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 |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
a4a4d9_n | alg_sum_ap_v1_1419126231_215 | A digital clock logs events every second, assigning each a sequential number starting from 1. During a test lasting $\sum_{k=0}^{683} (2k + 100)$ seconds, engineers monitor how many logged event numbers $j$ satisfy both $j \leq \sum_{k_1=0}^{12} (2k_1 + 601)$ and $j^4 \leq 4032880071611521$. The system reports the tota... | 1,649 | ALG | null | COMPUTE | sympy | ABS_INEQ | [
"SUM_AP/C3"
] | 9bc91a | alg_sum_ap_v1 | null | 4 | null | [
"ABS_INEQ",
"C3",
"SUM_AP"
] | 3 | 0.033 | 2026-02-25T09:46:18.859711Z | null | 736f95 | a4a4d9 | narrative | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 222,
"completion_tokens": 4559
},
"timestamp": "2026-03-31T03:20:44.793Z",
"answer": 1649
},
{
"i... | 1 | [
{
"lemma": "C3",
"status": "ok_later"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "SUM_AP",
"status": "ok"
}
] | {
"lo": -5.37,
"mid": 0.23,
"hi": 5.22
} | |
a82e6a_n | algebra_vieta_sum_v1_601307018_47 | A rectangular garden has area $1587600$ square meters, with integer side lengths. The smallest possible perimeter corresponds to sides $x_1$ and $y$ minimizing $x_1 + y$. This minimum sum is used as a constant in the quartic equation $x^4 - 30x^3 + 327x^2 - 1522x + (x_1 + y) = 0$. Let $M$ be the sum of all positive rea... | 92,816 | ALG | null | COMPUTE | sympy | POLY_ORBIT_COUNT | [
"B3"
] | 0cd20d | algebra_vieta_sum_v1 | null | 5 | null | [
"B3",
"POLY_ORBIT_COUNT"
] | 2 | 3.856 | 2026-03-10T00:43:46.125278Z | null | 20e3f2 | a82e6a | narrative | 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": 10593
},
"timestamp": "2026-03-29T13:52:11.286Z",
"answer": 92816
},
{
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
}
] | {
"lo": -5.36,
"mid": 0.27,
"hi": 5.45
} | |
fcc6ca | nt_count_digit_sum_v1_677425708_3776 | Let $n$ be a positive integer. Define $\alpha$ to be the number of positive integers $n$ at most 125 that are divisible by 5 and relatively prime to 21. Let $\beta$ be the number of positive integers $n$ at most 99999 such that the sum of the decimal digits of $n$ equals $\alpha$. Compute the remainder when $43915\beta... | 12,084 | graphs = [
Graph(
let={
"_n": Const(21),
"upper": Const(99999),
"target_sum": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Const(125)), Divides(divisor=Const(5), dividend=Var("n")), Eq(GCD(a=Var("n"), b=Ref("_n")), Const... | NT | null | COUNT | sympy | C5 | [
"C5"
] | 1d9668 | nt_count_digit_sum_v1 | null | 6 | 0 | [
"C5"
] | 1 | 4.044 | 2026-02-08T05:55:58.966237Z | {
"verified": true,
"answer": 12084,
"timestamp": "2026-02-08T05:56:03.009853Z"
} | f8789d | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 137,
"completion_tokens": 1772
},
"timestamp": "2026-02-12T16:51:18.833Z",
"answer": 12084
},
... | 1 | [
{
"lemma": "C5",
"status": "ok"
},
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"
}
] | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
2e41c8 | comb_catalan_compute_v1_458359167_2516 | Let $n = 10$. Define $C_n$ to be the $n$th Catalan number. Let $S$ be the set of all ordered pairs $(x_1, x_2)$ of positive odd integers such that $x_1 + x_2 = 13530$. Let $c$ be the number of elements in $S$. Compute the remainder when $c - C_n$ is divided by $80249$. | 70,218 | graphs = [
Graph(
let={
"_n": Const(13530),
"n": Const(10),
"result": Catalan(Ref("n")),
"_c": 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... | COMB | null | COMPUTE | sympy | COMB1 | [
"COMB1"
] | 9f12f1 | comb_catalan_compute_v1 | negation_mod | 4 | 0 | [
"COMB1"
] | 1 | 0.001 | 2026-02-08T06:18:41.012958Z | {
"verified": true,
"answer": 70218,
"timestamp": "2026-02-08T06:18:41.014429Z"
} | eff938 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 202,
"completion_tokens": 1061
},
"timestamp": "2026-02-24T05:54:40.566Z",
"answer": 70218
},
{
"... | 1 | [
{
"lemma": "COMB1",
"status": "ok"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "V7... | {
"lo": -5.98,
"mid": -3.97,
"hi": -1.94
} | ||
5a44e8 | lte_diff_endings_v1_168721529_793 | Let $a = 153$, $b = 3$, $p = 5$, and $T = 9$. Let $d = a - b$. Let $v_p(d)$ denote the largest integer $k$ such that $p^k$ divides $d$. Define $x = p^{T - v_p(d)}$. Compute $x$. | 78,125 | graphs = [
Graph(
let={
"a_val": Const(153),
"b_val": Const(3),
"p_val": Const(5),
"T_val": Const(9),
"diff": Sub(Ref("a_val"), Ref("b_val")),
"vp_diff": MaxKDivides(target=Ref("diff"), base=Ref("p_val")),
"exp": Sub(Ref("T_... | NT | null | COMPUTE | sympy | LTE_DIFF | [
"LTE_DIFF"
] | cf8260 | lte_diff_endings_v1 | null | 2 | null | [
"LTE_DIFF"
] | 1 | 0.001 | 2026-02-08T13:17:37.435579Z | {
"verified": true,
"answer": 78125,
"timestamp": "2026-02-08T13:17:37.436304Z"
} | 20bdc1 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 189,
"completion_tokens": 361
},
"timestamp": "2026-02-09T09:12:04.195Z",
"answer": 78125
},
{
"i... | 1 | [
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "ok"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
... | {
"lo": -6.69,
"mid": -2.39,
"hi": 1.83
} | ||
e63c17 | algebra_quadratic_discriminant_v1_717093673_1724 | Let $N$ be the number of nonnegative integers $j$ with $0 \leq j \leq 384$ such that $\binom{384}{j}$ is odd. Let $a = 1$, $b = 3$, and $c = -70$. Let $P$ be the number of positive integers $p$ for which there exists a positive integer $q$ such that $pq = 72$, $\gcd(p, q) = 1$, and $p < q$. Compute the value of $b^P - ... | 289 | graphs = [
Graph(
let={
"_n": CountOverSet(set=SolutionsSet(var=Var("j"), condition=And(Geq(Var("j"), Const(0)), Leq(Var("j"), Const(384)), Eq(Mod(value=Binom(n=Const(384), k=Var("j")), modulus=Const(2)), Const(1))), domain='nonnegative_integers')),
"a": Const(1),
"b": Co... | NT | null | COMPUTE | sympy | COPRIME_PAIRS | [
"V8/COPRIME_PAIRS"
] | cea98a | algebra_quadratic_discriminant_v1 | null | 6 | 0 | [
"COPRIME_PAIRS",
"V8"
] | 2 | 0.032 | 2026-02-08T16:17:12.234326Z | {
"verified": true,
"answer": 289,
"timestamp": "2026-02-08T16:17:12.266156Z"
} | 5696cd | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 168,
"completion_tokens": 1444
},
"timestamp": "2026-02-17T00:46:14.957Z",
"answer": 289
},
{
... | 1 | [
{
"lemma": "COPRIME_PAIRS",
"status": "ok_later"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "V3",
"status": "no"
},
{
"lemma": "V5",
"statu... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
b3541b_l | comb_sum_binomial_mod_v1_151522320_738 | Let $S$ be the set of all ordered pairs $(x, y)$ of positive integers such that $xy = 2829124$. Let $s$ be the minimum value of $x + y$ over all $(x, y) \in S$. Let $T$ be the set of all ordered pairs $(x, y)$ of positive integers such that $xy = s$. Let $m$ be the minimum value of $x + y$ over all $(x, y) \in T$. Defi... | 0 | ALG | COMB | COMPUTE | sympy | B3 | [
"B3/B3"
] | 8ffef9 | comb_sum_binomial_mod_v1 | null | 6 | 0 | [
"B3"
] | 1 | 0.01 | 2026-02-08T03:29:34.447527Z | {
"verified": false,
"answer": 2679,
"timestamp": "2026-02-08T03:29:34.457521Z"
} | 15cc0a | b3541b | 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": 253,
"completion_tokens": 32768
},
"timestamp": "2026-02-23T22:25:34.715Z",
"answer": null
},
{
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
}
] | {
"lo": 3.43,
"mid": 5.73,
"hi": 8.84
} | |
93e238 | antilemma_k2_v1_898971024_845 | Let $n = 164$. Define
$$
x = \sum_{k=1}^{n} \phi(k) \left\lfloor \frac{\sum_{d \mid n} \phi(d)}{k} \right\rfloor.
$$
Compute the value of $x$. | 13,530 | graphs = [
Graph(
let={
"_n": Const(164),
"x": Summation(var="k", start=Const(1), end=Ref("_n"), expr=Mul(EulerPhi(n=Var("k")), Floor(Div(SumOverDivisors(n=Const(value=164), var='d', expr=EulerPhi(n=Var(name='d'))), Var("k"))))),
},
goal=Ref("x"),
)
] | NT | COMB | COMPUTE | sympy | K13 | [
"K3/K2",
"K2"
] | c7f244 | antilemma_k2_v1 | null | 7 | 0 | [
"K13",
"K2",
"K3"
] | 3 | 0.006 | 2026-02-08T15:42:00.071707Z | {
"verified": true,
"answer": 13530,
"timestamp": "2026-02-08T15:42:00.077808Z"
} | 7274db | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 105,
"completion_tokens": 1184
},
"timestamp": "2026-02-16T11:57:19.666Z",
"answer": 13530
},
... | 1 | [
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "K2",
"status": "ok"
},
{
"lemma": "K3",
"status": "ok"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "V7",... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
000ae4 | modular_mod_compute_v1_1978505735_6349 | Let $m$ be the largest positive divisor of $1057792$ that is at most $1024$. Let $a = 49284$ and let $r = a \bmod m$. Let $c = 37919$ and $n = 88450$. Compute the value of $(c \cdot r) \bmod n$. | 52,108 | graphs = [
Graph(
let={
"_n": Const(88450),
"a": Const(49284),
"m": MaxOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Const(1)), Leq(Var("d"), Const(1024)), Divides(divisor=Var("d"), dividend=Const(1057792))))),
"result": Mod(value=Ref("a")... | NT | null | COMPUTE | sympy | MAX_DIVISOR | [
"MAX_DIVISOR"
] | 51757e | modular_mod_compute_v1 | null | 3 | 0 | [
"MAX_DIVISOR"
] | 1 | 0.002 | 2026-02-08T19:33:34.599004Z | {
"verified": true,
"answer": 52108,
"timestamp": "2026-02-08T19:33:34.600791Z"
} | 231caf | 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": 1298
},
"timestamp": "2026-02-18T22:37:45.391Z",
"answer": 52108
},
... | 1 | [
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MAX_DIVISOR",
"status": "ok"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "V3",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
916c7a | modular_count_residue_v1_458359167_227 | Let $n = 2$ and define $\text{upper} = 41616$. Let $m$ be the largest prime number $n$ such that $2 \leq n \leq 17$. Let $r = 2$. Determine the value of the number of integers $n$ such that $\phi(n) \leq n \leq \text{upper}$ and $n \equiv r \pmod{m}$. | 2,448 | graphs = [
Graph(
let={
"_n": Const(2),
"upper": Const(41616),
"m": MaxOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(2)), Leq(Var("n"), Const(17)), IsPrime(Var("n"))))),
"r": Const(2),
"result": CountOverSet(set=Solutions... | NT | null | COUNT | sympy | B3 | [
"MAX_PRIME_BELOW",
"ONE_PHI_2"
] | 256a94 | modular_count_residue_v1 | null | 4 | 0 | [
"B3",
"MAX_PRIME_BELOW",
"ONE_PHI_2"
] | 3 | 2.9 | 2026-02-08T03:05:09.440222Z | {
"verified": true,
"answer": 2448,
"timestamp": "2026-02-08T03:05:12.340342Z"
} | ad7986 | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 187,
"completion_tokens": 607
},
"timestamp": "2026-02-17T20:15:43.705Z",
"answer": 2448
}
] | 2 | [
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok"
},
{
"lemma": "ONE_PHI_2",
"status": "ok"
},
{
"lemma": "V5",
"status": "no"
},
{
... | {
"lo": -10,
"mid": -6.47,
"hi": -2.95
} | ||
48f6f3 | nt_gcd_compute_v1_124444284_897 | Let $p_1$ be the number of positive integers $n$ such that $1 \le n \le 47$ and $\gcd(n, 20) = 1$. Let $w = \Omega(p_1)$, where $\Omega(k)$ denotes the number of prime factors of $k$ counted with multiplicity. Define $p = 19$ and $q = 83$, and let $n = p \cdot q$. Let $u = \sum_{d \mid n} \mu(d)$, where $\mu$ is the M\... | 62,828 | graphs = [
Graph(
let={
"p1": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Const(47)), Eq(GCD(a=Var("n"), b=Const(20)), Const(1))))),
"w": BigOmega(n=Ref(name='p1')),
"p": Const(19),
"q": Const(83),
... | NT | null | COMPUTE | sympy | C4 | [
"C4/BIG_OMEGA_ONE",
"MOBIUS_SUM"
] | 402935 | nt_gcd_compute_v1 | null | 7 | 2 | [
"BIG_OMEGA_ONE",
"C4",
"MOBIUS_SUM"
] | 3 | 0.002 | 2026-02-08T03:34:34.539948Z | {
"verified": true,
"answer": 62828,
"timestamp": "2026-02-08T03:34:34.542347Z"
} | a1b062 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 288,
"completion_tokens": 4497
},
"timestamp": "2026-02-09T23:42:48.418Z",
"answer": 62828
},
{
"... | 1 | [
{
"lemma": "BIG_OMEGA_ONE",
"status": "ok_later"
},
{
"lemma": "C4",
"status": "ok"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
... | {
"lo": -6.51,
"mid": -0.31,
"hi": 5.43
} | ||
b852fb | comb_count_derangements_v1_677425708_3477 | Let $u = 7$. Define $n_2 = u + 1$ and compute
$$
m = \sum_{k=0}^{n_2} (-1)^k \binom{n_2}{k}.
$$
Let $n_1 = 0$ and compute
$$
f = \sum_{k=0}^{n_1} (-1)^k \binom{n_1}{k}.
$$
Let $n = 7$ and let $D$ be the number of derangements of $n$ elements. Let $d_0, d_1, \dots, d_{t-1}$ be the decimal digits of $D$, where $d_0$ is t... | 52,553 | graphs = [
Graph(
let={
"u": Const(7),
"n2": Sum(Ref("u"), Const(1)),
"m": Summation(var="k", start=Const(0), end=Ref("n2"), expr=Mul(Pow(Const(-1), Var("k")), Binom(n=Ref("n2"), k=Var("k")))),
"n1": Const(0),
"f": Summation(var="k", start=Const(0)... | COMB | null | COUNT | sympy | BINOMIAL_ALTERNATING | [
"BINOMIAL_ALTERNATING"
] | c21569 | comb_count_derangements_v1 | null | 6 | 2 | [
"BINOMIAL_ALTERNATING"
] | 1 | 0.001 | 2026-02-08T05:44:48.227628Z | {
"verified": true,
"answer": 52553,
"timestamp": "2026-02-08T05:44:48.228871Z"
} | 528983 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 315,
"completion_tokens": 1194
},
"timestamp": "2026-02-24T04:28:26.345Z",
"answer": 52553
},
{
"... | 1 | [
{
"lemma": "BINOMIAL_ALTERNATING",
"status": "ok"
},
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8_SUM",
"status... | {
"lo": -4.93,
"mid": -2.91,
"hi": -0.71
} | ||
53f2f7 | algebra_poly_eval_v1_124444284_7851 | Let $b = 11$. Let $P$ be the set of all positive integers $p$ for which there exists a positive integer $q$ such that $pq = 72$, $\gcd(p, q) = 1$, and $p < q$. Let $m$ be the number of elements in $P$. Compute the value of $$ b^4 \sum_{k=1}^{m} \varphi(k) \left\lfloor \frac{2}{k} \right\rfloor - b^3 - 8b^2 - 4b - 3. $$ | 41,577 | graphs = [
Graph(
let={
"b": Const(11),
"result": Sum(Mul(Summation(var="k", start=Const(1), end=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(val... | NT | null | COMPUTE | sympy | COPRIME_PAIRS | [
"COPRIME_PAIRS/K2"
] | 846647 | algebra_poly_eval_v1 | null | 6 | 0 | [
"COPRIME_PAIRS",
"K2"
] | 2 | 0.005 | 2026-02-08T09:23:37.274705Z | {
"verified": true,
"answer": 41577,
"timestamp": "2026-02-08T09:23:37.279336Z"
} | 47935b | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 170,
"completion_tokens": 1065
},
"timestamp": "2026-02-14T03:42:32.160Z",
"answer": 41577
},
... | 1 | [
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "K2",
"status": "ok_later"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma":... | {
"lo": -6.96,
"mid": -4.56,
"hi": -1.46
} | ||
37e2be | diophantine_fbi2_min_v1_809748730_1621 | Let $n$ be the minimum value of $x + y$ over all positive integers $x$ and $y$ such that $xy = 4$. Let $d$ be the smallest integer such that $d$ divides 35, $d$ is at least the minimum value of $x + y$ over all positive integers $x$ and $y$ such that $xy = n$, $d \leq 45$, and $\frac{35}{d} \geq 6$. Find the value of $... | 5 | graphs = [
Graph(
let={
"_m": Const(6),
"_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(4)))), expr=Sum(Var("x"), Var("y")))),
... | NT | null | EXTREMUM | sympy | SUM_DIVISIBLE | [
"B3/B3"
] | 8ffef9 | diophantine_fbi2_min_v1 | null | 6 | 0 | [
"B3",
"SUM_DIVISIBLE"
] | 2 | 0.051 | 2026-02-08T12:35:08.486696Z | {
"verified": true,
"answer": 5,
"timestamp": "2026-02-08T12:35:08.538109Z"
} | 6cdea9 | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 170,
"completion_tokens": 224
},
"timestamp": "2026-02-16T04:00:35.692Z",
"answer": 5
},
{
"id": 11,
"... | 2 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "VAL_SUM_EQ",
"status": "no... | {
"lo": -10,
"mid": -7.71,
"hi": -5.43
} | ||
f962df | nt_count_coprime_and_v1_1125832087_531 | Let $m = 2$. Define $d(n)$ as the sum of $\phi(d)$ over all positive divisors $d$ of $n$, where $\phi$ denotes Euler's totient function. Let $k_1 = 5$ and let $k_2$ be the largest prime number $n$ such that $d(m) \leq n \leq 12$. Determine the value of the number of positive integers $n$ with $1 \leq n \leq 34412$ such... | 25,027 | graphs = [
Graph(
let={
"_m": Const(2),
"_n": SumOverDivisors(n=Ref(name='_m'), var='d', expr=EulerPhi(n=Var(name='d'))),
"upper": Const(34412),
"k1": Const(5),
"k2": MaxOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Ref("_n")),... | NT | null | COUNT | sympy | K3 | [
"K3/MAX_PRIME_BELOW"
] | d8e8cc | nt_count_coprime_and_v1 | null | 5 | 0 | [
"K3",
"MAX_PRIME_BELOW"
] | 2 | 7.556 | 2026-02-08T03:08:39.124521Z | {
"verified": true,
"answer": 25027,
"timestamp": "2026-02-08T03:08:46.680978Z"
} | e6a840 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 248,
"completion_tokens": 917
},
"timestamp": "2026-02-10T12:52:15.046Z",
"answer": 25027
},
{
"... | 1 | [
{
"lemma": "K3",
"status": "ok"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok_later"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "V1",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
},
{
"lem... | {
"lo": -3.45,
"mid": 1.18,
"hi": 5.72
} | ||
e1cdcb | sequence_count_fib_divisible_v1_865884756_4491 | Let $\text{upper}$ be the minimum value of $x + y$ over all ordered pairs $(x, y)$ of positive integers such that $xy = 181476$. Let $d$ be the maximum value of $x_1 y_1$ over all ordered pairs $(x_1, y_1)$ of positive integers such that $x_1 + y_1 = 4$. Define $\text{result}$ to be the number of positive integers $n$ ... | 142 | graphs = [
Graph(
let={
"_n": Const(4),
"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(181476)))), expr=Sum(Var("x"), Var("y"))... | NT | null | COUNT | sympy | B3 | [
"B3",
"B1"
] | 655d51 | sequence_count_fib_divisible_v1 | null | 7 | 0 | [
"B1",
"B3"
] | 2 | 0.06 | 2026-02-08T17:57:48.630383Z | {
"verified": true,
"answer": 142,
"timestamp": "2026-02-08T17:57:48.690582Z"
} | 5b0d2f | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 190,
"completion_tokens": 1123
},
"timestamp": "2026-02-18T10:30:19.719Z",
"answer": 142
},
{
... | 1 | [
{
"lemma": "B1",
"status": "ok"
},
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "V3",
"status": "no"
},
{
"lemma": "V8",
"s... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
4d6d34 | nt_count_divisible_v1_717093673_2614 | Let $n = 6$. Define $$ d = \sum_{k=1}^{6} \phi(k) \left\lfloor \frac{6}{k} \right\rfloor, $$ where $\phi$ denotes Euler's totient function. Find the number of positive integers $m$ such that $1 \leq m \leq 51076$ and $m$ is divisible by $d$. | 2,432 | graphs = [
Graph(
let={
"_n": Const(6),
"upper": Const(51076),
"divisor": Summation(var="k", start=Const(1), end=Ref("_n"), expr=Mul(EulerPhi(n=Var("k")), Floor(Div(Const(6), Var("k"))))),
"result": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq... | NT | null | COUNT | sympy | K2 | [
"K2"
] | 6897ab | nt_count_divisible_v1 | null | 4 | 0 | [
"K2"
] | 1 | 1.638 | 2026-02-08T17:00:29.805708Z | {
"verified": true,
"answer": 2432,
"timestamp": "2026-02-08T17:00:31.444040Z"
} | 65f716 | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 148,
"completion_tokens": 497
},
"timestamp": "2026-02-16T08:43:16.251Z",
"answer": 2432
},
{
"id": 11,
... | 2 | [
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "K2",
"status": "ok"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "V3",
"status": "no"
}
] | {
"lo": -10,
"mid": -7.27,
"hi": -4.54
} | ||
566318 | algebra_poly_eval_v1_1874849503_935 | Compute the value of $$5 \cdot 7^4 - 7^3 - 3 \cdot 7^2 + m \cdot 7 + 2,$$ where $m$ is the largest integer $k$ such that $2^k$ divides $5^8 - 3^8$. | 11,559 | graphs = [
Graph(
let={
"_n": Const(4),
"m": Const(7),
"result": Sum(Mul(Const(5), Pow(Ref("m"), Ref("_n"))), Mul(Const(-1), Pow(Ref("m"), Const(3))), Mul(Const(-3), Pow(Ref("m"), Const(2))), Mul(MaxKDivides(target=Sub(Pow(Const(5), Const(8)), Pow(Const(3), Const(8))), ba... | NT | null | COMPUTE | sympy | LTE_DIFF_P2 | [
"LTE_DIFF_P2"
] | 6d866c | algebra_poly_eval_v1 | null | 5 | 0 | [
"LTE_DIFF_P2"
] | 1 | 0.003 | 2026-02-08T13:25:18.817224Z | {
"verified": true,
"answer": 11559,
"timestamp": "2026-02-08T13:25:18.820717Z"
} | f814bd | 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": 1087
},
"timestamp": "2026-02-09T22:53:36.724Z",
"answer": 11559
},
{
"... | 1 | [
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "ok"
},
{
"lemma": "V8",
"status": "no"
},
{
"lemma": "VAL_SUM_EQ",
"status": "no"
}
] | {
"lo": -6.5,
"mid": -0.2,
"hi": 6.11
} | ||
14b74c | nt_min_with_divisor_count_v1_124444284_8830 | Let $T$ be the set of all integers $t$ such that $24 \leq t \leq 19628$ and there exist positive integers $a \leq 2967$ and $b \leq 453$ for which $t = 6a + 4b + 14$. Let $u$ be the number of elements in $T$. Determine the smallest positive integer $n$ such that $1 \leq n \leq u$ and $n$ has exactly $2$ positive diviso... | 4,276 | graphs = [
Graph(
let={
"_n": Const(92),
"upper": CountOverSet(set=SolutionsSet(var=Var("t"), condition=Exists(var=Var(name='a'), condition=Exists(var=Var(name='b'), condition=And(Geq(left=Var(name='a'), right=Const(value=1)), Leq(left=Var(name='a'), right=Const(value=2967)), Geq(lef... | NT | null | EXTREMUM | sympy | K2 | [
"K2",
"LIN_FORM"
] | 822569 | nt_min_with_divisor_count_v1 | negation_mod | 7 | 0 | [
"K2",
"LIN_FORM"
] | 2 | 0.401 | 2026-02-08T11:56:02.406729Z | {
"verified": true,
"answer": 4276,
"timestamp": "2026-02-08T11:56:02.808194Z"
} | a72cf0 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 195,
"completion_tokens": 4207
},
"timestamp": "2026-02-14T20:34:20.429Z",
"answer": 4276
},
{... | 1 | [
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "K2",
"status": "ok"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "V8",
... | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
8163a7 | geo_count_lattice_rect_v1_458359167_1243 | Compute the number of lattice points $(x, y)$ such that $0 \leq x \leq 111$ and $0 \leq y \leq 443$. | 49,728 | graphs = [
Graph(
let={
"a": Const(111),
"b": Const(443),
"result": LatticePointsRect(a=Ref(name='a'), b=Ref(name='b')),
},
goal=Ref("result"),
)
] | GEOM | null | COUNT | sympy | [] | geo_count_lattice_rect_v1 | null | 2 | 0 | null | null | 0.001 | 2026-02-08T04:30:45.787616Z | {
"verified": true,
"answer": 49728,
"timestamp": "2026-02-08T04:30:45.788157Z"
} | 917d09 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 148,
"completion_tokens": 126
},
"timestamp": "2026-02-24T00:50:58.067Z",
"answer": 49728
},
{
"i... | 1 | [] | {
"lo": -4.92,
"mid": -2.9,
"hi": -0.7
} | ||||
ae7d05 | algebra_poly_eval_v1_677425708_1258 | Let $\mathcal{S}$ be the set of all integers $n$ such that $1 \leq n \leq 126$ and $n \equiv \left\lfloor \frac{n}{2} \right\rfloor \pmod{7}$. Let $m = 3$ and let $N = |\mathcal{S}|$. Let $\mathcal{T}$ be the set of all integers $t$ such that $10 \leq t \leq 30$ and $t = 4a + 6b$ for some integers $a, b$ with $1 \leq a... | 497 | graphs = [
Graph(
let={
"_m": Const(3),
"_n": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Const(126)), Congruent(a=Var(name='n'), b=Floor(arg=Div(left=Var(name='n'), right=Const(value=2))), modulus=Const(value=7))))),
"... | NT | null | COMPUTE | sympy | L3C | [
"L3C/LIN_FORM"
] | c79c9e | algebra_poly_eval_v1 | null | 4 | 0 | [
"L3C",
"LIN_FORM"
] | 2 | 0.006 | 2026-02-08T04:03:02.262607Z | {
"verified": true,
"answer": 497,
"timestamp": "2026-02-08T04:03:02.269009Z"
} | 238c62 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 303,
"completion_tokens": 970
},
"timestamp": "2026-02-09T17:40:50.819Z",
"answer": 497
},
{
"id"... | 1 | [
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "L3C",
"status": "ok"
},
{
"lemma": "LIN_FORM",
"status": "ok_later"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma"... | {
"lo": -3.46,
"mid": 1.03,
"hi": 5.49
} | ||
e7a294 | comb_catalan_compute_v1_1978505735_8407 | Let $A$ be the set of integers $t$ such that $13 \leq t \leq 25$ and there exist integers $a$ and $b$ with $1 \leq a \leq 4$, $1 \leq b \leq 3$, and $t = 2a + 3b + 8$. Let $n$ be the number of elements in $A$. Define $C_n$ to be the $n$-th Catalan number. Let $B$ be the set of integers $t_1$ such that $11 \leq t_1 \leq... | 35,114 | graphs = [
Graph(
let={
"_n": Const(93857),
"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=4)), Geq(left=Va... | COMB | null | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM"
] | 324ba4 | comb_catalan_compute_v1 | negation_mod | 5 | 0 | [
"LIN_FORM"
] | 1 | 0.003 | 2026-02-08T20:49:03.196975Z | {
"verified": true,
"answer": 35114,
"timestamp": "2026-02-08T20:49:03.200387Z"
} | 4c0074 | 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": 2646
},
"timestamp": "2026-02-19T01:11:50.430Z",
"answer": 35114
},
... | 1 | [
{
"lemma": "COUNT_INTEGER_RANGE",
"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": -3.12,
"mid": 1.47,
"hi": 6.57
} | ||
d621b8 | nt_sum_over_divisible_v1_1742523217_146 | Let $A$ be the set of all integers $t$ such that there exist integers $a$ and $b$ with $1 \le a \le 34$, $1 \le b \le 10$, $22 \le t \le 115$, and $t = 2a + 3b + 17$. Let $d$ be the number of elements in $A$. Let $S$ be the set of all positive integers $n$ such that $1 \le n \le 22222$ and $n \equiv \sum_{d \mid \gcd(8... | 70,260 | graphs = [
Graph(
let={
"upper": Const(22222),
"divisor": CountOverSet(set=SolutionsSet(var=Var("t"), condition=Exists(var=Var(name='a'), condition=Exists(var=Var(name='b'), condition=And(Geq(left=Var(name='a'), right=Const(value=1)), Leq(left=Var(name='a'), right=Const(value=34)), G... | NT | null | SUM | sympy | MOBIUS_COPRIME | [
"MOBIUS_COPRIME",
"LIN_FORM"
] | d8034f | nt_sum_over_divisible_v1 | null | 7 | 0 | [
"LIN_FORM",
"MOBIUS_COPRIME"
] | 2 | 1.29 | 2026-02-08T02:53:40.461620Z | {
"verified": true,
"answer": 70260,
"timestamp": "2026-02-08T02:53:41.751642Z"
} | 98c1cd | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 281,
"completion_tokens": 3015
},
"timestamp": "2026-02-09T14:07:48.875Z",
"answer": 23680
},
{
... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "MOBIUS_COPRIME",
"status": "ok"
},
{
"lemma": "V8",
"status": "no"
},
{
"lemma":... | {
"lo": 1.69,
"mid": 5.03,
"hi": 8.38
} | ||
a162df | nt_lcm_compute_v1_168721529_777 | Let $p=3$. Define
\[v\equiv (p-1)!+1\pmod p\qquad\text{with }0\le v<p,
\]
and let $n=1+v$. Let $f$ be the number of distinct prime factors of $n$.
Let $a$ be the minimum value of $x+y$ over all ordered pairs $(x,y)$ of positive integers such that
\[xy=499849.
\]
Let $b$ be the number of positive integers $k$ with $1\... | 39,052 | graphs = [
Graph(
let={
"_m": Const(78231),
"_n": Const(222),
"p": Const(3),
"v": Mod(value=Sum(Factorial(Sub(Ref("p"), Const(1))), Const(1)), modulus=Ref("p")),
"n": Sum(Const(1), Ref("v")),
"f": SmallOmega(n=Ref(name='n')),
... | NT | null | COMPUTE | sympy | C3 | [
"C3",
"OMEGA_ZERO",
"WILSON",
"B3",
"C2"
] | ffd55b | nt_lcm_compute_v1 | quadratic_mod | 8 | 2 | [
"B3",
"C2",
"C3",
"OMEGA_ZERO",
"WILSON"
] | 5 | 0.008 | 2026-02-08T13:17:25.910381Z | {
"verified": true,
"answer": 39052,
"timestamp": "2026-02-08T13:17:25.917898Z"
} | 0cfa40 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 379,
"completion_tokens": 2569
},
"timestamp": "2026-02-09T09:03:39.088Z",
"answer": 39052
},
{
"... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "C2",
"status": "ok"
},
{
"lemma": "C3",
"status": "ok"
},
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
... | {
"lo": -1.99,
"mid": 2.14,
"hi": 6.33
} | ||
829d82 | sequence_count_fib_divisible_v1_548369836_252 | Let $\phi(n)$ denote Euler's totient function. Define $d = 6$ and let $S$ be the set of all positive integers $n$ such that $2 \leq n \leq 246$ and $d$ divides the $n$th Fibonacci number. Let $k$ be the number of elements in $S$. Compute the value of
$$
\sum_{n=1}^{k} \tau(n),
$$
where $\tau(n)$ denotes the number of p... | 66 | graphs = [
Graph(
let={
"upper": Const(246),
"d": Const(6),
"result": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), EulerPhi(n=Const(2))), Leq(Var("n"), Ref("upper")), Divides(divisor=Ref("d"), dividend=Fibonacci(arg=Var(name='n')))))),
... | NT | null | COUNT | sympy | ONE_PHI_2 | [
"ONE_PHI_2"
] | e19278 | sequence_count_fib_divisible_v1 | null | 6 | 0 | [
"ONE_PHI_2"
] | 1 | 0.012 | 2026-02-08T02:49:42.162910Z | {
"verified": true,
"answer": 66,
"timestamp": "2026-02-08T02:49:42.174735Z"
} | 62aa56 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 226,
"completion_tokens": 3175
},
"timestamp": "2026-02-08T20:17:02.161Z",
"answer": 66
},
{
"id"... | 1 | [
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "ONE_PHI_2",
"status": "ok"
... | {
"lo": -2.08,
"mid": 1.77,
"hi": 4.93
} | ||
7159c9 | comb_factorial_compute_v1_1978505735_5475 | Let $c = 31603$ and define $m$ as the smallest divisor of $c$ that is at least $2$. Let $T$ be the set of all integers $t$ such that there exist integers $a$ and $b$ with $1 \leq a \leq 7$, $1 \leq b \leq 14$, $10 \leq t \leq 91$, and $t = 7a + 3b$. Let $n$ be the number of elements $t$ in $T$. Define $N$ as the number... | 5,040 | graphs = [
Graph(
let={
"_c": Const(31603),
"_m": MinOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Const(2)), Divides(divisor=Var("d"), dividend=Ref("_c"))))),
"_n": CountOverSet(set=SolutionsSet(var=Var("t"), condition=Exists(var=Var(name='a'), condi... | NT | null | COMPUTE | sympy | MIN_PRIME_FACTOR | [
"MIN_PRIME_FACTOR/LIN_FORM/COUNT_FIB_DIVISIBLE"
] | 7597d6 | comb_factorial_compute_v1 | null | 6 | 0 | [
"COUNT_FIB_DIVISIBLE",
"LIN_FORM",
"MIN_PRIME_FACTOR"
] | 3 | 0.005 | 2026-02-08T19:01:10.268236Z | {
"verified": true,
"answer": 5040,
"timestamp": "2026-02-08T19:01:10.273145Z"
} | 7ad64c | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 207,
"completion_tokens": 6144
},
"timestamp": "2026-02-18T21:08:54.112Z",
"answer": 5040
},
{... | 1 | [
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "ok_later"
},
{
"lemma": "LIN_FORM",
"status": "ok_later"
},
{
"lemma": "MIN_PRIME_FACTOR",
"status": "ok"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lem... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
bb1913 | antilemma_sum_equals_v1_971394319_1695 | Let $x$ be the number of ordered pairs $(i, j)$ of integers such that $1 \leq i \leq 21$, $1 \leq j \leq 21$, and $i + j = 22$. Find the remainder when $8588 \cdot x$ is divided by $54165$. | 17,853 | graphs = [
Graph(
let={
"x": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("i"), Var("j")]), condition=Eq(Sum(Var("i"), Var("j")), Const(22)), domain=CartesianProduct(left=IntegerRange(start=Const(1), end=Const(21)), right=IntegerRange(start=Const(1), end=Const(21))))),
"_c":... | COMB | GEOM | COMPUTE | sympy | COUNT_SUM_EQUALS | [
"COUNT_SUM_EQUALS"
] | 75ab0f | antilemma_sum_equals_v1 | null | 2 | 0 | [
"COUNT_SUM_EQUALS"
] | 1 | 0.066 | 2026-02-08T13:51:01.525804Z | {
"verified": true,
"answer": 17853,
"timestamp": "2026-02-08T13:51:01.591960Z"
} | 3f0fd7 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 181,
"completion_tokens": 634
},
"timestamp": "2026-02-24T19:10:36.819Z",
"answer": 17853
},
{
"i... | 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": -2.37,
"mid": 1.22,
"hi": 4.84
} | ||
640ac9 | nt_count_coprime_and_v1_655260480_4621 | Compute the number of positive integers $n$ such that $n \leq 26824$, $\gcd(n, 11) = 1$, and $\gcd(n, 13) = 1$. | 22,510 | graphs = [
Graph(
let={
"upper": Const(26824),
"k1": Const(11),
"k2": Const(13),
"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("k1")), Const(1)), Eq(GCD(a=Var(... | NT | null | COUNT | sympy | LTE_DIFF | [
"LTE_DIFF"
] | cf8260 | nt_count_coprime_and_v1 | null | 3 | 0 | [
"LTE_DIFF"
] | 1 | 15.908 | 2026-02-08T18:01:45.301211Z | {
"verified": true,
"answer": 22510,
"timestamp": "2026-02-08T18:02:01.209299Z"
} | 830576 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 89,
"completion_tokens": 1284
},
"timestamp": "2026-02-18T12:35:56.253Z",
"answer": 22510
},
{... | 1 | [
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "ok"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
04f53e | alg_poly_preperiod_count_v1_1218484723_5244 | For an integer $a$, define
$$N = a^{2} - 13 \bmod 43, \quad M = N^{2} - 13 \bmod 43, \quad R = M^{2} - 13 \bmod 43, \quad S = R^{2} - 13 \bmod 43.$$
Let $Q$ be the number of integers $a$ with $0 \le a \le 47772$ such that $S = M$ and $R \ne M$. Find $Q$. | 8,888 | graphs = [
Graph(
let={
"p1": Mod(value=Sum(Pow(Var("a"), Const(2)), Const(-13)), modulus=Const(43)),
"p2": Mod(value=Sum(Pow(Ref("p1"), Const(2)), Const(-13)), modulus=Const(43)),
"p3": Mod(value=Sum(Pow(Ref("p2"), Const(2)), Const(-13)), modulus=Const(43)),
... | ALG | null | COUNT | sympy | POLY_ORBIT_COUNT | [
"POLY_ORBIT_COUNT"
] | 4ad965 | alg_poly_preperiod_count_v1 | null | 7 | null | [
"POLY_ORBIT_COUNT"
] | 1 | 0.016 | 2026-02-25T06:54:06.543077Z | {
"verified": true,
"answer": 8888,
"timestamp": "2026-02-25T06:54:06.559214Z"
} | 3883eb | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 228,
"completion_tokens": 8963
},
"timestamp": "2026-03-29T20:10:21.688Z",
"answer": 8888
},
{
"i... | 1 | [
{
"lemma": "POLY_ORBIT_COUNT",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
}
] | {
"lo": -3.33,
"mid": 1.03,
"hi": 5.26
} | ||
904558 | algebra_vieta_sum_v1_1978505735_2647 | Let $S$ be the set of all real solutions $x$ to the equation $x^4 - 2x^3 - 77x^2 + 6x + 1080 = 0$. Compute the product of all elements of $S$. | 1,080 | graphs = [
Graph(
let={
"result": ProductOverSet(set=SolutionsSet(var=Var(name='x'), condition=Eq(left=Sum(Pow(base=Var(name='x'), exp=Const(value=4)), Mul(Const(value=-2), Pow(base=Var(name='x'), exp=Const(value=3))), Mul(Const(value=-77), Pow(base=Var(name='x'), exp=Const(value=2))), Mul(Const... | NT | null | COMPUTE | sympy | K14 | [
"SUM_ARITHMETIC/COPRIME_PAIRS"
] | 97106c | algebra_vieta_sum_v1 | null | 4 | 0 | [
"COPRIME_PAIRS",
"K14",
"SUM_ARITHMETIC"
] | 3 | 0.129 | 2026-02-08T17:02:31.742383Z | {
"verified": true,
"answer": 1080,
"timestamp": "2026-02-08T17:02:31.870885Z"
} | bfe38a | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 113,
"completion_tokens": 333
},
"timestamp": "2026-02-16T08:59:45.828Z",
"answer": 1080
},
{
"id": 11,
... | 2 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COPRIME_PAIRS",
"status": "ok_later"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": ... | {
"lo": -10,
"mid": -7.27,
"hi": -4.54
} | ||
ecf456 | modular_min_linear_v1_458359167_2478 | Let $a$ be the minimum value of $x + y$ over all pairs of positive integers $(x, y)$ such that $xy = 1155625$. Let $b = 81638$ and $m = 85509$. Let $Q$ be the smallest positive integer $x$ such that $1 \le x \le m$ and $ax \equiv b \pmod{m}$. Compute $Q$. | 28,594 | graphs = [
Graph(
let={
"a": 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(1155625)))), expr=Sum(Var("x"), Var("y")))),
"b": Const(8163... | NT | null | EXTREMUM | sympy | B3 | [
"B3"
] | 0cd20d | modular_min_linear_v1 | null | 6 | 0 | [
"B3"
] | 1 | 3.602 | 2026-02-08T05:26:30.554844Z | {
"verified": true,
"answer": 28594,
"timestamp": "2026-02-08T05:26:34.157131Z"
} | 262704 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 136,
"completion_tokens": 3647
},
"timestamp": "2026-02-12T22:43:06.223Z",
"answer": 28594
},
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "VAL_SUM_EQ",
"status": "no... | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
1be698 | antilemma_k3_v1_1978505735_7814 | Let $n = 74282$. Compute the sum of $\phi(d)$ over all positive divisors $d$ of $n$, where $\phi$ denotes Euler's totient function. | 74,282 | graphs = [
Graph(
let={
"_n": Const(74282),
"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 | 0.001 | 2026-02-08T20:28:36.303712Z | {
"verified": true,
"answer": 74282,
"timestamp": "2026-02-08T20:28:36.304257Z"
} | fdd35d | 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": 624
},
"timestamp": "2026-02-19T00:36:59.499Z",
"answer": 74282
},
{
... | 1 | [
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "K3",
"status": "ok"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "V1",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
30e2e6 | alg_poly_preperiod_count_v1_1218484723_446 | Let $N = (a^2 + a - 2) \bmod 83$, $M = (N^2 + N - 2) \bmod 83$, $R = (M^2 + M - 2) \bmod 83$, $S = (R^2 + R - 2) \bmod 83$, and $T = (S^2 + S - 2) \bmod 83$. Find the number of non-negative integers $a$ with $0 \le a \le 52538$ such that $T = N$, $M \ne N$, $R \ne N$, and $S \ne N$. | 5,064 | graphs = [
Graph(
let={
"p1": Mod(value=Sum(Pow(Var("a"), Const(2)), Var("a"), Const(-2)), modulus=Const(83)),
"p2": Mod(value=Sum(Pow(Ref("p1"), Const(2)), Ref("p1"), Const(-2)), modulus=Const(83)),
"p3": Mod(value=Sum(Pow(Ref("p2"), Const(2)), Ref("p2"), Const(-2)), mod... | ALG | null | COUNT | sympy | POLY_ORBIT_COUNT | [
"POLY_ORBIT_COUNT"
] | 4ad965 | alg_poly_preperiod_count_v1 | null | 7 | null | [
"POLY_ORBIT_COUNT"
] | 1 | 0.029 | 2026-02-25T02:09:41.600960Z | {
"verified": true,
"answer": 5064,
"timestamp": "2026-02-25T02:09:41.630367Z"
} | 507c63 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 255,
"completion_tokens": 29992
},
"timestamp": "2026-03-28T22:41:13.306Z",
"answer": 1266
},
{
... | 0 | [
{
"lemma": "POLY_ORBIT_COUNT",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
}
] | {
"lo": 5.81,
"mid": 8.21,
"hi": 10
} | ||
ee8ab5 | comb_count_surjections_v1_717093673_2917 | Let $n = 4$. Let $k$ be the number of ordered pairs $(x_1, x_2)$ of positive odd integers such that $x_1 + x_2 = 6$. Define $\text{result} = k! \cdot S(n, k)$, where $S(n, k)$ denotes the Stirling number of the second kind. Let $Q$ be the remainder when $68386 \cdot \text{result}$ is divided by $73287$. Compute $Q$. | 43,425 | graphs = [
Graph(
let={
"n": Const(4),
"k": 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")), Cons... | COMB | null | COUNT | sympy | COMB1 | [
"COMB1"
] | 567f58 | comb_count_surjections_v1 | null | 4 | 0 | [
"COMB1"
] | 1 | 0.003 | 2026-02-08T17:17:21.596605Z | {
"verified": true,
"answer": 43425,
"timestamp": "2026-02-08T17:17:21.599917Z"
} | f32188 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 152,
"completion_tokens": 867
},
"timestamp": "2026-02-17T23:06:53.581Z",
"answer": 43425
},
{... | 1 | [
{
"lemma": "COMB1",
"status": "ok"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
... | {
"lo": -2.38,
"mid": 1.74,
"hi": 6.59
} | ||
7bb588 | comb_count_partitions_v1_1978505735_4871 | Let $m = 2$. Let $S$ be the set of all positive integers $n_1$ such that $1 \leq n_1 \leq 111$ and $\gcd(n_1, 10) = 1$. Let $n$ be the largest prime number in the set of integers from $m$ to $|S|$, inclusive. Compute the number of integer partitions of $n$. | 63,261 | graphs = [
Graph(
let={
"_m": Const(2),
"_n": CountOverSet(set=SolutionsSet(var=Var("n1"), condition=And(Geq(Var("n1"), Const(1)), Leq(Var("n1"), Const(111)), Eq(GCD(a=Var("n1"), b=Const(10)), Const(1))))),
"n": MaxOverSet(set=SolutionsSet(var=Var("n2"), condition=And(Geq... | NT | COMB | COUNT | sympy | C4 | [
"C4/MAX_PRIME_BELOW"
] | 757853 | comb_count_partitions_v1 | null | 3 | 0 | [
"C4",
"MAX_PRIME_BELOW"
] | 2 | 0.004 | 2026-02-08T18:36:18.165312Z | {
"verified": true,
"answer": 63261,
"timestamp": "2026-02-08T18:36:18.169021Z"
} | affbd1 | 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": 933
},
"timestamp": "2026-02-18T18:01:53.278Z",
"answer": 63261
},
{... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "C4",
"status": "ok"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok_later"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
c03dec | alg_poly3_sum_v1_1218484723_1151 | Find the remainder when $$\sum_{\substack{a=1 \\ b=1 \\ c=1}}^{39} \left( 72a^2c - 124a^3 - 12ab^2 + \min_{\substack{a_1=1 \\ b_1=1}}^{14} \left( 20a_1^2 + \left| \left\{ (a_2,b_2) : \substack{1 \leq a_2 \leq 40,\, 1 \leq b_2 \leq 40 \\ 102a_2^2b_2^2 + 17b_2^4 + 17a_2^4 + 68a_2^3b_2 + 68a_2b_2^3 = 235379297} \right\} \... | 23,456 | graphs = [
Graph(
let={
"_m": Const(3),
"_n": Const(39),
"result": Mod(value=SumOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("a"), Var("b"), Var("c")]), condition=And(Geq(Var("a"), Const(1)), Leq(Var("a"), Const(39)), Geq(Var("b"), Const(1)), Leq(Var("b... | ALG | null | COMPUTE | sympy | POLY4_COUNT | [
"POLY4_COUNT/QF_PSD_MIN"
] | dce3a4 | alg_poly3_sum_v1 | null | 6 | 0 | [
"POLY4_COUNT",
"QF_PSD_MIN"
] | 2 | 0.171 | 2026-02-25T02:53:33.634839Z | {
"verified": true,
"answer": 23456,
"timestamp": "2026-02-25T02:53:33.806001Z"
} | f0bccc | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 355,
"completion_tokens": 6360
},
"timestamp": "2026-03-10T05:44:41.458Z",
"answer": 24456
},
{
... | 1 | [
{
"lemma": "POLY4_COUNT",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "QF_PSD_MIN",
"status": "ok_later"
}
] | {
"lo": 3.79,
"mid": 5.69,
"hi": 7.81
} | ||
9785fb | geo_count_lattice_rect_v1_151522320_1660 | Compute the number of lattice points in the rectangle $[0, 47] \times [0, 122]$. | 5,904 | graphs = [
Graph(
let={
"a": Const(47),
"b": Const(122),
"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 | 0.005 | 2026-02-08T04:10:19.132307Z | {
"verified": true,
"answer": 5904,
"timestamp": "2026-02-08T04:10:19.137181Z"
} | 34a45a | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 135,
"completion_tokens": 215
},
"timestamp": "2026-02-23T23:39:44.244Z",
"answer": 5904
},
{
"id... | 1 | [] | {
"lo": -4.92,
"mid": -2.9,
"hi": -0.7
} | ||||
f7e7d9 | comb_count_derangements_v1_168721529_217 | Let $N_0=10$.
Let $R$ be the set of all ordered pairs $(x,y)$ of positive integers such that
$$x+y=N_0.$$
Let $S$ be the set of all values of $xy$ as $(x,y)$ ranges over $R$, and let $M$ be the maximum element of $S$.
Let $T$ be the set of all integers $t$ for which there exist integers $a$ and $b$ such that
$$1\le ... | 14,833 | graphs = [
Graph(
let={
"_n": Const(10),
"n": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("i"), Var("j")]), condition=Eq(GCD(a=Var("i"), b=Var("j")), SumOverDivisors(n=GCD(a=CountOverSet(set=SolutionsSet(var=Var(name='t'), condition=Exists(var=Var(name='a'), condition=Exist... | NT | COMB | COUNT | sympy | LIN_FORM | [
"LIN_FORM/MOBIUS_COPRIME/COUNT_COPRIME_GRID",
"B1/MOBIUS_COPRIME/COUNT_COPRIME_GRID"
] | d59d24 | comb_count_derangements_v1 | null | 7 | 0 | [
"B1",
"COUNT_COPRIME_GRID",
"LIN_FORM",
"MOBIUS_COPRIME"
] | 4 | 0.004 | 2026-02-08T12:54:22.366553Z | {
"verified": true,
"answer": 14833,
"timestamp": "2026-02-08T12:54:22.370387Z"
} | ab0314 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 418,
"completion_tokens": 1102
},
"timestamp": "2026-02-09T02:33:46.742Z",
"answer": 14833
},
{
"... | 1 | [
{
"lemma": "B1",
"status": "ok"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "ok_later"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"l... | {
"lo": -6.69,
"mid": -2.4,
"hi": 1.77
} | ||
e6a2f6 | antilemma_k3_v1_1742523217_5274 | Compute the sum of $\phi(d)$ over all positive divisors $d$ of $30403$, where $\phi$ denotes Euler's totient function. | 30,403 | graphs = [
Graph(
let={
"x": SumOverDivisors(n=Const(value=30403), 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 | 2026-02-08T10:53:59.137830Z | {
"verified": true,
"answer": 30403,
"timestamp": "2026-02-08T10:53:59.138113Z"
} | 05da95 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 77,
"completion_tokens": 6527
},
"timestamp": "2026-02-14T09:14:47.482Z",
"answer": 30403
},
{... | 1 | [
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K3",
"status": "ok"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "V1",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
},
{
"lemma": "VAL_SUM_EQ",
"status": "no"
}
] | {
"lo": -5.49,
"mid": 0.22,
"hi": 6.51
} | ||
8d5efd | nt_euler_phi_compute_v1_1742523217_338 | Let $n = 68644$. Define $\text{result} = \varphi(n)$. Let $c$ be the largest prime number less than or equal to $5004$. Let $d_{\min}$ be the smallest divisor of $72243521606816531$ that is at least $2$. Define $$Q = \left( (\text{result} \bmod d_{\min}) + c \cdot (\text{result} \bmod 397) \right) \bmod 65374.$$ Find t... | 7,144 | graphs = [
Graph(
let={
"_n": Const(397),
"n": Const(68644),
"result": EulerPhi(n=Ref("n")),
"_c": MaxOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(2)), Leq(Var("n"), Const(5004)), IsPrime(Var("n"))))),
"Q": Mod(value=Sum... | NT | null | COMPUTE | sympy | MIN_PRIME_FACTOR | [
"MIN_PRIME_FACTOR",
"MAX_PRIME_BELOW"
] | ed95f3 | nt_euler_phi_compute_v1 | two_moduli | 6 | 0 | [
"MAX_PRIME_BELOW",
"MIN_PRIME_FACTOR"
] | 2 | 0.002 | 2026-02-08T02:58:45.964939Z | {
"verified": true,
"answer": 7144,
"timestamp": "2026-02-08T02:58:45.966839Z"
} | 1ae9f2 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 227,
"completion_tokens": 23046
},
"timestamp": "2026-02-23T15:19:44.283Z",
"answer": 7144
},
{
... | 1 | [
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok"
},
{
"lemma": "MIN_PRIME_FACTOR",
"status": "ok"
},
{
"lemma": "V3",
"status": "no"
},
{
"lemma": "V8_SUM",
... | {
"lo": 1.96,
"mid": 5.23,
"hi": 8.52
} | ||
29d6c3 | comb_bell_compute_v1_2051736721_5487 | Let $n$ be the number of ordered pairs $(x_1, x_2)$ of positive odd integers such that $x_1 + x_2 = 18$. Let $B_n$ denote the $n$th Bell number, which counts the number of partitions of a set of $n$ elements. Compute the remainder when $31 - B_n$ is divided by $57871$. | 36,755 | graphs = [
Graph(
let={
"_n": Const(31),
"n": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x1"), Var("x2")]), condition=And(IsPositive(arg=Var(name='x1')), IsPositive(arg=Var(name='x2')), IsOdd(arg=Var(name='x1')), IsOdd(arg=Var(name='x2')), Eq(Sum(Var("x1"), Var("x2")), Co... | COMB | null | COMPUTE | sympy | COMB1 | [
"COMB1"
] | 567f58 | comb_bell_compute_v1 | null | 4 | 0 | [
"COMB1"
] | 1 | 0.001 | 2026-02-08T18:36:57.047596Z | {
"verified": true,
"answer": 36755,
"timestamp": "2026-02-08T18:36:57.048748Z"
} | 0d167c | 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": 900
},
"timestamp": "2026-02-18T18:23:32.312Z",
"answer": 36755
},
{... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COMB1",
"status": "ok"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
}
] | {
"lo": -3.12,
"mid": 1.47,
"hi": 6.57
} | ||
5f56a7 | alg_sym_quad_system_v1_601307018_5216 | Let $k$ be the number of positive integers $p$ such that $p \mid 54$, $\gcd(p, 54/p) = 1$, and $p < 54/p$. Let $m = \min\{x + y : x, y > 0,\, xy = 8850625,\, x \leq y\}$. Let $M = \max\{d \geq 1 : d \mid 61811019,\, d^2 \leq 61811019\}$. Compute the sum $$S = \sum_{\substack{a,b,c \geq 1 \\ a^2 + b^2 + c^k = ab + bc + ... | 64,265 | graphs = [
Graph(
let={
"_c": Const(4),
"_m": Const(14317),
"_n": Const(4),
"result": Mod(value=SumOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("a"), Var("b"), Var("c")]), condition=And(Eq(Sum(Pow(Var("a"), Const(2)), Pow(Var("b"), Const(2))... | NT | null | COMPUTE | sympy | COPRIME_PAIRS | [
"COPRIME_PAIRS",
"B3_CLOSEST",
"B3"
] | 14e9b7 | alg_sym_quad_system_v1 | null | 7 | 0 | [
"B3",
"B3_CLOSEST",
"COPRIME_PAIRS"
] | 3 | 0.03 | 2026-03-10T05:54:28.965541Z | {
"verified": true,
"answer": 64265,
"timestamp": "2026-03-10T05:54:28.995642Z"
} | 83a984 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 313,
"completion_tokens": 13009
},
"timestamp": "2026-04-19T01:36:10.787Z",
"answer": 42951
},
{
... | 0 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "B3_CLOSEST",
"status": "ok"
},
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
}... | {
"lo": 2.12,
"mid": 5.37,
"hi": 8.63
} | ||
df55e2 | nt_count_coprime_and_v1_1742523217_306 | Let $k_1 = 8$. Let $k_2$ be the maximum value of $xy$ over all pairs of positive integers $(x, y)$ such that $x + y = 6$. Let $S$ be the set of all positive integers $n \leq 78858$ such that $\gcd(n, k_1) = 1$ and $\gcd(n, k_2) = 1$. Compute the remainder when $44121 \cdot |S|$ is divided by 79888. | 30,510 | graphs = [
Graph(
let={
"_n": Const(6),
"upper": Const(78858),
"k1": Const(8),
"k2": 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"... | NT | null | COUNT | sympy | B1 | [
"B1"
] | 5b950e | nt_count_coprime_and_v1 | null | 4 | 0 | [
"B1"
] | 1 | 9.958 | 2026-02-08T02:57:55.333630Z | {
"verified": true,
"answer": 30510,
"timestamp": "2026-02-08T02:58:05.291721Z"
} | 00cf2a | 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": 5661
},
"timestamp": "2026-02-09T16:14:20.083Z",
"answer": 30510
},
{
"... | 1 | [
{
"lemma": "B1",
"status": "ok"
},
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "V3",
"status": "no"
}
] | {
"lo": 2.08,
"mid": 3.62,
"hi": 5.18
} | ||
7df543 | antilemma_coprime_grid_v1_153355830_81 | Let $x$ be the number of ordered pairs $(i,j)$ with $1 \le i \le 57$ and $1 \le j \le 110$ such that $\gcd(i,j) = 1$. Compute
$$
x + \varphi(|x| + 1) + \tau\left(|x| + \sum_{d \mid \gcd(5,7)} \mu(d)\right),
$$
where $\varphi$ is Euler's totient function, $\tau(n)$ is the number of positive divisors of $n$, and $\mu$ is... | 5,910 | graphs = [
Graph(
let={
"x": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("i"), Var("j")]), condition=Eq(GCD(a=Var("i"), b=Var("j")), EulerPhi(n=Const(1))), domain=CartesianProduct(left=IntegerRange(start=Const(1), end=Const(57)), right=IntegerRange(start=Const(1), end=Const(110))))),
... | NT | null | COMPUTE | sympy | MOBIUS_COPRIME | [
"MOBIUS_COPRIME",
"COUNT_COPRIME_GRID",
"ONE_PHI_1"
] | 2c7d49 | antilemma_coprime_grid_v1 | null | 4 | 0 | [
"COUNT_COPRIME_GRID",
"MOBIUS_COPRIME",
"ONE_PHI_1"
] | 3 | 0.003 | 2026-02-08T02:53:00.409820Z | {
"verified": true,
"answer": 5910,
"timestamp": "2026-02-08T02:53:00.413052Z"
} | 904415 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 248,
"completion_tokens": 4133
},
"timestamp": "2026-02-08T22:44:41.692Z",
"answer": 7706
},
{
... | 0 | [
{
"lemma": "COUNT_COPRIME_GRID",
"status": "ok"
},
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "MOBIUS_COPRIME"... | {
"lo": 3.31,
"mid": 6.77,
"hi": 10
} | ||
f5a7ac | diophantine_fbi2_count_v1_151522320_2062 | Let $k = 240$. Consider the set of all integers $d$ such that $3 \leq d \leq 66$, $d$ divides $k$, and $4 \leq \frac{k}{d} \leq 67$. Let $r$ be the number of elements in this set. Compute $$\sum_{n=1}^{r} \tau(n),$$ where $\tau(n)$ denotes the number of positive divisors of $n$. | 41 | graphs = [
Graph(
let={
"k": Const(240),
"a": Const(2),
"b": Const(3),
"upper": Const(64),
"result": CountOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Const(3)), Leq(Var("d"), Const(66)), Divides(divisor=Var("d"), dividend=Ref... | NT | null | COUNT | sympy | COUNT_CARTESIAN | [
"COUNT_CARTESIAN",
"COPRIME_PAIRS"
] | 742a81 | diophantine_fbi2_count_v1 | null | 3 | 0 | [
"COPRIME_PAIRS",
"COUNT_CARTESIAN"
] | 2 | 0.04 | 2026-02-08T04:34:06.985807Z | {
"verified": true,
"answer": 41,
"timestamp": "2026-02-08T04:34:07.025744Z"
} | a0a14f | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 210,
"completion_tokens": 1571
},
"timestamp": "2026-02-10T17:10:31.082Z",
"answer": 41
},
{
"id... | 1 | [
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "ok"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K15",
"st... | {
"lo": -3.42,
"mid": 1.86,
"hi": 7.55
} | ||
3779a5 | modular_mod_compute_v1_865884756_2842 | Let $a$ be the number of ordered pairs $(i, j)$ of integers such that $1 \leq i \leq 112$, $1 \leq j \leq 112$, and $i + j = 114$. Let $m = 2520$ and let $r$ be the remainder when $a$ is divided by $m$. Let $Q$ be the remainder when $44121 \cdot r$ is divided by $75092$. Determine the value of $Q$. | 16,451 | graphs = [
Graph(
let={
"_n": Const(75092),
"a": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("i"), Var("j")]), condition=Eq(Sum(Var("i"), Var("j")), Const(114)), domain=CartesianProduct(left=IntegerRange(start=Const(1), end=Const(112)), right=IntegerRange(start=Const(1), en... | NT | null | COMPUTE | sympy | COUNT_SUM_EQUALS | [
"COUNT_SUM_EQUALS"
] | 75ab0f | modular_mod_compute_v1 | null | 2 | 0 | [
"COUNT_SUM_EQUALS"
] | 1 | 0.007 | 2026-02-08T16:58:14.810148Z | {
"verified": true,
"answer": 16451,
"timestamp": "2026-02-08T16:58:14.817582Z"
} | a8a915 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 150,
"completion_tokens": 848
},
"timestamp": "2026-02-17T16:20:26.241Z",
"answer": 16451
},
{... | 1 | [
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "ok"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
}... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
0e5a61 | antilemma_sum_equals_v1_2051736721_4236 | Let $m = 74$. Let $n$ be the number of ordered pairs $(x_1, x_2)$ of positive odd integers such that $x_1 + x_2 = m$. Let $x$ be the number of ordered pairs $(i, j)$ with $1 \le i \le 36$ and $1 \le j \le 36$ such that $i + j = n$. Compute the remainder when $87468 \cdot x$ is divided by $89935$. | 1,123 | graphs = [
Graph(
let={
"_m": Const(74),
"_n": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x1"), Var("x2")]), condition=And(IsPositive(arg=Var(name='x1')), IsPositive(arg=Var(name='x2')), IsOdd(arg=Var(name='x1')), IsOdd(arg=Var(name='x2')), Eq(Sum(Var("x1"), Var("x2")), R... | COMB | GEOM | COMPUTE | sympy | LIN_FORM | [
"COMB1/COUNT_SUM_EQUALS",
"COUNT_SUM_EQUALS"
] | 3e1adf | antilemma_sum_equals_v1 | null | 4 | 0 | [
"COMB1",
"COUNT_SUM_EQUALS",
"LIN_FORM"
] | 3 | 0.036 | 2026-02-08T17:50:14.889443Z | {
"verified": true,
"answer": 1123,
"timestamp": "2026-02-08T17:50:14.925519Z"
} | bcdd43 | 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": 901
},
"timestamp": "2026-02-18T08:37:58.624Z",
"answer": 1123
},
{
... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COMB1",
"status": "ok"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "ok"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
},
{... | {
"lo": -4.1,
"mid": -1.76,
"hi": 1.32
} | ||
a80436 | antilemma_product_of_sums_v1_124444284_32 | Let $S_1$ be the sum of all integers $j$ with $0 \leq j \leq 15$ such that $\binom{15}{j}$ is odd. Let $S_2$ be the sum of $k$ over all ordered pairs $(k, j)$ of positive integers with $1 \leq k \leq 11$ and $1 \leq j \leq 8$. Compute $S_1 \cdot S_2$. | 63,360 | graphs = [
Graph(
let={
"S1": SumOverSet(set=SolutionsSet(var=Var("j"), condition=And(Geq(Var("j"), Const(0)), Leq(Var("j"), Const(15)), Eq(Mod(value=Binom(n=Const(15), k=Var("j")), modulus=Const(2)), Const(1))))),
"S2": SumOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[... | NT | COMB | COMPUTE | sympy | PRODUCT_OF_SUMS | [
"PRODUCT_OF_SUMS"
] | f2b2b0 | antilemma_product_of_sums_v1 | null | 3 | 0 | [
"PRODUCT_OF_SUMS"
] | 1 | 0.001 | 2026-02-08T02:54:41.355546Z | {
"verified": true,
"answer": 63360,
"timestamp": "2026-02-08T02:54:41.356302Z"
} | 6e7861 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 218,
"completion_tokens": 1088
},
"timestamp": "2026-02-09T12:32:03.691Z",
"answer": 63360
},
{
"... | 1 | [
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "PRODUCT_OF_SUMS",
"status": "ok"
}... | {
"lo": -6.51,
"mid": -0.31,
"hi": 5.43
} | ||
400b8f | diophantine_fbi2_min_v1_1874849503_47 | Let $k = 12$ and $u = 22$. Find the smallest integer $d$ such that $2 \leq d \leq u$, $d$ divides $k$, and $\frac{k}{d} \geq 5$. | 2 | graphs = [
Graph(
let={
"k": Const(12),
"upper": Const(22),
"result": MinOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Const(2)), Leq(Var("d"), Ref("upper")), Divides(divisor=Var("d"), dividend=Ref("k")), Geq(Div(Ref("k"), Var("d")), Const(5))))),
... | NT | null | EXTREMUM | sympy | LTE_DIFF | [
"LTE_DIFF/DIVISOR_PARITY",
"WILSON"
] | 36e30d | diophantine_fbi2_min_v1 | null | 2 | 2 | [
"DIVISOR_PARITY",
"LTE_DIFF",
"WILSON"
] | 3 | 0.007 | 2026-02-08T12:46:31.853498Z | {
"verified": true,
"answer": 2,
"timestamp": "2026-02-08T12:46:31.860467Z"
} | fbe8ea | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 168,
"completion_tokens": 319
},
"timestamp": "2026-02-09T13:33:46.078Z",
"answer": 2
},
{
"id": ... | 1 | [
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "DIVISOR_PARITY",
"status": "ok_later"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "ok... | {
"lo": -6.51,
"mid": -0.38,
"hi": 5.12
} | ||
0c7111 | modular_mod_compute_v1_1520064083_6820 | Let $T$ be the set of all positive integers $t$ such that $9 \leq t \leq 1109$ and there exist positive integers $a$, $b$ with $1 \leq a \leq 21$, $1 \leq b \leq 251$, satisfying
$$
t = 5a + 4b.
$$
Let $m$ be the number of elements in $T$. Find the remainder when $66564$ is divided by $m$. | 135 | graphs = [
Graph(
let={
"a": Const(66564),
"m": CountOverSet(set=SolutionsSet(var=Var("t"), condition=Exists(var=Var(name='a'), condition=Exists(var=Var(name='b'), condition=And(Geq(left=Var(name='a'), right=Const(value=1)), Leq(left=Var(name='a'), right=Const(value=21)), Geq(left=Va... | NT | null | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | modular_mod_compute_v1 | null | 4 | 0 | [
"LIN_FORM"
] | 1 | 0.002 | 2026-02-08T08:21:52.007833Z | {
"verified": true,
"answer": 135,
"timestamp": "2026-02-08T08:21:52.009877Z"
} | e36045 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 147,
"completion_tokens": 3276
},
"timestamp": "2026-02-13T17:32:02.617Z",
"answer": 135
},
{
... | 1 | [
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
}
] | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
20ade6 | alg_qf_psd_min_v1_1218484723_5228 | Let $Q$ be the minimum value of $$40392b^2 + 32538a^2 - 26928ab - 85272bc + 47124c^2 + 22440ac$$ over all ordered triples $(a, b, c)$ of positive integers with $1 \leq a \leq 34$, $1 \leq c \leq 34$, and $1 \leq b \leq \min\{17a_1^2 + 17b_1^2 \mid a_1,b_1 = 1,2,\dots,14\}$. Find $Q$. | 30,294 | graphs = [
Graph(
let={
"_n": Const(17),
"result": 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(34)), Geq(Var("b"), Const(1)), Leq(Var("b"), MinOverSet(set=MapOverSet(set=Solu... | ALG | null | COMPUTE | sympy | QF_PSD_MIN | [
"QF_PSD_MIN"
] | c66ce3 | alg_qf_psd_min_v1 | null | 6 | 0 | [
"QF_PSD_MIN"
] | 1 | 0.139 | 2026-02-25T06:50:56.694717Z | {
"verified": true,
"answer": 30294,
"timestamp": "2026-02-25T06:50:56.833536Z"
} | 9b2594 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 246,
"completion_tokens": 23033
},
"timestamp": "2026-03-29T20:07:57.053Z",
"answer": 735734
},
{
... | 1 | [
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "QF_PSD_MIN",
"status": "ok"
}
] | {
"lo": -3.33,
"mid": 1.03,
"hi": 5.26
} | ||
60ebe2 | alg_sum_powers_v1_1218484723_5131 | Let $C = \left|\left\{ (a, b) : 1 \leq a, b \leq 40,\ 17a^2 - 8ab + 16b^2 \leq 27161 \right\}\right|$. Let $M = \left( \sum_{k=1}^{C} k^2 \right) \bmod 4325$. Find the remainder when $M^2 + 31M + 47$ is divided by $67087$. | 52,312 | graphs = [
Graph(
let={
"_n": Const(2),
"result": Mod(value=Summation(var="k", start=Const(1), end=CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("a"), Var("b")]), condition=And(Geq(Var("a"), Const(1)), Leq(Var("a"), Const(40)), Geq(Var("b"), Const(1)), Leq(Var("b"), Const(40)... | ALG | null | COMPUTE | sympy | QF_PSD_COUNT_LEQ | [
"QF_PSD_COUNT_LEQ"
] | 009d0f | alg_sum_powers_v1 | null | 4 | 0 | [
"QF_PSD_COUNT_LEQ"
] | 1 | 0.065 | 2026-02-25T06:44:59.220561Z | {
"verified": true,
"answer": 52312,
"timestamp": "2026-02-25T06:44:59.285076Z"
} | c68efa | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 220,
"completion_tokens": 19995
},
"timestamp": "2026-03-29T19:36:27.415Z",
"answer": 17078
},
{
... | 1 | [
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "QF_PSD_COUNT_LEQ",
"status": "ok"
}
] | {
"lo": 3.81,
"mid": 6.33,
"hi": 9.49
} | ||
8d57df | sequence_count_fib_divisible_v1_1431428450_206 | Let $N$ be the number of positive integers $n$ such that $1 \leq n \leq 576$ and $3$ divides the $n$th Fibonacci number. Let $P$ be the number of prime numbers $p$ such that $2 \leq p \leq 17579$. Compute $P - N$. | 1,877 | graphs = [
Graph(
let={
"upper": Const(576),
"d": Const(3),
"result": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Ref("upper")), Divides(divisor=Ref("d"), dividend=Fibonacci(arg=Var(name='n')))))),
"_c": Cou... | NT | null | COUNT | sympy | COUNT_PRIMES | [
"COUNT_PRIMES"
] | ad5c3c | sequence_count_fib_divisible_v1 | negation_mod | 4 | 0 | [
"COUNT_PRIMES"
] | 1 | 0.029 | 2026-02-08T13:17:44.430440Z | {
"verified": true,
"answer": 1877,
"timestamp": "2026-02-08T13:17:44.459489Z"
} | fe9a7e | 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": 2052
},
"timestamp": "2026-02-15T12:07:40.552Z",
"answer": 1877
},
{... | 1 | [
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "COUNT_PRIMES",
"status": "ok"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "V8",
"status":... | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
875100 | antilemma_count_primes_v1_677425708_28 | Compute the number of prime numbers $p$ such that $2 \leq p \leq 2447$. | 363 | graphs = [
Graph(
let={
"x": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(2)), Leq(Var("n"), Const(2447)), IsPrime(Var("n"))))),
},
goal=Ref("x"),
)
] | NT | null | COMPUTE | sympy | COUNT_PRIMES | [
"COUNT_PRIMES"
] | 07c874 | antilemma_count_primes_v1 | null | 4 | 0 | [
"COUNT_PRIMES"
] | 1 | 0.001 | 2026-02-08T03:01:03.028629Z | {
"verified": true,
"answer": 363,
"timestamp": "2026-02-08T03:01:03.029177Z"
} | b4ef65 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 69,
"completion_tokens": 1059
},
"timestamp": "2026-02-10T02:57:59.364Z",
"answer": 363
},
{
... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "COUNT_PRIMES",
"status": "ok"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
}
] | {
"lo": -6.5,
"mid": 0,
"hi": 6.5
} | ||
fd1194 | comb_count_surjections_v1_601307018_3157 | Let $M = (3a^4 + a^2 - 4a + 1) \bmod 4489$ and $R = (3M^4 + M^2 - 4M + 1) \bmod 4489$. Let $n$ be the number of integers $a$ with $0 \le a \le 4488$ such that $R = a$ and $M \ne a$. Compute $4! \cdot S(n, 4)$, where $S(n, 4)$ denotes the Stirling number of the second kind. | 40,824 | graphs = [
Graph(
let={
"_n": Const(3),
"n": CountOverSet(set=SolutionsSet(var=Var("a"), condition=And(Geq(Var("a"), Const(0)), Leq(Var("a"), Const(4488)), Eq(Ref("_po_p2"), Var("a")), Neq(Ref("_po_p1"), Var("a"))))),
"k": Const(4),
"result": Mul(Factorial(Ref... | COMB | null | COUNT | sympy | POLY_ORBIT_HENSEL | [
"POLY_ORBIT_HENSEL"
] | 53b6eb | comb_count_surjections_v1 | null | 6 | 0 | [
"POLY_ORBIT_HENSEL"
] | 1 | 0.003 | 2026-03-10T03:44:24.084693Z | {
"verified": true,
"answer": 40824,
"timestamp": "2026-03-10T03:44:24.087481Z"
} | 784930 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 236,
"completion_tokens": 19976
},
"timestamp": "2026-03-29T07:41:03.941Z",
"answer": 40824
},
{
... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "POLY_ORBIT_HENSEL",
"status": "ok"
},
{
"lemma": "V8",
"status": "no"
},
{
"lemma": "V8_SUM",
"status"... | {
"lo": 3.34,
"mid": 5.77,
"hi": 8.89
} | ||
8ff8c1 | alg_linear_system_2x2_v1_1218484723_3669 | Let $\det = 6 \cdot 7 - (-5) \cdot (-19)$. Let $S = 91063 \cdot \left|\left\{ (a, b) : 1 \leq a, b \leq 10,\ 102a^2b^2 + 68ab^3 + 17a^4 + N \cdot b^4 + 68a^3b = 69632 \right\}\right| - (-72750) \cdot (-19)$, where $N = \left|\left\{ (a_1, b_1) : 1 \leq a_1, b_1 \leq 30,\ 128a_1^3 + 384a_1b_1^2 + 384a_1^2b_1 + 128b_1^3 ... | 36,898 | graphs = [
Graph(
let={
"_m": Const(128),
"_n": Const(4),
"num_x": Sub(Mul(Const(91063), 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"), Const(1... | ALG | null | COMPUTE | sympy | POLY3_COUNT | [
"POLY3_COUNT/POLY4_COUNT"
] | 029046 | alg_linear_system_2x2_v1 | null | 5 | 0 | [
"POLY3_COUNT",
"POLY4_COUNT"
] | 2 | 0.01 | 2026-02-25T05:18:32.039757Z | {
"verified": true,
"answer": 36898,
"timestamp": "2026-02-25T05:18:32.050018Z"
} | 4114fe | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 374,
"completion_tokens": 4775
},
"timestamp": "2026-03-29T11:34:08.742Z",
"answer": 36898
},
{
"... | 1 | [
{
"lemma": "POLY3_COUNT",
"status": "ok"
},
{
"lemma": "POLY4_COUNT",
"status": "ok_later"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
}
] | {
"lo": -2.45,
"mid": 1.37,
"hi": 5.29
} | ||
1c9254 | nt_sum_over_divisible_v1_124444284_35 | Let $n$ be a positive integer. Define $N$ to be the number of positive integers $n \leq 60549$ such that $$n \equiv \left\lfloor \frac{n}{2} \right\rfloor \pmod{7}.$$ Let $S$ be the set of positive multiples of 44 that are at most $N$. Let $T = 40401 - \sum_{k \in S} k$. Compute the remainder when $T$ is divided by 606... | 39,659 | graphs = [
Graph(
let={
"_n": Const(60549),
"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=7))))),
... | NT | null | SUM | sympy | L3C | [
"L3C"
] | 73f8b0 | nt_sum_over_divisible_v1 | null | 6 | 0 | [
"L3C"
] | 1 | 0.277 | 2026-02-08T02:54:42.400923Z | {
"verified": true,
"answer": 39659,
"timestamp": "2026-02-08T02:54:42.678376Z"
} | d25dd3 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 226,
"completion_tokens": 2988
},
"timestamp": "2026-02-09T12:45:57.212Z",
"answer": 39659
},
{
"... | 1 | [
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "L3C",
"status": "ok"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"
}
] | {
"lo": 1.68,
"mid": 3.38,
"hi": 5.04
} | ||
7c2aab | modular_modexp_compute_v1_397696148_1714 | Let $m = 29000$. Define $n$ to be $11$ more than the number of nonnegative integers $j \leq m$ for which $\binom{29000}{j}$ is odd. Let $a$ be the number of positive integers at most $n$ whose digit sum is even. Let $e$ be the number of integers $t$ with $35 \leq t \leq 1737$ for which there exist integers $a$ and $b$ ... | 11,401 | graphs = [
Graph(
let={
"_m": Const(29000),
"_n": Sum(CountOverSet(set=SolutionsSet(var=Var("j"), condition=And(Geq(Var("j"), Const(0)), Leq(Var("j"), Ref("_m")), Eq(Mod(value=Binom(n=Const(29000), k=Var("j")), modulus=Const(2)), Const(1))), domain='nonnegative_integers')), Const(11)... | NT | null | COMPUTE | sympy | V8 | [
"V8/L3B",
"LIN_FORM"
] | 85cfde | modular_modexp_compute_v1 | null | 7 | 0 | [
"L3B",
"LIN_FORM",
"V8"
] | 3 | 0.01 | 2026-02-08T12:43:28.578131Z | {
"verified": true,
"answer": 11401,
"timestamp": "2026-02-08T12:43:28.587664Z"
} | 2622fa | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 201,
"completion_tokens": 6102
},
"timestamp": "2026-02-15T04:58:04.344Z",
"answer": 11401
},
... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "L3B",
"status": "ok_later"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"... | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
5c39ce | antilemma_v8_lucas_1116507919_287 | Let $n = 64431$. Determine the number of nonnegative integers $j$ such that $0 \leq j \leq n$ and $\binom{n}{j}$ is odd. | 8,192 | graphs = [
Graph(
let={
"_n": Const(64431),
"x": CountOverSet(set=SolutionsSet(var=Var("j"), condition=And(Geq(Var("j"), Const(0)), Leq(Var("j"), Const(64431)), Eq(Mod(value=Binom(n=Ref("_n"), k=Var("j")), modulus=Const(2)), Const(1))), domain='nonnegative_integers')),
},
... | NT | COMB | COMPUTE | sympy | V8 | [
"V8"
] | 86348e | antilemma_v8_lucas | null | 6 | 0 | [
"V8"
] | 1 | 0 | 2026-02-08T02:30:31.510871Z | {
"verified": true,
"answer": 8192,
"timestamp": "2026-02-08T02:30:31.511352Z"
} | 7f883e | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 157,
"completion_tokens": 906
},
"timestamp": "2026-02-08T19:21:01.395Z",
"answer": 8192
},
{
"id... | 1 | [
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "V8",
"status": "ok"
}
] | {
"lo": -4.6,
"mid": 0.19,
"hi": 4.77
} | ||
1525dc | antilemma_cartesian_v1_1874849503_1503 | Let $x$ be the number of ordered pairs $(a, b)$ where $a$ is an integer from $1$ to $10$, inclusive, and $b$ is an integer from $1$ to $25$, inclusive. Compute the remainder when $44121 \cdot x$ is divided by $76129$. | 67,674 | graphs = [
Graph(
let={
"x": CountOverSet(set=CartesianProduct(left=IntegerRange(start=Const(1), end=Const(10)), right=IntegerRange(start=Const(1), end=Const(25)))),
"Q": Mod(value=Mul(Const(44121), Ref("x")), modulus=Const(76129)),
},
goal=Ref("Q"),
)
] | COMB | GEOM | COMPUTE | sympy | COUNT_CARTESIAN | [
"COUNT_CARTESIAN"
] | 409d7d | antilemma_cartesian_v1 | null | 2 | 0 | [
"COUNT_CARTESIAN"
] | 1 | 0.001 | 2026-02-08T13:56:34.513639Z | {
"verified": true,
"answer": 67674,
"timestamp": "2026-02-08T13:56:34.514790Z"
} | e9bf41 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 178,
"completion_tokens": 1875
},
"timestamp": "2026-02-10T04:51:08.661Z",
"answer": 67674
},
{
"... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "ok"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
},
{
"lemma": "V8_SUM",
"statu... | {
"lo": -2.37,
"mid": 1.22,
"hi": 4.84
} | ||
b22d9e | comb_count_derangements_v1_677425708_936 | Let $n$ be the number of integers $t$ such that $5 \leq t \leq 14$ and there exist positive integers $a$ and $b$ with $1 \leq a \leq 4$, $1 \leq b \leq 2$, and $t = 2a + 3b$. Compute the subfactorial of $n$. | 14,833 | graphs = [
Graph(
let={
"n": CountOverSet(set=SolutionsSet(var=Var("t"), condition=Exists(var=Var(name='a'), condition=Exists(var=Var(name='b'), condition=And(Geq(left=Var(name='a'), right=Const(value=1)), Leq(left=Var(name='a'), right=Const(value=4)), Geq(left=Var(name='b'), right=Const(value=1... | COMB | null | COUNT | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | comb_count_derangements_v1 | null | 4 | 0 | [
"LIN_FORM"
] | 1 | 0.001 | 2026-02-08T03:52:53.803530Z | {
"verified": true,
"answer": 14833,
"timestamp": "2026-02-08T03:52:53.804807Z"
} | 6a3b46 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 198,
"completion_tokens": 1381
},
"timestamp": "2026-02-09T14:14:08.385Z",
"answer": 14833
},
{
"... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
}
] | {
"lo": -5.97,
"mid": -3.96,
"hi": -1.93
} | ||
7f1730 | antilemma_k3_v1_1915831931_234 | Compute the sum of $\phi(d)$ over all positive divisors $d$ of $54102$, where $\phi$ denotes Euler's totient function. | 54,102 | graphs = [
Graph(
let={
"x": SumOverDivisors(n=Const(value=54102), 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 | 2026-02-08T15:16:53.257246Z | {
"verified": true,
"answer": 54102,
"timestamp": "2026-02-08T15:16:53.257624Z"
} | f1e558 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 77,
"completion_tokens": 764
},
"timestamp": "2026-02-16T04:06:21.647Z",
"answer": 54102
},
{
... | 1 | [
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "K3",
"status": "ok"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "V1",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
4701e4 | nt_sum_totient_over_divisors_v1_677425708_2281 | Let $n$ be the number of ordered pairs $(x_1, x_2)$ of positive odd integers such that $x_1 + x_2 = 15204$. Let $s = \sum_{d \mid n} \phi(d)$, where $\phi$ is Euler's totient function. Compute $26335 - s$. | 18,733 | graphs = [
Graph(
let={
"_n": Const(15204),
"n": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x1"), Var("x2")]), condition=And(IsPositive(arg=Var(name='x1')), IsPositive(arg=Var(name='x2')), IsOdd(arg=Var(name='x1')), IsOdd(arg=Var(name='x2')), Eq(Sum(Var("x1"), Var("x2")),... | NT | null | COMPUTE | sympy | COMB1 | [
"COMB1"
] | 567f58 | nt_sum_totient_over_divisors_v1 | null | 5 | 0 | [
"COMB1"
] | 1 | 0.015 | 2026-02-08T04:58:12.963463Z | {
"verified": true,
"answer": 18733,
"timestamp": "2026-02-08T04:58:12.978249Z"
} | b7039e | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 183,
"completion_tokens": 719
},
"timestamp": "2026-02-11T22:35:46.593Z",
"answer": 18733
},
{
"... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COMB1",
"status": "ok"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "V3",
"status": "no"
}
] | {
"lo": -3.42,
"mid": 1.86,
"hi": 7.55
} | ||
764a64 | nt_count_divisible_and_v1_1742523217_4699 | Let $d_1$ be the minimum value of $x + y$ over all ordered pairs $(x, y)$ of positive integers such that $xy = 16$. Let $d_2$ be the minimum value of $x + y$ over all ordered pairs $(x, y)$ of positive integers such that $xy = 36$. Let $S$ be the set of all positive integers $n$ such that $1 \leq n \leq 34920$, $n$ is ... | 59,979 | graphs = [
Graph(
let={
"_n": Const(36),
"upper": Const(34920),
"d1": 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(16)))),... | NT | null | COUNT | sympy | B3 | [
"B3"
] | 0cd20d | nt_count_divisible_and_v1 | null | 5 | 0 | [
"B3"
] | 1 | 1.157 | 2026-02-08T09:05:35.599275Z | {
"verified": true,
"answer": 59979,
"timestamp": "2026-02-08T09:05:36.756533Z"
} | a0cfa0 | 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": 1116
},
"timestamp": "2026-02-14T00:16:19.229Z",
"answer": 59979
},
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
}... | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
53256e | nt_sum_divisors_mod_v1_677425708_2459 | Let $n$ be the sum of the first $15$ positive integers. Let $\sigma$ be the sum of all positive divisors of $n$. Compute the remainder when $\sigma$ is divided by $10753$. | 360 | graphs = [
Graph(
let={
"_n": Const(15),
"n": Summation(var="k", start=Const(1), end=Ref("_n"), expr=Var("k")),
"M": Const(10753),
"sigma": SumDivisors(n=Ref("n")),
"result": Mod(value=Ref("sigma"), modulus=Ref("M")),
},
goal=Ref("r... | NT | null | COMPUTE | sympy | SUM_ARITHMETIC | [
"SUM_ARITHMETIC"
] | eb34f0 | nt_sum_divisors_mod_v1 | null | 3 | 0 | [
"SUM_ARITHMETIC"
] | 1 | 0.001 | 2026-02-08T05:04:01.945665Z | {
"verified": true,
"answer": 360,
"timestamp": "2026-02-08T05:04:01.946938Z"
} | e1140b | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 106,
"completion_tokens": 417
},
"timestamp": "2026-02-11T22:13:25.524Z",
"answer": 360
},
{
"id": 11,
... | 2 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "SUM_ARITHMETIC",
"status": "ok"
},
{
"lemma": "V1",
"status": "no"
},
{
"lemma": "V3",
"status": "no"
},
{
"lemma": "VAL_SUM_EQ",
"status": "no"
}
... | {
"lo": -10,
"mid": -7.73,
"hi": -5.46
} | ||
571a7f | nt_count_phi_equals_v1_1742523217_935 | Let $S$ be the set of all ordered pairs $(x,y)$ of positive integers such that $x + y = 130$. Define $P$ to be the maximum value of $xy$ over all such pairs in $S$. Let $k = 300$. Determine the value of the number of positive integers $n$ such that $1 \leq n \leq P$ and $\phi(n) = k$. | 5 | graphs = [
Graph(
let={
"upper": 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(130)))), expr=Mul(Var("x"), Var("y")))),
"k": Const(300)... | NT | null | COUNT | sympy | B1 | [
"B1"
] | 5b950e | nt_count_phi_equals_v1 | null | 7 | 0 | [
"B1"
] | 1 | 0.363 | 2026-02-08T03:21:56.929162Z | {
"verified": true,
"answer": 5,
"timestamp": "2026-02-08T03:21:57.292512Z"
} | ce514c | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 1,
"correct": {
"strict": false,
"boxed": false,
"relaxed": true
},
"usage": {
"prompt_tokens": 199,
"completion_tokens": 8587
},
"timestamp": "2026-02-23T18:17:48.617Z",
"answer": 3
},
{
"i... | 1 | [
{
"lemma": "B1",
"status": "ok"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "V3",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
}
] | {
"lo": -3.45,
"mid": 1.18,
"hi": 5.72
} | ||
d2bcf7 | diophantine_fbi2_count_v1_1978505735_831 | Let $k = 360$, $a = 3$, and $b = 2$. Let the upper limit be $120$. Consider the set of all positive integers $d$ such that $4 \leq d \leq 123$, $d$ divides $k$, and $3 \leq \frac{k}{d} \leq 122$. Compute the number of elements in this set. | 19 | graphs = [
Graph(
let={
"k": Const(360),
"a": Const(3),
"b": Const(2),
"upper": Const(120),
"result": CountOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Const(4)), Leq(Var("d"), Const(123)), Divides(divisor=Var("d"), dividend=R... | NT | null | COUNT | sympy | VIETA_SUM | [
"VIETA_SUM"
] | b33a7a | diophantine_fbi2_count_v1 | null | 3 | 0 | [
"VIETA_SUM"
] | 1 | 0.065 | 2026-02-08T15:38:00.528750Z | {
"verified": true,
"answer": 19,
"timestamp": "2026-02-08T15:38:00.594159Z"
} | 97645d | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 129,
"completion_tokens": 1124
},
"timestamp": "2026-02-16T09:51:21.390Z",
"answer": 19
},
{
... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
},
{
"lemma": "VIETA_SUM",
"status": "ok"
}
... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
1bdb6a | modular_mod_compute_v1_1915831931_1964 | Let $S$ be the set of all ordered pairs $(x_1, x_2)$ of positive odd integers such that $x_1 + x_2 = 15554$. Let $m$ be the number of elements in $S$. Find the remainder when $-43681$ is divided by $m$. | 2,981 | graphs = [
Graph(
let={
"_n": Const(15554),
"a": Const(-43681),
"m": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x1"), Var("x2")]), condition=And(IsPositive(arg=Var(name='x1')), IsPositive(arg=Var(name='x2')), IsOdd(arg=Var(name='x1')), IsOdd(arg=Var(name='x2')... | NT | null | COMPUTE | sympy | COMB1 | [
"COMB1"
] | 567f58 | modular_mod_compute_v1 | null | 4 | 0 | [
"COMB1"
] | 1 | 0.007 | 2026-02-08T16:33:10.141878Z | {
"verified": true,
"answer": 2981,
"timestamp": "2026-02-08T16:33:10.148520Z"
} | e81f15 | 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": 778
},
"timestamp": "2026-02-17T06:51:09.155Z",
"answer": 2981
},
{
... | 1 | [
{
"lemma": "COMB1",
"status": "ok"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
f57ae4 | comb_bell_compute_v1_48377204_1289 | Let $n$ be the number of ordered pairs $(a, b)$ where $a$ and $b$ are integers satisfying $1 \leq a \leq 3$ and $1 \leq b \leq 3$. Let $B_n$ denote the $n$th Bell number, which counts the number of partitions of a set of $n$ elements. Compute the value of $69169 - B_n$. | 48,022 | graphs = [
Graph(
let={
"_n": Const(69169),
"n": CountOverSet(set=CartesianProduct(left=IntegerRange(start=Const(1), end=Const(3)), right=IntegerRange(start=Const(1), end=Const(3)))),
"result": Bell(Ref("n")),
"Q": Sub(Ref("_n"), Ref("result")),
},
... | COMB | null | COMPUTE | sympy | COUNT_CARTESIAN | [
"COUNT_CARTESIAN"
] | 409d7d | comb_bell_compute_v1 | null | 3 | 0 | [
"COUNT_CARTESIAN"
] | 1 | 0.003 | 2026-02-08T16:01:03.328827Z | {
"verified": true,
"answer": 48022,
"timestamp": "2026-02-08T16:01:03.331518Z"
} | ec8173 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 201,
"completion_tokens": 438
},
"timestamp": "2026-02-24T19:22:33.590Z",
"answer": 48022
},
{
"... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "ok"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
},
{
"lemma": "V8_SUM",
"status":... | {
"lo": -5.65,
"mid": -3.17,
"hi": -0.81
} | ||
25c852 | sequence_count_fib_divisible_v1_655260480_3245 | Let $ d = 20 $. Determine the number of positive integers $ n $ such that $ 1 \leq n \leq 563 $ and $ d $ divides the $ n $-th Fibonacci number. Compute this number. | 18 | graphs = [
Graph(
let={
"upper": Const(563),
"d": Const(20),
"result": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Ref("upper")), Divides(divisor=Ref("d"), dividend=Fibonacci(arg=Var(name='n')))))),
},
g... | NT | null | COUNT | sympy | MIN_PRIME_FACTOR | [
"L3B/K14"
] | ff1b67 | sequence_count_fib_divisible_v1 | null | 5 | 0 | [
"K14",
"L3B",
"MIN_PRIME_FACTOR"
] | 3 | 0.103 | 2026-02-08T17:17:06.134495Z | {
"verified": true,
"answer": 18,
"timestamp": "2026-02-08T17:17:06.237669Z"
} | 79f717 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 93,
"completion_tokens": 1947
},
"timestamp": "2026-02-17T22:45:25.789Z",
"answer": 18
},
{
... | 1 | [
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K14",
"status": "ok_later"
},
{
"lemma": "L3B",
"status": "ok"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
},... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
a7a534 | modular_sum_quadratic_residues_v1_124444284_2144 | Let $ m = 6 $. Define $ n $ to be the number of integers $ k $ with $ 1 \leq k \leq m $ such that $ k \equiv \left\lfloor \frac{k}{2} \right\rfloor \pmod{3} $. Let $ p $ be the smallest divisor of 265189 that is at least $ n $. Compute $ \frac{p(p-1)}{4} $. | 64,643 | graphs = [
Graph(
let={
"_m": Const(6),
"_n": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Ref("_m")), Congruent(a=Var(name='n'), b=Floor(arg=Div(left=Var(name='n'), right=Const(value=2))), modulus=Const(value=3))))),
"p... | NT | null | SUM | sympy | V8 | [
"L3C/MIN_PRIME_FACTOR",
"COUNT_CARTESIAN"
] | 9cabd8 | modular_sum_quadratic_residues_v1 | null | 6 | 0 | [
"COUNT_CARTESIAN",
"L3C",
"MIN_PRIME_FACTOR",
"V8"
] | 4 | 0.009 | 2026-02-08T04:20:48.775451Z | {
"verified": true,
"answer": 64643,
"timestamp": "2026-02-08T04:20:48.784128Z"
} | ccc483 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 206,
"completion_tokens": 5341
},
"timestamp": "2026-02-10T16:33:06.508Z",
"answer": 64643
},
{
... | 1 | [
{
"lemma": "COUNT_CARTESIAN",
"status": "ok"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "L3C",
"status": "ok"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
... | {
"lo": -3.42,
"mid": 1.86,
"hi": 7.55
} | ||
842c50 | lin_form_endings_v1_809748730_511 | Let $a = 9$, $b = 12$, $A = 49$, and $B = 29$. Let $g = \gcd(a, b)$. Define $n = \left\lfloor \frac{aA + bB - a - b}{g} \right\rfloor + 1$. Let $k = 18536$ and $M = 56436$. Compute the remainder when $k \cdot n$ is divided by $M$. | 23,128 | graphs = [
Graph(
let={
"a_coeff": Const(9),
"b_coeff": Const(12),
"A_val": Const(49),
"B_val": Const(29),
"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"), Re... | COMB | NT | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | lin_form_endings_v1 | null | 3 | null | [
"LIN_FORM"
] | 1 | 0.003 | 2026-02-08T11:33:20.358969Z | {
"verified": true,
"answer": 23128,
"timestamp": "2026-02-08T11:33:20.361817Z"
} | 0590ba | 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": 728
},
"timestamp": "2026-02-14T15:39:37.950Z",
"answer": 23128
},
{... | 1 | [
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": ... | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
e07d40 | comb_catalan_compute_v1_677425708_3312 | Let $n$ be the number of ordered pairs $(x_1, x_2)$ of positive odd integers such that $x_1 + x_2 = 22$. Let $r$ be the $n$-th Catalan number. Compute the remainder when $44121r$ is divided by $68869$. | 21,697 | graphs = [
Graph(
let={
"_n": Const(68869),
"n": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x1"), Var("x2")]), condition=And(IsPositive(arg=Var(name='x1')), IsPositive(arg=Var(name='x2')), IsOdd(arg=Var(name='x1')), IsOdd(arg=Var(name='x2')), Eq(Sum(Var("x1"), Var("x2")),... | COMB | null | COMPUTE | sympy | COMB1 | [
"COMB1"
] | 567f58 | comb_catalan_compute_v1 | null | 4 | 0 | [
"COMB1"
] | 1 | 0.002 | 2026-02-08T05:39:00.124641Z | {
"verified": true,
"answer": 21697,
"timestamp": "2026-02-08T05:39:00.126150Z"
} | 9beca8 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 1,
"correct": {
"strict": false,
"boxed": false,
"relaxed": true
},
"usage": {
"prompt_tokens": 178,
"completion_tokens": 32768
},
"timestamp": "2026-02-24T04:16:03.505Z",
"answer": null
},
{
... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COMB1",
"status": "ok"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
... | {
"lo": 1.97,
"mid": 4.36,
"hi": 6.69
} | ||
fc008a | comb_factorial_compute_v1_153355830_2558 | Let $S$ be the set of all integers $n$ such that $1 \leq n \leq 1079$ and the sum of the digits of $n$ is even. Let $m = 2$, and let $T$ be the set of all divisors $d$ of $|S|$ such that $d \geq m$. Let $k$ be the smallest element of $T$. Compute $k!$. | 5,040 | graphs = [
Graph(
let={
"_m": Const(2),
"_n": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Const(1079)), Eq(Mod(value=DigitSum(Var("n")), modulus=Const(2)), Const(0))))),
"n": MinOverSet(set=SolutionsSet(var=Var("d"), co... | NT | null | COMPUTE | sympy | L3B | [
"L3B/MIN_PRIME_FACTOR"
] | 2db982 | comb_factorial_compute_v1 | null | 4 | 0 | [
"L3B",
"MIN_PRIME_FACTOR"
] | 2 | 0.002 | 2026-02-08T07:13:46.332915Z | {
"verified": true,
"answer": 5040,
"timestamp": "2026-02-08T07:13:46.334561Z"
} | 334d9f | 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": 1134
},
"timestamp": "2026-02-13T08:59:31.133Z",
"answer": 5040
},
{... | 1 | [
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "L3B",
"status": "ok"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "MIN_PRIME_FACTOR",
"stat... | {
"lo": -5.55,
"mid": -3.01,
"hi": 0.32
} | ||
2235b6 | algebra_quadratic_discriminant_v1_865884756_2647 | Let $b$ be the number of nonnegative integers $j$ with $0 \leq j \leq 1088$ such that $\binom{1088}{j}$ is odd. Let $p$ be the number of prime numbers $n$ such that $2 \leq n \leq 3$. Define $\text{result} = b^p - 4 \cdot 1 \cdot (-60)$. Find the smallest positive integer $k$ such that the $k$-th Fibonacci number is di... | 132 | graphs = [
Graph(
let={
"_n": Const(1088),
"a": Const(1),
"b": CountOverSet(set=SolutionsSet(var=Var("j"), condition=And(Geq(Var("j"), Const(0)), Leq(Var("j"), Const(1088)), Eq(Mod(value=Binom(n=Ref("_n"), k=Var("j")), modulus=Const(2)), Const(1))), domain='nonnegative_in... | NT | null | COMPUTE | sympy | COUNT_PRIMES | [
"COUNT_PRIMES",
"V8"
] | 9c24d3 | algebra_quadratic_discriminant_v1 | null | 6 | 0 | [
"COUNT_PRIMES",
"V8"
] | 2 | 0.004 | 2026-02-08T16:51:51.808951Z | {
"verified": true,
"answer": 132,
"timestamp": "2026-02-08T16:51:51.813034Z"
} | 007a56 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 163,
"completion_tokens": 2277
},
"timestamp": "2026-02-17T12:53:47.251Z",
"answer": 132
},
{
... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "COUNT_PRIMES",
"status": "ok"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
}... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
092717 | comb_count_partitions_v1_717093673_469 | Let $n$ be the largest integer such that $2^n \leq 5914558133053$. Determine the number of integer partitions of $n$. | 53,174 | graphs = [
Graph(
let={
"_n": Const(2),
"n": MaxOverSet(set=SolutionsSet(var=Var("k"), condition=Leq(Pow(Ref("_n"), Var("k")), Const(5914558133053)))),
"result": Partition(arg=Ref(name='n')),
},
goal=Ref("result"),
)
] | COMB | null | COUNT | sympy | MAX_VAL | [
"MAX_VAL"
] | 1da621 | comb_count_partitions_v1 | null | 4 | 0 | [
"MAX_VAL"
] | 1 | 0.001 | 2026-02-08T15:28:07.038040Z | {
"verified": true,
"answer": 53174,
"timestamp": "2026-02-08T15:28:07.039214Z"
} | 388594 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 144,
"completion_tokens": 770
},
"timestamp": "2026-02-24T21:00:43.355Z",
"answer": 53174
},
{
"i... | 1 | [
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K16",
"status": "same_pattern_wrong"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "ok"
},
{
"lemma": "MOD_... | {
"lo": -2.43,
"mid": 1.2,
"hi": 4.84
} | ||
fb2df9 | antilemma_sum_equals_v1_1978505735_5344 | Let $m$ be the number of integers $t$ with $12 \leq t \leq 108$ for which there exist integers $a$ and $b$, each between $1$ and $9$ inclusive, such that $t = 5a + 7b$. Let $n$ be the number of ordered pairs $(i, j)$ of integers with $1 \leq i \leq 72$ and $1 \leq j \leq 72$ such that $i + j = m$. Compute the number of... | 71 | graphs = [
Graph(
let={
"_m": 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=9)), Geq(left=Var(name='b'), right=Const(value=... | COMB | GEOM | COMPUTE | sympy | COMB1 | [
"COUNT_SUM_EQUALS/COUNT_SUM_EQUALS",
"LIN_FORM/COUNT_SUM_EQUALS",
"COUNT_SUM_EQUALS"
] | b43a9c | antilemma_sum_equals_v1 | null | 5 | 0 | [
"COMB1",
"COUNT_SUM_EQUALS",
"LIN_FORM"
] | 3 | 0.116 | 2026-02-08T18:56:36.393335Z | {
"verified": true,
"answer": 71,
"timestamp": "2026-02-08T18:56:36.509580Z"
} | 1a14af | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 217,
"completion_tokens": 4699
},
"timestamp": "2026-02-25T00:59:15.924Z",
"answer": 71
},
{
... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "ok"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
},
... | {
"lo": -3.12,
"mid": 1.47,
"hi": 6.57
} | ||
c1d9ea | comb_count_surjections_v1_865884756_4506 | Let $n = 15$. Define $A$ as the set of all ordered pairs $(i, j)$ of integers such that $1 \leq i \leq 13$, $1 \leq j \leq 13$, and $i + j = n$. Let $n_1$ be the number of elements in $A$. Compute the sum
$$
\sum_{k=0}^{n_1} (-1)^k \binom{n_1}{k}.
$$Let $u$ be this sum. Define $n = 6 + u$. Now compute the sum
$$
\sum_{... | 1,800 | graphs = [
Graph(
let={
"_n": Const(15),
"u1": Const(0),
"n2": Sum(Ref("u1"), Const(1)),
"e": Summation(var="k1", start=Const(0), end=Ref("n2"), expr=Mul(Pow(Const(-1), Var("k1")), Binom(n=Ref("n2"), k=Var("k1")))),
"n1": CountOverSet(set=Solutions... | COMB | null | COUNT | sympy | COUNT_SUM_EQUALS | [
"COUNT_SUM_EQUALS/BINOMIAL_ALTERNATING"
] | ab0fe8 | comb_count_surjections_v1 | null | 5 | 2 | [
"BINOMIAL_ALTERNATING",
"COUNT_SUM_EQUALS"
] | 2 | 0.012 | 2026-02-08T17:58:07.388744Z | {
"verified": true,
"answer": 1800,
"timestamp": "2026-02-08T17:58:07.400451Z"
} | b7cd30 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 256,
"completion_tokens": 930
},
"timestamp": "2026-02-18T10:31:31.472Z",
"answer": 1800
},
{
... | 1 | [
{
"lemma": "BINOMIAL_ALTERNATING",
"status": "ok_later"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "ok"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma"... | {
"lo": -2.38,
"mid": 1.74,
"hi": 6.59
} | ||
929ed5 | comb_count_permutations_fixed_v1_677425708_2260 | Let $n$ be the number of integers $j$ with $0 \leq j \leq 66624$ such that $\binom{66624}{j}$ is odd. Compute the value of $\binom{n}{0} \cdot !n$, where $!n$ denotes the number of derangements of $n$ elements. | 14,833 | graphs = [
Graph(
let={
"_n": Const(2),
"n": CountOverSet(set=SolutionsSet(var=Var("j"), condition=And(Geq(Var("j"), Const(0)), Leq(Var("j"), Const(66624)), Eq(Mod(value=Binom(n=Const(66624), k=Var("j")), modulus=Ref("_n")), Const(1))), domain='nonnegative_integers')),
"k... | COMB | null | COUNT | sympy | C4 | [
"V8"
] | 86348e | comb_count_permutations_fixed_v1 | null | 6 | 0 | [
"C4",
"V8"
] | 2 | 0.017 | 2026-02-08T04:52:39.574043Z | {
"verified": true,
"answer": 14833,
"timestamp": "2026-02-08T04:52:39.590628Z"
} | b55981 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 185,
"completion_tokens": 1892
},
"timestamp": "2026-02-24T02:28:45.113Z",
"answer": 14833
},
{
"... | 1 | [
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
},
{
"lemma": "V8",
"status": "ok"
}
] | {
"lo": -2.46,
"mid": 0.47,
"hi": 3.59
} | ||
7eccc8 | lin_form_endings_v1_1520064083_8625 | Compute the value of $x$, where $x$ is the remainder when $5587 \cdot \left\lfloor \frac{35}{\gcd(35, \gcd(14, 4))} \right\rfloor$ is divided by $77316$. | 40,913 | graphs = [
Graph(
let={
"a_coeff": Const(14),
"b_coeff": Const(4),
"k_val": Const(35),
"step": GCD(a=Ref("a_coeff"), b=Ref("b_coeff")),
"_inner_result": Floor(Div(Ref("k_val"), GCD(a=Ref("k_val"), b=Ref("step")))),
"_scale_k": Const(558... | COMB | NT | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | lin_form_endings_v1 | null | 3 | null | [
"LIN_FORM"
] | 1 | 0.001 | 2026-02-08T10:16:15.795086Z | {
"verified": true,
"answer": 40913,
"timestamp": "2026-02-08T10:16:15.796532Z"
} | c22b49 | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 121,
"completion_tokens": 313
},
"timestamp": "2026-02-15T20:58:43.985Z",
"answer": 41413
},
{
"id": 11... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "V8",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no... | {
"lo": -6.96,
"mid": -4.56,
"hi": -1.46
} | ||
6999ff | comb_count_derangements_v1_1218484723_4233 | Let $N = 10$, $M = 0$, and define $f = \sum_{k=0}^{M} (-1)^k \binom{M}{k}$, $a = 4f$, $R = a + 2$, $m = \sum_{k=0}^{R} (-1)^k \binom{R}{k}$, $w = \sum_{k=0}^{N} (-1)^k \binom{N}{k}$, and $n = 8 + w + m$. Compute the number of derangements of $n$ elements. | 14,833 | graphs = [
Graph(
let={
"n3": Const(0),
"f": Summation(var="k", start=Const(0), end=Ref("n3"), expr=Mul(Pow(Const(-1), Var("k")), Binom(n=Ref("n3"), k=Var("k")))),
"n2": Const(10),
"w": Summation(var="k1", start=Const(0), end=Ref("n2"), expr=Mul(Pow(Const(-1),... | COMB | null | COUNT | sympy | BINOMIAL_ALTERNATING | [
"BINOMIAL_ALTERNATING"
] | c21569 | comb_count_derangements_v1 | null | 3 | 3 | [
"BINOMIAL_ALTERNATING"
] | 1 | 0.001 | 2026-02-25T05:53:34.294588Z | {
"verified": true,
"answer": 14833,
"timestamp": "2026-02-25T05:53:34.295988Z"
} | 3c9764 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 238,
"completion_tokens": 1183
},
"timestamp": "2026-03-29T14:25:15.671Z",
"answer": 14833
},
{
"... | 2 | [
{
"lemma": "BINOMIAL_ALTERNATING",
"status": "ok"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
},
{
"lemma": "V8_S... | {
"lo": -10,
"mid": -6.41,
"hi": -2.82
} | ||
4c2ffb | modular_min_linear_v1_1742523217_5584 | Let $a$ be the largest prime number at most $4226$. Let $m = 60207$ and $b = 56871$. Define $x$ to be the smallest positive integer such that $1 \le x \le m$ and $ax \equiv b \pmod{m}$. Compute the remainder when $44121x$ is divided by $73375$. | 47,568 | graphs = [
Graph(
let={
"_n": Const(73375),
"a": MaxOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(2)), Leq(Var("n"), Const(4226)), IsPrime(Var("n"))))),
"b": Const(56871),
"m": Const(60207),
"result": MinOverSet(set=Solut... | NT | null | EXTREMUM | sympy | MAX_PRIME_BELOW | [
"MAX_PRIME_BELOW"
] | dc3ad3 | modular_min_linear_v1 | null | 6 | 0 | [
"MAX_PRIME_BELOW"
] | 1 | 3.359 | 2026-02-08T11:05:01.821273Z | {
"verified": true,
"answer": 47568,
"timestamp": "2026-02-08T11:05:05.180535Z"
} | eb81aa | 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": 4211
},
"timestamp": "2026-02-14T10:27:32.330Z",
"answer": 47568
},
... | 1 | [
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok"
},
{
"lemma": "V5",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
}
] | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
6ca0c8 | nt_count_coprime_and_v1_1978505735_6687 | Let $m = 2$ and $n = 20449$. Let $k_1$ be the smallest divisor $d$ of $n$ such that $d \geq m$. Let $k_2$ be the largest prime number $n$ such that $2 \leq n \leq 16$. Let $S$ be the set of all positive integers $n_1$ such that $1 \leq n_1 \leq 18221$, $\gcd(n_1, k_1) = 1$, and $\gcd(n_1, k_2) = 1$. Compute the number ... | 40,584 | graphs = [
Graph(
let={
"_m": Const(2),
"_n": Const(20449),
"upper": Const(18221),
"k1": MinOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Ref("_m")), Divides(divisor=Var("d"), dividend=Ref("_n"))))),
"k2": MaxOverSet(set=Soluti... | NT | null | COUNT | sympy | MIN_PRIME_FACTOR | [
"MIN_PRIME_FACTOR",
"MAX_PRIME_BELOW"
] | 9f9e96 | nt_count_coprime_and_v1 | null | 5 | 0 | [
"MAX_PRIME_BELOW",
"MIN_PRIME_FACTOR"
] | 2 | 1.858 | 2026-02-08T19:44:54.859887Z | {
"verified": true,
"answer": 40584,
"timestamp": "2026-02-08T19:44:56.717670Z"
} | 5a7483 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 202,
"completion_tokens": 3164
},
"timestamp": "2026-02-18T23:25:07.379Z",
"answer": 40584
},
... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
8c0361 | sequence_count_fib_divisible_v1_655260480_1879 | Let $n$ be a positive integer such that $1 \leq n \leq 988$ and $15$ divides the $n$th Fibonacci number. Determine how many such integers $n$ satisfy this condition. Let $c$ be this count. Find the remainder when $7 - c$ is divided by $50755$. | 50,713 | graphs = [
Graph(
let={
"upper": Const(988),
"d": Const(15),
"result": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Ref("upper")), Divides(divisor=Ref("d"), dividend=Fibonacci(arg=Var(name='n')))))),
"Q": Mod... | NT | null | COUNT | sympy | C3 | [
"C3/C3",
"K2/C3"
] | 141a84 | sequence_count_fib_divisible_v1 | null | 6 | 0 | [
"C3",
"K2"
] | 2 | 0.076 | 2026-02-08T16:27:23.986940Z | {
"verified": true,
"answer": 50713,
"timestamp": "2026-02-08T16:27:24.063060Z"
} | 987f5b | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 116,
"completion_tokens": 1817
},
"timestamp": "2026-02-17T03:19:59.048Z",
"answer": 50713
},
... | 1 | [
{
"lemma": "C3",
"status": "ok"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "K2",
"status": "ok"
},
... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
e103ba | antilemma_sum_equals_v1_2051736721_3130 | Let $n$ be the number of ordered pairs $(i, j)$ of integers such that $1 \leq i \leq 2$ and $1 \leq j \leq 37$. Let $x$ be the number of ordered pairs $(i, j)$ of integers such that $1 \leq i \leq 72$, $1 \leq j \leq 73$, and $i + j = n$. Compute $x + \varphi(|x| + 0!) + \tau(|x| + 1)$, where $\varphi(k)$ denotes the n... | 146 | graphs = [
Graph(
let={
"_n": CountOverSet(set=CartesianProduct(left=IntegerRange(start=Const(1), end=Const(2)), right=IntegerRange(start=Const(1), end=Const(37)))),
"x": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("i"), Var("j")]), condition=Eq(Sum(Var("i"), Var("j")), Ref... | COMB | GEOM | COMPUTE | sympy | LIN_FORM | [
"COUNT_CARTESIAN/COUNT_SUM_EQUALS",
"COUNT_SUM_EQUALS",
"ONE_FACTORIAL_0"
] | b74536 | antilemma_sum_equals_v1 | null | 3 | 0 | [
"COUNT_CARTESIAN",
"COUNT_SUM_EQUALS",
"LIN_FORM",
"ONE_FACTORIAL_0"
] | 4 | 0.046 | 2026-02-08T17:08:08.615577Z | {
"verified": true,
"answer": 146,
"timestamp": "2026-02-08T17:08:08.661536Z"
} | 8a24d5 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 196,
"completion_tokens": 841
},
"timestamp": "2026-02-17T19:06:55.010Z",
"answer": 146
},
{
... | 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": "ok"
},
{
"lemma": "ONE_F... | {
"lo": -5.64,
"mid": -3.17,
"hi": -0.81
} | ||
922240 | geo_visible_lattice_v1_1431428450_89 | Let $n = 99$. A lattice point $(x, y)$ with $1 \leq x, y \leq n$ is said to be visible if $\gcd(x, y) = 1$. Let $V$ be the number of visible lattice points in this range. Compute the remainder when $44121 \cdot V$ is divided by $51253$. | 5,584 | graphs = [
Graph(
let={
"n": Const(99),
"result": VisibleLatticePoints(n=Ref(name='n')),
"Q": Mod(value=Mul(Const(44121), Ref("result")), modulus=Const(51253)),
},
goal=Ref("Q"),
)
] | GEOM | null | COUNT | sympy | [] | geo_visible_lattice_v1 | null | 3 | 0 | null | null | 0.218 | 2026-02-08T13:10:58.602926Z | {
"verified": true,
"answer": 5584,
"timestamp": "2026-02-08T13:10:58.821080Z"
} | e4f680 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 190,
"completion_tokens": 32768
},
"timestamp": "2026-02-24T17:35:52.597Z",
"answer": null
},
{
... | 1 | [] | {
"lo": 3.25,
"mid": 5.68,
"hi": 8.81
} | ||||
5211ad | modular_count_residue_v1_784195855_310 | Let $m = 8$. Define $n$ to be the number of positive integers $n$ such that $1 \le n \le 3016$, $m$ divides $n$, and $\gcd(n, 21) = 1$. Let $M$ be the number of positive integers $k$ such that $1 \le k \le n$ and $9$ divides $k$. Let $R = 10$. Compute the number of positive integers $n$ such that $1 \le n \le 49284$ an... | 36,233 | graphs = [
Graph(
let={
"_m": Const(8),
"_n": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Const(3016)), Divides(divisor=Ref("_m"), dividend=Var("n")), Eq(GCD(a=Var("n"), b=Const(21)), Const(1))))),
"upper": Const(49284)... | NT | null | COUNT | sympy | C5 | [
"C5/C2"
] | d5b84b | modular_count_residue_v1 | null | 5 | 0 | [
"C2",
"C5"
] | 2 | 4.682 | 2026-02-08T03:05:26.077838Z | {
"verified": true,
"answer": 36233,
"timestamp": "2026-02-08T03:05:30.759939Z"
} | 52107d | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 268,
"completion_tokens": 1752
},
"timestamp": "2026-02-10T12:51:38.063Z",
"answer": 35783
},
{
... | 1 | [
{
"lemma": "C2",
"status": "ok_later"
},
{
"lemma": "C5",
"status": "ok"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "V8_S... | {
"lo": 1.1,
"mid": 4.17,
"hi": 6.61
} | ||
d4c5ef | nt_min_coprime_above_v1_784195855_7525 | Let $m$ be the number of integers $t$ with $10 \leq t \leq 338$ that can be written as $3a + 7b$ for positive integers $a \leq 101$ and $b \leq 5$. Let $r$ be the smallest integer greater than 10404 and at most 10731 that is relatively prime to $m$. Compute the remainder when the Bell number $B_r$, where $r$ is taken m... | 18,155 | graphs = [
Graph(
let={
"_n": Const(2),
"start": Const(10404),
"upper": Const(10731),
"modulus": 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=Con... | NT | COMB | EXTREMUM | sympy | LIN_FORM | [
"MAX_PRIME_BELOW",
"LIN_FORM"
] | 4b337f | nt_min_coprime_above_v1 | bell_mod | 7 | 0 | [
"LIN_FORM",
"MAX_PRIME_BELOW"
] | 2 | 0.15 | 2026-02-08T09:22:49.019990Z | {
"verified": true,
"answer": 18155,
"timestamp": "2026-02-08T09:22:49.170291Z"
} | 5a7ae3 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 161,
"completion_tokens": 3586
},
"timestamp": "2026-02-14T03:28:57.709Z",
"answer": 18155
},
... | 1 | [
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
... | {
"lo": -5.49,
"mid": 0.22,
"hi": 6.51
} | ||
f89652 | modular_modexp_compute_v1_1125832087_316 | Let $a = 19$. Let $e$ be the minimum value of $x + y$ over all ordered pairs of positive integers $(x, y)$ such that $xy = 1000000$. Let $m = 77284$. Compute $a^e \bmod m$. | 56,829 | graphs = [
Graph(
let={
"a": Const(19),
"e": 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(1000000)))), expr=Sum(Var("x"), Var("y")))),... | NT | null | COMPUTE | sympy | B3 | [
"B3"
] | 0cd20d | modular_modexp_compute_v1 | null | 6 | 0 | [
"B3"
] | 1 | 0.002 | 2026-02-08T03:01:10.468043Z | {
"verified": true,
"answer": 56829,
"timestamp": "2026-02-08T03:01:10.469607Z"
} | d72e79 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 171,
"completion_tokens": 6151
},
"timestamp": "2026-02-10T12:29:57.494Z",
"answer": 56829
},
{
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
}
] | {
"lo": 1.96,
"mid": 5.23,
"hi": 8.52
} | ||
78e33d | alg_qf_psd_min_v1_601307018_8692 | Let $M$ be the minimum value of $x + y$ over all pairs of positive real numbers $(x, y)$ with $x \le y$ and $xy = 6170256$. Let $B$ be the largest positive integer $d$ such that $d^2 \le 1599$ and $d$ divides the largest divisor of $2559999$ whose square is at most $2559999$. Find the minimum value of $$M \cdot a \cdot... | 93,564 | graphs = [
Graph(
let={
"_m": Const(38088),
"_n": Const(17388),
"result": 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(39)), Geq(Var("b"), Const(1)), Leq(Var("b"),... | NT | null | COMPUTE | sympy | B3_CLOSEST | [
"B3_CLOSEST/B3_CLOSEST",
"B3"
] | fb6895 | alg_qf_psd_min_v1 | null | 5 | 0 | [
"B3",
"B3_CLOSEST"
] | 2 | 0.157 | 2026-03-10T09:10:25.120684Z | {
"verified": true,
"answer": 93564,
"timestamp": "2026-03-10T09:10:25.277225Z"
} | a92ab4 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 289,
"completion_tokens": 6231
},
"timestamp": "2026-04-19T09:31:12.370Z",
"answer": 93564
},
{
... | 2 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "B3_CLOSEST",
"status": "ok"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma":... | {
"lo": -10,
"mid": -5.89,
"hi": -1.79
} | ||
fee889 | diophantine_product_count_v1_784195855_7581 | Let $p_{\text{max}}$ be the largest prime number $p$ such that $2 \leq p \leq 338$. Determine the number of positive integers $x$ such that $1 \leq x \leq p_{\text{max}}$, $x$ divides $360$, and $\frac{360}{x} \leq p_{\text{max}}$. Compute the remainder when $96037$ times this count is divided by $72409$. | 12,953 | graphs = [
Graph(
let={
"_n": Const(2),
"k": Const(360),
"upper": MaxOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Ref("_n")), Leq(Var("n"), Const(338)), IsPrime(Var("n"))))),
"result": CountOverSet(set=SolutionsSet(var=Var("x"), condition... | NT | null | COUNT | sympy | MAX_PRIME_BELOW | [
"MAX_PRIME_BELOW"
] | dc3ad3 | diophantine_product_count_v1 | null | 4 | 0 | [
"MAX_PRIME_BELOW"
] | 1 | 0.012 | 2026-02-08T09:24:14.611601Z | {
"verified": true,
"answer": 12953,
"timestamp": "2026-02-08T09:24:14.623330Z"
} | 1ff085 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 142,
"completion_tokens": 1607
},
"timestamp": "2026-02-14T03:46:03.897Z",
"answer": 12953
},
... | 1 | [
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok"
},
{
"lemma": "V7",
"status": "no"
}
] | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
f81566 | nt_num_divisors_compute_v1_677425708_2643 | Consider the set of all ordered pairs $(x, y)$ of positive integers such that $xy = 20250000$. Let $n$ be the minimum value of $x + y$ over all such pairs. Let $d$ be the number of positive divisors of $n$. Compute
$$
\sum_{k=1}^{d} \phi(k),
$$
where $\phi(k)$ denotes Euler's totient function. | 712 | graphs = [
Graph(
let={
"n": MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(Mul(Var("x"), Var("y")), Const(20250000)))), expr=Sum(Var("x"), Var("y")))),
"result": NumD... | NT | null | COMPUTE | sympy | B3 | [
"B3"
] | 0cd20d | nt_num_divisors_compute_v1 | null | 6 | 0 | [
"B3"
] | 1 | 0.001 | 2026-02-08T05:10:17.049465Z | {
"verified": true,
"answer": 712,
"timestamp": "2026-02-08T05:10:17.050831Z"
} | fda48c | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 200,
"completion_tokens": 2413
},
"timestamp": "2026-02-11T22:59:09.317Z",
"answer": 712
},
{
"i... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
}
] | {
"lo": -3.42,
"mid": 1.86,
"hi": 7.55
} | ||
67b157 | sequence_count_fib_divisible_v1_1520064083_7056 | Let $u$ be the minimum value of $x + y$ over all ordered pairs $(x, y)$ of positive integers such that $xy = 93025$. Compute the number of positive integers $n$ with $1 \leq n \leq u$ for which the $n$th Fibonacci number is divisible by 3. | 152 | 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(93025)))), expr=Sum(Var("x"), Var("y")))),
"d": Const(3)... | NT | null | COUNT | sympy | B3 | [
"B3"
] | 0cd20d | sequence_count_fib_divisible_v1 | null | 5 | 0 | [
"B3"
] | 1 | 0.027 | 2026-02-08T08:43:46.604046Z | {
"verified": true,
"answer": 152,
"timestamp": "2026-02-08T08:43:46.631029Z"
} | a3f6f7 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 116,
"completion_tokens": 1319
},
"timestamp": "2026-02-13T20:56:41.265Z",
"answer": 152
},
{
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
}
] | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
9034cb | modular_mod_compute_v1_601307018_5795 | Let $a$ be the minimum value of $|x - y|$ over all ordered pairs $(x, y)$ of positive integers such that $xy = 24339252$. Find the remainder when $a$ is divided by $29241$. | 3,481 | graphs = [
Graph(
let={
"a": 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(24339252)))), expr=Abs(arg=Sub(left=Var(name='x'), right=Var(name='y')))... | NT | null | COMPUTE | sympy | B3_DIFF | [
"B3_DIFF"
] | b47ea7 | modular_mod_compute_v1 | null | 3 | 0 | [
"B3_DIFF"
] | 1 | 0.003 | 2026-03-10T06:20:21.661900Z | {
"verified": true,
"answer": 3481,
"timestamp": "2026-03-10T06:20:21.665394Z"
} | 8bcd4e | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 162,
"completion_tokens": 7464
},
"timestamp": "2026-04-19T02:55:49.278Z",
"answer": 26500
},
{
... | 0 | [
{
"lemma": "B3_DIFF",
"status": "ok"
},
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
}
] | {
"lo": 2.1,
"mid": 5.36,
"hi": 8.63
} | ||
eb9686 | lin_form_endings_v1_677425708_330 | Let $a = 4$ and $b = 14$. Let $A = 8$ and $B = 45$. Let $g = \gcd(a, b)$, and define $a' = \left\lfloor \frac{a}{g} \right\rfloor$ and $b' = \left\lfloor \frac{b}{g} \right\rfloor$. Let $T$ be a set whose size is given by
$$
|T| = a'A + b'B - a'b'.
$$
The total number of lattice points satisfying certain bounds is
$... | 51,388 | graphs = [
Graph(
let={
"a_coeff": Const(4),
"b_coeff": Const(14),
"A_val": Const(8),
"B_val": Const(45),
"g_step": GCD(a=Ref("a_coeff"), b=Ref("b_coeff")),
"ap_node": Floor(Div(Ref("a_coeff"), Ref("g_step"))),
"bp_node": Fl... | COMB | NT | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | lin_form_endings_v1 | null | 6 | null | [
"LIN_FORM"
] | 1 | 0.003 | 2026-02-08T03:13:22.820895Z | {
"verified": true,
"answer": 51388,
"timestamp": "2026-02-08T03:13:22.823839Z"
} | 292efa | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 299,
"completion_tokens": 478
},
"timestamp": "2026-02-08T20:27:51.405Z",
"answer": 51388
},
{
"i... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "LIN_F... | {
"lo": -3.46,
"mid": 1.03,
"hi": 5.49
} | ||
561b72 | nt_num_divisors_compute_v1_48377204_34 | Let $n = \sum_{k=1}^{88} \phi(k) \left\lfloor \frac{88}{k} \right\rfloor$, where $\phi(k)$ denotes Euler's totient function. Let $Q = 33856 - d(n)$, where $d(n)$ denotes the number of positive divisors of $n$. Compute $Q$. | 33,844 | graphs = [
Graph(
let={
"_n": Const(88),
"n": Summation(var="k", start=Const(1), end=Ref("_n"), expr=Mul(EulerPhi(n=Var("k")), Floor(Div(Const(88), Var("k"))))),
"result": NumDivisors(n=Ref("n")),
"_c": Const(33856),
"Q": Sub(Ref("_c"), Ref("result... | NT | null | COMPUTE | sympy | K2 | [
"K2"
] | 6897ab | nt_num_divisors_compute_v1 | null | 5 | 0 | [
"K2"
] | 1 | 0.003 | 2026-02-08T15:09:00.880679Z | {
"verified": true,
"answer": 33844,
"timestamp": "2026-02-08T15:09:00.883459Z"
} | e9a53d | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 121,
"completion_tokens": 993
},
"timestamp": "2026-02-16T01:40:34.486Z",
"answer": 33844
},
{... | 1 | [
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K2",
"status": "ok"
},
{
"lemma": "V8",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
40d9c4 | sequence_count_fib_divisible_v1_153355830_1256 | Let $n$ be a positive integer. Define $u$ to be the largest positive divisor of $707990$ that is at most $830$. Find the number of positive integers $n \leq u$ such that $16$ divides the $n$-th Fibonacci number. | 69 | graphs = [
Graph(
let={
"_n": Const(830),
"upper": MaxOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Const(1)), Leq(Var("d"), Ref("_n")), Divides(divisor=Var("d"), dividend=Const(707990))))),
"d": Const(16),
"result": CountOverSet(set=Solut... | NT | null | COUNT | sympy | MAX_DIVISOR | [
"MAX_DIVISOR"
] | 51757e | sequence_count_fib_divisible_v1 | null | 6 | 0 | [
"MAX_DIVISOR"
] | 1 | 0.051 | 2026-02-08T06:13:08.840384Z | {
"verified": true,
"answer": 69,
"timestamp": "2026-02-08T06:13:08.891460Z"
} | c0d456 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 104,
"completion_tokens": 1985
},
"timestamp": "2026-02-12T21:44:39.113Z",
"answer": 69
},
{
... | 1 | [
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "MAX_DIVISOR",
"status": "ok"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
}
] | {
"lo": -3.51,
"mid": 1.33,
"hi": 6.56
} | ||
ff7f5d | antilemma_sum_equals_v1_153355830_1357 | Let $N$ be the number of integers $t$ for which there exist integers $a$ and $b$ satisfying $1\le a\le 7$, $1\le b\le 11$, $16\le t\le 136$, and
$$t=10a+6b.$$
Let $X$ be the number of ordered pairs $(i,j)$ of integers with $1\le i\le 52$, $1\le j\le 52$, and
$$i+j=N.$$
Let $C$ be the number of ordered pairs $(u,v)$ of ... | 60,504 | graphs = [
Graph(
let={
"_n": CountOverSet(set=SolutionsSet(var=Var("t"), condition=Exists(var=Var(name='a'), condition=Exists(var=Var(name='b'), condition=And(Geq(left=Var(name='a'), right=Const(value=1)), Leq(left=Var(name='a'), right=Const(value=7)), Geq(left=Var(name='b'), right=Const(value=... | COMB | GEOM | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM/COUNT_CARTESIAN/COUNT_SUM_EQUALS",
"COUNT_CARTESIAN",
"COUNT_SUM_EQUALS"
] | 0c98fd | antilemma_sum_equals_v1 | two_stage_modexp | 4 | 0 | [
"COUNT_CARTESIAN",
"COUNT_SUM_EQUALS",
"LIN_FORM"
] | 3 | 0.01 | 2026-02-08T06:20:45.453982Z | {
"verified": true,
"answer": 60504,
"timestamp": "2026-02-08T06:20:45.464021Z"
} | 096847 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 304,
"completion_tokens": 32768
},
"timestamp": "2026-02-24T06:04:36.126Z",
"answer": null
},
{
... | 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": "ok"
},
{
"lemma": "LIN_F... | {
"lo": 3.43,
"mid": 5.73,
"hi": 8.84
} | ||
cad581 | antilemma_k3_v1_1918700295_320 | Compute the sum of $\phi(d)$ over all positive divisors $d$ of $40393$, where $\phi$ denotes Euler's totient function. | 40,393 | graphs = [
Graph(
let={
"x": SumOverDivisors(n=Const(value=40393), var='d', expr=EulerPhi(n=Var(name='d'))),
},
goal=Ref("x"),
)
] | NT | COMB | COMPUTE | sympy | K3 | [
"K3"
] | 54c41e | antilemma_k3_v1 | null | 4 | 0 | [
"K3"
] | 1 | 0.001 | 2026-02-08T03:09:30.031425Z | {
"verified": true,
"answer": 40393,
"timestamp": "2026-02-08T03:09:30.032483Z"
} | 937731 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 142,
"completion_tokens": 743
},
"timestamp": "2026-02-10T13:21:39.462Z",
"answer": 40393
},
{
"i... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "K3",
"status": "ok"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
}
] | {
"lo": -3.53,
"mid": 1.02,
"hi": 5.49
} | ||
984c67 | alg_sym_quad_system_v1_1218484723_4963 | Let $M$ be the number of ordered pairs $(a_1, b_1)$ of positive integers with $1 \leq a_1, b_1 \leq 30$ such that $20b_1^2 + 41a_1^2 - 12a_1b_1 \leq 33073$. Let $R$ be the sum of $a^4 + b^4 + c^4$ over all positive integer triples $(a, b, c)$ satisfying $a^2 + b^2 + c^2 = ab + bc + ca$, $4a + 5b + c = 4830$, taken modu... | 64,549 | graphs = [
Graph(
let={
"_n": Const(20),
"result": Mod(value=SumOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("a"), Var("b"), Var("c")]), condition=And(Eq(Sum(Pow(Var("a"), Const(2)), Pow(Var("b"), Const(2)), Pow(Var("c"), Const(2))), Sum(Mul(Var("a"), Var("b")), Mu... | ALG | null | COMPUTE | sympy | QF_PSD_COUNT_LEQ | [
"QF_PSD_COUNT_LEQ"
] | 81217a | alg_sym_quad_system_v1 | negation_mod | 6 | 0 | [
"QF_PSD_COUNT_LEQ"
] | 1 | 0.014 | 2026-02-25T06:35:34.758743Z | {
"verified": true,
"answer": 64549,
"timestamp": "2026-02-25T06:35:34.772972Z"
} | 651ba7 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 273,
"completion_tokens": 10751
},
"timestamp": "2026-03-29T18:46:34.676Z",
"answer": 64549
},
{
... | 1 | [
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "QF_PSD_COUNT_LEQ",
"status": "ok"
}
] | {
"lo": -3.33,
"mid": 1.03,
"hi": 5.26
} |
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