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 |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
9d4d6b | nt_sum_phi_v1_1520064083_3150 | Let $\phi(n)$ denote Euler's totient function. Define $n_0 = 2420$. Let $A$ be the set of all positive integers $n$ such that $1 \leq n \leq n_0$ and
$$
n \equiv \left\lfloor \frac{n}{2} \right\rfloor \pmod{5}.
$$
Let $m = |A|$, the number of elements in $A$. Now let $B$ be the set of all positive integers $n$ such tha... | 71,276 | graphs = [
Graph(
let={
"_n": Const(2420),
"upper": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Ref("_n")), Congruent(a=Var(name='n'), b=Floor(arg=Div(left=Var(name='n'), right=Const(value=2))), modulus=Const(value=5))))),
... | NT | null | SUM | sympy | L3C | [
"L3C"
] | 73f8b0 | nt_sum_phi_v1 | null | 6 | 0 | [
"L3C"
] | 1 | 0.028 | 2026-02-08T05:29:47.262429Z | {
"verified": true,
"answer": 71276,
"timestamp": "2026-02-08T05:29:47.290589Z"
} | 444aad | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 179,
"completion_tokens": 3928
},
"timestamp": "2026-02-12T09:28:55.136Z",
"answer": 71276
},
... | 1 | [
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "L3C",
"status": "ok"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
}
] | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
f9427a | comb_sum_binomial_row_v1_1918700295_2788 | Let $n = \sum_{k=1}^{5} k$. Compute $2^n$. Let this value be $a$. Find the remainder when $20160 - a$ is divided by 85242. | 72,634 | graphs = [
Graph(
let={
"_n": Const(2),
"n": Summation(var="k", start=Const(1), end=Const(5), expr=Var("k")),
"result": Pow(Ref("_n"), Ref("n")),
"_c": Const(20160),
"Q": Mod(value=Sub(Ref("_c"), Ref("result")), modulus=Const(85242)),
},
... | NT | null | SUM | sympy | SUM_ARITHMETIC | [
"SUM_ARITHMETIC"
] | eb34f0 | comb_sum_binomial_row_v1 | null | 2 | 0 | [
"SUM_ARITHMETIC"
] | 1 | 0.001 | 2026-02-08T08:12:24.010996Z | {
"verified": true,
"answer": 72634,
"timestamp": "2026-02-08T08:12:24.012158Z"
} | 2ccea7 | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 106,
"completion_tokens": 316
},
"timestamp": "2026-02-15T19:47:11.083Z",
"answer": 72634
},
{
"id": 11,
... | 2 | [
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "SUM_ARITHMETIC",
"status": "ok"
}
] | {
"lo": -9.14,
"mid": -6.05,
"hi": -3.73
} | ||
510e6d | comb_catalan_compute_v1_1915831931_742 | Let $S$ be the set of all ordered pairs $(i, j)$ of integers such that $1 \leq i \leq 12$, $1 \leq j \leq 12$, and $i + j = 12$. Let $n$ be the number of elements in $S$. Define $C_n$ to be the $n$th Catalan number, given by
$$
C_n = \frac{1}{n+1} \binom{2n}{n}.
$$
Compute the remainder when $44483 \cdot C_n$ is divide... | 5,334 | graphs = [
Graph(
let={
"_n": Const(63917),
"n": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("i"), Var("j")]), condition=Eq(Sum(Var("i"), Var("j")), Const(12)), domain=CartesianProduct(left=IntegerRange(start=Const(1), end=Const(12)), right=IntegerRange(start=Const(1), end=... | COMB | null | COMPUTE | sympy | COUNT_SUM_EQUALS | [
"COUNT_SUM_EQUALS"
] | 75ab0f | comb_catalan_compute_v1 | null | 3 | 0 | [
"COUNT_SUM_EQUALS"
] | 1 | 0.012 | 2026-02-08T15:39:05.521847Z | {
"verified": true,
"answer": 5334,
"timestamp": "2026-02-08T15:39:05.533378Z"
} | 6532f6 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 240,
"completion_tokens": 1746
},
"timestamp": "2026-02-24T18:14:25.489Z",
"answer": 5334
},
{
"... | 1 | [
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "ok"
},
{
"lemma": "V8",
"status": "no"
},
{
"lemma": "V8_SU... | {
"lo": -2.4,
"mid": 1.57,
"hi": 5.75
} | ||
b50672 | nt_min_crt_v1_397696148_499 | Let $m = 4$, $k = 7$, $a = 3$, and $b = 2$. Define
$$
S = \sum_{i=1}^{7} \phi(i) \left\lfloor \frac{7}{i} \right\rfloor,
$$
where $\phi(n)$ denotes Euler's totient function. Let $N$ be the set of all integers $n$ such that $1 \leq n \leq S$, $n \equiv a \pmod{m}$, and $n \equiv b \pmod{k}$. Compute the minimum value of... | 23 | graphs = [
Graph(
let={
"m": Const(4),
"k": Const(7),
"a": Const(3),
"b": Const(2),
"upper": Summation(var="k", start=Const(1), end=Const(7), expr=Mul(EulerPhi(n=Var("k")), Floor(Div(Const(7), Var("k"))))),
"result": MinOverSet(set=Solu... | NT | null | EXTREMUM | sympy | K2 | [
"K2"
] | 6897ab | nt_min_crt_v1 | null | 5 | 0 | [
"K2"
] | 1 | 0.009 | 2026-02-08T11:30:53.490721Z | {
"verified": true,
"answer": 23,
"timestamp": "2026-02-08T11:30:53.499829Z"
} | be0bf9 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 176,
"completion_tokens": 1079
},
"timestamp": "2026-02-14T15:18:49.058Z",
"answer": 23
},
{
... | 1 | [
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K2",
"status": "ok"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "V1",
"status": "no"
}
] | {
"lo": -6.96,
"mid": -4.56,
"hi": -1.46
} | ||
314932 | nt_min_with_divisor_count_v1_784195855_4158 | Let $S$ be the set of all integers $t$ such that there exist integers $a$ and $b$ satisfying the following conditions:
- $1 \leq a \leq 2$,
- $1 \leq b \leq 5$,
- $5 \leq t \leq 16$,
- $t = 3a + 2b$.
Let $d$ be the number of elements in $S$. Let $n$ be the smallest positive integer such that $2 \leq n \leq 32768$ and... | 48 | graphs = [
Graph(
let={
"upper": Const(32768),
"div_count": 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=2)), ... | NT | null | EXTREMUM | sympy | ONE_PHI_1 | [
"LIN_FORM",
"ONE_PHI_2"
] | 9858be | nt_min_with_divisor_count_v1 | null | 6 | 0 | [
"LIN_FORM",
"ONE_PHI_1",
"ONE_PHI_2"
] | 3 | 2.942 | 2026-02-08T06:52:30.579457Z | {
"verified": true,
"answer": 48,
"timestamp": "2026-02-08T06:52:33.521386Z"
} | e4f1f0 | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 236,
"completion_tokens": 1029
},
"timestamp": "2026-02-19T16:32:34.579Z",
"answer": 48
}
] | 2 | [
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "ONE_PHI_2",
"status": "ok"
},
{
"lemma": "V3",
"status": "no"
},
{
"le... | {
"lo": -10,
"mid": -6.47,
"hi": -2.95
} | ||
4f2e3e | algebra_quadratic_discriminant_v1_124444284_6461 | Let $a = -1$, $b = -9$, and $c = 0$. Let $r$ be the number of positive integers $p$ for which there exists an integer $q$ such that $pq = 108$, $\gcd(p, q) = 1$, and $p < q$. Define $\text{result} = b^r - 4ac$. Let $Q = 32761 - \text{result}$. Find the value of $Q$. | 32,680 | graphs = [
Graph(
let={
"_n": Const(32761),
"a": Const(-1),
"b": Const(-9),
"c": Const(0),
"result": Sub(Pow(Ref("b"), CountOverSet(set=SolutionsSet(var=Var("p"), condition=And(IsPositive(arg=Var(name='p')), Exists(var=Var(name='q'), condition=And(... | NT | null | COMPUTE | sympy | COPRIME_PAIRS | [
"COPRIME_PAIRS"
] | 2bb3aa | algebra_quadratic_discriminant_v1 | null | 4 | 0 | [
"COPRIME_PAIRS"
] | 1 | 0.002 | 2026-02-08T08:28:14.772427Z | {
"verified": true,
"answer": 32680,
"timestamp": "2026-02-08T08:28:14.773930Z"
} | eed42e | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 148,
"completion_tokens": 1021
},
"timestamp": "2026-02-13T18:52:42.840Z",
"answer": 32680
},
... | 1 | [
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "V1",
"status": "no"
},
{
"lemma": "V3",
"status": "no"
},
{
"lemma": "VAL_SUM_EQ",
"status": "no"
... | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
a18190 | alg_poly_orbit_count_v1_1218484723_1450 | Let $f(x) = (2x^3 - 2x) \bmod 37$. For a non-negative integer $a$, define the sequence $N = f(a)$, $M = f(N)$, $R = f(M)$, $S = f(R)$, $T = f(S)$, and $K = f(T)$. Find the number of integers $a$ with $0 \le a \le 33669$ such that $K = a$, but $N \ne a$, $M \ne a$, $R \ne a$, $S \ne a$, and $T \ne a$. | 10,920 | graphs = [
Graph(
let={
"p1": Mod(value=Sum(Mul(Const(2), Pow(Var("a"), Const(3))), Mul(Const(-2), Var("a"))), modulus=Const(37)),
"p2": Mod(value=Sum(Mul(Const(2), Pow(Ref("p1"), Const(3))), Mul(Const(-2), Ref("p1"))), modulus=Const(37)),
"p3": Mod(value=Sum(Mul(Const(2)... | ALG | null | COUNT | sympy | POLY_ORBIT_COUNT | [
"POLY_ORBIT_COUNT"
] | 4ad965 | alg_poly_orbit_count_v1 | null | 6 | null | [
"POLY_ORBIT_COUNT"
] | 1 | 0.034 | 2026-02-25T03:10:01.568775Z | {
"verified": true,
"answer": 10920,
"timestamp": "2026-02-25T03:10:01.602955Z"
} | fee2d0 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 245,
"completion_tokens": 4784
},
"timestamp": "2026-03-10T03:46:56.164Z",
"answer": 6
},
{
"i... | 0 | [
{
"lemma": "POLY_ORBIT_COUNT",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
}
] | {
"lo": 4.43,
"mid": 6.62,
"hi": 9.7
} | ||
1789cf | antilemma_cartesian_v1_784195855_6664 | Let $x$ be the number of ordered pairs $(a,b)$ where $a$ is an integer from 1 to 22, inclusive, and $b$ is an integer from 1 to 49, inclusive. Compute the remainder when $74867 \cdot x$ is divided by $64374$. | 46,004 | graphs = [
Graph(
let={
"x": CountOverSet(set=CartesianProduct(left=IntegerRange(start=Const(1), end=Const(22)), right=IntegerRange(start=Const(1), end=Const(49)))),
"Q": Mod(value=Mul(Const(74867), Ref("x")), modulus=Const(64374)),
},
goal=Ref("Q"),
)
] | COMB | GEOM | COMPUTE | sympy | COUNT_CARTESIAN | [
"COUNT_CARTESIAN"
] | 409d7d | antilemma_cartesian_v1 | null | 2 | 0 | [
"COUNT_CARTESIAN"
] | 1 | 0 | 2026-02-08T08:46:38.533664Z | {
"verified": true,
"answer": 46004,
"timestamp": "2026-02-08T08:46:38.534096Z"
} | 57f730 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 175,
"completion_tokens": 2518
},
"timestamp": "2026-02-24T10:01:35.971Z",
"answer": 46004
},
{
"... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "ok"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8_SUM",
"statu... | {
"lo": -2.35,
"mid": 1.22,
"hi": 4.84
} | ||
a3d7b8 | sequence_lucas_compute_v1_784195855_2068 | Let $m$ be the number of ordered pairs $(i,j)$ with $1 \leq i \leq 4$ and $1 \leq j \leq 7$ such that $\gcd(i,j) = 1$. Let $n_1$ be the maximum value of $xy$ over all ordered pairs $(x,y)$ of positive integers such that $x + y = m$. Let $n$ be the minimum value of $x + y$ over all ordered pairs $(x,y)$ of positive inte... | 15,127 | graphs = [
Graph(
let={
"_m": 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(4)), right=IntegerRange(start=Const(1), end=Const(7))))),
"_n... | NT | null | COMPUTE | sympy | COUNT_COPRIME_GRID | [
"COUNT_COPRIME_GRID/B1/B3"
] | e96e76 | sequence_lucas_compute_v1 | null | 7 | 0 | [
"B1",
"B3",
"COUNT_COPRIME_GRID"
] | 3 | 0.002 | 2026-02-08T05:27:51.702407Z | {
"verified": true,
"answer": 15127,
"timestamp": "2026-02-08T05:27:51.704776Z"
} | 7b1b44 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 171,
"completion_tokens": 1228
},
"timestamp": "2026-02-12T09:17:04.391Z",
"answer": 15127
},
... | 1 | [
{
"lemma": "B1",
"status": "ok_later"
},
{
"lemma": "B3",
"status": "ok_later"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "ok"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
... | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
b42bc2 | comb_bell_compute_v1_1915831931_3550 | Let $n$ be the number of integers $t$ such that $21 \leq t \leq 31$ and there exist integers $a$ and $b$ with $1 \leq a \leq 3$, $1 \leq b \leq 3$, and $t = 3a + 2b + 16$. Let $B_n$ be the $n$th Bell number. Compute the remainder when $44121 \cdot B_n$ is divided by 75329. | 1,793 | graphs = [
Graph(
let={
"_n": Const(75329),
"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=Va... | COMB | null | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | comb_bell_compute_v1 | null | 4 | 0 | [
"LIN_FORM"
] | 1 | 0.003 | 2026-02-08T17:45:18.485056Z | {
"verified": true,
"answer": 1793,
"timestamp": "2026-02-08T17:45:18.487636Z"
} | 194a91 | 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": 1641
},
"timestamp": "2026-02-18T07:05:08.302Z",
"answer": 1793
},
{... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
}
] | {
"lo": -2.38,
"mid": 1.74,
"hi": 6.59
} | ||
a504f6 | antilemma_cartesian_v1_1440796553_1386 | Let $x$ be the number of ordered pairs $(a, b)$ such that $1 \leq a \leq 9$ and $1 \leq b \leq 12$. Let $c$ be the number of integers $t$ with $33 \leq t \leq 21084$ for which there exist positive integers $a \leq 1456$ and $b \leq 172$ such that $t = 12a + 21b$. Compute $x^2 + 32x + c$. | 22,120 | graphs = [
Graph(
let={
"_n": Const(2),
"x": CountOverSet(set=CartesianProduct(left=IntegerRange(start=Const(1), end=Const(9)), right=IntegerRange(start=Const(1), end=Const(12)))),
"_c": CountOverSet(set=SolutionsSet(var=Var("t"), condition=Exists(var=Var(name='a'), condi... | COMB | GEOM | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM",
"COUNT_CARTESIAN"
] | 22e14d | antilemma_cartesian_v1 | quadratic_mod | 3 | 0 | [
"COUNT_CARTESIAN",
"LIN_FORM"
] | 2 | 0.002 | 2026-02-08T13:41:29.752482Z | {
"verified": true,
"answer": 22120,
"timestamp": "2026-02-08T13:41:29.754191Z"
} | 4287fa | 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": 28613
},
"timestamp": "2026-02-24T18:54:33.667Z",
"answer": 22120
},
{
... | 1 | [
{
"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": "no"
},
{
"lemma": "LIN_F... | {
"lo": 3.25,
"mid": 5.68,
"hi": 8.81
} | ||
8db8c5 | diophantine_product_count_v1_784195855_8386 | Let $k = 240$. Define $A$ to be the set of all positive integers $x$ such that $1 \leq x \leq 48$, $x$ divides $k$, and $\frac{k}{x} \leq 48$. Let $\text{result} = |A|$, the number of elements in $A$.
Let $P$ be the set of all ordered pairs $(x, y)$ of positive integers such that $x \cdot y = 6718464$. Define $S$ to b... | 5,172 | graphs = [
Graph(
let={
"k": Const(240),
"upper": Const(48),
"result": CountOverSet(set=SolutionsSet(var=Var("x"), condition=And(Geq(Var("x"), Const(1)), Leq(Var("x"), Ref("upper")), Divides(divisor=Var("x"), dividend=Ref("k")), Leq(Div(Ref("k"), Var("x")), Ref("upper")))... | NT | null | COUNT | sympy | B3 | [
"B3"
] | fc629c | diophantine_product_count_v1 | negation_mod | 5 | 0 | [
"B3"
] | 1 | 0.016 | 2026-02-08T16:02:46.273250Z | {
"verified": true,
"answer": 5172,
"timestamp": "2026-02-08T16:02:46.289389Z"
} | b870e1 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 205,
"completion_tokens": 1378
},
"timestamp": "2026-02-16T19:08:34.244Z",
"answer": 5172
},
{... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
4a26bd | nt_count_divisible_and_v1_971394319_245 | Let $S$ be the set of all ordered pairs $(x, y)$ of positive integers such that $xy = 8714304$. Let $u$ be the minimum value of $x + y$ over all such pairs. Determine the number of positive integers $n$ such that $1 \leq n \leq u$, $n$ is divisible by $4$, and $n$ is divisible by $6$. | 492 | graphs = [
Graph(
let={
"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")), Const(8714304)))), expr=Sum(Var("x"), Var("y")))),
"d1": Const... | NT | null | COUNT | sympy | B3 | [
"B3"
] | 0cd20d | nt_count_divisible_and_v1 | null | 4 | 0 | [
"B3"
] | 1 | 0.267 | 2026-02-08T12:54:59.520774Z | {
"verified": true,
"answer": 492,
"timestamp": "2026-02-08T12:54:59.788173Z"
} | 7efaa1 | 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": 1095
},
"timestamp": "2026-02-15T08:02:22.815Z",
"answer": 492
},
{
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
}
] | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
f8bd0e | nt_sum_totient_over_divisors_v1_784195855_2551 | Let $n = 60654$. Define $S = \sum_{d \mid n} \phi(d)$, where $\phi$ denotes Euler's totient function. Let $T$ be the set of all ordered pairs of positive integers $(x, y)$ such that $xy = 2250000$. Let $M$ be the minimum value of $x + y$ as $(x, y)$ ranges over $T$. Compute the remainder when $M - S$ is divided by $831... | 25,492 | graphs = [
Graph(
let={
"n": Const(60654),
"result": SumOverDivisors(n=Ref(name='n'), var='d', expr=EulerPhi(n=Var(name='d'))),
"Q": Mod(value=Sub(MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x... | NT | null | COMPUTE | sympy | B3 | [
"B3"
] | fc629c | nt_sum_totient_over_divisors_v1 | negation_mod | 5 | 0 | [
"B3"
] | 1 | 0.006 | 2026-02-08T05:51:14.528009Z | {
"verified": true,
"answer": 25492,
"timestamp": "2026-02-08T05:51:14.533604Z"
} | 5d04fd | 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": 1148
},
"timestamp": "2026-02-12T16:01:15.470Z",
"answer": 25492
},
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "V1",
"status": "no"
}
] | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
6c8ac9 | comb_catalan_compute_v1_1915831931_3766 | Let $m = 16$. Consider the set of all ordered pairs $(i, j)$ of positive integers such that $i + j = m$, where $1 \leq i \leq 14$ and $1 \leq j \leq 15$. Let $n$ be the number of elements in this set. Now consider the set of all ordered pairs $(i_1, j_1)$ of positive integers such that $i_1 + j_1 = n$, where $1 \leq i_... | 58,786 | graphs = [
Graph(
let={
"_m": Const(16),
"_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(14)), right=IntegerRange(start=Const(1), end=Co... | COMB | null | COMPUTE | sympy | COUNT_SUM_EQUALS | [
"COUNT_SUM_EQUALS/COUNT_SUM_EQUALS"
] | 756129 | comb_catalan_compute_v1 | null | 4 | 0 | [
"COUNT_SUM_EQUALS"
] | 1 | 0.019 | 2026-02-08T17:54:19.277832Z | {
"verified": true,
"answer": 58786,
"timestamp": "2026-02-08T17:54:19.296406Z"
} | f2f6ea | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 208,
"completion_tokens": 1414
},
"timestamp": "2026-02-18T09:27:38.515Z",
"answer": 58786
},
... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "ok"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8_SUM",
"status":... | {
"lo": -2.38,
"mid": 1.74,
"hi": 6.59
} | ||
9b2d20 | algebra_poly_eval_v1_1978505735_4286 | Let $z$ be the minimum value of $x + y$ over all ordered pairs $(x, y)$ of positive integers such that $xy = 144$. Define $$f(z) = \frac{40z^4 + 80z^3 + 40z^2 + 45z - 45}{235}.$$ Compute the remainder when $32400 - f(z)$ is divided by $96453$. | 67,572 | graphs = [
Graph(
let={
"_n": Const(40),
"z": 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(144)))), expr=Sum(Var("x"), Var("y")))),
... | NT | null | COMPUTE | sympy | B3 | [
"B3"
] | 0cd20d | algebra_poly_eval_v1 | null | 4 | 0 | [
"B3"
] | 1 | 0.004 | 2026-02-08T18:08:36.613644Z | {
"verified": true,
"answer": 67572,
"timestamp": "2026-02-08T18:08:36.617208Z"
} | 2e039f | 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": 1461
},
"timestamp": "2026-02-18T14:34:51.664Z",
"answer": 67572
},
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
699e59 | algebra_poly_eval_v1_601307018_3740 | Let $a$ be the number of ordered pairs $(a_1, b)$ of positive integers with $1 \le a_1, b \le 30$ such that $b^2 - 8a_1 b + 16a_1^2 = 81$. Compute $34596 - (2a^3 - a^2 - 8a - 8)$. | 31,388 | graphs = [
Graph(
let={
"_n": Const(3),
"a": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("a1"), Var("b")]), condition=And(Geq(Var("a1"), Const(1)), Leq(Var("a1"), Const(30)), Geq(Var("b"), Const(1)), Leq(Var("b"), Const(30)), Eq(Sum(Pow(Var("b"), Const(2)), Mul(Const(-8), V... | ALG | null | COMPUTE | sympy | QF_PSD_COUNT | [
"QF_PSD_COUNT"
] | 09ce67 | algebra_poly_eval_v1 | null | 5 | 0 | [
"QF_PSD_COUNT"
] | 1 | 0.005 | 2026-03-10T04:19:22.436182Z | {
"verified": true,
"answer": 31388,
"timestamp": "2026-03-10T04:19:22.440817Z"
} | 1d12f4 | 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": 1394
},
"timestamp": "2026-03-29T09:49:07.079Z",
"answer": 31388
},
{
"... | 2 | [
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "QF_PSD_COUNT",
"status": "ok"
}
] | {
"lo": -10,
"mid": -6.24,
"hi": -2.48
} | ||
9afa1a | sequence_fibonacci_compute_v1_153355830_1951 | Let $n$ be the number of integers $t$ such that $7 \leq t \leq 35$ and there exist positive integers $a$ and $b$ with $1 \leq a \leq 5$, $1 \leq b \leq 5$, and $t = 2a + 5b$. Let $F_n$ denote the $n$-th Fibonacci number, defined by $F_1 = F_2 = 1$ and $F_k = F_{k-1} + F_{k-2}$ for $k \geq 3$. Compute the remainder when... | 75,025 | graphs = [
Graph(
let={
"_n": Const(91125),
"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=5)), Geq(left=Va... | NT | null | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | sequence_fibonacci_compute_v1 | null | 4 | 0 | [
"LIN_FORM"
] | 1 | 0.002 | 2026-02-08T06:48:12.577150Z | {
"verified": true,
"answer": 75025,
"timestamp": "2026-02-08T06:48:12.578917Z"
} | 5b7112 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 187,
"completion_tokens": 2795
},
"timestamp": "2026-02-13T05:11:58.838Z",
"answer": 75025
},
... | 1 | [
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "V3",
"status": "no"
},
{
"lemma": "VAL_SUM_EQ",
"status": "no"
}
] | {
"lo": -3.51,
"mid": 1.33,
"hi": 6.56
} | ||
fa433d | nt_count_with_divisor_count_v1_655260480_834 | Let $d$ be the largest prime number less than or equal to $16$. Compute the number of positive integers $n_1$ with $1 \leq n_1 \leq 48828$ such that the number of positive divisors of $n_1$ is equal to $d$. | 1 | graphs = [
Graph(
let={
"_n": Const(16),
"upper": Const(48828),
"div_count": MaxOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(2)), Leq(Var("n"), Ref("_n")), IsPrime(Var("n"))))),
"result": CountOverSet(set=SolutionsSet(var=Var("n1"),... | NT | null | COUNT | sympy | MAX_PRIME_BELOW | [
"MAX_PRIME_BELOW"
] | dc3ad3 | nt_count_with_divisor_count_v1 | null | 4 | 0 | [
"MAX_PRIME_BELOW"
] | 1 | 9.41 | 2026-02-08T15:38:55.268218Z | {
"verified": true,
"answer": 1,
"timestamp": "2026-02-08T15:39:04.678309Z"
} | b1d123 | 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": 798
},
"timestamp": "2026-02-16T10:31:11.264Z",
"answer": 1
},
{
... | 1 | [
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
},
{
"lemma": "VAL_SUM_EQ",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
009b34 | comb_catalan_compute_v1_971394319_736 | Let $n$ be the number of positive integers $t$ such that $5 \leq t \leq 16$ and there exist positive integers $a$ and $b$ with $1 \leq a \leq 2$, $1 \leq b \leq 5$, and $$t = 3a + 2b.$$ Let $C_n$ denote the $n$-th Catalan number. Let $Q = 29929 - C_n$. Compute $Q$. | 13,133 | graphs = [
Graph(
let={
"_n": Const(29929),
"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=2)), Geq(left=Va... | COMB | null | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | comb_catalan_compute_v1 | null | 4 | 0 | [
"LIN_FORM"
] | 1 | 0.003 | 2026-02-08T13:17:14.470363Z | {
"verified": true,
"answer": 13133,
"timestamp": "2026-02-08T13:17:14.473503Z"
} | ca8d88 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 217,
"completion_tokens": 465
},
"timestamp": "2026-02-24T17:37:29.902Z",
"answer": 13133
},
{
"i... | 1 | [
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "V8",
"status": "no"
},
{
"lemma": "V8_SUM",
"s... | {
"lo": -7.18,
"mid": -5,
"hi": -3.01
} | ||
ea920c | sequence_lucas_compute_v1_151522320_1869 | Let $n$ be the largest prime number such that $2 \leq n \leq 19$. Let $L_n$ denote the $n$th Lucas number, defined by $L_1 = 1$, $L_2 = 3$, and $L_k = L_{k-1} + L_{k-2}$ for $k \geq 3$. Compute the remainder when $44121 \cdot L_n$ is divided by $53726$. | 32,727 | graphs = [
Graph(
let={
"_n": Const(2),
"n": MaxOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Ref("_n")), Leq(Var("n"), Const(19)), IsPrime(Var("n"))))),
"result": Lucas(arg=Ref(name='n')),
"Q": Mod(value=Mul(Const(44121), Ref("result")), ... | NT | null | COMPUTE | sympy | MAX_PRIME_BELOW | [
"MAX_PRIME_BELOW"
] | dc3ad3 | sequence_lucas_compute_v1 | null | 3 | 0 | [
"MAX_PRIME_BELOW"
] | 1 | 0.001 | 2026-02-08T04:26:27.990428Z | {
"verified": true,
"answer": 32727,
"timestamp": "2026-02-08T04:26:27.991282Z"
} | 4ec01c | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 212,
"completion_tokens": 1805
},
"timestamp": "2026-02-10T16:35:04.246Z",
"answer": 32727
},
{
... | 1 | [
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok"
},
{
"lemma": "MOD_SUB",
"status": "no"
}
... | {
"lo": -3.42,
"mid": 1.86,
"hi": 7.55
} | ||
d651fd | algebra_quadratic_discriminant_v1_1978505735_8225 | Let $a = -1$, $b = -16$, $c = -64$, and let $D = b^2 - 4ac$. Let $\alpha$ be the number of unordered pairs of positive integers $(p, q)$ such that $p < q$, $pq = 36$, and $\gcd(p, q) = 1$. Define $\beta = 1$ if $D > 0$, and $\beta = 0$ otherwise. Define $\gamma = 1$ if $D = 0$, and $\gamma = 0$ otherwise. Let $r = \alp... | 36,369 | graphs = [
Graph(
let={
"_n": Const(2),
"a": Const(-1),
"b": Const(-16),
"c": Const(-64),
"D": Sub(Pow(Ref("b"), Ref("_n")), Mul(Const(4), Ref("a"), Ref("c"))),
"result": Sum(Mul(CountOverSet(set=SolutionsSet(var=Var("p"), condition=And... | NT | null | COMPUTE | sympy | COPRIME_PAIRS | [
"COPRIME_PAIRS"
] | 2bb3aa | algebra_quadratic_discriminant_v1 | null | 4 | 0 | [
"COPRIME_PAIRS"
] | 1 | 0.003 | 2026-02-08T20:44:23.271907Z | {
"verified": true,
"answer": 36369,
"timestamp": "2026-02-08T20:44:23.275250Z"
} | daa075 | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 206,
"completion_tokens": 275
},
"timestamp": "2026-02-16T18:53:05.452Z",
"answer": 36369
},
{
"id": 11,
... | 2 | [
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "V3",
"status": "no"
}
] | {
"lo": -10,
"mid": -7.27,
"hi": -4.54
} | ||
7d0bcb | comb_factorial_compute_v1_48377204_124 | Let $ n $ be the number of nonnegative integers $ j $ at most $ 2816 $ such that $ \binom{2816}{j} $ is odd. Compute $ n! $. | 40,320 | graphs = [
Graph(
let={
"_n": Const(2),
"n": CountOverSet(set=SolutionsSet(var=Var("j"), condition=And(Geq(Var("j"), Const(0)), Leq(Var("j"), Const(2816)), Eq(Mod(value=Binom(n=Const(2816), k=Var("j")), modulus=Ref("_n")), Const(1))), domain='nonnegative_integers')),
"res... | ALG | COMB | COMPUTE | sympy | V8 | [
"V8"
] | 86348e | comb_factorial_compute_v1 | null | 6 | 0 | [
"V8"
] | 1 | 0.003 | 2026-02-08T15:14:29.288437Z | {
"verified": true,
"answer": 40320,
"timestamp": "2026-02-08T15:14:29.291073Z"
} | 3b8480 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 153,
"completion_tokens": 1018
},
"timestamp": "2026-02-24T20:13:52.914Z",
"answer": 40320
},
{
"... | 1 | [
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "V8",
"status": "ok"
},
{
"lemma": "V8_SUM",
"status": "no"
}
] | {
"lo": -4.1,
"mid": -1.76,
"hi": 1.26
} | ||
8b609e | diophantine_fbi2_min_v1_655260480_6117 | Let $d$ be an integer satisfying $3 \le d \le 34$ such that $d$ divides $24$ and $\frac{24}{d} \ge 3$. Determine the value of the smallest such $d$. | 3 | graphs = [
Graph(
let={
"k": Const(24),
"a": Const(2),
"b": Const(2),
"upper": Const(34),
"result": MinOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Const(3)), Leq(Var("d"), Ref("upper")), Divides(divisor=Var("d"), dividend=Ref... | NT | null | EXTREMUM | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | diophantine_fbi2_min_v1 | null | 3 | 0 | [
"LIN_FORM"
] | 1 | 0.025 | 2026-02-08T18:50:02.603849Z | {
"verified": true,
"answer": 3,
"timestamp": "2026-02-08T18:50:02.628814Z"
} | 7aa5f1 | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 109,
"completion_tokens": 165
},
"timestamp": "2026-02-16T17:38:46.715Z",
"answer": 3
},
{
"id": 11,
"... | 2 | [
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"... | {
"lo": -10,
"mid": -7.27,
"hi": -4.54
} | ||
c0f5db_l | antilemma_sum_equals_v1_124444284_3888 | Compute the number of ordered pairs $(i, j)$ of integers with $1 \leq i \leq 50$ and $1 \leq j \leq 50$ such that $i + j = 52$. | 50 | COMB | GEOM | COMPUTE | sympy | LIN_FORM | [
"COUNT_SUM_EQUALS"
] | 75ab0f | antilemma_sum_equals_v1 | null | 2 | 0 | [
"COUNT_SUM_EQUALS",
"LIN_FORM"
] | 2 | 0.034 | 2026-02-08T05:39:34.272049Z | {
"verified": false,
"answer": 49,
"timestamp": "2026-02-08T05:39:34.306411Z"
} | 2242fc | c0f5db | legacy_text | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 159,
"completion_tokens": 204
},
"timestamp": "2026-02-24T04:11:03.718Z",
"answer": 49
},
{
"id":... | 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",
"status": "n... | {
"lo": -4.93,
"mid": -2.91,
"hi": -0.71
} | |
c6d105 | nt_num_divisors_compute_v1_784195855_5810 | Let $S$ be the set of all ordered pairs $(x, y)$ of positive integers such that $xy = 25000000$. Let $T$ be the set of all values $x + y$ where $(x, y) \in S$. Let $m$ be the minimum value in $T$. Now, let $U$ be the set of all ordered pairs $(x, y)$ of positive integers such that $xy = m$. Let $V$ be the set of all va... | 6,093 | graphs = [
Graph(
let={
"_n": Const(44121),
"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")), MinOverSet(set=MapOverSet(set=SolutionsSet(var... | NT | null | COMPUTE | sympy | B3 | [
"B3/B3"
] | 8ffef9 | nt_num_divisors_compute_v1 | null | 6 | 0 | [
"B3"
] | 1 | 0.004 | 2026-02-08T08:07:23.257105Z | {
"verified": true,
"answer": 6093,
"timestamp": "2026-02-08T08:07:23.260916Z"
} | 0a3654 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 228,
"completion_tokens": 1571
},
"timestamp": "2026-02-13T15:14:55.125Z",
"answer": 6093
},
{... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
}
] | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
8e7713 | nt_lcm_compute_v1_1915831931_199 | Let $a = 2002$ and $b = 2543$. Compute the least common multiple of $a$ and $b$. Let $r_1$ be the remainder when this least common multiple is divided by $251$, and let $r_2$ be the remainder when it is divided by $397$. Compute the remainder when $r_1 + 1009 \cdot r_2$ is divided by $77756$. | 47,224 | graphs = [
Graph(
let={
"a": Const(2002),
"b": Const(2543),
"result": LCM(a=Ref("a"), b=Ref("b")),
"Q": Mod(value=Sum(Mod(value=Ref("result"), modulus=Const(251)), Mul(Const(1009), Mod(value=Ref("result"), modulus=Const(397)))), modulus=Const(77756)),
... | NT | null | COMPUTE | sympy | MIN_PRIME_FACTOR | [
"MIN_PRIME_FACTOR",
"MAX_PRIME_BELOW"
] | ed95f3 | nt_lcm_compute_v1 | two_moduli | 2 | 0 | [
"MAX_PRIME_BELOW",
"MIN_PRIME_FACTOR"
] | 2 | 0.114 | 2026-02-08T15:13:48.873483Z | {
"verified": true,
"answer": 47224,
"timestamp": "2026-02-08T15:13:48.987328Z"
} | 535da2 | 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": 3770
},
"timestamp": "2026-02-16T02:02:18.030Z",
"answer": 47224
},
... | 1 | [
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok"
},
{
"lemma": "MIN_PRIME_FACTOR",
"status": "ok"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "MOD_SU... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
086140 | nt_min_coprime_above_v1_1520064083_4205 | Let $S$ be the set of all ordered pairs of positive integers $(x, y)$ such that $x + y = 102$. Let $M$ be the maximum value of $xy$ over all pairs in $S$. Determine the smallest integer $n$ such that $M < n \le 3039$ and $\gcd(n, 428) = 1$. | 2,603 | graphs = [
Graph(
let={
"start": 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(102)))), expr=Mul(Var("x"), Var("y")))),
"upper": Const(... | NT | null | EXTREMUM | sympy | B1 | [
"B1"
] | 5b950e | nt_min_coprime_above_v1 | null | 4 | 0 | [
"B1"
] | 1 | 0.038 | 2026-02-08T06:08:32.778108Z | {
"verified": true,
"answer": 2603,
"timestamp": "2026-02-08T06:08:32.815883Z"
} | 8ad634 | 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": 920
},
"timestamp": "2026-02-12T20:12:40.732Z",
"answer": 2603
},
{
... | 1 | [
{
"lemma": "B1",
"status": "ok"
},
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
}
] | {
"lo": -7.01,
"mid": -4.68,
"hi": -2.15
} | ||
9dc5fa | algebra_vieta_sum_v1_784195855_8716 | Let $f(x) = x^3 + \left( \sum_{k=1}^{3} \phi(k) \left\lfloor \frac{3}{k} \right\rfloor \right) x^2 - 52x - 120$. Let $S$ be the set of all real numbers $x$ such that $f(x) = 0$. Compute the absolute value of the product of all elements in $S$. | 120 | graphs = [
Graph(
let={
"_n": Const(3),
"result": ProductOverSet(set=SolutionsSet(var=Var(name='x'), condition=Eq(left=Sum(Pow(base=Var(name='x'), exp=Ref(name='_n')), Mul(Summation(expr=Mul(EulerPhi(n=Var(name='k')), Floor(arg=Div(left=Const(value=3), right=Var(name='k')))), var='k'... | NT | null | COMPUTE | sympy | LIN_FORM | [
"K2"
] | 6897ab | algebra_vieta_sum_v1 | null | 6 | 0 | [
"K2",
"LIN_FORM"
] | 2 | 0.13 | 2026-02-08T16:17:20.075152Z | {
"verified": true,
"answer": 120,
"timestamp": "2026-02-08T16:17:20.204740Z"
} | 056f24 | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 156,
"completion_tokens": 357
},
"timestamp": "2026-02-16T07:17:11.173Z",
"answer": 120
},
{
"id": 11,
... | 2 | [
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "K2",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "VAL_SUM_EQ",
"status": "no"
}
] | {
"lo": -10,
"mid": -7.27,
"hi": -4.54
} | ||
84b152 | comb_count_permutations_fixed_v1_124444284_1542 | Let $n$ be the largest prime number satisfying $2 \leq n \leq 7$. Let $k = 1$. Compute the value of $\binom{n}{k} \cdot !(n - k)$, where $!m$ denotes the number of derangements of $m$ elements. | 1,855 | graphs = [
Graph(
let={
"_n": Const(2),
"n": MaxOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Ref("_n")), Leq(Var("n"), Const(7)), IsPrime(Var("n"))))),
"k": Const(1),
"result": Mul(Binom(n=Ref("n"), k=Ref("k")), Subfactorial(arg=Sub(left=... | NT | COMB | COUNT | sympy | COUNT_FIB_DIVISIBLE | [
"MAX_PRIME_BELOW"
] | dc3ad3 | comb_count_permutations_fixed_v1 | null | 3 | 0 | [
"COUNT_FIB_DIVISIBLE",
"MAX_PRIME_BELOW"
] | 2 | 0.019 | 2026-02-08T03:59:03.967291Z | {
"verified": true,
"answer": 1855,
"timestamp": "2026-02-08T03:59:03.985930Z"
} | 58ac35 | 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": 631
},
"timestamp": "2026-02-10T16:38:16.347Z",
"answer": 1855
},
{
"id... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "VAL_SUM_EQ",
"status": "no"
}
] | {
"lo": -7.01,
"mid": -4.68,
"hi": -2.15
} | ||
93e036 | antilemma_sum_equals_v1_124444284_6804 | Let $x$ be the number of ordered pairs $(i, j)$ of positive integers such that $i + j = 62$, $1 \leq i \leq 61$, and $1 \leq j \leq 61$. Let $y$ be the number of ordered pairs $(x_1, x_2)$ of positive odd integers such that $x_1 + x_2 = 10006$. Compute the remainder when $$x \bmod 199 + y \cdot (x \bmod 499)$$ is divid... | 36,492 | graphs = [
Graph(
let={
"_m": Const(499),
"_n": Const(62),
"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(61)), right=Intege... | COMB | GEOM | COMPUTE | sympy | COMB1 | [
"COMB1",
"COUNT_SUM_EQUALS"
] | 128824 | antilemma_sum_equals_v1 | two_moduli | 4 | 0 | [
"COMB1",
"COUNT_SUM_EQUALS"
] | 2 | 0.006 | 2026-02-08T08:38:42.374866Z | {
"verified": true,
"answer": 36492,
"timestamp": "2026-02-08T08:38:42.381048Z"
} | 44c7ad | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 233,
"completion_tokens": 935
},
"timestamp": "2026-02-24T09:47:47.351Z",
"answer": 36492
},
{
"i... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COMB1",
"status": "ok"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "ok"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
},
... | {
"lo": -3.84,
"mid": -1.67,
"hi": 1.32
} | ||
f290be | nt_min_coprime_above_v1_784195855_8371 | Let $A$ be the set of all integers $n$ such that $31329 < n \leq 31469$ and $\gcd(n, 130) = 1$. Let $r$ be the minimum element of $A$. Now, consider the set of all ordered pairs $(x,y)$ of positive integers such that $x + y = 42$. Let $P$ be the set of all values of $xy$ for such pairs. Let $c$ be the maximum element o... | 68,731 | graphs = [
Graph(
let={
"_n": Const(99621),
"start": Const(31329),
"upper": Const(31469),
"modulus": Const(130),
"result": MinOverSet(set=SolutionsSet(var=Var("n"), condition=And(Gt(Var("n"), Ref("start")), Leq(Var("n"), Ref("upper")), Eq(GCD(a=Var... | NT | null | EXTREMUM | sympy | B1 | [
"B1"
] | d2b6e1 | nt_min_coprime_above_v1 | negation_mod | 6 | 0 | [
"B1"
] | 1 | 0.015 | 2026-02-08T16:02:04.444057Z | {
"verified": true,
"answer": 68731,
"timestamp": "2026-02-08T16:02:04.458945Z"
} | f31fe2 | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 194,
"completion_tokens": 452
},
"timestamp": "2026-02-16T06:51:23.962Z",
"answer": 30915
},
{
"id": 11... | 1 | [
{
"lemma": "B1",
"status": "ok"
},
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "... | {
"lo": -8.26,
"mid": -5.01,
"hi": -1.76
} | ||
889b19 | antilemma_sum_equals_v1_48377204_750 | Compute the number of ordered pairs $(i, j)$ of positive integers such that $i + j = 88$, $1 \leq i \leq 87$, and $1 \leq j \leq 88$. | 87 | graphs = [
Graph(
let={
"x": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("i"), Var("j")]), condition=Eq(Sum(Var("i"), Var("j")), Const(88)), domain=CartesianProduct(left=IntegerRange(start=Const(1), end=Const(87)), right=IntegerRange(start=Const(1), end=Const(88))))),
},
... | COMB | GEOM | COMPUTE | sympy | COMB1 | [
"COUNT_SUM_EQUALS"
] | 75ab0f | antilemma_sum_equals_v1 | null | 2 | 0 | [
"COMB1",
"COUNT_SUM_EQUALS"
] | 2 | 0.312 | 2026-02-08T15:40:59.139618Z | {
"verified": true,
"answer": 87,
"timestamp": "2026-02-08T15:40:59.451890Z"
} | dd58a2 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 159,
"completion_tokens": 359
},
"timestamp": "2026-02-24T18:15:14.707Z",
"answer": 87
},
{
"id"... | 2 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "ok"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
}
] | {
"lo": -10,
"mid": -7.42,
"hi": -4.85
} | ||
a3e05e | diophantine_product_count_v1_1520064083_6282 | Let $S$ be the set of all ordered pairs $(x,y)$ of positive integers such that $xy = 129600$. Let $k$ be the minimum value of $x + y$ over all such pairs. Let $U$ be the number of positive integers $n$ with $1 \leq n \leq 1269$ such that $9$ divides $n$ and $\gcd(n, 10) = 1$. Let $R$ be the number of positive integers ... | 22,854 | graphs = [
Graph(
let={
"_n": Const(65895),
"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")), Const(129600)))), expr=Sum(Var("x"), Var("y"))... | NT | null | COUNT | sympy | B3 | [
"B3",
"C5"
] | 2a47df | diophantine_product_count_v1 | null | 7 | 0 | [
"B3",
"C5"
] | 2 | 0.007 | 2026-02-08T07:59:17.865950Z | {
"verified": true,
"answer": 22854,
"timestamp": "2026-02-08T07:59:17.873077Z"
} | 01ccf3 | 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": 1721
},
"timestamp": "2026-02-13T13:57:57.516Z",
"answer": 22854
},
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "C5",
"status": "ok"
},
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lem... | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
83086d | comb_count_derangements_v1_717093673_3104 | Let $n = 7$. Define $d_n$ to be the number of derangements of $n$ elements. Let $S$ be the set of all ordered pairs $(x,y)$ of positive integers such that $xy = 11108889$. Let $m$ be the minimum value of $x + y$ over all such pairs. Compute $m - d_n$. | 4,812 | graphs = [
Graph(
let={
"n": Const(7),
"result": Subfactorial(arg=Ref(name='n')),
"Q": Sub(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... | COMB | null | COUNT | sympy | B3 | [
"B3"
] | fc629c | comb_count_derangements_v1 | negation_mod | 4 | 0 | [
"B3"
] | 1 | 0.002 | 2026-02-08T17:22:32.894376Z | {
"verified": true,
"answer": 4812,
"timestamp": "2026-02-08T17:22:32.896543Z"
} | b0454d | 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": 1710
},
"timestamp": "2026-02-18T01:17:39.766Z",
"answer": 4812
},
{... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
}
] | {
"lo": -2.38,
"mid": 1.74,
"hi": 6.59
} | ||
58d6dc | nt_num_divisors_compute_v1_1470522791_806 | Let $n = 2000$. Let $d(n)$ denote the number of positive divisors of $n$. Let $c$ be the number of positive integers $p$ for which there exists a positive integer $q$ such that $p < q$, $pq = 9000$, and $\gcd(p, q) = 1$. Compute the remainder when $c - d(n)$ is divided by 50650. | 50,634 | graphs = [
Graph(
let={
"n": Const(2000),
"result": NumDivisors(n=Ref("n")),
"_c": 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... | NT | null | COMPUTE | sympy | COPRIME_PAIRS | [
"COPRIME_PAIRS"
] | c90628 | nt_num_divisors_compute_v1 | negation_mod | 4 | 0 | [
"COPRIME_PAIRS"
] | 1 | 0.001 | 2026-02-08T13:15:52.697629Z | {
"verified": true,
"answer": 50634,
"timestamp": "2026-02-08T13:15:52.699066Z"
} | b316f9 | 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": 1553
},
"timestamp": "2026-02-15T11:52:44.403Z",
"answer": 50634
},
... | 1 | [
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "V3",
"status": "no"
}
] | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
041db8 | comb_factorial_compute_v1_1218484723_1862 | Find the number $n$ of ordered pairs $(a, b)$ of positive integers with $1 \le a \le b \le 10$ such that $32b^2 - 64ab + 32a^2 = 128$. Compute $n!$. | 40,320 | graphs = [
Graph(
let={
"_n": Const(10),
"n": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("a"), Var("b")]), condition=And(Geq(Var("a"), Const(1)), Leq(Var("a"), Const(10)), Geq(Var("b"), Const(1)), Leq(Var("b"), Ref("_n")), Leq(Var("a"), Var("b")), Eq(Sum(Mul(Const(32), Pow... | COMB | null | COMPUTE | sympy | QF_PSD_ORBIT | [
"QF_PSD_ORBIT"
] | 1d37f3 | comb_factorial_compute_v1 | null | 3 | 0 | [
"QF_PSD_ORBIT"
] | 1 | 0.002 | 2026-02-25T03:33:16.219123Z | {
"verified": true,
"answer": 40320,
"timestamp": "2026-02-25T03:33:16.220642Z"
} | 38ddf0 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 167,
"completion_tokens": 413
},
"timestamp": "2026-03-29T01:48:44.702Z",
"answer": 40320
},
{
"i... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "QF_PSD_ORBIT",
"status": "ok"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "... | {
"lo": -6.5,
"mid": -3.34,
"hi": -0.89
} | ||
bcec0a | algebra_quadratic_discriminant_v1_1520064083_4437 | Let $a$ be the number of positive integers $p$ for which there exists a positive integer $q > p$ such that $pq = 180$ and $\gcd(p, q) = 1$. Let $b = -3$ and $c = -7$, and define $D = b^2 - 4ac$. Let $r$ be the number of positive integers $p$ for which there exists a positive integer $q > p$ such that $pq = 216$ and $\g... | 87,982 | graphs = [
Graph(
let={
"_n": Const(2),
"a": 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=180)), Eq(left=GCD(a=Var(name='p'), b=Var(name='q... | NT | null | COMPUTE | sympy | COPRIME_PAIRS | [
"COPRIME_PAIRS"
] | 2bb3aa | algebra_quadratic_discriminant_v1 | null | 6 | 0 | [
"COPRIME_PAIRS"
] | 1 | 0.005 | 2026-02-08T06:16:14.477762Z | {
"verified": true,
"answer": 87982,
"timestamp": "2026-02-08T06:16:14.482286Z"
} | 907aee | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 237,
"completion_tokens": 1749
},
"timestamp": "2026-02-12T22:09:05.236Z",
"answer": 87982
},
... | 1 | [
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
... | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
bb28ab | nt_count_divisible_v1_397696148_658 | Let $n$ be a positive integer. Consider the set of all positive integers $n$ such that $1 \leq n \leq 38809$ and $n$ is divisible by 20. Let $A$ be the number of elements in that set.
Let $d$ be a positive integer satisfying $d \geq 2$ and $d$ divides 352843. Let $B$ be the smallest such $d$.
Compute the remainder wh... | 49,105 | graphs = [
Graph(
let={
"_n": Const(2),
"upper": Const(38809),
"divisor": Const(20),
"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")), Const... | NT | null | COUNT | sympy | MIN_PRIME_FACTOR | [
"MIN_PRIME_FACTOR"
] | fd27b3 | nt_count_divisible_v1 | negation_mod | 3 | 0 | [
"MIN_PRIME_FACTOR"
] | 1 | 2.136 | 2026-02-08T11:39:17.055038Z | {
"verified": true,
"answer": 49105,
"timestamp": "2026-02-08T11:39:19.191158Z"
} | 1d5bc4 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 154,
"completion_tokens": 1232
},
"timestamp": "2026-02-14T17:20:38.945Z",
"answer": 49105
},
... | 1 | [
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "MIN_PRIME_FACTOR",
"status": "ok"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "V1",
"status": "no"
}
] | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
17a935_l | antilemma_sum_equals_v1_784195855_6285 | Let $ m = 75 $. Compute the number of ordered pairs $ (i, j) $ of positive integers such that $ i + j = m $, $ 1 \leq i \leq 73 $, and $ 1 \leq j \leq 74 $. Denote this number by $ n $. Now compute the number of ordered pairs $ (i, j) $ of positive integers such that $ i + j = n $, $ 1 \leq i \leq 71 $, and $ 1 \leq j ... | 20,954 | COMB | GEOM | COMPUTE | sympy | COUNT_SUM_EQUALS | [
"COUNT_SUM_EQUALS/COUNT_SUM_EQUALS",
"COUNT_SUM_EQUALS"
] | ae9919 | antilemma_sum_equals_v1 | null | 3 | 0 | [
"COUNT_SUM_EQUALS"
] | 1 | 0.009 | 2026-02-08T08:32:18.904123Z | {
"verified": false,
"answer": 20955,
"timestamp": "2026-02-08T08:32:18.913033Z"
} | 22d05b | 17a935 | legacy_text | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 250,
"completion_tokens": 3068
},
"timestamp": "2026-02-24T09:40:53.865Z",
"answer": 20955
},
{
"... | 1 | [
{
"lemma": "COUNT_CARTESIAN",
"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":... | {
"lo": -3.84,
"mid": -1.67,
"hi": 1.32
} | |
eec634 | modular_mod_compute_v1_717093673_3606 | Let $S$ be the set of all ordered pairs $(x, y)$ of positive integers such that $xy = 23425600$. Define $m_0$ to be the minimum value of $x + y$ as $(x, y)$ ranges over $S$. Let $T$ be the set of all positive integers $n$ such that $1 \le n \le m_0$ and $n \equiv \left\lfloor \frac{n}{2} \right\rfloor \pmod{5}$. Define... | 22,871 | graphs = [
Graph(
let={
"_m": Const(73855),
"_n": Const(44121),
"a": Const(39601),
"m": 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"), Va... | NT | null | COMPUTE | sympy | B3 | [
"B3/L3C"
] | 345f3b | modular_mod_compute_v1 | null | 6 | 0 | [
"B3",
"L3C"
] | 2 | 0.008 | 2026-02-08T17:43:11.070279Z | {
"verified": true,
"answer": 22871,
"timestamp": "2026-02-08T17:43:11.077847Z"
} | 82971b | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 194,
"completion_tokens": 1755
},
"timestamp": "2026-02-18T07:10:05.482Z",
"answer": 22871
},
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "L3C",
"status": "ok_later"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
},
{
"lemma": "... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
70066f | nt_count_divisors_in_range_v1_784195855_3819 | Let $n = 15120$. Define $a = \sum_{k=1}^{8} \varphi(k) \left\lfloor \frac{8}{k} \right\rfloor$. Let $b$ be the number of integers $t$ with $33 \leq t \leq 5775$ for which there exist positive integers $a$ and $b$ such that $1 \leq a \leq 112$, $1 \leq b \leq 211$, and $t = 12a + 21b$. Determine the number of positive d... | 51 | graphs = [
Graph(
let={
"_n": Const(8),
"n": Const(15120),
"a": Summation(var="k", start=Const(1), end=Const(8), expr=Mul(EulerPhi(n=Var("k")), Floor(Div(Ref("_n"), Var("k"))))),
"b": CountOverSet(set=SolutionsSet(var=Var("t"), condition=Exists(var=Var(name='a... | NT | null | COUNT | sympy | LIN_FORM | [
"LIN_FORM",
"K2"
] | b46b5e | nt_count_divisors_in_range_v1 | null | 6 | 0 | [
"K2",
"LIN_FORM"
] | 2 | 0.021 | 2026-02-08T06:39:24.064163Z | {
"verified": true,
"answer": 51,
"timestamp": "2026-02-08T06:39:24.085318Z"
} | d2395c | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 183,
"completion_tokens": 5749
},
"timestamp": "2026-02-13T03:06:26.223Z",
"answer": 51
},
{
... | 1 | [
{
"lemma": "K2",
"status": "ok"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "V3",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "... | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
d0e5cd | modular_min_linear_v1_1874849503_660 | Let $c = 2$ and let $q$ be the smallest prime divisor of $385$. Let $r$ be the largest prime number $n$ such that $2 \leq n \leq q$. Let $m$ be the smallest prime divisor of $13013$. Define $\delta$ to be the sum of $\mu(d)$ over all positive divisors $d$ of $\gcd(r, m)$, where $\mu$ denotes the Möbius function. Let $a... | 31,212 | graphs = [
Graph(
let={
"_c": Const(2),
"_m": MinOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Const(2)), Divides(divisor=Var("d"), dividend=Const(13013))))),
"_n": Const(2),
"a": Const(23643),
"b": Const(44082),
"m... | NT | null | EXTREMUM | sympy | MIN_PRIME_FACTOR | [
"MIN_PRIME_FACTOR/MIN_PRIME_FACTOR/MOBIUS_COPRIME",
"MIN_PRIME_FACTOR/MAX_PRIME_BELOW/MOBIUS_COPRIME"
] | eda59d | modular_min_linear_v1 | null | 7 | 0 | [
"MAX_PRIME_BELOW",
"MIN_PRIME_FACTOR",
"MOBIUS_COPRIME"
] | 3 | 2.661 | 2026-02-08T13:14:38.984549Z | {
"verified": true,
"answer": 31212,
"timestamp": "2026-02-08T13:14:41.645449Z"
} | d01008 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 270,
"completion_tokens": 1836
},
"timestamp": "2026-02-09T19:30:30.032Z",
"answer": 31212
},
{
"... | 1 | [
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok_later"
},
{
"lemma": "MIN_PRIME_FACTOR",
"status": "ok"
},
{
"lemma": "MOBIUS_COPRIME",
"status": "ok_later"
},
{
"lemma": "V7",... | {
"lo": -6.5,
"mid": -0.2,
"hi": 6.11
} | ||
e0b7f1 | nt_count_gcd_equals_v1_124444284_3018 | Let $k = 441$ and $U = 7056$. Define $r$ to be the number of positive integers $n \leq U$ such that $\gcd(n, k) = 1$. Let $s$ be the number of ordered pairs $(p, q)$ of positive integers such that $pq = 108$, $\gcd(p, q) = 1$, and $p < q$. Compute the value of
$$
r + \left( s^{r \bmod 14} \bmod 89903 \right).$$ | 4,033 | graphs = [
Graph(
let={
"_n": Const(89903),
"upper": Const(7056),
"k": Const(441),
"d": Const(1),
"result": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Ref("upper")), Eq(GCD(a=Var("n"), b=Ref("k"... | NT | null | COUNT | sympy | COPRIME_PAIRS | [
"COPRIME_PAIRS"
] | 64a51e | nt_count_gcd_equals_v1 | mod_exp | 4 | 0 | [
"COPRIME_PAIRS"
] | 1 | 0.711 | 2026-02-08T05:08:41.561759Z | {
"verified": true,
"answer": 4033,
"timestamp": "2026-02-08T05:08:42.272744Z"
} | 1efe2b | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 230,
"completion_tokens": 1405
},
"timestamp": "2026-02-11T23:05:53.840Z",
"answer": 4033
},
{
"i... | 1 | [
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
}
] | {
"lo": -3.45,
"mid": 1.15,
"hi": 6.18
} | ||
b11fa1 | geo_count_lattice_rect_v1_1918700295_620 | Compute the number of lattice points in the rectangle $[0, 60] \times [0, 17]$, including the boundary. | 1,098 | graphs = [
Graph(
let={
"a": Const(60),
"b": Const(17),
"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 | 2026-02-08T03:21:08.343170Z | {
"verified": true,
"answer": 1098,
"timestamp": "2026-02-08T03:21:08.344178Z"
} | fb8986 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 140,
"completion_tokens": 226
},
"timestamp": "2026-02-10T13:56:49.614Z",
"answer": 1098
},
{
"id... | 2 | [] | {
"lo": -9.23,
"mid": -6.18,
"hi": -4.06
} | ||||
9f5765 | comb_binomial_compute_v1_548369836_397 | Let $S$ be the set of all ordered pairs of positive integers $(x, y)$ such that $x + y = 8$. Define $n$ to be the maximum value of $xy$ over all such pairs.
Let $k = 9$. Compute $\binom{n}{k}$. | 11,440 | graphs = [
Graph(
let={
"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(8)))), expr=Mul(Var("x"), Var("y")))),
"k": Const(9),
... | ALG | COMB | COMPUTE | sympy | B1 | [
"B1"
] | 5b950e | comb_binomial_compute_v1 | null | 4 | 0 | [
"B1"
] | 1 | 0.001 | 2026-02-08T02:53:49.460471Z | {
"verified": true,
"answer": 11440,
"timestamp": "2026-02-08T02:53:49.461750Z"
} | 58a379 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 179,
"completion_tokens": 765
},
"timestamp": "2026-02-08T20:26:02.018Z",
"answer": 11440
},
{
"i... | 1 | [
{
"lemma": "B1",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
}
] | {
"lo": -1.87,
"mid": 0.05,
"hi": 1.73
} | ||
bf4098 | modular_modexp_compute_v1_2051736721_2272 | Let $a = 13$. Let $S$ be the set of all ordered pairs $(x_1, x_2)$ of positive odd integers such that $x_1 + x_2 = 2664$. Let $N$ be the number of positive integers $n$ such that $1 \leq n \leq |S|$ and $n \equiv \left\lfloor \frac{n}{2} \right\rfloor \pmod{3}$. Compute the remainder when $a^N$ is divided by $88888$. | 69,889 | graphs = [
Graph(
let={
"a": Const(13),
"e": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x1"), Var("x2")]), condition=And(IsPositive(arg=Var(name='x1')), IsPositive(arg=Var(nam... | NT | null | COMPUTE | sympy | COMB1 | [
"COMB1/L3C"
] | 5e9660 | modular_modexp_compute_v1 | null | 7 | 0 | [
"COMB1",
"L3C"
] | 2 | 0.003 | 2026-02-08T16:33:23.970268Z | {
"verified": true,
"answer": 69889,
"timestamp": "2026-02-08T16:33:23.973398Z"
} | 6c5d37 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 160,
"completion_tokens": 3146
},
"timestamp": "2026-02-17T06:33:35.165Z",
"answer": 69889
},
... | 1 | [
{
"lemma": "COMB1",
"status": "ok"
},
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "L3C",
"status": "ok_later"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
57fb75_n | algebra_poly_eval_v1_601307018_6406 | A treasure chest unlocks only when a dial is turned to the smallest positive divisor of 1001. Once unlocked, the mechanism computes the value $7d^3 - 4d^2 + 7d - 4$, where $d$ is the number used to unlock it. What is the computed value? | 2,250 | graphs = [
Graph(
let={
"_n": Const(7),
"m": MinOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Const(2)), Divides(divisor=Var("d"), dividend=Const(1001))))),
"result": Sum(Mul(Const(7), Pow(Ref("m"), Const(3))), Mul(Const(-4), Pow(Ref("m"), Const(2))),... | NT | null | COMPUTE | sympy | MIN_PRIME_FACTOR | [
"MIN_PRIME_FACTOR"
] | bc3776 | algebra_poly_eval_v1 | null | 2 | null | [
"MIN_PRIME_FACTOR"
] | 1 | 0.007 | 2026-03-10T07:04:58.613161Z | null | d5ad14 | 57fb75 | narrative | CC BY 4.0 | [
{
"id": 36,
"model": "qwen2.5:3b-32k",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 123,
"completion_tokens": 461
},
"timestamp": "2026-04-23T12:07:19.581Z",
"answer": 2250
}
] | 2 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MIN_PRIME_FACTOR",
"status": "ok"
},
{
"lemma": "V3",
"status": "no"
}
] | {
"lo": -10,
"mid": -5.89,
"hi": -1.79
} |
ac8824 | alg_poly4_count_v1_1218484723_224 | Find the number of ordered pairs $(a, b)$ of positive integers with $1 \le a, b \le 444$ such that $$
\left(\min_{\substack{a_1,b_1 \ge 1 \\ a_1,b_1 \le 11}} \left(257a_1^4 - 244a_1^3b_1 + 150a_1^2b_1^2 + 92a_1b_1^3 + 82b_1^4\right)\right) b^4 + \left(\min_{\substack{x,y > 0 \\ xy = 1022121}} (x + y)\right) a^2b^2 + 33... | 576 | graphs = [
Graph(
let={
"_m": Const(11),
"_n": Const(4),
"result": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("a"), Var("b")]), condition=And(Geq(Var("a"), Const(1)), Leq(Var("a"), Const(444)), Geq(Var("b"), Const(1)), Leq(Var("b"), Const(444)), Eq(Sum(Mul(MinO... | ALG | null | COUNT | sympy | POLY4_MIN | [
"POLY4_MIN",
"B3"
] | a2070e | alg_poly4_count_v1 | null | 6 | 0 | [
"B3",
"POLY4_MIN"
] | 2 | 2.315 | 2026-02-25T01:54:51.658802Z | {
"verified": true,
"answer": 576,
"timestamp": "2026-02-25T01:54:53.974228Z"
} | 86338b | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 1,
"correct": {
"strict": false,
"boxed": false,
"relaxed": true
},
"usage": {
"prompt_tokens": 294,
"completion_tokens": 32768
},
"timestamp": "2026-03-10T08:58:58.146Z",
"answer": null
},
{
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "POLY4_MIN",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
}
] | {
"lo": 2.74,
"mid": 4.78,
"hi": 6.68
} | ||
bfe9ba | nt_count_gcd_equals_v1_717093673_2353 | Let $m = 28224$ and $n = 55997$. Let $\text{upper}$ be the number of positive integers $k$ such that $1 \leq k \leq 14110$ and the sum of the decimal digits of $k$ is odd.
Let $S$ be the set of all ordered pairs $(x, y)$ of positive integers such that $xy = m$. Let $T$ be the set of all values $x + y$ where $(x, y) \i... | 53,463 | graphs = [
Graph(
let={
"_m": Const(28224),
"_n": Const(55997),
"upper": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Const(14110)), Eq(Mod(value=DigitSum(Var("n")), modulus=Const(2)), Const(1))))),
"k": MaxO... | NT | null | COUNT | sympy | B3 | [
"B3/MAX_PRIME_BELOW",
"L3B"
] | 5268a6 | nt_count_gcd_equals_v1 | null | 6 | 0 | [
"B3",
"L3B",
"MAX_PRIME_BELOW"
] | 3 | 0.558 | 2026-02-08T16:46:29.476475Z | {
"verified": true,
"answer": 53463,
"timestamp": "2026-02-08T16:46:30.034698Z"
} | 0cbccd | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 265,
"completion_tokens": 2876
},
"timestamp": "2026-02-17T12:23:58.507Z",
"answer": 53463
},
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "L3B",
"status": "ok"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok_later"
},
{
"lemma": "MOD_SUB",
"status": "no"... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
c25ecc | lin_form_endings_v1_397696148_1384 | Let $a = 84$, $b = 24$, $A = 34$, and $B = 51$. Compute $\gcd(a, b)$, and let $g = \gcd(a, b)$. Define
$$
n = aA + bB - (a + b).
$$
Let $k = \left\lfloor \frac{n}{g} \right\rfloor + 1$. Compute the remainder when $6538 \cdot k$ is divided by $73792$. | 30,648 | graphs = [
Graph(
let={
"a_coeff": Const(84),
"b_coeff": Const(24),
"A_val": Const(34),
"B_val": Const(51),
"g_step": GCD(a=Ref("a_coeff"), b=Ref("b_coeff")),
"numerator": Sub(Sum(Mul(Ref("a_coeff"), Ref("A_val")), Mul(Ref("b_coeff"), R... | COMB | NT | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | lin_form_endings_v1 | null | 3 | null | [
"LIN_FORM"
] | 1 | 0.001 | 2026-02-08T12:31:59.965131Z | {
"verified": true,
"answer": 30648,
"timestamp": "2026-02-08T12:31:59.965979Z"
} | 2b8864 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 148,
"completion_tokens": 1370
},
"timestamp": "2026-02-15T01:47:15.462Z",
"answer": 30648
},
... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "V7",
"status... | {
"lo": -5.49,
"mid": 0.22,
"hi": 6.51
} | ||
a36405 | sequence_count_fib_divisible_v1_601307018_2685 | Let $F_n$ denote the $n$-th Fibonacci number. Let $M$ be the minimum value of $x + y$ over all ordered pairs $(x, y)$ of positive integers with $xy = 121$. Let $R$ be the minimum value of $|x - y|$ over all ordered pairs $(x, y)$ of positive integers with $xy = 169061$. Let $S$ be the number of positive integers $n$ wi... | 79,697 | graphs = [
Graph(
let={
"_n": Const(121),
"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")), Const(169061)))), expr=Abs(arg=Sub(left=Var(... | NT | null | COUNT | sympy | B3 | [
"B3",
"B3_DIFF"
] | 08028d | sequence_count_fib_divisible_v1 | negation_mod | 6 | 0 | [
"B3",
"B3_DIFF"
] | 2 | 0.014 | 2026-03-10T03:21:32.294177Z | {
"verified": true,
"answer": 79697,
"timestamp": "2026-03-10T03:21:32.308371Z"
} | b0a619 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 242,
"completion_tokens": 26629
},
"timestamp": "2026-03-29T06:11:49.330Z",
"answer": 79697
},
{
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "B3_DIFF",
"status": "ok"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
... | {
"lo": 1.23,
"mid": 4.27,
"hi": 6.7
} | ||
414d2d | alg_qf_psd_count_v1_601307018_6819 | Let $A$ be the number of integer pairs $(a_3, b_3)$ with $1 \leq a_3, b_3 \leq 35$ such that $17b_3^4 = 1377$. Let $B$ be the number of integer pairs $(a_2, b_2)$ with $1 \leq a_2 \leq A$, $1 \leq b_2 \leq 35$ such that $13a_2^2 - 2a_2b_2 + 2b_2^2 \leq 2297$. Let $C$ be the number of integer pairs $(a_1, b_1)$ with $1 ... | 10 | graphs = [
Graph(
let={
"_c": Const(384),
"_m": Const(2),
"_n": Const(128),
"result": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("a"), Var("b")]), condition=And(Geq(Var("a"), Const(1)), Leq(Var("a"), Const(452)), Geq(Var("b"), Const(1)), Leq(Var("b"... | ALG | null | COUNT | sympy | POLY4_COUNT | [
"POLY4_COUNT/QF_PSD_COUNT_LEQ/POLY3_COUNT"
] | 8b1cd0 | alg_qf_psd_count_v1 | null | 7 | 0 | [
"POLY3_COUNT",
"POLY4_COUNT",
"QF_PSD_COUNT_LEQ"
] | 3 | 1.813 | 2026-03-10T07:27:53.330633Z | {
"verified": true,
"answer": 10,
"timestamp": "2026-03-10T07:27:55.143678Z"
} | 9b6770 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 380,
"completion_tokens": 7139
},
"timestamp": "2026-04-19T05:23:20.598Z",
"answer": 10
},
{
"id... | 1 | [
{
"lemma": "POLY3_COUNT",
"status": "ok_later"
},
{
"lemma": "POLY4_COUNT",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "QF_PSD_COUNT_LEQ",
"status": "ok_later"
}
] | {
"lo": -5.34,
"mid": 1.1,
"hi": 7.53
} | ||
e5d024 | modular_sum_quadratic_residues_v1_2051736721_1434 | Let $p = 317$ and define $\text{result} = \frac{p(p-1)}{4}$. Let $S$ be the set of all ordered pairs $(x, y)$ of positive integers such that $x + y = 8$. Define $P$ to be the set of all products $xy$ as $(x, y)$ ranges over $S$. Let $m = \max(P)$ and define $e = \text{result} \bmod m$. Compute the value of
$$
\text{re... | 25,051 | graphs = [
Graph(
let={
"p": Const(317),
"result": Div(Mul(Ref("p"), Sub(Ref("p"), Const(1))), Const(4)),
"Q": Sum(Ref("result"), Mod(value=Pow(Const(2), Mod(value=Ref("result"), modulus=MaxOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), ... | NT | null | SUM | sympy | B1 | [
"B1"
] | 876f42 | modular_sum_quadratic_residues_v1 | mod_exp | 5 | 0 | [
"B1"
] | 1 | 0.003 | 2026-02-08T16:02:43.823719Z | {
"verified": true,
"answer": 25051,
"timestamp": "2026-02-08T16:02:43.826279Z"
} | 702ba4 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 181,
"completion_tokens": 755
},
"timestamp": "2026-02-16T19:45:25.096Z",
"answer": 25051
},
{... | 1 | [
{
"lemma": "B1",
"status": "ok"
},
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "V1",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
b6d199 | algebra_quadratic_discriminant_v1_124444284_1625 | Let $a = -2$, $b = -28$, and $c = -96$. Define $\text{result} = b^2 - 4ac$. Compute the value of $3588 \times \text{result}$. | 57,408 | graphs = [
Graph(
let={
"a": Const(-2),
"b": Const(-28),
"c": Const(-96),
"result": Sub(Pow(Ref("b"), Const(2)), Mul(Const(4), Ref("a"), Ref("c"))),
"Q": Mul(Const(3588), Ref("result")),
},
goal=Ref("Q"),
)
] | NT | null | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM",
"MOBIUS_SUM"
] | b2327f | algebra_quadratic_discriminant_v1 | affine_mod | 2 | 0 | [
"LIN_FORM",
"MOBIUS_SUM"
] | 2 | 0.02 | 2026-02-08T04:03:47.666354Z | {
"verified": true,
"answer": 57408,
"timestamp": "2026-02-08T04:03:47.686246Z"
} | bbcb4a | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 160,
"completion_tokens": 241
},
"timestamp": "2026-02-11T16:11:17.106Z",
"answer": 57408
},
{
"i... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "MOBIUS_SUM",
"status": "ok"
},
{
"lemma": "V1",
"status": "no"
},
{
"le... | {
"lo": -5.55,
"mid": -3.02,
"hi": 0.31
} | ||
085b05 | modular_min_linear_v1_865884756_1576 | Let $a = 31615$. Define $b$ to be the number of ordered pairs $(x_1, x_2)$ of positive odd integers such that $x_1 + x_2 = 19352$. Let $m = 57834$. Determine the value of $x$, the smallest positive integer such that $1 \le x \le m$ and $a \cdot x \equiv b \pmod{m}$. | 54,022 | graphs = [
Graph(
let={
"a": Const(31615),
"b": 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")), ... | NT | null | EXTREMUM | sympy | COMB1 | [
"COMB1"
] | 567f58 | modular_min_linear_v1 | null | 5 | 0 | [
"COMB1"
] | 1 | 4.921 | 2026-02-08T16:09:31.391293Z | {
"verified": true,
"answer": 54022,
"timestamp": "2026-02-08T16:09:36.311986Z"
} | 67271b | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 138,
"completion_tokens": 3146
},
"timestamp": "2026-02-16T21:41:52.537Z",
"answer": 54022
},
... | 1 | [
{
"lemma": "COMB1",
"status": "ok"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "V1",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
814311 | antilemma_k3_v1_458359167_340 | Let $n = 86871$. Compute
$$
x = \sum_{d \mid n} \phi(d),
$$
where $\phi$ is Euler's totient function. Let $m = |x| + 2$. Find the smallest positive integer $k$ such that the $k$th Fibonacci number is divisible by $m$. Compute this $k$. | 513 | graphs = [
Graph(
let={
"_n": Const(86871),
"x": SumOverDivisors(n=Ref(name='_n'), var='d', expr=EulerPhi(n=Var(name='d'))),
"Q": FibonacciEntryPoint(modulus=Sum(Abs(arg=Ref(name='x')), Const(value=2))),
},
goal=Ref("Q"),
)
] | NT | COMB | COMPUTE | sympy | K3 | [
"K3"
] | 54c41e | antilemma_k3_v1 | null | 4 | 0 | [
"K3"
] | 1 | 0.001 | 2026-02-08T03:13:09.702934Z | {
"verified": true,
"answer": 513,
"timestamp": "2026-02-08T03:13:09.703996Z"
} | 330c0a | 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": 4496
},
"timestamp": "2026-02-10T13:39:00.668Z",
"answer": 513
},
{
"id... | 1 | [
{
"lemma": "K3",
"status": "ok"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
},
{
"lemma": "VAL_SUM_EQ",
"status": "no"
}
] | {
"lo": -3.46,
"mid": 1.03,
"hi": 5.49
} | ||
b9139e | sequence_lucas_compute_v1_601307018_3484 | Let $n$ be the largest positive integer $d$ such that $d^2 \le 667$ and $d \mid 667$. Let $Q = L_n$, where $L_n$ denotes the $n$-th Lucas number. Compute $Q$. | 64,079 | graphs = [
Graph(
let={
"_n": Const(667),
"n": MaxOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Const(1)), Divides(divisor=Var("d"), dividend=Const(667)), Leq(Mul(Var("d"), Var("d")), Ref("_n"))))),
"result": Lucas(arg=Ref(name='n')),
},
... | NT | null | COMPUTE | sympy | B3_CLOSEST | [
"B3_CLOSEST"
] | 25e610 | sequence_lucas_compute_v1 | null | 3 | 0 | [
"B3_CLOSEST"
] | 1 | 0.005 | 2026-03-10T04:05:48.179950Z | {
"verified": true,
"answer": 64079,
"timestamp": "2026-03-10T04:05:48.184564Z"
} | 614bc0 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 167,
"completion_tokens": 1087
},
"timestamp": "2026-03-29T08:52:34.555Z",
"answer": 64079
},
{
"... | 2 | [
{
"lemma": "B3_CLOSEST",
"status": "ok"
},
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
}
] | {
"lo": -10,
"mid": -6.41,
"hi": -2.82
} | ||
a3d8c9_l | nt_sum_totient_over_divisors_v1_798873815_440 | Let $T$ be the set of all integers $t$ such that $43 \leq t \leq 24520$ and there exist positive integers $a$ and $b$ with $1 \leq a \leq 530$, $1 \leq b \leq 1839$, and $t = 15a + 9b + 19$. Let $n$ be the number of elements in $T$. Compute the sum of $\phi(d)$ over all positive divisors $d$ of $n$, where $\phi$ denote... | 8,160 | NT | null | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | nt_sum_totient_over_divisors_v1 | null | 5 | 0 | [
"LIN_FORM"
] | 1 | 0.003 | 2026-02-08T02:38:35.483949Z | {
"verified": false,
"answer": 8152,
"timestamp": "2026-02-08T02:38:35.487036Z"
} | bfa8ba | a3d8c9 | 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": 239,
"completion_tokens": 5197
},
"timestamp": "2026-02-08T19:31:46.571Z",
"answer": 8160
},
{
... | 1 | [
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "V3",
"status": "no"
},
{
"lemma": "V8",
"status": "no"... | {
"lo": 3.82,
"mid": 5.54,
"hi": 7.58
} | |
08a96d | modular_sum_quadratic_residues_v1_124444284_3033 | Let $c = 2$, $m = 2$, and $n = 4$. Let $D$ be the set of all positive integers $d$ such that $d \geq m$ and $d$ divides $171371$. Define $d_{\text{min}}$ to be the minimum element of $D$. Let $P$ be the set of all positive integers $j$ such that $1 \leq j \leq d_{\text{min}}$ and $j^e \leq 11445019581049$, where $e$ is... | 4,440 | graphs = [
Graph(
let={
"_c": Const(2),
"_m": Const(2),
"_n": Const(4),
"p": CountOverSet(set=SolutionsSet(var=Var("j"), condition=And(Geq(Var("j"), Const(1)), Leq(Var("j"), MinOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Ref("_m")), Divi... | NT | null | SUM | sympy | MIN_PRIME_FACTOR | [
"MIN_PRIME_FACTOR/C3",
"MAX_PRIME_BELOW/C3"
] | 6c9e47 | modular_sum_quadratic_residues_v1 | null | 5 | 0 | [
"C3",
"MAX_PRIME_BELOW",
"MIN_PRIME_FACTOR"
] | 3 | 0.005 | 2026-02-08T05:09:50.010358Z | {
"verified": true,
"answer": 4440,
"timestamp": "2026-02-08T05:09:50.015289Z"
} | 8e9e5a | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 318,
"completion_tokens": 7680
},
"timestamp": "2026-02-11T23:06:29.090Z",
"answer": 4440
},
{
"... | 1 | [
{
"lemma": "C3",
"status": "ok_later"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "MAX_PRIM... | {
"lo": -3.49,
"mid": 1.84,
"hi": 7.55
} | ||
02ca1c | geo_count_lattice_rect_v1_971394319_78 | Let $a = 367$ and $b = 227$. Compute the number of lattice points in the rectangle $[0, a] \times [0, b]$. | 83,904 | graphs = [
Graph(
let={
"a": Const(367),
"b": Const(227),
"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 | 0.003 | 2026-02-08T12:49:08.544369Z | {
"verified": true,
"answer": 83904,
"timestamp": "2026-02-08T12:49:08.547498Z"
} | b93868 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 147,
"completion_tokens": 401
},
"timestamp": "2026-02-24T16:25:29.450Z",
"answer": 83904
},
{
"i... | 1 | [] | {
"lo": -5.97,
"mid": -3.97,
"hi": -1.93
} | ||||
8315f0 | alg_qf_psd_orbit_v1_1218484723_5633 | Find the number of ordered pairs $(a, b)$ of positive integers with $1 \leq a \leq b \leq 297$ such that $20a^2 - 32ab + 20b^2 = 170820$. | 6 | graphs = [
Graph(
let={
"result": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("a"), Var("b")]), condition=And(Geq(Var("a"), Const(1)), Leq(Var("a"), Const(297)), Geq(Var("b"), Const(1)), Leq(Var("b"), Const(297)), Leq(Var("a"), Var("b")), Eq(Sum(Mul(Const(-32), Var("a"), Var("b")), Mul... | ALG | null | COUNT | sympy | QF_PSD_DISTINCT | [
"MAX_PRIME_BELOW/QF_PSD_COUNT_LEQ",
"SUM_GEOM/QF_PSD_COUNT_LEQ"
] | c57319 | alg_qf_psd_orbit_v1 | null | 4 | null | [
"MAX_PRIME_BELOW",
"QF_PSD_COUNT_LEQ",
"QF_PSD_DISTINCT",
"SUM_GEOM"
] | 4 | 1.97 | 2026-02-25T07:10:19.380784Z | {
"verified": true,
"answer": 6,
"timestamp": "2026-02-25T07:10:21.351275Z"
} | 3b02b5 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 163,
"completion_tokens": 19020
},
"timestamp": "2026-03-29T22:04:12.257Z",
"answer": 6
},
{
"id"... | 1 | [
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok"
},
{
"lemma": "QF_PSD_COUNT_LEQ",
"status": ... | {
"lo": -3.33,
"mid": 1.03,
"hi": 5.26
} | ||
dc1fcb | nt_count_phi_equals_v1_124444284_8820 | Let $x$ and $y$ be positive integers such that $xy = 1234321$. Define $S$ to be the set of all values of $x + y$ for such pairs $(x, y)$. Let $u$ be the minimum value in $S$. Determine the number of positive integers $n$ such that $1 \leq n \leq u$ and $\phi(n) = 128$. Let this count be $c$. Compute the remainder when ... | 30,663 | graphs = [
Graph(
let={
"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")), Const(1234321)))), expr=Sum(Var("x"), Var("y")))),
"k": Const(... | NT | null | COUNT | sympy | B3 | [
"B3"
] | 0cd20d | nt_count_phi_equals_v1 | null | 7 | 0 | [
"B3"
] | 1 | 0.169 | 2026-02-08T11:55:23.702007Z | {
"verified": true,
"answer": 30663,
"timestamp": "2026-02-08T11:55:23.870936Z"
} | da358a | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 159,
"completion_tokens": 3454
},
"timestamp": "2026-02-14T20:34:32.921Z",
"answer": 30663
},
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
}
] | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
3a4d4d_l | nt_count_gcd_equals_v1_1918700295_1996 | Let $d$ be the sum of all integers $k$ from 1 to 21, inclusive. Let $k = 462$ and let $n$ be a positive integer such that $1 \leq n \leq 25281$ and $\gcd(n, k) = d$. Compute the number of such integers $n$. | 109 | NT | null | COUNT | sympy | EULER_TOTIENT_SUM | [
"SUM_ARITHMETIC"
] | eb34f0 | nt_count_gcd_equals_v1 | null | 4 | 0 | [
"EULER_TOTIENT_SUM",
"SUM_ARITHMETIC"
] | 2 | 9.257 | 2026-02-08T07:36:29.834379Z | {
"verified": false,
"answer": 55,
"timestamp": "2026-02-08T07:36:39.091096Z"
} | dce68a | 3a4d4d | legacy_text | 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": 1199
},
"timestamp": "2026-02-13T11:29:55.694Z",
"answer": 55
},
{
... | 1 | [
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "SUM_ARITHMETIC",
"status": "ok"
}
... | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | |
916331 | comb_factorial_compute_v1_1915831931_2642 | Let $S_1$ be the set of all ordered pairs $(x_1, y_1)$ of positive integers such that $x_1 y_1 = 64$. Let $s_1$ be the minimum value of $x_1 + y_1$ as $(x_1, y_1)$ ranges over $S_1$. Let $S_2$ be the set of all ordered pairs $(x, y)$ of positive integers such that $xy = s_1$. Let $n$ be the minimum value of $x + y$ as ... | 49,090 | graphs = [
Graph(
let={
"_n": Const(74769),
"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")), MinOverSet(set=MapOverSet(set=SolutionsSet(var... | ALG | COMB | COMPUTE | sympy | B3 | [
"B3/B3"
] | 8ffef9 | comb_factorial_compute_v1 | null | 5 | 0 | [
"B3"
] | 1 | 0.003 | 2026-02-08T17:00:55.381027Z | {
"verified": true,
"answer": 49090,
"timestamp": "2026-02-08T17:00:55.384200Z"
} | 2bcae4 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 197,
"completion_tokens": 743
},
"timestamp": "2026-02-17T17:16:41.937Z",
"answer": 49090
},
{... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
}
] | {
"lo": -5.64,
"mid": -3.17,
"hi": -0.81
} | ||
910927 | modular_count_residue_v1_784195855_4851 | Let $m = \sum_{k=1}^{3} \phi(k) \left\lfloor \frac{3}{k} \right\rfloor$, where $\phi$ denotes Euler's totient function. Determine the number of positive integers $n$ such that $1 \le n \le 33489$ and $n \equiv 3 \pmod{m}$. Multiply this count by $44121$, and find the remainder when the result is divided by $64286$. | 3,756 | graphs = [
Graph(
let={
"_n": Const(64286),
"upper": Const(33489),
"m": Summation(var="k", start=Const(1), end=Const(3), expr=Mul(EulerPhi(n=Var("k")), Floor(Div(Const(3), Var("k"))))),
"r": Const(3),
"result": CountOverSet(set=SolutionsSet(var=Var... | NT | null | COUNT | sympy | K2 | [
"K2"
] | 6897ab | modular_count_residue_v1 | null | 4 | 0 | [
"K2"
] | 1 | 1.192 | 2026-02-08T07:26:10.609749Z | {
"verified": true,
"answer": 3756,
"timestamp": "2026-02-08T07:26:11.801666Z"
} | 9f117d | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 146,
"completion_tokens": 950
},
"timestamp": "2026-02-13T10:03:07.696Z",
"answer": 3756
},
{
... | 1 | [
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "K2",
"status": "ok"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "V1",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
}
] | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
bd4d4b | nt_count_coprime_v1_458359167_1897 | Let $T$ be the set of all integers $t$ such that $16 \leq t \leq 126$ and there exist positive integers $a$, $b$ with $1 \leq a \leq 16$, $1 \leq b \leq 3$, satisfying $t = 6a + 10b$. Let $k$ be the number of elements in $T$. Determine the number of positive integers $n \leq 12321$ such that $\gcd(n, k) = 1$. | 4,107 | graphs = [
Graph(
let={
"upper": Const(12321),
"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(left=Var(name='a'), right=Const(value=16)), Geq(lef... | NT | null | COUNT | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | nt_count_coprime_v1 | null | 5 | 0 | [
"LIN_FORM"
] | 1 | 0.953 | 2026-02-08T04:55:37.875472Z | {
"verified": true,
"answer": 4107,
"timestamp": "2026-02-08T04:55:38.828461Z"
} | 6b4dda | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 226,
"completion_tokens": 2186
},
"timestamp": "2026-02-11T22:27:12.727Z",
"answer": 4107
},
{
"... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
}
] | {
"lo": -3.42,
"mid": 1.86,
"hi": 7.55
} | ||
4651ef | comb_binomial_compute_v1_153355830_1213 | Let $n = 12$. Define $k$ to be the sum $\sum_{i=1}^{3} i$. Compute $\binom{n}{k}$. | 924 | graphs = [
Graph(
let={
"n": Const(12),
"k": Summation(var="k", start=Const(1), end=Const(3), expr=Var("k")),
"result": Binom(n=Ref("n"), k=Ref("k")),
},
goal=Ref("result"),
)
] | ALG | COMB | COMPUTE | sympy | SUM_ARITHMETIC | [
"SUM_ARITHMETIC"
] | eb34f0 | comb_binomial_compute_v1 | null | 2 | 0 | [
"SUM_ARITHMETIC"
] | 1 | 0.002 | 2026-02-08T06:11:39.798470Z | {
"verified": true,
"answer": 924,
"timestamp": "2026-02-08T06:11:39.800875Z"
} | 1123e5 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 146,
"completion_tokens": 373
},
"timestamp": "2026-02-24T05:40:20.703Z",
"answer": 924
},
{
"id"... | 2 | [
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "SUM_ARITHMETIC",
"status": "ok"
}
] | {
"lo": -10,
"mid": -7.79,
"hi": -5.57
} | ||
06f392_n | comb_sum_binomial_row_v1_601307018_2466 | A square solar panel array is being designed using a total of $1055744$ panels. The array must be a perfect square or smaller, but still use a number of panels per side that divides evenly into the total. The largest possible side length $d$ satisfying $d^2 \leq 1055744$ and $d \mid 1055744$ is chosen. If the base desi... | 53,878 | COMB | null | SUM | sympy | B3_CLOSEST | [
"B3_CLOSEST"
] | ff7764 | comb_sum_binomial_row_v1 | negation_mod | 3 | null | [
"B3_CLOSEST"
] | 1 | 0.004 | 2026-03-10T03:12:09.014949Z | null | e1f734 | 06f392 | narrative | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 224,
"completion_tokens": 2310
},
"timestamp": "2026-03-29T16:11:49.751Z",
"answer": 53878
},
{
"... | 1 | [
{
"lemma": "B3_CLOSEST",
"status": "ok"
},
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no... | {
"lo": -5.36,
"mid": 0.27,
"hi": 5.45
} | |
d349c1 | alg_qf_psd_sum_v1_601307018_8213 | Compute the remainder when $$\sum_{a=1}^{6} \sum_{b=1}^{6} \sum_{c=1}^{6} \sum_{d=1}^{6} \left( 60a^2 + 39d^2 + 31c^2 + 22ac + 56cd - 36ab - 14bc - 26ad - 10bd + N \cdot b^2 \right)$$ is divided by $50146$, where $N = \left|\{ (a_1, b_1) \mid 1 \leq a_1 \leq b_1 \leq 40,\ 2a_1^2 - 4a_1b_1 + 2b_1^2 = 968 \}\right|$ | 24,050 | graphs = [
Graph(
let={
"_n": Const(39),
"result": Mod(value=SumOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("a"), Var("b"), Var("c"), Var("d")]), condition=And(Geq(Var("a"), Const(1)), Leq(Var("a"), Const(6)), Geq(Var("b"), Const(1)), Leq(Var("b"), Const(6)), Geq(... | ALG | null | COMPUTE | sympy | QF_PSD_ORBIT | [
"QF_PSD_ORBIT"
] | 1d37f3 | alg_qf_psd_sum_v1 | null | 5 | 0 | [
"QF_PSD_ORBIT"
] | 1 | 0.024 | 2026-03-10T08:44:11.043236Z | {
"verified": true,
"answer": 24050,
"timestamp": "2026-03-10T08:44:11.067565Z"
} | d53bc1 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 285,
"completion_tokens": 3887
},
"timestamp": "2026-04-19T08:31:24.817Z",
"answer": 24050
},
{
... | 1 | [
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "QF_PSD_ORBIT",
"status": "ok"
}
] | {
"lo": -5.34,
"mid": 1.1,
"hi": 7.53
} | ||
bdd0b3 | comb_count_derangements_v1_784195855_7557 | Let $n$ be the number of prime numbers $p$ such that $2 \leq p \leq 17$. Compute the number of derangements of $n$ elements. | 1,854 | graphs = [
Graph(
let={
"_n": Const(2),
"n": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Ref("_n")), Leq(Var("n"), Const(17)), IsPrime(Var("n"))))),
"result": Subfactorial(arg=Ref(name='n')),
},
goal=Ref("result"),
)
] | NT | COMB | COUNT | sympy | COUNT_PRIMES | [
"COUNT_PRIMES"
] | 07c874 | comb_count_derangements_v1 | null | 3 | 0 | [
"COUNT_PRIMES"
] | 1 | 0.001 | 2026-02-08T09:23:51.363684Z | {
"verified": true,
"answer": 1854,
"timestamp": "2026-02-08T09:23:51.364575Z"
} | 9d5dbe | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 84,
"completion_tokens": 5143
},
"timestamp": "2026-02-14T03:36:02.758Z",
"answer": 1854
},
{
... | 1 | [
{
"lemma": "COUNT_PRIMES",
"status": "ok"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
}
] | {
"lo": -8.26,
"mid": -5.01,
"hi": -1.76
} | ||
8f4fef | comb_binomial_compute_v1_168721529_1227 | Let $n = 16$. A positive integer $t$ is called admissible if there exist integers $a$ and $b$ such that $1 \leq a \leq 2$, $1 \leq b \leq 4$, $24 \leq t \leq 42$, and $t = 6a + 4b + 14$. Let $k$ be the number of admissible integers $t$. Compute $\binom{n}{k}$. | 12,870 | graphs = [
Graph(
let={
"n": Const(16),
"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(left=Var(name='a'), right=Const(value=2)), Geq(left=Var(na... | ALG | COMB | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | comb_binomial_compute_v1 | null | 4 | 0 | [
"LIN_FORM"
] | 1 | 0.003 | 2026-02-08T13:32:49.236956Z | {
"verified": true,
"answer": 12870,
"timestamp": "2026-02-08T13:32:49.240005Z"
} | 31f436 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 219,
"completion_tokens": 697
},
"timestamp": "2026-02-09T14:51:37.672Z",
"answer": 12870
},
{
"i... | 1 | [
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
}
] | {
"lo": -5.98,
"mid": -3.99,
"hi": -2
} | ||
7c8c67 | comb_factorial_compute_v1_349078426_1414 | Let $n$ be the number of positive integers $p$ for which there exists a positive integer $q$ such that $p < q$, $\gcd(p, q) = 1$, and $pq = 10290$. Let $r = n!$. Compute the remainder when $44121 \cdot r$ is divided by $83774$. | 17,830 | graphs = [
Graph(
let={
"_n": Const(44121),
"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=10290)), Eq(left=GCD(a=Var(name='p'), b=Var(n... | NT | null | COMPUTE | sympy | COPRIME_PAIRS | [
"COPRIME_PAIRS"
] | 2bb3aa | comb_factorial_compute_v1 | null | 5 | 0 | [
"COPRIME_PAIRS"
] | 1 | 0.011 | 2026-02-08T13:38:00.230821Z | {
"verified": true,
"answer": 17830,
"timestamp": "2026-02-08T13:38:00.242069Z"
} | 468d82 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 120,
"completion_tokens": 2612
},
"timestamp": "2026-02-15T19:06:43.556Z",
"answer": 17830
},
... | 1 | [
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "V1",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
}
] | {
"lo": -5.49,
"mid": 0.22,
"hi": 6.51
} | ||
510c29 | comb_sum_binomial_row_v1_1742523217_1697 | Let $n = 13$ and let $r = 2^n$. Let $c$ be the smallest divisor of $669938385421$ that is at least $2$. Compute the remainder when $c - r$ is divided by $51669$. | 43,566 | graphs = [
Graph(
let={
"n": Const(13),
"result": Pow(Const(2), Ref("n")),
"_c": MinOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Const(2)), Divides(divisor=Var("d"), dividend=Const(669938385421))))),
"Q": Mod(value=Sub(Ref("_c"), Ref("res... | NT | null | SUM | sympy | MIN_PRIME_FACTOR | [
"MIN_PRIME_FACTOR"
] | fd27b3 | comb_sum_binomial_row_v1 | negation_mod | 4 | 0 | [
"MIN_PRIME_FACTOR"
] | 1 | 0.001 | 2026-02-08T04:06:31.685930Z | {
"verified": true,
"answer": 43566,
"timestamp": "2026-02-08T04:06:31.687141Z"
} | 74a0ca | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 165,
"completion_tokens": 6229
},
"timestamp": "2026-02-10T15:18:39.747Z",
"answer": 43566
},
{
... | 1 | [
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "MIN_PRIME... | {
"lo": -3.42,
"mid": 1.86,
"hi": 7.55
} | ||
9626cc | algebra_poly_eval_v1_784195855_9075 | Let $n = 6$. Define
$$
Q = 10n^4 + 8n^3 + k \cdot n^2 - 2n + 2,
$$
where $k$ is the largest prime number in the interval $[2, 4]$. Compute the value of $Q$. | 14,786 | graphs = [
Graph(
let={
"n": Const(6),
"result": Sum(Mul(Const(10), Pow(Ref("n"), Const(4))), Mul(Const(8), Pow(Ref("n"), Const(3))), Mul(MaxOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(2)), Leq(Var("n"), Const(4)), IsPrime(Var("n"))))), Pow(Ref("n"), Cons... | NT | null | COMPUTE | sympy | MAX_PRIME_BELOW | [
"MAX_PRIME_BELOW"
] | dc3ad3 | algebra_poly_eval_v1 | null | 2 | 0 | [
"MAX_PRIME_BELOW"
] | 1 | 0.002 | 2026-02-08T16:30:53.148641Z | {
"verified": true,
"answer": 14786,
"timestamp": "2026-02-08T16:30:53.151062Z"
} | ff8bf0 | 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": 515
},
"timestamp": "2026-02-17T05:31:11.956Z",
"answer": 14786
},
{... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok"
},
{
"lemma": "V5",
"status"... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
d6cbc3 | comb_sum_binomial_row_v1_50713871_51 | Let $ n $ be the largest prime number satisfying $ 2 \leq n \leq 15 $. Compute the value of $ 2^n $. | 8,192 | graphs = [
Graph(
let={
"_n": Const(2),
"n": MaxOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Ref("_n")), Leq(Var("n"), Const(15)), IsPrime(Var("n"))))),
"result": Pow(Const(2), Ref("n")),
"Q": Ref("result"),
},
goal=Ref("Q... | NT | null | SUM | sympy | K2 | [
"MAX_PRIME_BELOW"
] | dc3ad3 | comb_sum_binomial_row_v1 | null | 3 | 0 | [
"K2",
"MAX_PRIME_BELOW"
] | 2 | 0.008 | 2026-02-08T02:43:54.627441Z | {
"verified": true,
"answer": 8192,
"timestamp": "2026-02-08T02:43:54.635529Z"
} | bf54b0 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 147,
"completion_tokens": 117
},
"timestamp": "2026-02-08T19:45:15.662Z",
"answer": 8192
},
{
"id... | 2 | [
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "VAL_SUM_EQ",
"status": "no"
}
... | {
"lo": -6.62,
"mid": -4.76,
"hi": -2.89
} | ||
618af9 | nt_num_divisors_compute_v1_1520064083_9194 | Let $n = 61009$. Define $r$ to be the number of positive divisors of $n$. Let $S$ be the set of all integers $t$ such that there exist integers $a$ and $b$ satisfying $1 \leq a \leq 8$, $1 \leq b \leq 2$, $7 \leq t \leq 26$, and $t = 2a + 5b$. Compute $r^2 + r \cdot |S| + 8$. | 233 | graphs = [
Graph(
let={
"_n": Const(2),
"n": Const(61009),
"result": NumDivisors(n=Ref("n")),
"_c": Const(8),
"Q": Sum(Pow(Ref("result"), Ref("_n")), Mul(CountOverSet(set=SolutionsSet(var=Var("t"), condition=Exists(var=Var(name='a'), condition=Exis... | NT | null | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM"
] | 2ba0ea | nt_num_divisors_compute_v1 | quadratic_mod | 3 | 0 | [
"LIN_FORM"
] | 1 | 0.003 | 2026-02-08T10:35:39.488783Z | {
"verified": true,
"answer": 233,
"timestamp": "2026-02-08T10:35:39.491594Z"
} | 40072b | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 154,
"completion_tokens": 1238
},
"timestamp": "2026-02-14T07:50:14.715Z",
"answer": 233
},
{
... | 1 | [
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "V3",
"status": "no"... | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
206673 | nt_min_with_divisor_count_v1_1431428450_0 | Let $m = 123$. Consider the set of all ordered pairs $(i,j)$ of positive integers such that $i + j = m$, where $1 \le i \le 122$ and $1 \le j \le 122$. Let $n$ be the number of such pairs. Let $u$ be the maximum value of $xy$ over all ordered pairs $(x,y)$ of positive integers such that $x + y = n$. Determine the small... | 12 | graphs = [
Graph(
let={
"_m": Const(123),
"_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(122)), right=IntegerRange(start=Const(1), end=... | NT | null | EXTREMUM | sympy | COUNT_SUM_EQUALS | [
"COUNT_SUM_EQUALS/B1"
] | 8f58d2 | nt_min_with_divisor_count_v1 | null | 6 | 0 | [
"B1",
"COUNT_SUM_EQUALS"
] | 2 | 0.894 | 2026-02-08T13:07:01.692422Z | {
"verified": true,
"answer": 12,
"timestamp": "2026-02-08T13:07:02.586795Z"
} | 480389 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 171,
"completion_tokens": 1198
},
"timestamp": "2026-02-15T10:57:18.873Z",
"answer": 12
},
{
... | 1 | [
{
"lemma": "B1",
"status": "ok_later"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "ok"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "... | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
6186cd | nt_sum_over_divisible_v1_153355830_749 | Let $n$ be a positive integer such that $1 \leq n \leq 65536$ and $n$ is divisible by 85. Compute the sum of all such $n$. Let this sum be $S$.\\
Let $T$ be the set of all ordered pairs $(x, y)$ of positive integers such that $x + y = 100$. Define $P$ to be the maximum value of $xy$ over all such pairs.\\
Compute the... | 17,876 | graphs = [
Graph(
let={
"_n": Const(100),
"upper": Const(65536),
"divisor": Const(85),
"result": SumOverSet(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")), Const... | NT | null | SUM | sympy | B1 | [
"B1"
] | bf138c | nt_sum_over_divisible_v1 | quadratic_mod | 3 | 0 | [
"B1"
] | 1 | 2.393 | 2026-02-08T04:09:47.488051Z | {
"verified": true,
"answer": 17876,
"timestamp": "2026-02-08T04:09:49.881528Z"
} | 910284 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 232,
"completion_tokens": 2751
},
"timestamp": "2026-02-10T15:31:50.097Z",
"answer": 17876
},
{
... | 1 | [
{
"lemma": "B1",
"status": "ok"
},
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
}
] | {
"lo": -3.49,
"mid": 1.84,
"hi": 7.55
} | ||
0b2596 | nt_count_coprime_v1_1915831931_2631 | Let $n$ be an integer. Define $k$ to be the largest prime number such that $2 \leq n \leq 29$. Let $S$ be the set of all positive integers $n_1$ such that $1 \leq n_1 \leq 22801$ and $\gcd(n_1, k) = 1$. Compute the number of elements in $S$. | 22,015 | graphs = [
Graph(
let={
"_n": Const(29),
"upper": Const(22801),
"k": MaxOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(2)), Leq(Var("n"), Ref("_n")), IsPrime(Var("n"))))),
"result": CountOverSet(set=SolutionsSet(var=Var("n1"), conditi... | NT | null | COUNT | sympy | MAX_PRIME_BELOW | [
"MAX_PRIME_BELOW"
] | dc3ad3 | nt_count_coprime_v1 | null | 4 | 0 | [
"MAX_PRIME_BELOW"
] | 1 | 3.004 | 2026-02-08T17:00:39.360398Z | {
"verified": true,
"answer": 22015,
"timestamp": "2026-02-08T17:00:42.364705Z"
} | 2ba793 | 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": 1890
},
"timestamp": "2026-02-17T17:13:37.621Z",
"answer": 22015
},
... | 1 | [
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok"
},
{
"lemma": "V3",
"st... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
ecf609 | antilemma_k3_v1_458359167_2960 | Compute the sum of $\phi(d)$ over all positive divisors $d$ of $47998$, where $\phi$ denotes Euler's totient function. Determine the value of this sum. | 47,998 | graphs = [
Graph(
let={
"_n": Const(47998),
"x": SumOverDivisors(n=Ref(name='_n'), 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 | 2026-02-08T06:52:03.500384Z | {
"verified": true,
"answer": 47998,
"timestamp": "2026-02-08T06:52:03.500779Z"
} | 123bd6 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 84,
"completion_tokens": 2380
},
"timestamp": "2026-02-13T05:27:53.944Z",
"answer": 47998
},
{... | 1 | [
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "K3",
"status": "ok"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "MOD_AD... | {
"lo": -5.92,
"mid": -3.14,
"hi": 0.26
} | ||
1ec025 | nt_count_with_divisor_count_v1_865884756_1986 | Compute the number of positive integers $n \le 8281$ such that $n$ has exactly $11$ positive divisors. | 1 | graphs = [
Graph(
let={
"upper": Const(8281),
"div_count": Const(11),
"result": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Ref("upper")), Eq(NumDivisors(n=Var("n")), Ref("div_count"))))),
},
goal=Ref("r... | NT | null | COUNT | sympy | LIN_FORM | [
"LIN_FORM/MIN_PRIME_FACTOR"
] | bb1a13 | nt_count_with_divisor_count_v1 | null | 4 | 0 | [
"LIN_FORM",
"MIN_PRIME_FACTOR"
] | 2 | 9.08 | 2026-02-08T16:25:20.376908Z | {
"verified": true,
"answer": 1,
"timestamp": "2026-02-08T16:25:29.456537Z"
} | dfe8f3 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 74,
"completion_tokens": 1175
},
"timestamp": "2026-02-17T03:26:46.139Z",
"answer": 1
},
{
... | 1 | [
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "MIN_PRIME_FACTOR",
"status": "ok_later"
},
{
"lemma": "MOD_ADD",
"s... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
70d409 | geo_count_lattice_triangle_v1_1918700295_1316 | Let $A$ be twice the area of the triangle with vertices at $(0,0)$, $(120,233)$, and $(77,128)$. Let $B$ be the number of lattice points on the boundary of this triangle, computed as the sum of the greatest common divisors of the absolute differences of coordinates along each edge. Compute the number of interior lattic... | 1,290 | graphs = [
Graph(
let={
"_n": Const(128),
"area_2x": Abs(arg=Sum(Mul(Const(value=120), Const(value=128)), Mul(Const(value=77), Sub(left=Const(value=0), right=Const(value=233))))),
"boundary": Sum(GCD(a=Abs(arg=Const(value=120)), b=Abs(arg=Const(value=233))), GCD(a=Abs(arg... | NT | null | COUNT | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | geo_count_lattice_triangle_v1 | null | 7 | 0 | [
"LIN_FORM"
] | 1 | 0.005 | 2026-02-08T05:46:36.230561Z | {
"verified": true,
"answer": 1290,
"timestamp": "2026-02-08T05:46:36.235897Z"
} | 59d6ec | 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": 1811
},
"timestamp": "2026-02-12T14:09:11.315Z",
"answer": 1290
},
{... | 1 | [
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "V8",
"status": "no"
}
] | {
"lo": -3.51,
"mid": 1.33,
"hi": 6.56
} | ||
d17eac | nt_min_with_divisor_count_v1_151522320_2200 | Let $u = 19321$ and $d = 9$. Let $N$ be the set of all positive integers $n \le u$ such that the number of positive divisors of $n$ is exactly $9$. Let $m$ be the smallest element of $N$. Let $T$ be the set of all integers $t$ such that $27 \le t \le 195$ and there exist positive integers $a \le 8$, $b \le 7$ satisfyin... | 2,996 | graphs = [
Graph(
let={
"_n": Const(2),
"upper": Const(19321),
"div_count": Const(9),
"result": MinOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Ref("upper")), Eq(NumDivisors(n=Var("n")), Ref("div_count"))))),
... | NT | null | EXTREMUM | sympy | LIN_FORM | [
"LIN_FORM/MAX_PRIME_BELOW"
] | 699466 | nt_min_with_divisor_count_v1 | quadratic_mod | 6 | 0 | [
"LIN_FORM",
"MAX_PRIME_BELOW"
] | 2 | 0.759 | 2026-02-08T04:40:57.836330Z | {
"verified": true,
"answer": 2996,
"timestamp": "2026-02-08T04:40:58.594832Z"
} | c6ecde | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 297,
"completion_tokens": 3143
},
"timestamp": "2026-02-11T21:40:55.003Z",
"answer": 2996
},
{
"... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok_later"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "V8",
"status":... | {
"lo": -3.42,
"mid": 1.86,
"hi": 7.55
} | ||
d32df6 | nt_count_intersection_v1_1915831931_1654 | 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 maximum value of $x_1 y_1$ over all pairs of positive integers $(x_1, y_1)$ such that $x_1 + y_1 = 6$. Determine the number of positive integers $n$ such that $1 \leq n \leq N$, $a$ divides $n$... | 64,544 | graphs = [
Graph(
let={
"_n": Const(30349),
"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 | B1 | [
"B1",
"B3"
] | 655d51 | nt_count_intersection_v1 | null | 6 | 0 | [
"B1",
"B3"
] | 2 | 0.513 | 2026-02-08T16:21:05.873104Z | {
"verified": true,
"answer": 64544,
"timestamp": "2026-02-08T16:21:06.385865Z"
} | 118848 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 185,
"completion_tokens": 1678
},
"timestamp": "2026-02-17T02:02:34.653Z",
"answer": 64544
},
... | 1 | [
{
"lemma": "B1",
"status": "ok"
},
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "MOD_SUB",
... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
c9d430_l | antilemma_sum_equals_v1_349078426_852 | Let $S$ be the set of all integers $t$ such that $22 \leq t \leq 242$ and there exist positive integers $a$ and $b$ with $1 \leq a \leq 7$, $1 \leq b \leq 18$, and $t = 14a + 8b$. Let $n$ be the number of elements in $S$. Let $x$ be the number of ordered pairs of positive integers $(i, j)$ such that $1 \leq i \leq 93$,... | 0 | COMB | GEOM | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM/COUNT_SUM_EQUALS",
"COUNT_SUM_EQUALS"
] | ada383 | antilemma_sum_equals_v1 | null | 4 | 0 | [
"COUNT_SUM_EQUALS",
"LIN_FORM"
] | 2 | 0.031 | 2026-02-08T13:18:33.244881Z | {
"verified": false,
"answer": 18144,
"timestamp": "2026-02-08T13:18:33.276051Z"
} | 0c4329 | c9d430 | legacy_text | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 270,
"completion_tokens": 4834
},
"timestamp": "2026-02-24T17:45:47.082Z",
"answer": 18144
},
{
"... | 1 | [
{
"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_FORM",
"status": "ok"
},
{
"lemma": ... | {
"lo": 3.25,
"mid": 5.68,
"hi": 8.81
} | |
55bfa1 | alg_poly3_min_v1_601307018_9041 | Find the minimum value of the expression
$$
48a^2c - 24b^2c - 72bc^2 + 192abc + 48a^2b - 56c^3 - 8b^3 + \left|\left\{ (a_1, b_1) \middle| \begin{array}{c}
1 \leq a_1 \leq 40,\ 1 \leq b_1 \leq M, \\
-2048a_1b_1^3 - 2048a_1^3b_1 + 512a_1^4 + 512b_1^4 + a_1^2b_1^2 \cdot S = 2097152
\end{array} \right\}\right| \cdot a^3 + ... | 75,044 | graphs = [
Graph(
let={
"_c": Const(40),
"_m": Const(512),
"_n": Const(2),
"result": Mod(value=MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("a"), Var("b"), Var("c")]), condition=And(Geq(Var("a"), Const(1)), Leq(Var("a"), Const(10)), Geq(V... | ALG | null | COMPUTE | sympy | SUM_SQUARES_IDENTITY | [
"SUM_SQUARES_IDENTITY/POLY4_COUNT",
"POLY4_COUNT/POLY4_COUNT"
] | a565b9 | alg_poly3_min_v1 | null | 7 | 0 | [
"POLY4_COUNT",
"SUM_SQUARES_IDENTITY"
] | 2 | 0.122 | 2026-03-10T09:27:40.465099Z | {
"verified": true,
"answer": 75044,
"timestamp": "2026-03-10T09:27:40.586655Z"
} | f9b8c7 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 522,
"completion_tokens": 8079
},
"timestamp": "2026-04-19T10:31:00.863Z",
"answer": 75044
},
{
... | 1 | [
{
"lemma": "POLY4_COUNT",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "SUM_SQUARES_IDENTITY",
"status": "ok"
}
] | {
"lo": -5.34,
"mid": 1.1,
"hi": 7.53
} | ||
756563 | comb_count_derangements_v1_124444284_877 | Let $n$ be the number of positive integers $p$ for which there exists a positive integer $q$ such that $p \cdot q = 2940$, $\gcd(p, q) = 1$, and $p < q$. Compute the subfactorial of $n$, denoted $!n$, which is the number of derangements of $n$ elements. | 14,833 | 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=2940)), Eq(left=GCD(a=Var(name='p'), b=Var(name='q')), right=Const(value=1)),... | NT | COMB | COUNT | sympy | COPRIME_PAIRS | [
"COPRIME_PAIRS"
] | 2bb3aa | comb_count_derangements_v1 | null | 6 | 0 | [
"COPRIME_PAIRS"
] | 1 | 0.001 | 2026-02-08T03:33:25.702056Z | {
"verified": true,
"answer": 14833,
"timestamp": "2026-02-08T03:33:25.703137Z"
} | 179217 | 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": 1673
},
"timestamp": "2026-02-09T23:17:40.838Z",
"answer": 14833
},
{
"... | 1 | [
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "V1",
"status": "no"
}
] | {
"lo": -3.46,
"mid": 1.03,
"hi": 5.49
} | ||
ab32d0 | nt_count_gcd_equals_v1_168721529_420 | Let $n = 511$. Define $u = \left( \sum_{d \mid n} \phi(d) \right) - n$, where $\phi$ denotes Euler's totient function. Let $a = 52$ and $b = 39$, and define $t = \sum_{d \mid \gcd(a,b)} \mu(d)$, where $\mu$ is the M\"obius function. Let $k = 338 + t$ and $\text{upper} = 45369 + u$. Determine the number of positive inte... | 1,610 | graphs = [
Graph(
let={
"n": Const(511),
"u": Sub(SumOverDivisors(n=Ref(name='n'), var='d', expr=EulerPhi(n=Var(name='d'))), Ref("n")),
"a": Const(52),
"b": Const(39),
"t": SumOverDivisors(n=GCD(a=Ref(name='a'), b=Ref(name='b')), var='d', expr=Moeb... | NT | null | COUNT | sympy | EULER_TOTIENT_SUM | [
"EULER_TOTIENT_SUM",
"MOBIUS_COPRIME"
] | 0bcbf0 | nt_count_gcd_equals_v1 | null | 6 | 2 | [
"EULER_TOTIENT_SUM",
"MOBIUS_COPRIME"
] | 2 | 5.508 | 2026-02-08T13:02:41.773409Z | {
"verified": true,
"answer": 1610,
"timestamp": "2026-02-08T13:02:47.281526Z"
} | 3bdbf5 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 264,
"completion_tokens": 1305
},
"timestamp": "2026-02-09T04:51:55.200Z",
"answer": 1610
},
{
"i... | 1 | [
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "EULER_TOTIENT_SUM",
"status": "ok"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "MOBIUS_COPRIME",
"status": "ok"
},
{
"lemma": "MOD_FACTORIAL",... | {
"lo": -2.06,
"mid": 1.85,
"hi": 5.2
} | ||
302481 | algebra_poly_eval_v1_1218484723_3565 | Let $m$ be the number of ordered pairs $(a, b)$ of positive integers with $1 \le a, b \le 30$ satisfying $27b^3 + 108ab^2 + 64a^3 + 144a^2b = 857375$. Let $e$ be the number of such pairs satisfying $24ab^2 - 24a^2b + 8a^3 = 46592$. Compute $7m^e + 9m^3 - 4m^2 + 7m - 9$. | 33,071 | graphs = [
Graph(
let={
"_m": Const(24),
"_n": Const(8),
"m": 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)), Eq(Sum(Mul(Const(27), ... | ALG | null | COMPUTE | sympy | POLY3_COUNT | [
"POLY3_COUNT"
] | 355dbe | algebra_poly_eval_v1 | null | 6 | 0 | [
"POLY3_COUNT"
] | 1 | 0.017 | 2026-02-25T05:11:34.280136Z | {
"verified": true,
"answer": 33071,
"timestamp": "2026-02-25T05:11:34.296865Z"
} | 9c1676 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 231,
"completion_tokens": 3591
},
"timestamp": "2026-03-29T11:00:40.168Z",
"answer": 33071
},
{
"... | 1 | [
{
"lemma": "POLY3_COUNT",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
}
] | {
"lo": -2.45,
"mid": 1.37,
"hi": 5.29
} | ||
d46968 | nt_count_phi_equals_v1_1440796553_509 | Compute the number of positive integers $n$ such that $1 \leq n \leq 1260$ and $\phi(n) = 840$, where $\phi$ denotes Euler's totient function. | 5 | graphs = [
Graph(
let={
"upper": Const(1260),
"k": Const(840),
"result": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Ref("upper")), Eq(EulerPhi(n=Var("n")), Ref("k"))))),
},
goal=Ref("result"),
)
] | NT | null | COUNT | sympy | BIG_OMEGA_ZERO | [
"COUNT_FIB_DIVISIBLE",
"LIN_FORM"
] | 0f3003 | nt_count_phi_equals_v1 | null | 7 | 0 | [
"BIG_OMEGA_ZERO",
"COUNT_FIB_DIVISIBLE",
"LIN_FORM"
] | 3 | 3.196 | 2026-02-08T11:50:00.977572Z | {
"verified": true,
"answer": 5,
"timestamp": "2026-02-08T11:50:04.173298Z"
} | c151ff | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 1,
"correct": {
"strict": false,
"boxed": false,
"relaxed": true
},
"usage": {
"prompt_tokens": 88,
"completion_tokens": 5730
},
"timestamp": "2026-02-14T19:26:48.208Z",
"answer": 0
},
{
... | 1 | [
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "ok"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "MOD_ADD",
"statu... | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
22f67d | algebra_quadratic_discriminant_v1_124444284_6128 | Let $a = 2$ and $b = 38$. Let $c$ be the number of integers $t$ such that $9 \leq t \leq 200$ and there exist integers $a'$ and $b'$ satisfying $1 \leq a' \leq 45$, $1 \leq b' \leq 4$, and $t = 4a' + 5b'$. Compute $b^2 - 4ac$. | 4 | graphs = [
Graph(
let={
"_n": Const(2),
"a": Const(2),
"b": Const(38),
"c": 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(lef... | NT | null | COMPUTE | sympy | B1 | [
"LIN_FORM"
] | 7b2633 | algebra_quadratic_discriminant_v1 | null | 5 | 0 | [
"B1",
"LIN_FORM"
] | 2 | 0.026 | 2026-02-08T08:08:55.401380Z | {
"verified": true,
"answer": 4,
"timestamp": "2026-02-08T08:08:55.427147Z"
} | 3e9f9e | 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": 2514
},
"timestamp": "2026-02-13T15:28:50.861Z",
"answer": 4
},
{
... | 1 | [
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "VAL_SUM_... | {
"lo": -3.51,
"mid": 1.33,
"hi": 6.56
} | ||
614d2e | antilemma_k3_v1_349078426_749 | Let $ n = 39044 $. Compute the sum of $ \phi(d) $ over all positive divisors $ d $ of $ n $. | 39,044 | graphs = [
Graph(
let={
"x": SumOverDivisors(n=Const(value=39044), 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 | 2026-02-08T13:16:07.808909Z | {
"verified": true,
"answer": 39044,
"timestamp": "2026-02-08T13:16:07.809289Z"
} | 080794 | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 1,
"correct": {
"strict": false,
"boxed": false,
"relaxed": true
},
"usage": {
"prompt_tokens": 89,
"completion_tokens": 879
},
"timestamp": "2026-02-16T04:28:51.140Z",
"answer": 28056
},
{
"id": 11,
... | 1 | [
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "K3",
"status": "ok"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
}
] | {
"lo": -6.96,
"mid": -4.56,
"hi": -1.46
} | ||
a09213 | nt_count_divisible_v1_2051736721_5556 | Let $S$ be the set of all ordered pairs $(x_1, y_1)$ of positive integers such that $x_1 y_1 = 1028196$. Let $m$ be the minimum value of $x_1 + y_1$ over all pairs $(x_1, y_1) \in S$. Let $T$ be the set of all positive integers $n$ such that $1 \le n \le m$ and $24$ divides the $n$th Fibonacci number. Let $U$ be the se... | 2,680 | graphs = [
Graph(
let={
"_n": Const(24),
"upper": Const(69696),
"divisor": 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")), CountOve... | NT | null | COUNT | sympy | B3 | [
"B3/COUNT_FIB_DIVISIBLE/B3"
] | 55c832 | nt_count_divisible_v1 | null | 6 | 0 | [
"B3",
"COUNT_FIB_DIVISIBLE"
] | 2 | 2.083 | 2026-02-08T18:39:57.949091Z | {
"verified": true,
"answer": 2680,
"timestamp": "2026-02-08T18:40:00.031640Z"
} | 540577 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 250,
"completion_tokens": 2395
},
"timestamp": "2026-02-18T18:35:41.954Z",
"answer": 2680
},
{... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "ok_later"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": ... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
5164ca | diophantine_fbi2_min_v1_1978505735_5810 | Let $S$ be the set of all ordered pairs $(x_1, y_1)$ of positive integers such that $x_1 + y_1 = 180$. Let $P$ be the maximum value of $x_1 y_1$ over all such pairs. Let $T$ be the set of all ordered pairs $(x, y)$ of positive integers such that $xy = P$. Let $k$ be the minimum value of $x + y$ over all such pairs in $... | 4 | graphs = [
Graph(
let={
"_c": Const(4),
"_m": Const(19),
"_n": Const(19),
"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... | NT | null | EXTREMUM | sympy | B1 | [
"B1/B3",
"K2"
] | dd6f52 | diophantine_fbi2_min_v1 | null | 7 | 0 | [
"B1",
"B3",
"K2"
] | 3 | 0.012 | 2026-02-08T19:14:46.033310Z | {
"verified": true,
"answer": 4,
"timestamp": "2026-02-08T19:14:46.045284Z"
} | f12496 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 239,
"completion_tokens": 2088
},
"timestamp": "2026-02-18T21:43:34.579Z",
"answer": 4
},
{
... | 1 | [
{
"lemma": "B1",
"status": "ok"
},
{
"lemma": "B3",
"status": "ok_later"
},
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K2",
"status": "ok"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
16721d | nt_min_coprime_above_v1_168721529_1368 | Let $s$ be the number of positive integers $n \leq 4916$ such that $3$ divides the $n$-th Fibonacci number. Let $u$ be the number of prime numbers $n$ such that $2 \leq n \leq 11243$. Let $m = 120$. Determine the value of the smallest integer $n$ such that $s < n \leq u$ and $\gcd(n, m) = 1$. | 1,231 | graphs = [
Graph(
let={
"_n": Const(3),
"start": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Const(4916)), Divides(divisor=Ref("_n"), dividend=Fibonacci(arg=Var(name='n')))))),
"upper": CountOverSet(set=SolutionsSet(var... | NT | null | EXTREMUM | sympy | COUNT_FIB_DIVISIBLE | [
"COUNT_FIB_DIVISIBLE",
"COUNT_PRIMES"
] | 2fa833 | nt_min_coprime_above_v1 | null | 5 | 0 | [
"COUNT_FIB_DIVISIBLE",
"COUNT_PRIMES"
] | 2 | 0.076 | 2026-02-08T13:39:03.381573Z | {
"verified": true,
"answer": 1231,
"timestamp": "2026-02-08T13:39:03.457087Z"
} | c46d62 | CC BY 4.0 | [
{
"id": 4,
"model": "NousResearch/Hermes-4-405B",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 158,
"completion_tokens": 515
},
"timestamp": "2026-02-10T05:57:41.439Z",
"answer": 1229
},
... | 1 | [
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "ok"
},
{
"lemma": "COUNT_PRIMES",
"status": "ok"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
... | {
"lo": -5.65,
"mid": -2.14,
"hi": 1.97
} | ||
4cd27d | nt_lcm_compute_v1_168721529_443 | Let $a$ be the sum of $\phi(d)$ over all positive divisors $d$ of $2356$. Let $b = 2918$. Define $\ell$ to be the least common multiple of $a$ and $b$.
Find the remainder when $19901 \times \ell$ is divided by $56496$. | 47,372 | graphs = [
Graph(
let={
"a": SumOverDivisors(n=Const(value=2356), var='d', expr=EulerPhi(n=Var(name='d'))),
"b": Const(2918),
"result": LCM(a=Ref("a"), b=Ref("b")),
"_c": Const(19901),
"Q": Mod(value=Mul(Ref("_c"), Ref("result")), modulus=Const(564... | NT | null | COMPUTE | sympy | K3 | [
"K3"
] | 54c41e | nt_lcm_compute_v1 | null | 5 | 0 | [
"K3"
] | 1 | 0.002 | 2026-02-08T13:03:26.945818Z | {
"verified": true,
"answer": 47372,
"timestamp": "2026-02-08T13:03:26.947849Z"
} | 4e6f66 | CC BY 4.0 | [
{
"id": 4,
"model": "NousResearch/Hermes-4-405B",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 128,
"completion_tokens": 643
},
"timestamp": "2026-02-09T17:00:03.914Z",
"answer": 3520
},
... | 1 | [
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K3",
"status": "ok"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
},
{
"lemma": "VAL_SUM_EQ",
"status": "no"
}
] | {
"lo": -1.9,
"mid": 2.34,
"hi": 6.68
} | ||
eb1077 | comb_factorial_compute_v1_1218484723_1171 | Let $M = 8!$. Compute the remainder when $$\min_{\substack{a,b \in \mathbb{Z}^+ \\ 1 \le a, b \le 11}} \left( \sum_{\substack{n_1 = 25, 50, 75, 100}} n_1 a^3 + 750a b^2 \right) - M$$ is divided by $73141$. | 33,821 | graphs = [
Graph(
let={
"_n": Const(2),
"n": Const(8),
"result": Factorial(Ref("n")),
"Q": Mod(value=Sub(MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("a"), Var("b")]), condition=And(Geq(Var("a"), Const(1)), Leq(Var("a"), Const(11)), Geq(V... | COMB | null | COMPUTE | sympy | SUM_DIVISIBLE | [
"SUM_DIVISIBLE/POLY3_MIN"
] | 568d9a | comb_factorial_compute_v1 | negation_mod | 5 | 0 | [
"POLY3_MIN",
"SUM_DIVISIBLE"
] | 2 | 0.007 | 2026-02-25T02:55:35.851328Z | {
"verified": true,
"answer": 33821,
"timestamp": "2026-02-25T02:55:35.857860Z"
} | 4a6035 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 205,
"completion_tokens": 1418
},
"timestamp": "2026-03-10T05:50:26.535Z",
"answer": 33821
},
{
"... | 1 | [
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "POLY3_MIN",
"status": "ok_later"
},
{
"lemma": "SUM_DIVISIBLE",
"status": "ok"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8",
... | {
"lo": -4.26,
"mid": -1.81,
"hi": 1.21
} | ||
36c3bb | sequence_count_fib_divisible_v1_1978505735_778 | Let $n = 64667$. Consider the set of all ordered pairs $(x,y)$ of positive integers such that $xy = 45796$. Let $S$ be the set of all values of $x + y$ for such pairs. Let $u$ be the minimum value in $S$. Let $d = 14$. Determine the number of positive integers $n'$ such that $1 \leq n' \leq u$ and $d$ divides the $n'$-... | 38,720 | graphs = [
Graph(
let={
"_n": Const(64667),
"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")), Const(45796)))), expr=Sum(Var("x"), Var("y... | NT | null | COUNT | sympy | B3 | [
"B3"
] | 0cd20d | sequence_count_fib_divisible_v1 | null | 6 | 0 | [
"B3"
] | 1 | 0.021 | 2026-02-08T15:35:31.454953Z | {
"verified": true,
"answer": 38720,
"timestamp": "2026-02-08T15:35:31.475698Z"
} | 2fc64d | 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": 1987
},
"timestamp": "2026-02-16T09:48:33.517Z",
"answer": 38720
},
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "VAL_SUM_EQ",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
4e468e | modular_sum_quadratic_residues_v1_1470522791_373 | Let $p$ be the largest prime number satisfying $2 \leq p \leq 269$. Define $r = \frac{p(p-1)}{4}$. Compute the remainder when $44121 \cdot r$ is divided by $92066$. | 18,741 | graphs = [
Graph(
let={
"_n": Const(92066),
"p": MaxOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(2)), Leq(Var("n"), Const(269)), 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 | 0.002 | 2026-02-08T12:58:41.255702Z | {
"verified": true,
"answer": 18741,
"timestamp": "2026-02-08T12:58:41.257464Z"
} | b5f839 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 98,
"completion_tokens": 1467
},
"timestamp": "2026-02-15T08:22:55.686Z",
"answer": 18741
},
{... | 1 | [
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"... | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} |
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