-02-08T03:32:57.374005Z | {
"verified": true,
"answer": 45412,
"timestamp": "2026-02-08T03:32:57.377073Z"
} | c3ece4 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 222,
"completion_tokens": 6915
},
"timestamp": "2026-02-10T15:02:47.275Z",
"answer": 45412
},
{
"... | 1 | [
{
"lemma": "K3",
"status": "ok"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "V1",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "VIETA_S... | {
"lo": -3.46,
"mid": 1.03,
"hi": 5.49
} | ||
6a88db | modular_product_range_v1_898971024_2210 | Let $n$ be an integer satisfying $2 \leq n \leq 499$ and such that $n$ is prime. Let $S$ be the set of all such integers $n$. Let $P$ be the product of all integers from 40 to $|S|$, inclusive. Let $R$ be the remainder when $P$ is divided by 10133. Compute the remainder when $24285 \cdot R$ is divided by 80018. | 78,110 | graphs = [
Graph(
let={
"_n": Const(2),
"prod": MathProduct(expr=Var("i"), var="i", start=Const(40), end=CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Ref("_n")), Leq(Var("n"), Const(499)), IsPrime(Var("n")))))),
"result": Mod(value=Ref("prod"), ... | NT | null | COMPUTE | sympy | COUNT_PRIMES | [
"COUNT_PRIMES"
] | 07c874 | modular_product_range_v1 | null | 4 | 0 | [
"COUNT_PRIMES"
] | 1 | 0.002 | 2026-02-08T16:36:10.653404Z | {
"verified": true,
"answer": 78110,
"timestamp": "2026-02-08T16:36:10.655851Z"
} | b9fb4b | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 145,
"completion_tokens": 4125
},
"timestamp": "2026-02-17T07:50:13.088Z",
"answer": 78110
},
... | 1 | [
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_PRIMES",
"status": "ok"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
df113b | nt_max_prime_below_v1_1520064083_4243 | Let $S$ be the set of all positive integers $p$ for which there exists a positive integer $q$ such that $p \cdot q = 12$, $\gcd(p, q) = 1$, and $p < q$. Let $m$ be the number of elements in $S$. Let $N$ be the largest prime number $n$ such that $m \le n \le 37636$. Determine the value of $N$. | 37,633 | graphs = [
Graph(
let={
"upper": Const(37636),
"result": MaxOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), CountOverSet(set=SolutionsSet(var=Var("p"), condition=And(IsPositive(arg=Var(name='p')), Exists(var=Var(name='q'), condition=And(Eq(left=Mul(Var(name='p'), V... | NT | null | EXTREMUM | sympy | COPRIME_PAIRS | [
"COPRIME_PAIRS"
] | 2bb3aa | nt_max_prime_below_v1 | null | 4 | 0 | [
"COPRIME_PAIRS"
] | 1 | 0.921 | 2026-02-08T06:10:26.147593Z | {
"verified": true,
"answer": 37633,
"timestamp": "2026-02-08T06:10:27.068480Z"
} | faea4d | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 143,
"completion_tokens": 1724
},
"timestamp": "2026-02-12T20:18:40.567Z",
"answer": 37633
},
... | 1 | [
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
}
] | {
"lo": -5.55,
"mid": -3.01,
"hi": 0.32
} | ||
0b27a7 | nt_max_prime_below_v1_124444284_2469 | Let $S$ be the set of all positive integers $p$ for which there exists a positive integer $q$ such that $p \cdot q = 6$, $\gcd(p, q) = 1$, and $p < q$. Let $m$ be the number of elements in $S$. Determine the largest prime number $n$ such that $m \le n \le 66666$. | 66,653 | graphs = [
Graph(
let={
"upper": Const(66666),
"result": MaxOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), CountOverSet(set=SolutionsSet(var=Var("p"), condition=And(IsPositive(arg=Var(name='p')), Exists(var=Var(name='q'), condition=And(Eq(left=Mul(Var(name='p'), V... | NT | null | EXTREMUM | sympy | COPRIME_PAIRS | [
"COPRIME_PAIRS"
] | 2bb3aa | nt_max_prime_below_v1 | null | 3 | 0 | [
"COPRIME_PAIRS"
] | 1 | 1.713 | 2026-02-08T04:42:28.443300Z | {
"verified": true,
"answer": 66653,
"timestamp": "2026-02-08T04:42:30.156393Z"
} | 5c6360 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 197,
"completion_tokens": 3673
},
"timestamp": "2026-02-11T21:42:26.286Z",
"answer": 66653
},
{
... | 1 | [
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "MOD_ADD",
"stat... | {
"lo": -5.55,
"mid": -3.01,
"hi": 0.33
} | ||
164d78 | comb_factorial_compute_v1_1520064083_9803 | Let $n$ be the largest prime number less than or equal to 8. Compute the remainder when $44121 \cdot n!$ is divided by 81472. | 32,752 | graphs = [
Graph(
let={
"_n": Const(8),
"n": MaxOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(2)), Leq(Var("n"), Ref("_n")), IsPrime(Var("n"))))),
"result": Factorial(Ref("n")),
"Q": Mod(value=Mul(Const(44121), Ref("result")), modulu... | NT | null | COMPUTE | sympy | MAX_PRIME_BELOW | [
"MAX_PRIME_BELOW"
] | dc3ad3 | comb_factorial_compute_v1 | null | 3 | 0 | [
"MAX_PRIME_BELOW"
] | 1 | 0.001 | 2026-02-08T11:00:34.143967Z | {
"verified": true,
"answer": 32752,
"timestamp": "2026-02-08T11:00:34.145045Z"
} | 532be1 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 83,
"completion_tokens": 825
},
"timestamp": "2026-02-14T09:58:25.793Z",
"answer": 32752
},
{
... | 1 | [
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
}... | {
"lo": -5.49,
"mid": 0.22,
"hi": 6.51
} | ||
609f9d | nt_sum_divisors_mod_v1_124444284_2578 | Let $S$ be the set of all ordered pairs $(x, y)$ of positive integers such that $xy = 14288400$. Let $n$ be the minimum value of $x + y$ over all pairs $(x, y) \in S$. Compute the remainder when the sum of all positive divisors of $n$ is divided by $10007$. | 8,786 | graphs = [
Graph(
let={
"n": MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(Mul(Var("x"), Var("y")), Const(14288400)))), expr=Sum(Var("x"), Var("y")))),
"M": Const(100... | NT | null | COMPUTE | sympy | B3 | [
"B3"
] | 0cd20d | nt_sum_divisors_mod_v1 | null | 6 | 0 | [
"B3"
] | 1 | 0.004 | 2026-02-08T04:46:19.368214Z | {
"verified": true,
"answer": 8786,
"timestamp": "2026-02-08T04:46:19.371894Z"
} | 7804dd | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 187,
"completion_tokens": 1977
},
"timestamp": "2026-02-11T22:03:31.027Z",
"answer": 8786
},
{
"... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "V1",
"status": "no"
},
{
"lemma": "V3",
"status": "no"
}
] | {
"lo": -3.42,
"mid": 1.86,
"hi": 7.55
} | ||
3ae8e0 | comb_count_derangements_v1_784195855_4187 | Let $n = 8$. Define $d_n$ to be the number of derangements of $n$ elements. Let $C$ be the maximum value of $xy$ over all pairs of positive integers $(x, y)$ such that $x + y = 194$. Compute $C - d_n$, then find the remainder when this value is divided by $91357$. Report this remainder. | 85,933 | graphs = [
Graph(
let={
"_n": Const(194),
"n": Const(8),
"result": Subfactorial(arg=Ref(name='n')),
"_c": MaxOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name=... | COMB | null | COUNT | sympy | B1 | [
"B1"
] | d2b6e1 | comb_count_derangements_v1 | negation_mod | 4 | 0 | [
"B1"
] | 1 | 0.002 | 2026-02-08T06:54:16.386008Z | {
"verified": true,
"answer": 85933,
"timestamp": "2026-02-08T06:54:16.388221Z"
} | 90d7be | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 193,
"completion_tokens": 1110
},
"timestamp": "2026-02-24T07:14:33.934Z",
"answer": 85933
},
{
"... | 1 | [
{
"lemma": "B1",
"status": "ok"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "V8_SU... | {
"lo": -4.93,
"mid": -2.91,
"hi": -0.71
} | ||
bd7b13 | antilemma_k3_v1_677425708_2367 | Let $m = 16146$ and $n = 76760$. Define $x$ to be the sum of Euler's totient function $\phi(d)$ over all positive divisors $d$ of $n$. Let $c = 7001$. Let $S$ be the set of all integers $x$ such that $x^2 - 397x + m = 0$. Compute the value of $$
\left( x \bmod 251 + c \cdot \left( x \bmod \sum S \right) \right) \bmod 7... | 31,533 | graphs = [
Graph(
let={
"_m": Const(16146),
"_n": Const(76760),
"x": SumOverDivisors(n=Ref(name='_n'), var='d', expr=EulerPhi(n=Var(name='d'))),
"_c": Const(7001),
"Q": Mod(value=Sum(Mod(value=Ref("x"), modulus=Const(251)), Mul(Ref("_c"), Mod(value... | NT | COMB | COMPUTE | sympy | VIETA_SUM | [
"VIETA_SUM",
"K3"
] | 4765cd | antilemma_k3_v1 | two_moduli | 5 | 0 | [
"K3",
"VIETA_SUM"
] | 2 | 0.001 | 2026-02-08T05:01:19.791820Z | {
"verified": true,
"answer": 31533,
"timestamp": "2026-02-08T05:01:19.792822Z"
} | 0325a0 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 237,
"completion_tokens": 1249
},
"timestamp": "2026-02-11T22:44:34.143Z",
"answer": 31533
},
{
... | 1 | [
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "K3",
"status": "ok"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{... | {
"lo": -3.42,
"mid": 1.86,
"hi": 7.55
} | ||
b1f01f | comb_count_partitions_v1_865884756_3830 | Let $d$ be a positive integer such that $1 \leq d \leq 39$ and $d$ divides 1677. Let $n$ be the largest such $d$. Compute the number of integer partitions of $n$. Then, find the remainder when $94475$ times this number is divided by 75738. | 70,413 | graphs = [
Graph(
let={
"_n": Const(75738),
"n": MaxOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Const(1)), Leq(Var("d"), Const(39)), Divides(divisor=Var("d"), dividend=Const(1677))))),
"result": Partition(arg=Ref(name='n')),
"_c": Const(... | NT | COMB | COUNT | sympy | MAX_DIVISOR | [
"MAX_DIVISOR"
] | 51757e | comb_count_partitions_v1 | null | 4 | 0 | [
"MAX_DIVISOR"
] | 1 | 0.002 | 2026-02-08T17:35:25.941150Z | {
"verified": true,
"answer": 70413,
"timestamp": "2026-02-08T17:35:25.943429Z"
} | 2bd6aa | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 117,
"completion_tokens": 1963
},
"timestamp": "2026-02-18T05:24:09.133Z",
"answer": 70413
},
... | 1 | [
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "MAX_DIVISOR",
"status": "ok"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
2d40fb | geo_count_lattice_triangle_v1_1218484723_4208 | Let $M = |128 \cdot 180 + 120 \cdot (-64)|$ and $R = \gcd(128, 64) + \gcd(|120 - 128|, |180 - 64|) + \gcd(|0 - 120|, |0 - 180|)$. Compute $\frac{M + 2 - R}{2}$. | 7,617 | graphs = [
Graph(
let={
"_n": Const(4),
"area_2x": Abs(arg=Sum(Mul(Const(value=128), Const(value=180)), Mul(Const(value=120), Sub(left=Const(value=0), right=Const(value=64))))),
"boundary": Sum(GCD(a=Abs(arg=Const(value=128)), b=Abs(arg=Const(value=64))), GCD(a=Abs(arg=Su... | GEOM | NT | COUNT | sympy | POLY_ORBIT_HENSEL | [
"POLY_ORBIT_HENSEL"
] | 53b6eb | geo_count_lattice_triangle_v1 | null | 3 | 0 | [
"POLY_ORBIT_HENSEL"
] | 1 | 0.021 | 2026-02-25T05:52:23.937763Z | {
"verified": true,
"answer": 7617,
"timestamp": "2026-02-25T05:52:23.958341Z"
} | d56e35 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 195,
"completion_tokens": 566
},
"timestamp": "2026-03-29T14:19:09.038Z",
"answer": 7617
},
{
"id... | 2 | [
{
"lemma": "POLY_ORBIT_HENSEL",
"status": "ok"
}
] | {
"lo": -10,
"mid": -6.41,
"hi": -2.82
} | ||
4e1597 | nt_sum_divisors_mod_v1_1520064083_9477 | Let $n$ be the minimum value of $x + y$ over all ordered pairs $(x, y)$ of positive integers such that $xy = 1587600$. Let $\sigma$ be the sum of the positive divisors of $n$, and let $M = 11399$. Define $\text{result} = \sigma \bmod M$. Find the value of $21904 - \text{result}$. | 12,544 | graphs = [
Graph(
let={
"n": MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(Mul(Var("x"), Var("y")), Const(1587600)))), expr=Sum(Var("x"), Var("y")))),
"M": Const(1139... | NT | null | COMPUTE | sympy | B3 | [
"B3"
] | 0cd20d | nt_sum_divisors_mod_v1 | null | 6 | 0 | [
"B3"
] | 1 | 0.001 | 2026-02-08T10:47:05.746608Z | {
"verified": true,
"answer": 12544,
"timestamp": "2026-02-08T10:47:05.747847Z"
} | 687cad | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 134,
"completion_tokens": 1674
},
"timestamp": "2026-02-14T08:50:53.702Z",
"answer": 12544
},
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "V3",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
}
] | {
"lo": -5.49,
"mid": 0.22,
"hi": 6.51
} | ||
c837b6 | antilemma_coprime_grid_v1_1248542787_847 | Let $x$ be the number of ordered pairs $(i, j)$ of positive integers with $1 \leq i \leq 37$ and $1 \leq j \leq 200$ such that $\gcd(i, j) = 1$. Let $d_k$ denote the $k$th decimal digit of $x$ (with $k=0$ being the units digit). Compute
$$
\sum_{i=0}^{t} d_i (i+1)^2 + 2916,
$$
where $t$ is the number of decimal digits ... | 3,065 | graphs = [
Graph(
let={
"x": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("i"), Var("j")]), condition=Eq(GCD(a=Var("i"), b=Var("j")), Const(1)), domain=CartesianProduct(left=IntegerRange(start=Const(1), end=Const(37)), right=IntegerRange(start=Const(1), end=Const(200))))),
"... | NT | COMB | COMPUTE | sympy | COUNT_COPRIME_GRID | [
"COUNT_COPRIME_GRID"
] | 20ec03 | antilemma_coprime_grid_v1 | null | 6 | 0 | [
"COUNT_COPRIME_GRID"
] | 1 | 0.001 | 2026-02-08T03:27:35.422872Z | {
"verified": true,
"answer": 3065,
"timestamp": "2026-02-08T03:27:35.424046Z"
} | e9b4e4 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 245,
"completion_tokens": 2650
},
"timestamp": "2026-02-09T09:03:14.219Z",
"answer": 3065
},
{
"i... | 1 | [
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "ok"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
},
{
"lemma": "VAL_SUM_EQ",
"stat... | {
"lo": -6.51,
"mid": -0.31,
"hi": 5.43
} | ||
778fbb | modular_inverse_v1_784195855_9529 | Let $N = 11056$. Compute the number of positive integers $n$ such that $1 \leq n \leq N$, $8$ divides $n$, and $\gcd(n, 15) = 1$. Denote this count by $u$. Let $a = 126$ and $m = 739$. Find the smallest positive integer $x$ such that $1 \leq x \leq u$ and $126x \equiv 1 \pmod{739}$. Compute the remainder when $44121$ t... | 34,590 | graphs = [
Graph(
let={
"_n": Const(11056),
"a": Const(126),
"m": Const(739),
"upper": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Ref("_n")), Divides(divisor=Const(8), dividend=Var("n")), Eq(GCD(a=Var("n"),... | NT | null | EXTREMUM | sympy | C5 | [
"C5"
] | 1d9668 | modular_inverse_v1 | null | 6 | 0 | [
"C5"
] | 1 | 0.033 | 2026-02-08T16:53:03.804102Z | {
"verified": true,
"answer": 34590,
"timestamp": "2026-02-08T16:53:03.837489Z"
} | 79d6d9 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 169,
"completion_tokens": 1929
},
"timestamp": "2026-02-17T15:25:05.622Z",
"answer": 34590
},
... | 1 | [
{
"lemma": "C5",
"status": "ok"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "V1",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
f579f6 | antilemma_sum_equals_v1_1978505735_6484 | Let $T$ be the number of integers $t$ such that there exist positive integers $a \leq 10$ and $b \leq 13$ satisfying $t = 15a + 6b + 5$ and $26 \leq t \leq 233$. Compute the number of ordered pairs $(i, j)$ with $1 \leq i \leq 64$ and $1 \leq j \leq 65$ such that $i + j = T$. | 64 | graphs = [
Graph(
let={
"_n": CountOverSet(set=SolutionsSet(var=Var("t"), condition=Exists(var=Var(name='a'), condition=Exists(var=Var(name='b'), condition=And(Geq(left=Var(name='a'), right=Const(value=1)), Leq(left=Var(name='a'), right=Const(value=10)), Geq(left=Var(name='b'), right=Const(value... | COMB | GEOM | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM/COUNT_SUM_EQUALS",
"COUNT_SUM_EQUALS"
] | ada383 | antilemma_sum_equals_v1 | null | 5 | 0 | [
"COUNT_SUM_EQUALS",
"LIN_FORM"
] | 2 | 0.008 | 2026-02-08T19:36:30.884134Z | {
"verified": true,
"answer": 64,
"timestamp": "2026-02-08T19:36:30.891650Z"
} | 5d5421 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 1,
"correct": {
"strict": false,
"boxed": false,
"relaxed": true
},
"usage": {
"prompt_tokens": 148,
"completion_tokens": 3574
},
"timestamp": "2026-02-18T22:59:36.792Z",
"answer": 60
},
{... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "ok"
},
{
"lemma": "LIN_F... | {
"lo": -5.39,
"mid": -2.64,
"hi": 0.63
} | ||
655d4b | comb_count_derangements_v1_151522320_2007 | Let $A$ be the set of all integers $t$ such that $7 \leq t \leq 549$ and there exist positive integers $a \leq 47$, $b \leq 157$ satisfying $t = 5a + 2b$. Let $m$ be the number of elements in $A$. Let $d$ be the smallest integer greater than or equal to $2$ that divides $m$. Compute the number of derangements of $d$ el... | 1,854 | graphs = [
Graph(
let={
"_m": Const(2),
"_n": CountOverSet(set=SolutionsSet(var=Var("t"), condition=Exists(var=Var(name='a'), condition=Exists(var=Var(name='b'), condition=And(Geq(left=Var(name='a'), right=Const(value=1)), Leq(left=Var(name='a'), right=Const(value=47)), Geq(left=Var(... | NT | COMB | COUNT | sympy | LIN_FORM | [
"LIN_FORM/MIN_PRIME_FACTOR"
] | bb1a13 | comb_count_derangements_v1 | null | 5 | 0 | [
"LIN_FORM",
"MIN_PRIME_FACTOR"
] | 2 | 0.002 | 2026-02-08T04:31:02.607416Z | {
"verified": true,
"answer": 1854,
"timestamp": "2026-02-08T04:31:02.609021Z"
} | 722ba3 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 216,
"completion_tokens": 4311
},
"timestamp": "2026-02-10T16:50:14.388Z",
"answer": 1854
},
{
"... | 1 | [
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "MIN_PRIME_FACTOR",
"status": "ok_la... | {
"lo": -3.42,
"mid": 1.86,
"hi": 7.55
} | ||
2cdd08 | nt_euler_phi_compute_v1_1918700295_2089 | Let $n = 38809$. Compute $\phi(n)$, where $\phi$ denotes Euler's totient function. Let $r = \phi(n)$. Let $t$ be the number of positive integers $p$ for which there exists a positive integer $q > p$ such that $pq = 2490180$ and $\gcd(p, q) = 1$. Compute $$ r + \left( 2^{r \bmod{t}} \bmod{88029} \right). $$ Determine th... | 38,628 | graphs = [
Graph(
let={
"n": Const(38809),
"result": EulerPhi(n=Ref("n")),
"Q": Sum(Ref("result"), Mod(value=Pow(Const(2), Mod(value=Ref("result"), modulus=CountOverSet(set=SolutionsSet(var=Var("p"), condition=And(IsPositive(arg=Var(name='p')), Exists(var=Var(name='q'), c... | NT | null | COMPUTE | sympy | COPRIME_PAIRS | [
"COPRIME_PAIRS"
] | 64a51e | nt_euler_phi_compute_v1 | mod_exp | 6 | 0 | [
"COPRIME_PAIRS"
] | 1 | 0.002 | 2026-02-08T07:40:57.501882Z | {
"verified": true,
"answer": 38628,
"timestamp": "2026-02-08T07:40:57.503809Z"
} | d386df | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 158,
"completion_tokens": 2437
},
"timestamp": "2026-02-13T11:53:18.988Z",
"answer": 38628
},
... | 1 | [
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
}
] | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} |
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