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 |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
0871c4 | algebra_poly_eval_v1_124444284_7685 | Let $b = 7$ and $n = 6$. Define
$$
r = 2b^4 + 3b^3 + 4b^2 + n b + 1.
$$
Let $M$ be the largest positive divisor $d$ of $4124897$ such that $1 \leq d \leq 2023$. Compute the remainder when $M - r$ is divided by $75164$. | 71,117 | graphs = [
Graph(
let={
"_n": Const(6),
"b": Const(7),
"result": Sum(Mul(Const(2), Pow(Ref("b"), Const(4))), Mul(Const(3), Pow(Ref("b"), Const(3))), Mul(Const(4), Pow(Ref("b"), Const(2))), Mul(Ref("_n"), Ref("b")), Const(1)),
"Q": Mod(value=Sub(MaxOverSet(set=... | NT | null | COMPUTE | sympy | MAX_DIVISOR | [
"MAX_DIVISOR"
] | ad1a9b | algebra_poly_eval_v1 | negation_mod | 4 | 0 | [
"MAX_DIVISOR"
] | 1 | 0.002 | 2026-02-08T09:17:01.934172Z | {
"verified": true,
"answer": 71117,
"timestamp": "2026-02-08T09:17:01.936142Z"
} | e7d93f | 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": 7382
},
"timestamp": "2026-02-14T02:57:26.178Z",
"answer": 71117
},
... | 1 | [
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "MAX_DIVISOR",
"status": "ok"
}... | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
04d355 | comb_bell_compute_v1_397696148_271 | Let $n$ be the number of integers $t$ with $5 \le t \le 14$ for which there exist positive integers $a$ and $b$ such that $1 \le a \le 2$, $1 \le b \le 4$, and $t = 3a + 2b$. Let $B_n$ denote the $n$th Bell number, which counts the number of partitions of a set of $n$ elements. Define $Q$ to be the remainder when $8541... | 15,732 | graphs = [
Graph(
let={
"_n": Const(82656),
"n": CountOverSet(set=SolutionsSet(var=Var("t"), condition=Exists(var=Var(name='a'), condition=Exists(var=Var(name='b'), condition=And(Geq(left=Var(name='a'), right=Const(value=1)), Leq(left=Var(name='a'), right=Const(value=2)), Geq(left=Va... | COMB | null | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | comb_bell_compute_v1 | null | 4 | 0 | [
"LIN_FORM"
] | 1 | 0.001 | 2026-02-08T11:24:10.667746Z | {
"verified": true,
"answer": 15732,
"timestamp": "2026-02-08T11:24:10.668874Z"
} | 35dd80 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 242,
"completion_tokens": 1311
},
"timestamp": "2026-02-24T13:41:17.692Z",
"answer": 15732
},
{
"... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
}
] | {
"lo": -2.35,
"mid": 1.22,
"hi": 4.84
} | ||
53da6f | nt_count_intersection_v1_458359167_4986 | Let $N_0$ be the number of integers $t$ with $9\le t\le 55$ for which there exist integers $a$ and $b$ satisfying $1\le a\le 7$, $1\le b\le 5$, and
$$t=5a+4b.$$
Let $S$ be the set of all integers $n$ with $1\le n\le 348$ such that $3$ divides the $n$th Fibonacci number $F_n$. Let $M$ be the number of elements of $S$.
... | 6,666 | 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=... | NT | null | COUNT | sympy | LIN_FORM | [
"LIN_FORM/SUM_DIVISIBLE/C5",
"COUNT_FIB_DIVISIBLE/C5"
] | 35d971 | nt_count_intersection_v1 | null | 8 | 0 | [
"C5",
"COUNT_FIB_DIVISIBLE",
"LIN_FORM",
"SUM_DIVISIBLE"
] | 4 | 2.771 | 2026-02-08T12:10:08.841156Z | {
"verified": true,
"answer": 6666,
"timestamp": "2026-02-08T12:10:11.612192Z"
} | 0abe25 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 324,
"completion_tokens": 2985
},
"timestamp": "2026-02-14T23:07:11.532Z",
"answer": 6666
},
{... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "C5",
"status": "ok_later"
},
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "ok"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status":... | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
0498c2 | nt_num_divisors_compute_v1_655260480_3703 | Let $S$ be the set of all ordered pairs $(x_1, y_1)$ of positive integers such that $x_1 y_1 = 144$. Let $T$ be the set of all values $x_1 + y_1$ where $(x_1, y_1) \in S$. Define $m$ to be the minimum value in $T$. Now, let $U$ be the set of all ordered pairs $(x, y)$ of positive integers such that $x + y = m$. Define ... | 15,225 | graphs = [
Graph(
let={
"_m": Const(85559),
"_n": Const(86574),
"n": MaxOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(Sum(Var("x"), Var("y")), MinOverSet(set... | NT | null | COMPUTE | sympy | B3 | [
"B3/B1"
] | 7f76f7 | nt_num_divisors_compute_v1 | null | 4 | 0 | [
"B1",
"B3"
] | 2 | 0.005 | 2026-02-08T17:30:40.897079Z | {
"verified": true,
"answer": 15225,
"timestamp": "2026-02-08T17:30:40.901792Z"
} | 551472 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 219,
"completion_tokens": 985
},
"timestamp": "2026-02-18T03:26:23.331Z",
"answer": 15225
},
{... | 1 | [
{
"lemma": "B1",
"status": "ok_later"
},
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
},
... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
a85270 | comb_count_partitions_v1_655260480_3174 | Let $n$ be the number of integers $t$ such that $10 \leq t \leq 100$ and there exist positive integers $a$ and $b$ with $1 \leq a \leq 4$, $1 \leq b \leq 19$, and $t = 6a + 4b$. Let $p(n)$ denote the number of integer partitions of $n$. Find the value of $p(n)$. | 75,175 | 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_partitions_v1 | null | 5 | 0 | [
"LIN_FORM"
] | 1 | 0.001 | 2026-02-08T17:13:47.755965Z | {
"verified": true,
"answer": 75175,
"timestamp": "2026-02-08T17:13:47.757443Z"
} | 61ed7b | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 139,
"completion_tokens": 2607
},
"timestamp": "2026-02-17T22:41:59.284Z",
"answer": 75175
},
... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "V8",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
... | {
"lo": -2.38,
"mid": 1.74,
"hi": 6.59
} | ||
b19bfb | algebra_poly_eval_v1_151522320_233 | Compute the value of
$$
\left( \sum_{k=1}^{4} \phi(k) \left\lfloor \frac{4}{k} \right\rfloor \right) \cdot 7^3 - 3 \cdot 7^2 + 8 \cdot 7 - 9.
$$ | 3,330 | graphs = [
Graph(
let={
"_n": Const(2),
"k": Const(7),
"result": Sum(Mul(Summation(var="k", start=Const(1), end=Const(4), expr=Mul(EulerPhi(n=Var("k")), Floor(Div(Const(4), Var("k"))))), Pow(Ref("k"), Const(3))), Mul(Const(-3), Pow(Ref("k"), Ref("_n"))), Mul(Const(8), Ref... | NT | null | COMPUTE | sympy | K2 | [
"K2"
] | 6897ab | algebra_poly_eval_v1 | null | 4 | 0 | [
"K2"
] | 1 | 0.002 | 2026-02-08T03:05:28.716018Z | {
"verified": true,
"answer": 3330,
"timestamp": "2026-02-08T03:05:28.718326Z"
} | 615fcc | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 183,
"completion_tokens": 354
},
"timestamp": "2026-02-10T13:05:30.134Z",
"answer": 3330
},
{
"id... | 1 | [
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "K2",
"status": "ok"
},
{
"lemma": "V3",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
}
] | {
"lo": -7.01,
"mid": -4.68,
"hi": -2.15
} | ||
25ee83 | sequence_fibonacci_compute_v1_458359167_1195 | Let $n$ be the number of positive integers $t$ such that $10 \leq t \leq 56$ and there exist positive integers $a$ and $b$ with $1 \leq a \leq 4$, $1 \leq b \leq 8$, and $t = 6a + 4b$. Compute the $n$th Fibonacci number. (Define the Fibonacci sequence by $F_1 = 1$, $F_2 = 1$, and $F_k = F_{k-1} + F_{k-2}$ for $k \geq 3... | 17,711 | 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... | NT | null | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | sequence_fibonacci_compute_v1 | null | 5 | 0 | [
"LIN_FORM"
] | 1 | 0.001 | 2026-02-08T04:29:19.549440Z | {
"verified": true,
"answer": 17711,
"timestamp": "2026-02-08T04:29:19.550295Z"
} | f57060 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 245,
"completion_tokens": 2150
},
"timestamp": "2026-02-10T16:53:22.069Z",
"answer": 17711
},
{
... | 1 | [
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "V3",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
}
] | {
"lo": -3.42,
"mid": 1.86,
"hi": 7.55
} | ||
21041d | comb_sum_binomial_mod_v1_458359167_1686 | Let $m = 3353$. Define $n$ to be the number of nonnegative integers $j \leq m$ such that $\binom{3353}{j}$ is odd. For each positive integer $k \leq n$, define $t_k = \binom{s}{k}$, where $s$ is the number of integers $t$ with $8 \leq t \leq 90$ that can be expressed as $3a + 5b$ for positive integers $a \leq 5$ and $b... | 2,118 | graphs = [
Graph(
let={
"_m": Const(3353),
"_n": CountOverSet(set=SolutionsSet(var=Var("j"), condition=And(Geq(Var("j"), Const(0)), Leq(Var("j"), Ref("_m")), Eq(Mod(value=Binom(n=Const(3353), k=Var("j")), modulus=Const(2)), Const(1))), domain='nonnegative_integers')),
"su... | ALG | COMB | COMPUTE | sympy | V8 | [
"V8/LIN_FORM"
] | e9c298 | comb_sum_binomial_mod_v1 | null | 6 | 0 | [
"LIN_FORM",
"V8"
] | 2 | 0.007 | 2026-02-08T04:48:05.487132Z | {
"verified": true,
"answer": 2118,
"timestamp": "2026-02-08T04:48:05.493924Z"
} | 235371 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 256,
"completion_tokens": 32768
},
"timestamp": "2026-02-24T01:53:41.216Z",
"answer": null
},
{
... | 1 | [
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok_later"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "V8",
"status": "ok"
... | {
"lo": 3.43,
"mid": 5.73,
"hi": 8.84
} | ||
a868a3 | algebra_poly_eval_v1_1470522791_1636 | Let $p$ and $q$ be positive integers. Define $b$ as the number of positive integers $p$ for which there exists a positive integer $q$ such that $pq = 17640$, $\gcd(p, q) = 1$, and $p < q$. Let $T$ be the set of all ordered pairs $(x, y)$ of positive integers such that $xy = 4$. For each such pair, compute $x + y$, and ... | 28,082 | graphs = [
Graph(
let={
"_n": Const(4),
"b": CountOverSet(set=SolutionsSet(var=Var("p"), condition=And(IsPositive(arg=Var(name='p')), Exists(var=Var(name='q'), condition=And(Eq(left=Mul(Var(name='p'), Var(name='q')), right=Const(value=17640)), Eq(left=GCD(a=Var(name='p'), b=Var(name=... | NT | null | COMPUTE | sympy | COPRIME_PAIRS | [
"COPRIME_PAIRS",
"B3"
] | 1999ea | algebra_poly_eval_v1 | null | 6 | 0 | [
"B3",
"COPRIME_PAIRS"
] | 2 | 0.007 | 2026-02-08T13:47:33.813953Z | {
"verified": true,
"answer": 28082,
"timestamp": "2026-02-08T13:47:33.821041Z"
} | ab16f0 | 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": 1678
},
"timestamp": "2026-02-15T21:10:15.084Z",
"answer": 28082
},
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
... | {
"lo": -5.49,
"mid": 0.22,
"hi": 6.51
} | ||
fae003 | comb_bell_compute_v1_153355830_1258 | Let $n$ be the number of positive integers $p$ for which there exists a positive integer $q$ such that $pq = 2520$, $\gcd(p, q) = 1$, and $p < q$. 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 $44121 \cdot B_n$ is divided by $84934$. | 52,840 | graphs = [
Graph(
let={
"_n": Const(44121),
"n": CountOverSet(set=SolutionsSet(var=Var("p"), condition=And(IsPositive(arg=Var(name='p')), Exists(var=Var(name='q'), condition=And(Eq(left=Mul(Var(name='p'), Var(name='q')), right=Const(value=2520)), Eq(left=GCD(a=Var(name='p'), b=Var(na... | NT | COMB | COMPUTE | sympy | COPRIME_PAIRS | [
"COPRIME_PAIRS"
] | 2bb3aa | comb_bell_compute_v1 | null | 5 | 0 | [
"COPRIME_PAIRS"
] | 1 | 0.002 | 2026-02-08T06:13:08.914114Z | {
"verified": true,
"answer": 52840,
"timestamp": "2026-02-08T06:13:08.916009Z"
} | 5fe7ce | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 143,
"completion_tokens": 2728
},
"timestamp": "2026-02-12T21:46:04.169Z",
"answer": 52840
},
... | 1 | [
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "V1",
"status": "no"
}
] | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
42a32a | modular_modexp_compute_v1_458359167_1042 | Let $a = 41$. Define $e$ to be the number of integers $n$ such that $1 \leq n \leq 8701$ and $\gcd(n, 10) = 1$. Let $m = 52900$ and let $r$ be the remainder when $a^e$ is divided by $m$. Compute the remainder when $44121 \cdot r$ is divided by $71759$. Find the value of this remainder. | 5,935 | graphs = [
Graph(
let={
"_n": Const(71759),
"a": Const(41),
"e": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Const(8701)), Eq(GCD(a=Var("n"), b=Const(10)), Const(1))))),
"m": Const(52900),
"resul... | NT | null | COMPUTE | sympy | C4 | [
"C4"
] | 08d162 | modular_modexp_compute_v1 | null | 5 | 0 | [
"C4"
] | 1 | 0.002 | 2026-02-08T04:14:46.567172Z | {
"verified": true,
"answer": 5935,
"timestamp": "2026-02-08T04:14:46.569101Z"
} | 4d5624 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 212,
"completion_tokens": 5191
},
"timestamp": "2026-02-10T15:53:48.423Z",
"answer": 5935
},
{
"... | 1 | [
{
"lemma": "C4",
"status": "ok"
},
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
}
] | {
"lo": -3.42,
"mid": 1.86,
"hi": 7.55
} | ||
afbcbd | modular_sum_quadratic_residues_v1_677425708_2169 | Let $n = 4$ and let $p$ be the largest prime number not exceeding $101$. Define $r = \frac{p(p-1)}{n}$. Find the value of $r$. | 2,525 | graphs = [
Graph(
let={
"_n": Const(4),
"p": MaxOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(2)), Leq(Var("n"), Const(101)), IsPrime(Var("n"))))),
"result": Div(Mul(Ref("p"), Sub(Ref("p"), Const(1))), Ref("_n")),
},
goal=Ref("re... | NT | null | SUM | sympy | MAX_PRIME_BELOW | [
"MAX_PRIME_BELOW"
] | dc3ad3 | modular_sum_quadratic_residues_v1 | null | 3 | 0 | [
"MAX_PRIME_BELOW"
] | 1 | 0.001 | 2026-02-08T04:49:54.854554Z | {
"verified": true,
"answer": 2525,
"timestamp": "2026-02-08T04:49:54.855638Z"
} | 4ff85a | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 155,
"completion_tokens": 211
},
"timestamp": "2026-02-11T22:08:57.476Z",
"answer": 2525
},
{
"i... | 1 | [
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "V3",
"status": "no"
}
] | {
"lo": -7.01,
"mid": -4.68,
"hi": -2.15
} | ||
ff25d7 | modular_mod_compute_v1_1820931509_286 | Let $S$ be the set of all ordered pairs of positive integers $(x, y)$ such that $xy = 9$. Let $s_{\min}$ be the minimum value of $x + y$ over all pairs $(x, y) \in S$. Let $A$ be the set of all ordered pairs of positive integers $(x, y)$ such that $x + y = s_{\min}$. Let $a$ be the maximum value of $xy$ over all pairs ... | 4,819 | graphs = [
Graph(
let={
"_m": Const(58715),
"_n": Const(65452),
"a": MaxOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(Sum(Var("x"), Var("y")), MinOverSet(set... | NT | null | COMPUTE | sympy | B3 | [
"B3/B1"
] | 7f76f7 | modular_mod_compute_v1 | null | 4 | 0 | [
"B1",
"B3"
] | 2 | 0.007 | 2026-02-08T11:28:02.830283Z | {
"verified": true,
"answer": 4819,
"timestamp": "2026-02-08T11:28:02.836849Z"
} | 43553f | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 251,
"completion_tokens": 1738
},
"timestamp": "2026-02-14T14:39:02.480Z",
"answer": 4819
},
{... | 1 | [
{
"lemma": "B1",
"status": "ok_later"
},
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "V3",
"status": "no"
},
{
... | {
"lo": -8.26,
"mid": -5.01,
"hi": -1.76
} | ||
2c54bb | comb_count_permutations_fixed_v1_1419126231_195 | Let $D_n$ denote the number of derangements of $n$ elements. Let $S$ be the set of integers $a$ with $0 \leq a \leq 7920$ such that $\left((a^2 - 1437) \bmod 7921\right)^2 - 1437 \equiv a \pmod{7921}$ and $(a^2 - 1437) \not\equiv a \pmod{7921}$. Let $k = \binom{|S|}{0} - 1$ and $n = 8$. Compute $\binom{n}{k} \cdot D_{n... | 14,833 | graphs = [
Graph(
let={
"_n": Const(2),
"n": Const(8),
"k": Sub(Binom(n=CountOverSet(set=SolutionsSet(var=Var("a"), condition=And(Geq(Var("a"), Const(0)), Leq(Var("a"), Const(7920)), Eq(Mod(value=Sum(Pow(Mod(value=Sum(Pow(Var("a"), Const(2)), Const(-1437)), modulus=Const(... | COMB | null | COUNT | sympy | COMB1 | [
"POLY_ORBIT_HENSEL/ZERO_BINOM_0"
] | 4267fe | comb_count_permutations_fixed_v1 | null | 6 | 0 | [
"COMB1",
"POLY_ORBIT_HENSEL",
"ZERO_BINOM_0"
] | 3 | 0.434 | 2026-02-25T09:45:32.740626Z | {
"verified": true,
"answer": 14833,
"timestamp": "2026-02-25T09:45:33.174479Z"
} | b2d8fa | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 257,
"completion_tokens": 1286
},
"timestamp": "2026-03-30T07:27:24.916Z",
"answer": 14833
},
{
"... | 1 | [
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "POLY_ORBIT_HENSEL",
"status": "ok"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8_SUM"... | {
"lo": -5.37,
"mid": 0.23,
"hi": 5.22
} | ||
1bb2f5 | antilemma_sum_equals_v1_655260480_2421 | Let $n$ be the number of ordered pairs $(i, j)$ such that $1 \leq i \leq 5$ and $1 \leq j \leq 11$. Compute the number of ordered pairs $(i, j)$ of integers such that $1 \leq i \leq 53$, $1 \leq j \leq 53$, and $i + j = n$. | 52 | graphs = [
Graph(
let={
"_n": CountOverSet(set=CartesianProduct(left=IntegerRange(start=Const(1), end=Const(5)), right=IntegerRange(start=Const(1), end=Const(11)))),
"x": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("i"), Var("j")]), condition=Eq(Sum(Var("i"), Var("j")), Ref... | COMB | GEOM | COMPUTE | sympy | COMB1 | [
"COUNT_CARTESIAN/COUNT_SUM_EQUALS",
"COUNT_SUM_EQUALS"
] | 8bee9e | antilemma_sum_equals_v1 | null | 3 | 0 | [
"COMB1",
"COUNT_CARTESIAN",
"COUNT_SUM_EQUALS"
] | 3 | 0.063 | 2026-02-08T16:42:47.708388Z | {
"verified": true,
"answer": 52,
"timestamp": "2026-02-08T16:42:47.770984Z"
} | 6c46cd | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 128,
"completion_tokens": 608
},
"timestamp": "2026-02-17T11:17:32.604Z",
"answer": 52
},
{
... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "ok"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "ok"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8",
"status": "no... | {
"lo": -5.64,
"mid": -3.17,
"hi": -0.81
} | ||
578145 | diophantine_fbi2_count_v1_784195855_9309 | Let $k$ be the number of positive integers $n$ with $1 \leq n \leq 10800$ such that $10$ divides the $n$-th Fibonacci number. Determine the number of positive integers $d$ with $2 \leq d \leq 112$ such that $d$ divides $k$, and $\frac{k}{d}$ is an integer between $3$ and $113$, inclusive. | 18 | graphs = [
Graph(
let={
"k": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Const(10800)), Divides(divisor=Const(10), dividend=Fibonacci(arg=Var(name='n')))))),
"result": CountOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(V... | NT | null | COUNT | sympy | COUNT_FIB_DIVISIBLE | [
"COUNT_FIB_DIVISIBLE"
] | 66de3c | diophantine_fbi2_count_v1 | null | 7 | 0 | [
"COUNT_FIB_DIVISIBLE"
] | 1 | 0.009 | 2026-02-08T16:41:01.174283Z | {
"verified": true,
"answer": 18,
"timestamp": "2026-02-08T16:41:01.183163Z"
} | 6b49d4 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 135,
"completion_tokens": 2114
},
"timestamp": "2026-02-17T09:29:25.270Z",
"answer": 18
},
{
... | 1 | [
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "ok"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
}... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
77c8d7 | nt_count_divisible_and_v1_1456120455_44 | Let $S$ be the set of all positive integers $n$ such that $1 \le n \le 65196$, $n$ is divisible by $6$, and the remainder when $n$ is divided by $9$ equals $\sum_{d \mid 46} \mu(d)$, where $\mu$ denotes the Möbius function. Let $N = |S|$. Compute the remainder when $98381 \cdot N$ is divided by $65808$. | 51,470 | graphs = [
Graph(
let={
"upper": Const(65196),
"d1": Const(6),
"d2": Const(9),
"result": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Ref("upper")), Eq(Mod(value=Var("n"), modulus=Ref("d1")), Const(0)), Eq(Mo... | NT | null | COUNT | sympy | MOBIUS_SUM | [
"MOBIUS_SUM"
] | 518e32 | nt_count_divisible_and_v1 | null | 4 | 0 | [
"MOBIUS_SUM"
] | 1 | 8.472 | 2026-02-08T02:51:22.513120Z | {
"verified": true,
"answer": 51470,
"timestamp": "2026-02-08T02:51:30.984896Z"
} | b44a4f | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 216,
"completion_tokens": 5916
},
"timestamp": "2026-02-08T19:55:01.807Z",
"answer": 51470
},
{
"... | 1 | [
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "MOBIUS_SUM",
"status": "ok"
},
{
"lemma": "V8_SUM",
"status": "no"
}
] | {
"lo": -6.51,
"mid": -0.53,
"hi": 4.75
} | ||
cac18b | nt_min_coprime_above_v1_397696148_1581 | Let $s = 1936$ and let $d_{\min}$ be the smallest divisor of $14687919293$ that is at least $2$. Let $r$ be the smallest integer $n$ such that $n > s$, $n \leq d_{\min}$, and $\gcd(n, 495) = 1$. Let $c$ be the maximum value of $xy$ over all pairs of positive integers $(x, y)$ such that $x + y = 46$. Find the remainder ... | 77,178 | graphs = [
Graph(
let={
"_n": Const(78586),
"start": Const(1936),
"upper": MinOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Const(2)), Divides(divisor=Var("d"), dividend=Const(14687919293))))),
"modulus": Const(495),
"result": ... | NT | null | EXTREMUM | sympy | B1 | [
"B1",
"MIN_PRIME_FACTOR"
] | 58e2b8 | nt_min_coprime_above_v1 | negation_mod | 6 | 0 | [
"B1",
"MIN_PRIME_FACTOR"
] | 2 | 0.067 | 2026-02-08T12:39:14.973861Z | {
"verified": true,
"answer": 77178,
"timestamp": "2026-02-08T12:39:15.040845Z"
} | 0fc181 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 167,
"completion_tokens": 7256
},
"timestamp": "2026-02-15T03:11:38.749Z",
"answer": 77178
},
... | 1 | [
{
"lemma": "B1",
"status": "ok"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "MIN_PRIME_FACTOR",
"status": "ok"
},
{
"lemma": "V1",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
},
{
"lemma"... | {
"lo": -6.96,
"mid": -4.56,
"hi": -1.46
} | ||
d80a3b | algebra_poly_eval_v1_601307018_4439 | Let $m$ be the number of non-negative integers $a$ with $0 \le a \le 528$ such that $M = a^5 + 5a^4 + 5a^3 + 4a^2 - 5a + 2 \bmod 529$, $R = M^5 + 5M^4 + 5M^3 + 4M^2 - 5M + 2 \bmod 529$, and $R = a$ but $M \ne a$. Let $S = m^3 - 8m^2 + 9m + 9$. Find the remainder when $50261S$ is divided by $98889$. | 15,502 | graphs = [
Graph(
let={
"_n": Const(4),
"m": CountOverSet(set=SolutionsSet(var=Var("a"), condition=And(Geq(Var("a"), Const(0)), Leq(Var("a"), Const(528)), Eq(Ref("_po_p2"), Var("a")), Neq(Ref("_po_p1"), Var("a"))))),
"result": Sum(Pow(Ref("m"), Const(3)), Mul(Const(-8), P... | ALG | null | COMPUTE | sympy | POLY_ORBIT_HENSEL | [
"POLY_ORBIT_HENSEL"
] | 53b6eb | algebra_poly_eval_v1 | null | 7 | 0 | [
"POLY_ORBIT_HENSEL"
] | 1 | 2.328 | 2026-03-10T04:59:56.681863Z | {
"verified": true,
"answer": 15502,
"timestamp": "2026-03-10T04:59:59.009811Z"
} | f6c4e0 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 261,
"completion_tokens": 32768
},
"timestamp": "2026-03-29T12:14:37.787Z",
"answer": null
},
{
... | 1 | [
{
"lemma": "POLY_ORBIT_HENSEL",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
}
] | {
"lo": 3.34,
"mid": 5.77,
"hi": 8.89
} | ||
bd8c67 | diophantine_sum_product_min_v1_151522320_2572 | Let $S = 38$ and $P = 361$. Let $T$ be the set of all integers $n$ such that $1 \leq n \leq 37$ and $n \equiv 0 \pmod{37}$. Define $U$ to be the sum of all elements of $T$. Determine the smallest positive integer $x$ such that $1 \leq x \leq U$ and $x(S - x) = P$. | 19 | graphs = [
Graph(
let={
"S": Const(38),
"P": Const(361),
"result": MinOverSet(set=SolutionsSet(var=Var("x"), condition=And(Geq(Var("x"), Const(1)), Leq(Var("x"), SumOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Const(37)), Eq(... | NT | null | EXTREMUM | sympy | LIN_FORM | [
"SUM_DIVISIBLE"
] | 02dbe3 | diophantine_sum_product_min_v1 | null | 4 | 0 | [
"LIN_FORM",
"SUM_DIVISIBLE"
] | 2 | 0.132 | 2026-02-08T04:52:55.891391Z | {
"verified": true,
"answer": 19,
"timestamp": "2026-02-08T04:52:56.023401Z"
} | 272120 | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 158,
"completion_tokens": 697
},
"timestamp": "2026-02-11T22:01:46.497Z",
"answer": 19
},
{
"id": 11,
... | 2 | [
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "SUM_DIVISIBLE",
"status": "ok"
},
{
"lemma": "V5",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
}
] | {
"lo": -10,
"mid": -7.73,
"hi": -5.46
} | ||
f27f6d | modular_count_residue_v1_153355830_1436 | Let $S$ be the set of all integers $t$ such that $26 \leq t \leq 62$ and there exist positive integers $a$ and $b$ with $1 \leq a \leq 3$, $1 \leq b \leq 5$, and $t = 10a + 4b + 12$. Let $m = |S|$. Let $r = \varphi(2)$, where $\varphi$ is Euler's totient function. Let $T$ be the set of all integers $n$ such that $r \le... | 2,641 | graphs = [
Graph(
let={
"upper": Const(39601),
"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=3)), Geq(left... | NT | null | COUNT | sympy | LIN_FORM | [
"LIN_FORM",
"ONE_PHI_2"
] | 9858be | modular_count_residue_v1 | null | 4 | 0 | [
"LIN_FORM",
"ONE_PHI_2"
] | 2 | 1.896 | 2026-02-08T06:23:36.952152Z | {
"verified": true,
"answer": 2641,
"timestamp": "2026-02-08T06:23:38.848315Z"
} | b2304d | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 252,
"completion_tokens": 1077
},
"timestamp": "2026-02-19T07:48:11.615Z",
"answer": 2641
}
] | 2 | [
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "ONE_PHI_2",
"status": "ok"
},
... | {
"lo": -10,
"mid": -6.47,
"hi": -2.95
} | ||
f624db | lin_form_endings_v1_1742523217_3423 | Let $a = 36$ and $b = 27$. Let $d = \gcd(a, b)$. Let $k = 15839$ and define $s = k \times d$. Compute the remainder when $s$ is divided by $55518$. | 31,515 | graphs = [
Graph(
let={
"a_coeff": Const(36),
"b_coeff": Const(27),
"_inner_result": GCD(a=Ref("a_coeff"), b=Ref("b_coeff")),
"_scale_k": Const(15839),
"_scaled": Mul(Ref("_scale_k"), Ref("_inner_result")),
"_mod_M": Const(55518),
... | COMB | NT | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | lin_form_endings_v1 | null | 2 | null | [
"LIN_FORM"
] | 1 | 0 | 2026-02-08T05:52:00.091607Z | {
"verified": true,
"answer": 31515,
"timestamp": "2026-02-08T05:52:00.092091Z"
} | d953a7 | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 121,
"completion_tokens": 309
},
"timestamp": "2026-02-11T23:18:37.754Z",
"answer": 31815
},
{
"id": 11... | 1 | [
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8_SUM",
... | {
"lo": -5.55,
"mid": -3.01,
"hi": 0.34
} | ||
51f03b | diophantine_product_count_v1_865884756_4144 | Let $m$ be the number of integers $n$ with $1\le n\le 7217$ such that $\gcd(n,15)=1$.
Let $k$ be the smallest possible value of $x+y$, where $x$ and $y$ are positive integers satisfying $xy=396900$.
Let $u$ be the sum of all integers $r$ such that
$$r^2-125r+m=0.$$
Let $U$ be the greatest prime number $p$ with $2\le ... | 18 | graphs = [
Graph(
let={
"_c": Const(15),
"_m": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Const(7217)), Eq(GCD(a=Var("n"), b=Ref("_c")), Const(1))))),
"_n": Const(2),
"k": MinOverSet(set=MapOverSet(set=Solu... | NT | null | COUNT | sympy | C4 | [
"C4/VIETA_SUM/MAX_PRIME_BELOW",
"B3"
] | 8d2515 | diophantine_product_count_v1 | null | 7 | 0 | [
"B3",
"C4",
"MAX_PRIME_BELOW",
"VIETA_SUM"
] | 4 | 0.012 | 2026-02-08T17:45:55.233323Z | {
"verified": true,
"answer": 18,
"timestamp": "2026-02-08T17:45:55.245465Z"
} | d93c4a | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 209,
"completion_tokens": 1738
},
"timestamp": "2026-02-18T08:11:14.929Z",
"answer": 18
},
{
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "C4",
"status": "ok"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
09b55f | comb_count_derangements_v1_1218484723_1803 | Let $D_n$ denote the number of derangements of $n$ elements. Define $h = \sum_{k=0}^{0} (-1)^k \binom{0}{k}$, $n = 7h$, $m = \sum_{k=0}^{7} (-1)^k \binom{7}{k}$, $S = 47961 + m$, $T = D_n$, and $v = \sum_{k=0}^{0} (-1)^k \binom{0}{k}$. Compute $S - T$. | 46,107 | graphs = [
Graph(
let={
"n3": Const(7),
"m": 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(0),
"v": 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 | 2 | 3 | [
"BINOMIAL_ALTERNATING"
] | 1 | 0.002 | 2026-02-25T03:27:59.738148Z | {
"verified": true,
"answer": 46107,
"timestamp": "2026-02-25T03:27:59.740495Z"
} | 7c0a57 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 232,
"completion_tokens": 1088
},
"timestamp": "2026-03-29T01:27:03.245Z",
"answer": 46107
},
{
"... | 1 | [
{
"lemma": "BINOMIAL_ALTERNATING",
"status": "ok"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
},
{
"lemma": "V8_... | {
"lo": -4.26,
"mid": -1.81,
"hi": 1.23
} | ||
9dacbd | antilemma_k3_v1_124444284_5078 | Let $x = \sum_{d \mid 66909} \phi(d)$, where $\phi$ denotes Euler's totient function. Let $r$ be the remainder when $|x|$ is divided by $11$. Compute the Bell number $B_r$, which is the number of partitions of a set of $r$ elements. | 877 | graphs = [
Graph(
let={
"x": SumOverDivisors(n=Const(value=66909), var='d', expr=EulerPhi(n=Var(name='d'))),
"Q": Bell(Mod(value=Abs(arg=Ref(name='x')), modulus=Const(11))),
},
goal=Ref("Q"),
)
] | NT | COMB | COMPUTE | sympy | K3 | [
"K3"
] | 54c41e | antilemma_k3_v1 | null | 4 | 0 | [
"K3"
] | 1 | 0.006 | 2026-02-08T06:23:08.225592Z | {
"verified": true,
"answer": 877,
"timestamp": "2026-02-08T06:23:08.231879Z"
} | 47e211 | 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": 480
},
"timestamp": "2026-02-12T23:37:00.856Z",
"answer": 877
},
{
... | 1 | [
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "K3",
"status": "ok"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
},
{
"lemma": "VAL_SUM_EQ",
"status": "no"
}
] | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
300eca | lin_form_endings_v1_458359167_4677 | Let $a = 24$, $b = 56$, $A = 25$, and $B = 14$. Let $g = \gcd(a, b)$ and define
$$
n = \left\lfloor \frac{aA + bB - a - b}{g} \right\rfloor + 1.
$$
Compute the remainder when $14461 \cdot n$ is divided by $99170$. | 90,694 | graphs = [
Graph(
let={
"a_coeff": Const(24),
"b_coeff": Const(56),
"A_val": Const(25),
"B_val": Const(14),
"g_step": GCD(a=Ref("a_coeff"), b=Ref("b_coeff")),
"numerator": Sub(Sum(Mul(Ref("a_coeff"), Ref("A_val")), Mul(Ref("b_coeff"), R... | COMB | NT | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | lin_form_endings_v1 | null | 3 | null | [
"LIN_FORM"
] | 1 | 0.002 | 2026-02-08T11:58:39.571849Z | {
"verified": true,
"answer": 90694,
"timestamp": "2026-02-08T11:58:39.573644Z"
} | 41fac3 | 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": 794
},
"timestamp": "2026-02-14T21:41:51.470Z",
"answer": 90694
},
{... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "V8_SUM",
"st... | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
c76b34 | comb_factorial_compute_v1_865884756_4573 | Let $n$ be the largest prime number such that $2 \leq n \leq 9$. Compute the remainder when $87031 \cdot n!$ is divided by $94558$. | 76,236 | graphs = [
Graph(
let={
"_n": Const(94558),
"n": MaxOverSet(set=SolutionsSet(var=Var("n1"), condition=And(Geq(Var("n1"), Const(2)), Leq(Var("n1"), Const(9)), IsPrime(Var("n1"))))),
"result": Factorial(Ref("n")),
"Q": Mod(value=Mul(Const(87031), Ref("result")),... | NT | null | COMPUTE | sympy | MAX_PRIME_BELOW | [
"MAX_PRIME_BELOW"
] | dc3ad3 | comb_factorial_compute_v1 | null | 3 | 0 | [
"MAX_PRIME_BELOW"
] | 1 | 0.004 | 2026-02-08T17:59:40.932909Z | {
"verified": true,
"answer": 76236,
"timestamp": "2026-02-08T17:59:40.936562Z"
} | 1bdf1a | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 87,
"completion_tokens": 1358
},
"timestamp": "2026-02-18T11:48:28.709Z",
"answer": 76236
},
{... | 1 | [
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "V1",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
79739b | nt_lcm_compute_v1_1918700295_663 | Let $N$ be the number of integers $t$ with $20 \leq t \leq 1400$ for which there exist positive integers $a$ and $b$ such that $1 \leq a \leq 219$, $1 \leq b \leq 146$, and
$$
t = 5a + 2b + 13.
$$
Let $a$ be the number of positive integers $n$ such that $1 \leq n \leq N$ and $\gcd(n, 10) = 1$. Let $b = 1537$, and defin... | 26,584 | graphs = [
Graph(
let={
"_n": Const(10),
"a": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), CountOverSet(set=SolutionsSet(var=Var("t"), condition=Exists(var=Var(name='a'), condition=Exists(var=Var(name='b'), condition=And(Geq(left=Va... | NT | null | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM/C4"
] | 067e5d | nt_lcm_compute_v1 | null | 5 | 0 | [
"C4",
"LIN_FORM"
] | 2 | 0.003 | 2026-02-08T03:22:09.003683Z | {
"verified": true,
"answer": 26584,
"timestamp": "2026-02-08T03:22:09.006839Z"
} | 6fb882 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 290,
"completion_tokens": 7640
},
"timestamp": "2026-02-10T14:10:18.074Z",
"answer": 26584
},
{
"... | 1 | [
{
"lemma": "C4",
"status": "ok_later"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemm... | {
"lo": 1.71,
"mid": 5.04,
"hi": 8.38
} | ||
40c4bf | geo_count_lattice_triangle_v1_124444284_4602 | Let $A$ be the area of a triangle with vertices at $(128, 9)$, $(21, 100)$, and $(0, 0)$, multiplied by 2. Let $B$ be the sum of the greatest common divisors of the absolute differences in coordinates along each side of the triangle, specifically:
$$
B = \gcd(|128 - 21|, |9 - 100|) + \gcd(|21 - 0|, |100 - 0|) + \gcd(|... | 6,305 | graphs = [
Graph(
let={
"area_2x": Abs(arg=Sum(Mul(Const(value=128), Const(value=100)), Mul(Const(value=21), Sub(left=Const(value=0), right=Const(value=9))))),
"boundary": Sum(GCD(a=Abs(arg=Const(value=128)), b=Abs(arg=Const(value=9))), GCD(a=Abs(arg=Sub(left=Const(value=21), right=C... | ALG | NT | COUNT | sympy | [] | geo_count_lattice_triangle_v1 | null | 5 | 0 | null | null | 0.003 | 2026-02-08T06:06:26.243143Z | {
"verified": true,
"answer": 6305,
"timestamp": "2026-02-08T06:06:26.245992Z"
} | d754bd | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 1,
"correct": {
"strict": false,
"boxed": false,
"relaxed": true
},
"usage": {
"prompt_tokens": 212,
"completion_tokens": 664
},
"timestamp": "2026-02-15T17:05:55.027Z",
"answer": 3153
},
{
"id": 11,
... | 1 | [] | {
"lo": -7.01,
"mid": -4.68,
"hi": -2.15
} | ||||
adefe5 | alg_qf_psd_sum_v1_1218484723_2956 | Find the remainder when $$\sum_{\substack{a=1 \\ b=1 \\ c=1 \\ d=1}}^{16} \left( 34d^2 + \left| \left\{ (a_1, b_1) : 1 \leq a_1 \leq 35,\ 1 \leq b_1 \leq \left| \left\{ (a_2, b_2) : 1 \leq a_2, b_2 \leq 35,\ -189a_2^3 = -137781 \right\} \right|,\ 16b_1^2 + 16a_1^2 - 32a_1b_1 = 256 \right\} \right| \cdot a \cdot d + 33a... | 17,134 | graphs = [
Graph(
let={
"_m": Const(2),
"_n": Const(2),
"result": Mod(value=SumOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("a"), Var("b"), Var("c"), Var("d")]), condition=And(Geq(Var("a"), Const(1)), Leq(Var("a"), Const(16)), Geq(Var("b"), Const(1)), L... | ALG | null | COMPUTE | sympy | POLY3_COUNT | [
"POLY3_COUNT/QF_PSD_COUNT"
] | 682a6e | alg_qf_psd_sum_v1 | null | 6 | 0 | [
"POLY3_COUNT",
"QF_PSD_COUNT"
] | 2 | 0.222 | 2026-02-25T04:42:02.556967Z | {
"verified": true,
"answer": 17134,
"timestamp": "2026-02-25T04:42:02.778809Z"
} | f32ddc | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 336,
"completion_tokens": 5025
},
"timestamp": "2026-03-29T07:30:46.388Z",
"answer": 37419
},
{
... | 1 | [
{
"lemma": "POLY3_COUNT",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "QF_PSD_COUNT",
"status": "ok_later"
}
] | {
"lo": 1.55,
"mid": 4.7,
"hi": 7.23
} | ||
a9f4c5 | nt_gcd_compute_v1_1742523217_1043 | Let $p = 7$, $h = ( (p-1)! + 1 ) \bmod p$, and $n = 485$. Define $s = \left( \sum_{d \mid n} \phi(d) \right) - n$, where $\phi$ is Euler's totient function. Let $a = 599963$ and $b = 1114217 + h + s$. Let $g = \gcd(a, b)$. Find the remainder when $44121 \cdot g$ is divided by $92410$. | 57,179 | graphs = [
Graph(
let={
"p": Const(7),
"h": Mod(value=Sum(Factorial(Sub(Ref("p"), Const(1))), Const(1)), modulus=Ref("p")),
"n": Const(485),
"s": Sub(SumOverDivisors(n=Ref(name='n'), var='d', expr=EulerPhi(n=Var(name='d'))), Ref("n")),
"a": Const(5... | NT | null | COMPUTE | sympy | EULER_TOTIENT_SUM | [
"EULER_TOTIENT_SUM",
"WILSON"
] | bd04a1 | nt_gcd_compute_v1 | null | 4 | 2 | [
"EULER_TOTIENT_SUM",
"WILSON"
] | 2 | 0.002 | 2026-02-08T03:23:53.773573Z | {
"verified": true,
"answer": 57179,
"timestamp": "2026-02-08T03:23:53.775193Z"
} | 3fa953 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 230,
"completion_tokens": 2688
},
"timestamp": "2026-02-10T02:29:47.324Z",
"answer": 57179
},
{
"... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "EULER_TOTIENT_SUM",
"status": "ok"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
},
{
"le... | {
"lo": 1.69,
"mid": 5.03,
"hi": 8.38
} | ||
9654c2 | antilemma_sum_equals_v1_458359167_5464 | Let $n = 23$. Let $x$ be the number of ordered pairs $(i, j)$ of positive integers such that $1 \le i \le 21$, $1 \le j \le 22$, and $i + j = n$. Define $s = \binom{6}{0}$ and $t = |x|$. Compute $\sum_{k=s}^{t} \phi(k)$, where $\phi$ denotes Euler's totient function. | 140 | graphs = [
Graph(
let={
"_n": Const(23),
"x": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("i"), Var("j")]), condition=Eq(Sum(Var("i"), Var("j")), Ref("_n")), domain=CartesianProduct(left=IntegerRange(start=Const(1), end=Const(21)), right=IntegerRange(start=Const(1), end=Con... | COMB | GEOM | COMPUTE | sympy | COMB1 | [
"COUNT_SUM_EQUALS",
"ONE_BINOM_0"
] | ec98de | antilemma_sum_equals_v1 | null | 4 | 0 | [
"COMB1",
"COUNT_SUM_EQUALS",
"ONE_BINOM_0"
] | 3 | 0.042 | 2026-02-08T12:32:04.836253Z | {
"verified": true,
"answer": 140,
"timestamp": "2026-02-08T12:32:04.877947Z"
} | 448313 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 210,
"completion_tokens": 1170
},
"timestamp": "2026-02-24T15:49:45.711Z",
"answer": 140
},
{
"id... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "ok"
},
{
"lemma": "ONE_BINOM_0",
"status": "ok"
},
{
"lemma": "V7",
"sta... | {
"lo": -2.35,
"mid": 1.22,
"hi": 4.84
} | ||
2a7e4a | nt_lcm_compute_v1_397696148_805 | Let $n = 44121$, $a = 1013$, and let $b$ be the sum of $\phi(d)$ over all positive divisors $d$ of $2776$. Let $r$ be the least common multiple of $a$ and $b$. Compute the remainder when $n \cdot r$ is divided by $57677$. | 25,390 | graphs = [
Graph(
let={
"_n": Const(44121),
"a": Const(1013),
"b": SumOverDivisors(n=Const(value=2776), var='d', expr=EulerPhi(n=Var(name='d'))),
"result": LCM(a=Ref("a"), b=Ref("b")),
"Q": Mod(value=Mul(Ref("_n"), Ref("result")), modulus=Const(576... | NT | null | COMPUTE | sympy | K3 | [
"K3"
] | 54c41e | nt_lcm_compute_v1 | null | 3 | 0 | [
"K3"
] | 1 | 0.002 | 2026-02-08T11:45:34.955705Z | {
"verified": true,
"answer": 25390,
"timestamp": "2026-02-08T11:45:34.957336Z"
} | ed9e39 | 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": 2196
},
"timestamp": "2026-02-14T18:08:19.353Z",
"answer": 25390
},
... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "K3",
"status": "ok"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "V1",
"status": "no"
}... | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
3c401a | modular_count_residue_v1_124444284_1904 | Let $m = 89$. Let $s$ be the minimum value of $x + y$ over all ordered pairs $(x,y)$ of positive integers such that $xy = 126736$. Let $r$ be the number of positive integers $k$ such that $1 \leq k \leq s$ and $m$ divides $k$. Compute the number of positive integers $n$ such that $1 \leq n \leq 83160$ and $n \equiv r \... | 2,772 | graphs = [
Graph(
let={
"_m": Const(89),
"_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(126736)))), expr=Sum(Var("x"), Var("y"))))... | NT | null | COUNT | sympy | B3 | [
"B3/C2"
] | dcbe93 | modular_count_residue_v1 | null | 6 | 0 | [
"B3",
"C2"
] | 2 | 2.944 | 2026-02-08T04:12:30.580388Z | {
"verified": true,
"answer": 2772,
"timestamp": "2026-02-08T04:12:33.524662Z"
} | aa99f3 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 223,
"completion_tokens": 1157
},
"timestamp": "2026-02-10T15:43:20.777Z",
"answer": 2772
},
{
"... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "C2",
"status": "ok_later"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": ... | {
"lo": -7.01,
"mid": -4.68,
"hi": -2.15
} | ||
44eb3f | modular_inverse_v1_655260480_6 | Let $a = 483$ and $m = 613$. Let $S$ be the set of all integers $x$ such that $1 \leq x \leq 612$ and $ax \equiv 1 \pmod{m}$. Let $r$ be the smallest element of $S$.
Let $T$ be the set of all ordered pairs $(x_1, y)$ of positive integers such that $x_1 + y$ equals the number of integers $t$ satisfying $15 \leq t \leq ... | 40,322 | graphs = [
Graph(
let={
"a": Const(483),
"m": Const(613),
"upper": Const(612),
"result": MinOverSet(set=SolutionsSet(var=Var("x"), condition=And(Geq(Var("x"), Const(1)), Leq(Var("x"), Ref("upper")), Eq(Mod(value=Mul(Ref("a"), Var("x")), modulus=Ref("m")), Cons... | ALG | NT | EXTREMUM | sympy | LIN_FORM | [
"LIN_FORM/B1"
] | 259044 | modular_inverse_v1 | two_stage_modexp | 7 | 0 | [
"B1",
"LIN_FORM"
] | 2 | 0.035 | 2026-02-08T15:07:46.148170Z | {
"verified": true,
"answer": 40322,
"timestamp": "2026-02-08T15:07:46.182916Z"
} | 4ddbe9 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 258,
"completion_tokens": 3757
},
"timestamp": "2026-02-16T00:24:50.399Z",
"answer": 40322
},
... | 1 | [
{
"lemma": "B1",
"status": "ok_later"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
b7cd68 | modular_sum_quadratic_residues_v1_1978505735_7621 | Let $p$ be the largest positive divisor of $166343$ that is at most $397$. Let $r = \frac{p(p-1)}{4}$. Find the smallest positive integer $k$ such that $F_k \equiv 0 \pmod{|r| + 2}$, where $F_k$ is the $k$-th Fibonacci number. | 11,240 | graphs = [
Graph(
let={
"_n": Const(4),
"p": MaxOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Const(1)), Leq(Var("d"), Const(397)), Divides(divisor=Var("d"), dividend=Const(166343))))),
"result": Div(Mul(Ref("p"), Sub(Ref("p"), Const(1))), Ref("_n")),... | NT | null | SUM | sympy | MAX_DIVISOR | [
"MAX_DIVISOR"
] | 51757e | modular_sum_quadratic_residues_v1 | null | 3 | 0 | [
"MAX_DIVISOR"
] | 1 | 0.003 | 2026-02-08T20:21:53.510310Z | {
"verified": true,
"answer": 11240,
"timestamp": "2026-02-08T20:21:53.512829Z"
} | 8a2ad2 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 122,
"completion_tokens": 4535
},
"timestamp": "2026-02-19T00:24:48.553Z",
"answer": 11240
},
... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "MAX_DIVISOR",
"status": "ok"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "VAL_SUM_EQ",
"status": "no"
... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
476ebb | comb_bell_compute_v1_1520064083_1026 | Let $m = 81$. Consider the set of all ordered pairs $(x, y)$ of positive integers such that $x + y = 6$. Define $\text{_n}$ to be the maximum value of $xy$ over all such pairs. Let $n$ be the number of positive integers $j$ such that $1 \leq j \leq \text{_n}$ and $j^2 \leq m$. Compute the Bell number $B_n$, which is th... | 21,147 | graphs = [
Graph(
let={
"_m": Const(81),
"_n": MaxOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(Sum(Var("x"), Var("y")), Const(6)))), expr=Mul(Var("x"), Var("y")))),
... | COMB | null | COMPUTE | sympy | B1 | [
"B1/C3"
] | 0a705f | comb_bell_compute_v1 | null | 6 | 0 | [
"B1",
"C3"
] | 2 | 0.002 | 2026-02-08T03:43:27.078098Z | {
"verified": true,
"answer": 21147,
"timestamp": "2026-02-08T03:43:27.079750Z"
} | d967af | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 234,
"completion_tokens": 815
},
"timestamp": "2026-02-10T15:37:08.327Z",
"answer": 21147
},
{
"i... | 1 | [
{
"lemma": "B1",
"status": "ok"
},
{
"lemma": "C3",
"status": "ok_later"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "V7",
"st... | {
"lo": -3.83,
"mid": -1.68,
"hi": 1.09
} | ||
8396f2 | antilemma_k2_v1_48377204_2422 | Let $$ x = \sum_{k=1}^{404} \phi(k) \left\lfloor \frac{404}{k} \right\rfloor. $$ Let $a = \phi(|x| + 1)$ and $b = \tau(|x| + 9^0)$, where $\tau(n)$ denotes the number of positive divisors of $n$. Compute the remainder when $x + a + b$ is divided by $85208$. | 74,838 | graphs = [
Graph(
let={
"x": Summation(var="k", start=Const(1), end=Const(404), expr=Mul(EulerPhi(n=Var("k")), Floor(Div(Const(404), Var("k"))))),
"Q": Mod(value=Sum(Ref("x"), EulerPhi(n=Sum(Abs(arg=Ref(name='x')), Const(1))), NumDivisors(n=Sum(Abs(arg=Ref(name='x')), Pow(Const(9), C... | NT | COMB | COMPUTE | sympy | K13 | [
"IDENTITY_POW_ZERO",
"K2"
] | fce51d | antilemma_k2_v1 | null | 5 | 0 | [
"IDENTITY_POW_ZERO",
"K13",
"K2"
] | 3 | 0.006 | 2026-02-08T16:46:16.985701Z | {
"verified": true,
"answer": 74838,
"timestamp": "2026-02-08T16:46:16.991489Z"
} | b7c5ee | 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": 1660
},
"timestamp": "2026-02-17T10:44:48.660Z",
"answer": 74838
},
... | 1 | [
{
"lemma": "IDENTITY_POW_ZERO",
"status": "ok"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "K2",
"status": "ok"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
fd932a | geo_count_lattice_triangle_v1_1820931509_718 | A triangle has vertices at $(0,0)$, $(180,33)$, and $(90,121)$. Let $A$ be twice the area of this triangle, and let $B$ be the number of lattice points on the boundary of the triangle, counting all three vertices and all points on the edges. Compute the value of
$$
56169 - \frac{A + 2 - B}{2}.
$$ | 46,766 | graphs = [
Graph(
let={
"area_2x": Abs(arg=Sum(Mul(Const(value=180), Const(value=121)), Mul(Const(value=90), Sub(left=Const(value=0), right=Const(value=33))))),
"boundary": Sum(GCD(a=Abs(arg=Const(value=180)), b=Abs(arg=Const(value=33))), GCD(a=Abs(arg=Sub(left=Const(value=90), right... | ALG | NT | COUNT | sympy | [] | geo_count_lattice_triangle_v1 | null | 4 | 0 | null | null | 0.005 | 2026-02-08T11:50:16.462221Z | {
"verified": true,
"answer": 46766,
"timestamp": "2026-02-08T11:50:16.467042Z"
} | d8c56f | 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": 1476
},
"timestamp": "2026-02-14T19:32:55.005Z",
"answer": 46766
},
... | 1 | [] | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||||
204b85 | nt_num_divisors_compute_v1_1125832087_992 | Let $n$ be the maximum value of $xy$ over all ordered pairs $(x,y)$ of positive integers such that $x + y = 90$. Compute the number of positive divisors of $n$. | 15 | graphs = [
Graph(
let={
"_n": Const(90),
"n": MaxOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(Sum(Var("x"), Var("y")), Ref("_n")))), expr=Mul(Var("x"), Var("y")))),
... | NT | null | COMPUTE | sympy | B1 | [
"B1"
] | 5b950e | nt_num_divisors_compute_v1 | null | 4 | 0 | [
"B1"
] | 1 | 0.007 | 2026-02-08T03:24:44.311025Z | {
"verified": true,
"answer": 15,
"timestamp": "2026-02-08T03:24:44.318506Z"
} | 5c68ac | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 154,
"completion_tokens": 350
},
"timestamp": "2026-02-10T14:28:33.566Z",
"answer": 15
},
{
"id":... | 1 | [
{
"lemma": "B1",
"status": "ok"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
}
] | {
"lo": -9.14,
"mid": -6.05,
"hi": -3.74
} | ||
7a0af6 | nt_sum_gcd_range_mod_v1_48377204_2332 | Let $N = 8778$. Let $S$ be the set of all ordered pairs $(x,y)$ of positive integers such that $xy = 44100$. Define $k$ to be the minimum value of $x + y$ over all pairs $(x,y) \in S$. Let
$$
\sum_{n=1}^{N} \gcd(n, k)
$$
denote the sum of $\gcd(n, k)$ for $n$ from 1 to $N$. Compute the remainder when this sum is divide... | 5,159 | graphs = [
Graph(
let={
"N": Const(8778),
"k": MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(Mul(Var("x"), Var("y")), Const(44100)))), expr=Sum(Var("x"), Var("y")))),... | NT | null | COMPUTE | sympy | B3 | [
"B3"
] | 0cd20d | nt_sum_gcd_range_mod_v1 | null | 5 | 0 | [
"B3"
] | 1 | 0.533 | 2026-02-08T16:43:56.259405Z | {
"verified": true,
"answer": 5159,
"timestamp": "2026-02-08T16:43:56.792647Z"
} | 309042 | 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": 2938
},
"timestamp": "2026-02-17T10:16:19.465Z",
"answer": 5159
},
{... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
6987be | comb_bell_compute_v1_1470522791_9 | Let $n$ be the number of positive integers $p$ for which there exists a positive integer $q$ such that $p \cdot q = 205800$, $\gcd(p, q) = 1$, and $p < q$. Compute the remainder when $44121$ times the $n$-th Bell number is divided by $54305$. | 33,225 | graphs = [
Graph(
let={
"_n": Const(44121),
"n": CountOverSet(set=SolutionsSet(var=Var("p"), condition=And(IsPositive(arg=Var(name='p')), Exists(var=Var(name='q'), condition=And(Eq(left=Mul(Var(name='p'), Var(name='q')), right=Const(value=205800)), Eq(left=GCD(a=Var(name='p'), b=Var(... | NT | COMB | COMPUTE | sympy | COPRIME_PAIRS | [
"COPRIME_PAIRS"
] | 2bb3aa | comb_bell_compute_v1 | null | 4 | 0 | [
"COPRIME_PAIRS"
] | 1 | 0.003 | 2026-02-08T12:47:31.261524Z | {
"verified": true,
"answer": 33225,
"timestamp": "2026-02-08T12:47:31.264865Z"
} | 5e9e2e | 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": 2778
},
"timestamp": "2026-02-15T05:04:45.855Z",
"answer": 33225
},
... | 1 | [
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "V1",
"status": "no"
},
{
"lemma": "VAL_SUM_EQ",
"status": "no"
}
] | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
106d0e_n | comb_count_partitions_v1_1218484723_6294 | A composer writes a piece made up of rhythmic units of varying lengths that sum to a total duration of $n$ beats, where $n = \sum_{k=0}^{3} 3^k$ (since $\binom{7}{7} - 1 = 0$). The number of distinct ways to arrange the rhythms (ignoring order of equal-length units) is $p(n)$, the partition function. Let $M = p(n)$. Ho... | 14,483 | COMB | null | COUNT | sympy | SUM_GEOM | [
"SUM_GEOM",
"ZERO_BINOM_N"
] | 4e18d8 | comb_count_partitions_v1 | null | 3 | null | [
"SUM_GEOM",
"ZERO_BINOM_N"
] | 2 | 0.003 | 2026-02-25T07:51:54.262762Z | null | a2db34 | 106d0e | narrative | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 234,
"completion_tokens": 3997
},
"timestamp": "2026-03-31T01:06:03.880Z",
"answer": 14483
},
{
"... | 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": "SUM_GEOM",
"status": "ok"
},
{
"lemma": ... | {
"lo": -5.37,
"mid": 0.23,
"hi": 5.22
} | |
46ab39 | diophantine_fbi2_count_v1_2051736721_590 | Let $k = 420$. Compute the number of integers $d$ such that $2 \leq d \leq 101$, $d$ divides $k$, $\frac{k}{d} \geq 6$, and
$$
\frac{k}{d} \leq \sum_{k_1=1}^{14} \phi(k_1) \left\lfloor \frac{14}{k_1} \right\rfloor.
$$ | 16 | graphs = [
Graph(
let={
"_n": Const(101),
"k": Const(420),
"result": CountOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Const(2)), Leq(Var("d"), Ref("_n")), Divides(divisor=Var("d"), dividend=Ref("k")), Geq(Div(Ref("k"), Var("d")), Const(6)), Leq(Div(... | NT | null | COUNT | sympy | K2 | [
"K2"
] | 6897ab | diophantine_fbi2_count_v1 | null | 5 | 0 | [
"K2"
] | 1 | 0.016 | 2026-02-08T15:33:01.033288Z | {
"verified": true,
"answer": 16,
"timestamp": "2026-02-08T15:33:01.048797Z"
} | f93072 | 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": 1317
},
"timestamp": "2026-02-16T09:06:03.667Z",
"answer": 16
},
{
... | 1 | [
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "K2",
"status": "ok"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
fe462f | nt_count_intersection_v1_784195855_1488 | Let $s$ be the minimum value of $x + y$ over all ordered pairs $(x, y)$ of positive integers such that $xy = 25000000$. Let $N$ be the number of ordered pairs $(x_1, x_2)$ of positive odd integers such that $x_1 + x_2 = s$. Compute the number of positive integers $n$ such that $1 \leq n \leq N$, $11$ divides $n$, and $... | 151 | graphs = [
Graph(
let={
"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")), MinOverSet(set=MapOverSet(set=S... | NT | null | COUNT | sympy | B3 | [
"B3/COMB1"
] | e26f7e | nt_count_intersection_v1 | null | 6 | 0 | [
"B3",
"COMB1"
] | 2 | 0.165 | 2026-02-08T05:02:19.762281Z | {
"verified": true,
"answer": 151,
"timestamp": "2026-02-08T05:02:19.927218Z"
} | 2c1803 | 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": 2948
},
"timestamp": "2026-02-11T22:56:28.450Z",
"answer": 151
},
{
"id... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "COMB1",
"status": "ok_later"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
... | {
"lo": -3.52,
"mid": 1.14,
"hi": 6.18
} | ||
baabc8 | alg_poly_preperiod_count_v1_1419126231_531 | For a non-negative integer $a$, define $N = (3a^5 - a^4 + 5a^3 - 1) \bmod 47$, $M = (3N^5 - N^4 + 5N^3 - 1) \bmod 47$, $R = (3M^5 - M^4 + 5M^3 - 1) \bmod 47$, $S = (3R^5 - R^4 + 5R^3 - 1) \bmod 47$, and $T = (3S^5 - S^4 + 5S^3 - 1) \bmod 47$. Find the number of integers $a$ with $0 \leq a \leq 1080$ such that $T = N$, ... | 184 | graphs = [
Graph(
let={
"p1": Mod(value=Sum(Mul(Const(3), Pow(Var("a"), Const(5))), Mul(Const(-1), Pow(Var("a"), Const(4))), Mul(Const(5), Pow(Var("a"), Const(3))), Const(-1)), modulus=Const(47)),
"p2": Mod(value=Sum(Mul(Const(3), Pow(Ref("p1"), Const(5))), Mul(Const(-1), Pow(Ref("p1... | ALG | null | COUNT | sympy | POLY_ORBIT_COUNT | [
"POLY_ORBIT_COUNT"
] | 4ad965 | alg_poly_preperiod_count_v1 | null | 6 | null | [
"POLY_ORBIT_COUNT"
] | 1 | 0.097 | 2026-02-25T10:03:40.724932Z | {
"verified": true,
"answer": 184,
"timestamp": "2026-02-25T10:03:40.821692Z"
} | 1c2ec9 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 309,
"completion_tokens": 14029
},
"timestamp": "2026-03-30T08:53:53.974Z",
"answer": 184
},
{
"i... | 1 | [
{
"lemma": "POLY_ORBIT_COUNT",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
}
] | {
"lo": 3.8,
"mid": 6.33,
"hi": 9.49
} | ||
e1668e | comb_count_derangements_v1_124444284_542 | Let $u = 9$ and $n_2 = u + 1$. Define $e = \sum_{k=0}^{n_2} (-1)^k \binom{n_2}{k}$. Let $n_1 = \binom{4}{4} - 1 + e$. Define $h = \sum_{k=0}^{n_1} (-1)^k \binom{n_1}{k}$. Let $n = 8h$. Compute the subfactorial of $n$, denoted $!n$. Find the value of $!n$. | 14,833 | graphs = [
Graph(
let={
"u": Const(9),
"n2": Sum(Ref("u"), Const(1)),
"e": Summation(var="k", start=Const(0), end=Ref("n2"), expr=Mul(Pow(Const(-1), Var("k")), Binom(n=Ref("n2"), k=Var("k")))),
"n1": Sum(Sub(Binom(n=Const(4), k=Const(4)), Const(1)), Ref("e")),... | COMB | null | COUNT | sympy | BINOMIAL_ALTERNATING | [
"BINOMIAL_ALTERNATING",
"ZERO_BINOM_N"
] | ba7829 | comb_count_derangements_v1 | null | 5 | 2 | [
"BINOMIAL_ALTERNATING",
"ZERO_BINOM_N"
] | 2 | 0.001 | 2026-02-08T03:20:56.992904Z | {
"verified": true,
"answer": 14833,
"timestamp": "2026-02-08T03:20:56.994288Z"
} | 6ac1b9 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 239,
"completion_tokens": 517
},
"timestamp": "2026-02-09T18:59:47.547Z",
"answer": 14833
},
{
"i... | 1 | [
{
"lemma": "BINOMIAL_ALTERNATING",
"status": "ok"
},
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8",
"status... | {
"lo": -4.92,
"mid": -2.9,
"hi": -0.7
} | ||
52187f | alg_poly_orbit_hensel_v1_1218484723_2279 | For a non-negative integer $a$, define $N = (a^2 - 2170) \bmod 6241$, $M = (N^2 - 2170) \bmod 6241$, and $R = (M^2 - 2170) \bmod 6241$. Find the number of integers $a$ with $0 \le a \le 11202594$ such that $R = a$, $N \ne a$, and $M \ne a$. | 5,385 | graphs = [
Graph(
let={
"p1": Mod(value=Sum(Pow(Var("a"), Const(2)), Const(-2170)), modulus=Const(6241)),
"p2": Mod(value=Sum(Pow(Ref("p1"), Const(2)), Const(-2170)), modulus=Const(6241)),
"p3": Mod(value=Sum(Pow(Ref("p2"), Const(2)), Const(-2170)), modulus=Const(6241)),
... | ALG | null | COUNT | sympy | POLY_ORBIT_COUNT | [
"POLY_ORBIT_COUNT"
] | 4ad965 | alg_poly_orbit_hensel_v1 | null | 6 | null | [
"POLY_ORBIT_COUNT"
] | 1 | 0.024 | 2026-02-25T04:07:06.097177Z | {
"verified": true,
"answer": 5385,
"timestamp": "2026-02-25T04:07:06.120836Z"
} | b0ec01 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 218,
"completion_tokens": 32768
},
"timestamp": "2026-03-29T03:55:27.247Z",
"answer": null
},
{
... | 1 | [
{
"lemma": "POLY_ORBIT_COUNT",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
}
] | {
"lo": 1.55,
"mid": 4.7,
"hi": 7.23
} | ||
73e9d2 | antilemma_k2_v1_48377204_1274 | Let $x = \sum_{k=1}^{58} \phi(k) \cdot \left\lfloor \frac{58}{k} \right\rfloor$, where $\phi$ denotes Euler's totient function. Compute the remainder when $44121 \cdot x$ is divided by $93928$. | 66,847 | graphs = [
Graph(
let={
"x": Summation(var="k", start=Const(1), end=Const(58), expr=Mul(EulerPhi(n=Var("k")), Floor(Div(Const(58), Var("k"))))),
"Q": Mod(value=Mul(Const(44121), Ref("x")), modulus=Const(93928)),
},
goal=Ref("Q"),
)
] | NT | COMB | COMPUTE | sympy | K2 | [
"K2"
] | 6897ab | antilemma_k2_v1 | null | 6 | 0 | [
"K2"
] | 1 | 0.001 | 2026-02-08T16:00:19.625894Z | {
"verified": true,
"answer": 66847,
"timestamp": "2026-02-08T16:00:19.626876Z"
} | a73516 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 110,
"completion_tokens": 2063
},
"timestamp": "2026-02-16T18:32:03.672Z",
"answer": 66847
},
... | 1 | [
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "K2",
"status": "ok"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
6b4079 | sequence_lucas_compute_v1_2051736721_1495 | Let $t$ be an integer such that $17 \leq t \leq 77$. Suppose there exist positive integers $a$ and $b$ with $1 \leq a \leq 6$ and $1 \leq b \leq 4$ such that $t = 6a + 10b + 1$. Let $n$ be the number of integers $t$ satisfying these conditions. Compute the $n$-th Lucas number. | 64,079 | 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=6)), Geq(left=Var(name='b'), right=Const(value=1... | NT | null | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | sequence_lucas_compute_v1 | null | 4 | 0 | [
"LIN_FORM"
] | 1 | 0.001 | 2026-02-08T16:04:09.292880Z | {
"verified": true,
"answer": 64079,
"timestamp": "2026-02-08T16:04:09.294295Z"
} | 719cdf | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 141,
"completion_tokens": 2621
},
"timestamp": "2026-02-16T20:43:40.850Z",
"answer": 64079
},
... | 1 | [
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
c08b30 | nt_count_divisors_in_range_v1_124444284_6430 | Let $n$ be the minimum value of $x + y$ over all pairs of positive integers $(x,y)$ such that $xy = 176400$. Let $b$ be the number of nonnegative integers $j$ with $0 \leq j \leq 686$ for which $\binom{686}{j}$ is odd. Compute the number of positive divisors $d$ of $n$ such that $1 \leq d \leq b$. | 22 | graphs = [
Graph(
let={
"_n": Const(686),
"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(176400)))), expr=Sum(Var("x"), Var("y"))))... | NT | null | COUNT | sympy | V8 | [
"B3",
"V8"
] | 5b3848 | nt_count_divisors_in_range_v1 | null | 7 | 0 | [
"B3",
"V8"
] | 2 | 0.024 | 2026-02-08T08:22:59.715014Z | {
"verified": true,
"answer": 22,
"timestamp": "2026-02-08T08:22:59.738914Z"
} | 278e09 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 141,
"completion_tokens": 2525
},
"timestamp": "2026-02-13T18:50:12.100Z",
"answer": 22
},
{
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "V3",
"status": "no"
},
{
"lemma": "V5",
"status": "... | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
f43193 | modular_count_residue_v1_1520064083_328 | Let $n$ be a positive integer. Define $r$ to be the largest integer $k$ such that $47^k$ divides the number of positive integers $n \leq 24309$ satisfying
$$
n \equiv \left\lfloor \frac{n}{2} \right\rfloor \pmod{11}.
$$
Let $S$ be the set of all positive integers $n \leq 87616$ such that $n \equiv r \pmod{11}$. The num... | 27,004 | graphs = [
Graph(
let={
"_n": Const(47),
"upper": Const(87616),
"m": Const(11),
"r": MaxKDivides(target=Mul(CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Const(24309)), Congruent(a=Var(name='n'), b=Floor(arg=D... | NT | null | COUNT | sympy | L3C | [
"L3C/K13"
] | 338801 | modular_count_residue_v1 | null | 6 | 0 | [
"K13",
"L3C"
] | 2 | 10.105 | 2026-02-08T03:15:19.713496Z | {
"verified": true,
"answer": 27004,
"timestamp": "2026-02-08T03:15:29.818783Z"
} | 0e0fa5 | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 245,
"completion_tokens": 697
},
"timestamp": "2026-02-17T22:23:51.095Z",
"answer": 27004
}
] | 2 | [
{
"lemma": "K13",
"status": "ok_later"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "L3C",
"status": "ok"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"le... | {
"lo": -10,
"mid": -6.47,
"hi": -2.95
} | ||
37ea21 | antilemma_k3_v1_124444284_730 | Let $n = 29790$. Compute the sum
$$
\sum_{d \mid n} \phi(d),
$$
where $\phi$ denotes Euler's totient function and the sum is taken over all positive divisors $d$ of $n$. | 29,790 | graphs = [
Graph(
let={
"_n": Const(29790),
"x": SumOverDivisors(n=Ref(name='_n'), var='d', expr=EulerPhi(n=Var(name='d'))),
},
goal=Ref("x"),
)
] | NT | COMB | COMPUTE | sympy | K3 | [
"K3"
] | 54c41e | antilemma_k3_v1 | null | 3 | 0 | [
"K3"
] | 1 | 0 | 2026-02-08T03:28:42.312064Z | {
"verified": true,
"answer": 29790,
"timestamp": "2026-02-08T03:28:42.312498Z"
} | 301ca4 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 165,
"completion_tokens": 351
},
"timestamp": "2026-02-09T21:10:08.171Z",
"answer": 29790
},
{
"i... | 1 | [
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "K3",
"status": "ok"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
}
] | {
"lo": -5.55,
"mid": -3.02,
"hi": 0.31
} | ||
0c2cb4 | nt_sum_totient_over_divisors_v1_677425708_557 | Let $T$ be the set of all integers $t$ such that $9 \leq t \leq 6262$ and there exist positive integers $a$ and $b$ with $1 \leq a \leq 842$, $1 \leq b \leq 184$, and $t = 7a + 2b$. Let $n$ be the number of elements in $T$. Compute $$\sum_{d \mid n} \phi(d),$$ where the sum is over all positive divisors $d$ of $n$, and... | 6,248 | 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=842)), Geq(left=Var(name='b'), right=Const(value... | NT | null | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | nt_sum_totient_over_divisors_v1 | null | 6 | 0 | [
"LIN_FORM"
] | 1 | 0.003 | 2026-02-08T03:35:53.341030Z | {
"verified": true,
"answer": 6248,
"timestamp": "2026-02-08T03:35:53.344490Z"
} | d8b284 | 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": 8106
},
"timestamp": "2026-02-08T20:45:56.237Z",
"answer": 6093
},
{
... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
}
] | {
"lo": 1.71,
"mid": 5.04,
"hi": 8.38
} | ||
0a1c65 | nt_num_divisors_compute_v1_971394319_1459 | Let $S$ 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 $k$ be the number of elements in $S$. Let $d_{\text{min}}$ be the smallest divisor of $7527397589$ that is at least $k$. Let $r$ be the number of positive divisors of $d_... | 3 | graphs = [
Graph(
let={
"_n": CountOverSet(set=SolutionsSet(var=Var("p"), condition=And(IsPositive(arg=Var(name='p')), Exists(var=Var(name='q'), condition=And(Eq(left=Mul(Var(name='p'), Var(name='q')), right=Const(value=72)), Eq(left=GCD(a=Var(name='p'), b=Var(name='q')), right=Const(value=1)), ... | NT | null | COMPUTE | sympy | B3 | [
"COPRIME_PAIRS/MIN_PRIME_FACTOR"
] | 52cee2 | nt_num_divisors_compute_v1 | null | 5 | 0 | [
"B3",
"COPRIME_PAIRS",
"MIN_PRIME_FACTOR"
] | 3 | 0.069 | 2026-02-08T13:41:59.833585Z | {
"verified": true,
"answer": 3,
"timestamp": "2026-02-08T13:41:59.903084Z"
} | 860c74 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 183,
"completion_tokens": 3657
},
"timestamp": "2026-02-15T19:41:33.008Z",
"answer": 3
},
{
... | 1 | [
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "MIN_PRIME_FACTOR",
"status": "ok_later"
},
{
"lemma": "V3",
"status": "no"
},
{
"lemma": "V7",... | {
"lo": -8.26,
"mid": -5.01,
"hi": -1.76
} | ||
a0894e | antilemma_sum_equals_v1_1470522791_1785 | Let $d = 73$. Define $c$ to be the number of ordered pairs $(i,j)$ of positive integers such that $i + j = d$ and $1 \leq i, j \leq 72$. Define $m$ to be the number of ordered pairs $(i,j)$ of positive integers such that $i + j = c$ and $1 \leq i, j \leq 71$. Define $n$ to be the number of ordered pairs $(i,j)$ of posi... | 18 | graphs = [
Graph(
let={
"_d": Const(73),
"_c": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("i"), Var("j")]), condition=Eq(Sum(Var("i"), Var("j")), Ref("_d")), domain=CartesianProduct(left=IntegerRange(start=Const(1), end=Const(72)), right=IntegerRange(start=Const(1), end=Co... | COMB | GEOM | COMPUTE | sympy | LIN_FORM | [
"COUNT_SUM_EQUALS/COUNT_SUM_EQUALS",
"COUNT_SUM_EQUALS"
] | ae9919 | antilemma_sum_equals_v1 | null | 6 | 0 | [
"COUNT_SUM_EQUALS",
"LIN_FORM"
] | 2 | 0.294 | 2026-02-08T13:57:48.032993Z | {
"verified": true,
"answer": 18,
"timestamp": "2026-02-08T13:57:48.326533Z"
} | 6ff171 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 332,
"completion_tokens": 1896
},
"timestamp": "2026-02-24T19:27:26.496Z",
"answer": 18
},
{
"id"... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "ok"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8",
"status": "no... | {
"lo": -2.37,
"mid": 1.22,
"hi": 4.84
} | ||
a29012 | nt_count_intersection_v1_2051736721_2137 | Let $N = 50000$ and $a = 9$. Let $s$ be the sum $\sum_{k=0}^{3} (-1)^k \binom{3}{k}$. Let $t_{\text{max}}$ be the number of integers $t$ such that $20 \leq t \leq 8530$ and there exist positive integers $a'$ and $b'$ with $1 \leq a' \leq 185$, $1 \leq b' \leq 990$, and $t = 14a' + 6b'$. Let $b$ be the number of nonnega... | 2,778 | graphs = [
Graph(
let={
"_n": Const(2),
"N": Const(50000),
"a": Const(9),
"b": CountOverSet(set=SolutionsSet(var=Var("j"), condition=And(Geq(Var("j"), Summation(var="k", start=Const(0), end=Const(3), expr=Mul(Pow(Const(-1), Var("k")), Binom(n=Const(3), k=Var("... | COMB | NT | COUNT | sympy | BINOMIAL_ALTERNATING | [
"BINOMIAL_ALTERNATING",
"LIN_FORM/V8",
"B3/V8"
] | 1ddcd8 | nt_count_intersection_v1 | null | 7 | 0 | [
"B3",
"BINOMIAL_ALTERNATING",
"LIN_FORM",
"V8"
] | 4 | 1.782 | 2026-02-08T16:30:01.561067Z | {
"verified": true,
"answer": 2778,
"timestamp": "2026-02-08T16:30:03.343329Z"
} | ad632a | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 284,
"completion_tokens": 6292
},
"timestamp": "2026-02-17T05:23:05.929Z",
"answer": 2778
},
{... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "BINOMIAL_ALTERNATING",
"status": "ok"
},
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "LIN_FORM",
"stat... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
00aa69 | nt_lcm_compute_v1_1431428450_74 | Let $a = 1476$. Let $S$ be the set of all ordered pairs $(x, y)$ of positive integers such that $xy = 284089$. Define $b$ to be the minimum value of $x + y$ over all pairs $(x, y) \in S$. Compute the least common multiple of $a$ and $b$. | 19,188 | graphs = [
Graph(
let={
"a": Const(1476),
"b": 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(284089)))), expr=Sum(Var("x"), Var("y"))))... | NT | null | COMPUTE | sympy | COMB1 | [
"B3"
] | 0cd20d | nt_lcm_compute_v1 | null | 4 | 0 | [
"B3",
"COMB1"
] | 2 | 0.006 | 2026-02-08T13:10:45.071544Z | {
"verified": true,
"answer": 19188,
"timestamp": "2026-02-08T13:10:45.077782Z"
} | 33830f | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 123,
"completion_tokens": 915
},
"timestamp": "2026-02-15T11:05:30.903Z",
"answer": 19188
},
{... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
}
] | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
031b78 | nt_num_divisors_compute_v1_898971024_742 | Let $P(x) = x^2 - 9x - 1170$. Let $s$ be the sum of all roots of $P(x) = 0$. Let $n$ be the minimum value of $x_1 + y$ over all pairs of positive integers $(x_1, y)$ such that $x_1 y = s$. Let $d$ be the number of positive divisors of $n$. Compute $77284 - d$. | 77,280 | graphs = [
Graph(
let={
"_n": SumOverSet(set=SolutionsSet(var=Var("x"), condition=Eq(Sum(Pow(Var("x"), Const(2)), Mul(Const(-9), Var("x")), Const(-1170)), Const(0)))),
"n": MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x1"), Var("y")]), condition=And(IsPositive(... | NT | null | COMPUTE | sympy | VIETA_SUM | [
"VIETA_SUM/B3"
] | d036a4 | nt_num_divisors_compute_v1 | null | 5 | 0 | [
"B3",
"VIETA_SUM"
] | 2 | 0.003 | 2026-02-08T15:37:41.168860Z | {
"verified": true,
"answer": 77280,
"timestamp": "2026-02-08T15:37:41.172058Z"
} | 689c7b | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 161,
"completion_tokens": 333
},
"timestamp": "2026-02-16T06:09:57.578Z",
"answer": 77280
},
{
"id": 11,
... | 2 | [
{
"lemma": "B3",
"status": "ok_later"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
},
{
"lemma": "VAL_SUM_EQ",
"status": "no"
},
{
... | {
"lo": -10,
"mid": -7.27,
"hi": -4.54
} | ||
67a1f9 | comb_binomial_compute_v1_349078426_1171 | Let $a = 1$ and $b = 2$. Define $n_2 = a + b$. Let $m = \sum_{k=0}^{n_2} (-1)^k \binom{n_2}{k}$ and $h = \sum_{k=0}^{0} (-1)^k \binom{0}{k}$. Let $n = 14 + m$ and $k = 7$. Define $Q = 49729 \cdot h - \binom{n}{k}$. Find the value of $Q$. | 46,297 | graphs = [
Graph(
let={
"a": Const(1),
"b": Const(2),
"n2": Sum(Ref("a"), Ref("b")),
"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),
"h": Summat... | COMB | null | COMPUTE | sympy | BINOMIAL_ALTERNATING | [
"BINOMIAL_ALTERNATING"
] | c21569 | comb_binomial_compute_v1 | null | 4 | 2 | [
"BINOMIAL_ALTERNATING"
] | 1 | 0.002 | 2026-02-08T13:27:15.372926Z | {
"verified": true,
"answer": 46297,
"timestamp": "2026-02-08T13:27:15.374873Z"
} | 99db2f | 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": 627
},
"timestamp": "2026-02-24T18:23:01.531Z",
"answer": 46297
},
{
"i... | 1 | [
{
"lemma": "BINOMIAL_ALTERNATING",
"status": "ok"
},
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8",
"stat... | {
"lo": -7.18,
"mid": -5,
"hi": -3.01
} | ||
ea7c1f | nt_count_divisors_in_range_v1_677425708_1245 | Let $n = 10080$, $a = 6$, and $b = 511$. Determine the number of positive divisors $d$ of $n$ such that $a \leq d \leq b$. Let $k$ be the absolute value of this count. Compute the sum
$$
\sum_{m=1}^{k} \varphi(m),
$$
where $\varphi$ denotes Euler's totient function. | 830 | graphs = [
Graph(
let={
"n": Const(10080),
"a": Const(6),
"b": Const(511),
"result": CountOverSet(set=SolutionsSet(var=Var("d"), condition=And(Divides(divisor=Var("d"), dividend=Ref("n")), Geq(Var("d"), Ref("a")), Leq(Var("d"), Ref("b"))))),
"Q": S... | NT | null | COUNT | sympy | ONE_PHI_1 | [
"ONE_PHI_1"
] | f6b5a5 | nt_count_divisors_in_range_v1 | null | 5 | 0 | [
"ONE_PHI_1"
] | 1 | 0.009 | 2026-02-08T04:02:56.412831Z | {
"verified": true,
"answer": 830,
"timestamp": "2026-02-08T04:02:56.421585Z"
} | 9ab0b5 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 204,
"completion_tokens": 4224
},
"timestamp": "2026-02-09T17:28:37.061Z",
"answer": 830
},
{
"id... | 1 | [
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "ONE_PHI_1",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "V5",
"status... | {
"lo": -6.5,
"mid": -0.2,
"hi": 6.11
} | ||
821669 | antilemma_k2_v1_1918700295_120 | Compute the value of
$$
\sum_{k=1}^{353} \phi(k) \left\lfloor \frac{353}{k} \right\rfloor,
$$
where $\phi(k)$ denotes Euler's totient function. | 62,481 | graphs = [
Graph(
let={
"_n": Const(353),
"x": Summation(var="k", start=Const(1), end=Ref("_n"), expr=Mul(EulerPhi(n=Var("k")), Floor(Div(Const(353), Var("k"))))),
},
goal=Ref("x"),
)
] | NT | COMB | COMPUTE | sympy | K2 | [
"K2"
] | 6897ab | antilemma_k2_v1 | null | 6 | 0 | [
"K2"
] | 1 | 0.001 | 2026-02-08T03:00:41.354614Z | {
"verified": true,
"answer": 62481,
"timestamp": "2026-02-08T03:00:41.355294Z"
} | 610e74 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 162,
"completion_tokens": 947
},
"timestamp": "2026-02-10T12:35:37.188Z",
"answer": 62481
},
{
"i... | 1 | [
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K2",
"status": "ok"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "V3",
"status": "no"
}
] | {
"lo": -3.47,
"mid": 0.81,
"hi": 4.81
} | ||
21c3c3 | antilemma_k2_v1_124444284_6576 | Let $n = 340$. Compute the value of $$\sum_{k=1}^{340} \phi(k) \left\lfloor \frac{1}{k} \sum_{d \mid n} \phi(d) \right\rfloor,$$ where $\phi$ denotes Euler's totient function. | 57,970 | graphs = [
Graph(
let={
"_n": Const(340),
"x": Summation(var="k", start=Const(1), end=Const(340), expr=Mul(EulerPhi(n=Var("k")), Floor(Div(SumOverDivisors(n=Ref(name='_n'), 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 | 0.002 | 2026-02-08T08:32:28.990691Z | {
"verified": true,
"answer": 57970,
"timestamp": "2026-02-08T08:32:28.992238Z"
} | 0a3c8b | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 110,
"completion_tokens": 1460
},
"timestamp": "2026-02-13T19:21:05.087Z",
"answer": 57970
},
... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "K2",
"status": "ok"
},
{
"lemma": "K3",
"status": "ok"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "MOD... | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
420478 | nt_min_phi_inverse_v1_1978505735_224 | Let $n = 2$, $k = 16$, and $\text{upper} = 70$. Let $S$ be the set of all positive integers $n$ such that $1 \leq n \leq 70$ and $\varphi(n) = 16$, where $\varphi$ denotes Euler's totient function. Let $r$ be the minimum element of $S$. Define
\[
Q = \sum_{i=0}^{d-1} \left( \text{digit}_i(r) \cdot (i+1)^2 \right) + \su... | 6,006 | graphs = [
Graph(
let={
"_n": Const(2),
"upper": Const(70),
"k": Const(16),
"result": MinOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Ref("upper")), Eq(EulerPhi(n=Var("n")), Ref("k"))))),
"Q": Sum(Summ... | NT | null | EXTREMUM | sympy | SUM_ARITHMETIC | [
"SUM_ARITHMETIC"
] | 2c0c6e | nt_min_phi_inverse_v1 | digits_weighted_mod | 5 | 0 | [
"SUM_ARITHMETIC"
] | 1 | 0.009 | 2026-02-08T15:13:59.203412Z | {
"verified": true,
"answer": 6006,
"timestamp": "2026-02-08T15:13:59.212293Z"
} | 653c7f | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 238,
"completion_tokens": 1980
},
"timestamp": "2026-02-16T02:08:15.628Z",
"answer": 6006
},
{... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "SUM_ARITHMETIC",
"status": "ok"
},
{
"lemma": "V1",
"status": "no"... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
69d2aa | nt_count_divisible_and_v1_784195855_8952 | Let $d_1 = 9$. Let $S$ be the set of all ordered pairs $(x,y)$ of positive integers such that $xy = 36$. Let $d_2$ be the minimum value of $x + y$ over all pairs $(x,y) \in S$. Compute the number of positive integers $n$ such that $1 \le n \le 11124$, $n$ is divisible by $d_1$, and $n$ is divisible by $d_2$. | 309 | graphs = [
Graph(
let={
"upper": Const(11124),
"d1": Const(9),
"d2": 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(36)))), ... | NT | null | COUNT | sympy | B3 | [
"B3"
] | 0cd20d | nt_count_divisible_and_v1 | null | 3 | 0 | [
"B3"
] | 1 | 0.379 | 2026-02-08T16:25:45.241447Z | {
"verified": true,
"answer": 309,
"timestamp": "2026-02-08T16:25:45.620390Z"
} | 139218 | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 172,
"completion_tokens": 406
},
"timestamp": "2026-02-16T07:24:49.536Z",
"answer": 309
},
{
"id": 11,
... | 2 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "V1",
"status": "no"
},
{
"lemma": "VAL_SUM_EQ",
... | {
"lo": -10,
"mid": -7.27,
"hi": -4.54
} | ||
c446a3 | nt_num_divisors_compute_v1_168721529_1683 | Let $n_1 = 67$ and $w = \lambda(n_1) + 1$, where $\lambda$ denotes the Liouville function. Let $d_{\max}$ be the largest positive divisor of $6059$ that is at most $73$. Define $p = d_{\max} + w$. Let $f = \Omega(p)$, the number of prime factors of $p$ counted with multiplicity. Define $n = 99f$ and let $r = \tau(n)$, ... | 6 | graphs = [
Graph(
let={
"_n": Const(73),
"n1": Const(67),
"w": Sum(LiouvilleLambda(n=Ref(name='n1')), Const(1)),
"p": Sum(MaxOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Const(1)), Leq(Var("d"), Ref("_n")), Divides(divisor=Var("d"), divid... | NT | null | COMPUTE | sympy | MAX_DIVISOR | [
"MAX_DIVISOR/LIOUVILLE_MINUS_ONE/BIG_OMEGA_ONE"
] | 9f27a6 | nt_num_divisors_compute_v1 | null | 5 | 2 | [
"BIG_OMEGA_ONE",
"LIOUVILLE_MINUS_ONE",
"MAX_DIVISOR"
] | 3 | 0.006 | 2026-02-08T13:50:43.565596Z | {
"verified": true,
"answer": 6,
"timestamp": "2026-02-08T13:50:43.571388Z"
} | be5e9f | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 257,
"completion_tokens": 1006
},
"timestamp": "2026-02-09T20:19:42.789Z",
"answer": 6
},
{
"id":... | 2 | [
{
"lemma": "BIG_OMEGA_ONE",
"status": "ok_later"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "LIOUVILLE_MINUS_ONE",
"st... | {
"lo": -10,
"mid": -6.47,
"hi": -2.95
} | ||
4a97d0 | comb_count_permutations_fixed_v1_898971024_2079 | Let $n$ be the largest prime number such that $2 \leq n \leq 12$. Let $S$ be the set of all ordered pairs $(x,y)$ of positive integers such that $x + y = 6$. Define $k$ to be the maximum value of $xy$ over all pairs $(x,y) \in S$. Compute
$$
\binom{n}{k} \cdot !(n - k),
$$
where $!m$ denotes the number of derangements ... | 55 | graphs = [
Graph(
let={
"_n": Const(2),
"n": MaxOverSet(set=SolutionsSet(var=Var("n1"), condition=And(Geq(Var("n1"), Ref("_n")), Leq(Var("n1"), Const(12)), IsPrime(Var("n1"))))),
"k": MaxOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), con... | NT | COMB | COUNT | sympy | MAX_PRIME_BELOW | [
"MAX_PRIME_BELOW",
"B1"
] | 7086d0 | comb_count_permutations_fixed_v1 | null | 6 | 0 | [
"B1",
"MAX_PRIME_BELOW"
] | 2 | 0.005 | 2026-02-08T16:31:40.462038Z | {
"verified": true,
"answer": 55,
"timestamp": "2026-02-08T16:31:40.466956Z"
} | 49b4f6 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 155,
"completion_tokens": 533
},
"timestamp": "2026-02-17T06:41:59.255Z",
"answer": 55
},
{
... | 1 | [
{
"lemma": "B1",
"status": "ok"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"statu... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
f4af21 | antilemma_sum_primes_v1_1742523217_104 | Let $S$ be the set of all nonnegative integers $j$ with $0 \leq j \leq 2080$ such that $\binom{2080}{j} \equiv 1 \pmod{2}$. Let $T$ be the set of all prime numbers $n$ such that $2 \leq n \leq |S|$. Let $x$ be the sum of all elements in $T$. Compute the remainder when $29773x$ is divided by 53579. | 41,707 | graphs = [
Graph(
let={
"_n": Const(2),
"x": SumOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Ref("_n")), Leq(Var("n"), CountOverSet(set=SolutionsSet(var=Var("j"), condition=And(Geq(Var("j"), Const(0)), Leq(Var("j"), Const(2080)), Eq(Mod(value=Binom(n=Const(2080)... | NT | null | COMPUTE | sympy | V8 | [
"V8/SUM_PRIMES",
"SUM_PRIMES"
] | 4a3626 | antilemma_sum_primes_v1 | null | 6 | 0 | [
"SUM_PRIMES",
"V8"
] | 2 | 0.003 | 2026-02-08T02:53:10.463777Z | {
"verified": true,
"answer": 41707,
"timestamp": "2026-02-08T02:53:10.466750Z"
} | 399a20 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 225,
"completion_tokens": 795
},
"timestamp": "2026-02-09T13:47:24.770Z",
"answer": 41707
},
{
"i... | 1 | [
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "SUM_PRIMES",
... | {
"lo": -6.51,
"mid": -0.31,
"hi": 5.43
} | ||
31ac9d | nt_count_coprime_and_v1_124444284_9158 | Let $A$ be the set of all positive integers $d$ such that $d \geq 2$ and $d$ divides $4725$. Define $k_1$ to be the minimum element of $A$, and let $k_2 = 7$. Let $U = 34104$. Define $S$ as the set of all positive integers $n$ such that $1 \leq n \leq U$, $\gcd(n, k_1) = 1$, and $\gcd(n, k_2) = 1$. Let $Q = (44121 \cdo... | 40,092 | graphs = [
Graph(
let={
"upper": Const(34104),
"k1": MinOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Const(2)), Divides(divisor=Var("d"), dividend=Const(4725))))),
"k2": Const(7),
"result": CountOverSet(set=SolutionsSet(var=Var("n"), cond... | NT | null | COUNT | sympy | MIN_PRIME_FACTOR | [
"MIN_PRIME_FACTOR"
] | bc3776 | nt_count_coprime_and_v1 | null | 4 | 0 | [
"MIN_PRIME_FACTOR"
] | 1 | 5.159 | 2026-02-08T12:15:07.984086Z | {
"verified": true,
"answer": 40092,
"timestamp": "2026-02-08T12:15:13.142755Z"
} | 52f25e | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 188,
"completion_tokens": 2430
},
"timestamp": "2026-02-14T23:29:44.415Z",
"answer": 40092
},
... | 1 | [
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "MIN_PRIME_FACTOR",
"status": "ok"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "V1",
"status": "no"
},
{
"lemma": "V7",
"status": "no... | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
a11ea4 | sequence_fibonacci_compute_v1_48377204_2777 | Let $S$ be the set of all ordered pairs $(k, j)$ of integers with $1 \leq k \leq 6$ and $1 \leq j \leq 7$. Define $n = \frac{7}{49} \sum_{(k,j) \in S} k$. Compute the $n$-th Fibonacci number, where the Fibonacci sequence is defined by $F_1 = 1$, $F_2 = 1$, and $F_m = F_{m-1} + F_{m-2}$ for $m \geq 3$. | 10,946 | graphs = [
Graph(
let={
"n": Div(Mul(Const(7), SumOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("k"), Var("_j")]), condition=Const(1), domain=CartesianProduct(left=IntegerRange(start=Const(1), end=Const(6)), right=IntegerRange(start=Const(1), end=Const(7)))), expr=Var("k")))), ... | NT | null | COMPUTE | sympy | SUM_INDEPENDENT | [
"SUM_INDEPENDENT",
"SUM_ARITHMETIC"
] | 9f7183 | sequence_fibonacci_compute_v1 | null | 2 | 0 | [
"SUM_ARITHMETIC",
"SUM_INDEPENDENT"
] | 2 | 0.002 | 2026-02-08T16:57:28.022510Z | {
"verified": true,
"answer": 10946,
"timestamp": "2026-02-08T16:57:28.024263Z"
} | 8d2cbb | 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": 718
},
"timestamp": "2026-02-17T15:49:48.996Z",
"answer": 10946
},
{... | 1 | [
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "SUM_ARITHMETIC",
"status": "ok"
},
{
"lemma": "SUM_INDEPENDENT",
... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
95c429 | nt_count_divisible_and_v1_1353956133_415 | Let $d_1 = 6$ and let
$$
d_2 = \sum_{k=1}^{4} \varphi(k) \left\lfloor \frac{4}{k} \right\rfloor,
$$
where $\varphi$ denotes Euler's totient function. Determine the number of positive integers $n$ such that $n \leq 122370$, $n$ is divisible by $d_1$, and $n$ is divisible by $d_2$. | 4,079 | graphs = [
Graph(
let={
"upper": Const(122370),
"d1": Const(6),
"d2": Summation(var="k", start=Const(1), end=Const(4), expr=Mul(EulerPhi(n=Var("k")), Floor(Div(Const(4), Var("k"))))),
"result": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var(... | NT | null | COUNT | sympy | K2 | [
"K2"
] | 6897ab | nt_count_divisible_and_v1 | null | 4 | 0 | [
"K2"
] | 1 | 4.475 | 2026-02-08T11:26:18.188387Z | {
"verified": true,
"answer": 4079,
"timestamp": "2026-02-08T11:26:22.663772Z"
} | 340f6c | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 170,
"completion_tokens": 561
},
"timestamp": "2026-02-15T22:01:45.123Z",
"answer": 4079
},
{
"id": 11,
... | 2 | [
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K2",
"status": "ok"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
}... | {
"lo": -9.12,
"mid": -6.02,
"hi": -3.62
} | ||
aa92cb | comb_catalan_compute_v1_898971024_227 | Let $N$ be the number of integers $t$ such that $18\le t\le88$ and there exist integers $a$ and $b$ with $1\le a\le6$, $1\le b\le4$, and
$$t=8a+10b.$$
Let $n=11$, and let
$$C_{n}$$
be the $n$th Catalan number. Define $R=C_{n}$.
Let $S$ be the number of ordered pairs $(x_1,x_2)$ of positive odd integers such that
$$x_... | 2 | 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=6)), Geq(left=Var(name='b'), right=Const(value=... | COMB | null | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM/COMB1/COUNT_SUM_EQUALS"
] | 2d95e6 | comb_catalan_compute_v1 | bell_mod | 7 | 0 | [
"COMB1",
"COUNT_SUM_EQUALS",
"LIN_FORM"
] | 3 | 0.095 | 2026-02-08T15:18:17.636497Z | {
"verified": true,
"answer": 2,
"timestamp": "2026-02-08T15:18:17.731348Z"
} | c093b8 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 380,
"completion_tokens": 1444
},
"timestamp": "2026-02-24T20:24:16.437Z",
"answer": 2
},
{
"id":... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COMB1",
"status": "ok_later"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "ok_later"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "V7",
"stat... | {
"lo": -2.43,
"mid": 1.2,
"hi": 4.84
} | ||
cd90b0 | modular_mod_compute_v1_2051736721_828 | Let $a = 47961$. Let $m$ be the number of nonnegative integers $j$ such that $0 \le j \le 97758$ and $\binom{97758}{j}$ is odd. Compute the remainder when $a$ is divided by $m$. | 7,001 | graphs = [
Graph(
let={
"a": Const(47961),
"m": CountOverSet(set=SolutionsSet(var=Var("j"), condition=And(Geq(Var("j"), Const(0)), Leq(Var("j"), Const(97758)), Eq(Mod(value=Binom(n=Const(97758), k=Var("j")), modulus=Const(2)), Const(1))), domain='nonnegative_integers')),
... | ALG | COMB | COMPUTE | sympy | V8 | [
"V8"
] | 86348e | modular_mod_compute_v1 | null | 5 | 0 | [
"V8"
] | 1 | 0.004 | 2026-02-08T15:41:53.008649Z | {
"verified": true,
"answer": 7001,
"timestamp": "2026-02-08T15:41:53.012518Z"
} | d09428 | 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": 1082
},
"timestamp": "2026-02-24T18:19:41.349Z",
"answer": 7001
},
{
"... | 1 | [
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "V8",
"status": "ok"
}
] | {
"lo": -2.4,
"mid": 1.57,
"hi": 5.75
} | ||
57ce9c | diophantine_fbi2_min_v1_151522320_1256 | Let $k = 360$. Compute the smallest positive integer $d$ such that $3 \leq d \leq 370$, $d$ divides $k$, and $\frac{k}{d} \geq 5$. | 3 | graphs = [
Graph(
let={
"k": Const(360),
"a": Const(2),
"b": Const(4),
"upper": Const(370),
"result": MinOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Const(3)), Leq(Var("d"), Ref("upper")), Divides(divisor=Var("d"), dividend=R... | NT | null | EXTREMUM | sympy | LIN_FORM | [
"B3"
] | 0cd20d | diophantine_fbi2_min_v1 | null | 3 | 0 | [
"B3",
"LIN_FORM"
] | 2 | 0.068 | 2026-02-08T03:51:42.904251Z | {
"verified": true,
"answer": 3,
"timestamp": "2026-02-08T03:51:42.972242Z"
} | ecf50b | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 159,
"completion_tokens": 361
},
"timestamp": "2026-02-10T15:54:42.145Z",
"answer": 3
},
{
"id": ... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "V3",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
}
] | {
"lo": -7.01,
"mid": -4.68,
"hi": -2.15
} | ||
40db56 | geo_count_lattice_triangle_v1_784195855_8327 | Let $A = 128$ and $B = 324$. Let $P$ be the set of all ordered pairs of positive integers $(x, y)$ such that $xy = N$, where $N$ is the number of positive integers $p$ for which there exists a positive integer $q > p$ with $pq = 22777695978964576650$ and $\gcd(p, q) = 1$. Let $s = x + y$ over all such pairs $(x, y) \in... | 9,329 | graphs = [
Graph(
let={
"_c": Const(190),
"_m": Const(190),
"_n": Const(120),
"area_2x": Abs(arg=Sum(Mul(Const(value=128), Const(value=324)), Mul(Ref(name='_n'), Sub(left=Const(value=0), right=Const(value=190))))),
"boundary": Sum(GCD(a=Abs(arg=Con... | NT | null | COUNT | sympy | COPRIME_PAIRS | [
"COPRIME_PAIRS/B3",
"LIN_FORM"
] | 08b7b0 | geo_count_lattice_triangle_v1 | null | 7 | 0 | [
"B3",
"COPRIME_PAIRS",
"LIN_FORM"
] | 3 | 0.016 | 2026-02-08T16:00:45.495008Z | {
"verified": true,
"answer": 9329,
"timestamp": "2026-02-08T16:00:45.510786Z"
} | 3cbf48 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 322,
"completion_tokens": 6014
},
"timestamp": "2026-02-16T19:06:19.418Z",
"answer": 9329
},
{... | 1 | [
{
"lemma": "B3",
"status": "ok_later"
},
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
c46ded | algebra_poly_eval_v1_1439011603_455 | Let $ z = 25 $. Consider the set of all integers $ t $ such that $ 8 \leq t \leq 182 $ and there exist positive integers $ a $ and $ b $ with $ 1 \leq a \leq 7 $, $ 1 \leq b \leq 49 $, and $ t = 5a + 3b $. Let $ d_1, d_2, \dots, d_k $ be the positive divisors of the number of elements in this set. Define $ S = \sum_{i=... | 731 | graphs = [
Graph(
let={
"_n": Const(10),
"z": Const(25),
"result": Div(Sum(Mul(Const(7), Pow(Ref("z"), Const(3))), Mul(Const(20), Pow(Ref("z"), Const(2))), Mul(Ref("_n"), Ref("z")), Const(-48)), SumOverDivisors(n=CountOverSet(set=SolutionsSet(var=Var(name='t'), condition=... | NT | null | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM/K3"
] | c7df50 | algebra_poly_eval_v1 | null | 6 | 0 | [
"K3",
"LIN_FORM"
] | 2 | 0.005 | 2026-02-08T15:30:16.684942Z | {
"verified": true,
"answer": 731,
"timestamp": "2026-02-08T15:30:16.690200Z"
} | d3e040 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 210,
"completion_tokens": 4350
},
"timestamp": "2026-02-16T07:49:39.846Z",
"answer": 731
},
{
... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "K3",
"status": "ok_later"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
420a6c | antilemma_k3_v1_865884756_6376 | Let $n = 75295$. Compute the sum of $\phi(d)$ over all positive divisors $d$ of $n$. | 75,295 | graphs = [
Graph(
let={
"_n": Const(75295),
"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 | 2026-02-08T19:10:10.682924Z | {
"verified": true,
"answer": 75295,
"timestamp": "2026-02-08T19:10:10.683597Z"
} | a05f72 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 74,
"completion_tokens": 387
},
"timestamp": "2026-02-18T21:27:21.605Z",
"answer": 75295
},
{
... | 1 | [
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "K3",
"status": "ok"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
950997 | lte_diff_endings_v1_168721529_246 | Let $a = 41$, $b = 11$, $p = 5$, and $n = 95165$. Let $C$ be the largest integer $k$ such that $p^k$ divides $a - b$. Let $F = n!$, and let $v$ be the largest integer $k$ such that $p^k$ divides $F$. Define $T = n \cdot C + v$. Find the remainder when $T$ is divided by $100000$. | 18,954 | graphs = [
Graph(
let={
"a_val": Const(41),
"b_val": Const(11),
"p_val": Const(5),
"n_val": Const(95165),
"ab_diff": Sub(Ref("a_val"), Ref("b_val")),
"vp_ab": MaxKDivides(target=Ref("ab_diff"), base=Ref("p_val")),
"n_times_C... | NT | null | COMPUTE | sympy | LTE_DIFF | [
"LTE_DIFF"
] | cf8260 | lte_diff_endings_v1 | null | 6 | null | [
"LTE_DIFF"
] | 1 | 0.001 | 2026-02-08T12:55:46.935142Z | {
"verified": true,
"answer": 18954,
"timestamp": "2026-02-08T12:55:46.935882Z"
} | 418eb2 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 221,
"completion_tokens": 1564
},
"timestamp": "2026-02-09T02:51:26.901Z",
"answer": 18953
},
{
... | 1 | [
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "ok"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
}
] | {
"lo": -2.06,
"mid": 1.85,
"hi": 5.2
} | ||
fb198b | algebra_poly_eval_v1_124444284_10286 | Let $z = 21$. Compute the value of the expression
$$
16z^5 + 8z^4 - 143z^3 + 23z^2 + 316z - 220.
$$
divided by the number of integers $t$ such that $8 \leq t \leq 7520$ and $t = 5a + 3b$ for some integers $a$ and $b$ with $1 \leq a \leq 1474$ and $1 \leq b \leq 50$. Let $\text{result}$ be this quotient. Find the remain... | 76,140 | graphs = [
Graph(
let={
"_n": Const(8),
"z": Const(21),
"result": Div(Sum(Mul(Const(16), Pow(Ref("z"), Const(5))), Mul(Ref("_n"), Pow(Ref("z"), Const(4))), Mul(Const(-143), Pow(Ref("z"), Const(3))), Mul(Const(23), Pow(Ref("z"), Const(2))), Mul(Const(316), Ref("z")), Const... | NT | null | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | algebra_poly_eval_v1 | null | 5 | 0 | [
"LIN_FORM"
] | 1 | 0.003 | 2026-02-08T12:56:24.376270Z | {
"verified": true,
"answer": 76140,
"timestamp": "2026-02-08T12:56:24.379457Z"
} | c397a2 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 191,
"completion_tokens": 4415
},
"timestamp": "2026-02-15T07:50:49.341Z",
"answer": 76140
},
... | 1 | [
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "... | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
4515f6 | algebra_poly_eval_v1_238844314_603 | Compute the value of $$7 \cdot 9^4 + 10 \cdot 9^{\sum_{k=1}^{2} \phi(k) \left\lfloor \frac{2}{k} \right\rfloor} + 7 \cdot 9^2 - 2 \cdot 9 - 8.$$ | 53,758 | graphs = [
Graph(
let={
"_n": Const(2),
"z": Const(9),
"result": Sum(Mul(Const(7), Pow(Ref("z"), Const(4))), Mul(Const(10), Pow(Ref("z"), Summation(var="k", start=Const(1), end=Const(2), expr=Mul(EulerPhi(n=Var("k")), Floor(Div(Const(2), Var("k"))))))), Mul(Const(7), Pow(... | NT | null | COMPUTE | sympy | K2 | [
"K2"
] | 6897ab | algebra_poly_eval_v1 | null | 2 | 0 | [
"K2"
] | 1 | 0.002 | 2026-02-08T13:25:39.941538Z | {
"verified": true,
"answer": 53758,
"timestamp": "2026-02-08T13:25:39.943535Z"
} | d372c6 | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 128,
"completion_tokens": 351
},
"timestamp": "2026-02-16T04:35:16.000Z",
"answer": 5360398
},
{
"id": ... | 1 | [
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K2",
"status": "ok"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
}
] | {
"lo": -8.26,
"mid": -5.01,
"hi": -1.76
} | ||
11dca0 | lin_form_endings_v1_1520064083_9920 | Let $a_{\text{coeff}} = 50$ and $b_{\text{coeff}} = 30$. Define $\text{step} = \gcd(a_{\text{coeff}}, b_{\text{coeff}})$. Let $k_{\text{val}} = 132$. Compute
$$
\left\lfloor \frac{k_{\text{val}}}{\gcd(k_{\text{val}}, \text{step})} \right\rfloor.
$$
Multiply this result by 17000, and then find the remainder when this pr... | 32,295 | graphs = [
Graph(
let={
"a_coeff": Const(50),
"b_coeff": Const(30),
"k_val": Const(132),
"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(1... | COMB | NT | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | lin_form_endings_v1 | null | 3 | null | [
"LIN_FORM"
] | 1 | 0.001 | 2026-02-08T11:02:47.386330Z | {
"verified": true,
"answer": 32295,
"timestamp": "2026-02-08T11:02:47.386839Z"
} | b0cc8d | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 166,
"completion_tokens": 478
},
"timestamp": "2026-02-14T10:11:30.568Z",
"answer": 32295
},
{... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "V8",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
... | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
efaac7 | nt_count_divisors_in_range_v1_1978505735_785 | Let $n = 45360$ and $a = 11$. Let $b$ be the number of positive integers $n_1$ such that $1 \leq n_1 \leq 121080$ and $14$ divides the $n_1$-th Fibonacci number. Determine the number of positive divisors $d$ of $n$ such that $a \leq d \leq b$. Let $c = 26569$. Compute $c$ minus this count. Find the value of this result... | 26,487 | graphs = [
Graph(
let={
"_n": Const(14),
"n": Const(45360),
"a": Const(11),
"b": CountOverSet(set=SolutionsSet(var=Var("n1"), condition=And(Geq(Var("n1"), Const(1)), Leq(Var("n1"), Const(121080)), Divides(divisor=Ref("_n"), dividend=Fibonacci(arg=Var(name='n1'... | NT | null | COUNT | sympy | COUNT_FIB_DIVISIBLE | [
"COUNT_FIB_DIVISIBLE"
] | 66de3c | nt_count_divisors_in_range_v1 | null | 6 | 0 | [
"COUNT_FIB_DIVISIBLE"
] | 1 | 0.082 | 2026-02-08T15:35:37.356017Z | {
"verified": true,
"answer": 26487,
"timestamp": "2026-02-08T15:35:37.437586Z"
} | e3fd0f | 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": 2459
},
"timestamp": "2026-02-16T09:50:34.554Z",
"answer": 26487
},
... | 1 | [
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "ok"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "VAL_SUM_EQ",
"status": "... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
704beb | nt_max_prime_below_v1_124444284_3483 | Let $p$ and $q$ be positive integers such that $pq = 12$, $\gcd(p, q) = 1$, and $p < q$. Let $m$ be the number of such integers $p$. Let $S$ be the set of all prime numbers $n$ such that $m \leq n \leq 11351$. Determine the value of the largest element in $S$. | 11,351 | graphs = [
Graph(
let={
"upper": Const(11351),
"result": MaxOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), CountOverSet(set=SolutionsSet(var=Var("p"), condition=And(IsPositive(arg=Var(name='p')), Exists(var=Var(name='q'), condition=And(Eq(left=Mul(Var(name='p'), V... | NT | null | EXTREMUM | sympy | COPRIME_PAIRS | [
"COPRIME_PAIRS"
] | 2bb3aa | nt_max_prime_below_v1 | null | 4 | 0 | [
"COPRIME_PAIRS"
] | 1 | 1.289 | 2026-02-08T05:25:23.475806Z | {
"verified": true,
"answer": 11351,
"timestamp": "2026-02-08T05:25:24.764511Z"
} | 3f2dbc | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 133,
"completion_tokens": 1300
},
"timestamp": "2026-02-12T08:32:41.528Z",
"answer": 11351
},
... | 1 | [
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"
}
] | {
"lo": -5.92,
"mid": -3.14,
"hi": 0.26
} | ||
d51ac0 | algebra_poly_eval_v1_601307018_6056 | Let $D = \max \{ d \ge 1 : d \mid 4204544 \text{ and } d^2 \le 4204544 \}$. Find the number $n$ of ordered pairs $(a, b)$ of positive integers with $1 \le a \le b \le 20$ such that $32a^2 - 64ab + 32b^2 = D$. Let $R = 2n^4 + n^3 + 3n^2 + 4n + 7$. Compute $R$. | 43,687 | graphs = [
Graph(
let={
"_m": Const(4),
"_n": Const(2),
"n": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("a"), Var("b")]), condition=And(Geq(Var("a"), Const(1)), Leq(Var("a"), Const(20)), Geq(Var("b"), Const(1)), Leq(Var("b"), Const(20)), Leq(Var("a"), Var("b"))... | NT | null | COMPUTE | sympy | B3_CLOSEST | [
"B3_CLOSEST/QF_PSD_ORBIT"
] | 82592c | algebra_poly_eval_v1 | null | 5 | 0 | [
"B3_CLOSEST",
"QF_PSD_ORBIT"
] | 2 | 0.011 | 2026-03-10T06:39:05.650863Z | {
"verified": true,
"answer": 43687,
"timestamp": "2026-03-10T06:39:05.662301Z"
} | 2bddc4 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 230,
"completion_tokens": 1802
},
"timestamp": "2026-04-19T03:29:20.576Z",
"answer": 43687
},
{
... | 1 | [
{
"lemma": "B3_CLOSEST",
"status": "ok"
},
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "QF_PSD_ORBIT",
"status": "ok_later"
},
{
"lemma": "V8",
"status": "no... | {
"lo": -5.35,
"mid": 0.52,
"hi": 5.84
} | ||
6fb9cb | sequence_fibonacci_compute_v1_655260480_5749 | Let $\_n = 72712$. Let $S$ be the set of all integers $t$ such that $7 \leq t \leq 30$ and there exist positive integers $a$ and $b$ with $1 \leq a \leq 5$, $1 \leq b \leq 4$, and $t = 2a + 5b$. Let $n$ be the number of elements in $S$. Define $\text{result} = F_n$, the $n$-th Fibonacci number. Compute the remainder wh... | 68,517 | graphs = [
Graph(
let={
"_n": Const(72712),
"n": CountOverSet(set=SolutionsSet(var=Var("t"), condition=Exists(var=Var(name='a'), condition=Exists(var=Var(name='b'), condition=And(Geq(left=Var(name='a'), right=Const(value=1)), Leq(left=Var(name='a'), right=Const(value=5)), Geq(left=Va... | NT | null | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | sequence_fibonacci_compute_v1 | null | 3 | 0 | [
"LIN_FORM"
] | 1 | 0.002 | 2026-02-08T18:38:45.100174Z | {
"verified": true,
"answer": 68517,
"timestamp": "2026-02-08T18:38:45.102377Z"
} | 588349 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 193,
"completion_tokens": 2641
},
"timestamp": "2026-02-18T18:17:32.916Z",
"answer": 68517
},
... | 1 | [
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
194f30 | comb_count_permutations_fixed_v1_898971024_88 | Compute $\binom{10}{6} \cdot !4$, where $!4$ denotes the number of derangements of four elements. | 1,890 | graphs = [
Graph(
let={
"n": Const(10),
"k": Const(6),
"result": Mul(Binom(n=Ref("n"), k=Ref("k")), Subfactorial(arg=Sub(left=Ref(name='n'), right=Ref(name='k')))),
},
goal=Ref("result"),
)
] | COMB | null | COUNT | sympy | MAX_PRIME_BELOW | [
"MAX_PRIME_BELOW/L3B/B1"
] | 2f3b2a | comb_count_permutations_fixed_v1 | null | 3 | 0 | [
"B1",
"L3B",
"MAX_PRIME_BELOW"
] | 3 | 0.018 | 2026-02-08T15:10:52.454243Z | {
"verified": true,
"answer": 1890,
"timestamp": "2026-02-08T15:10:52.471767Z"
} | 74b678 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 140,
"completion_tokens": 415
},
"timestamp": "2026-02-24T20:01:20.380Z",
"answer": 1890
},
{
"id... | 2 | [
{
"lemma": "B1",
"status": "ok_later"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "L3B",
"status": "ok_later"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok"
},
{
"lemma": "MAX_VAL",
"status... | {
"lo": -10,
"mid": -7.42,
"hi": -4.85
} | ||
f510cf | geo_visible_lattice_v1_2051736721_1275 | Let $n = 199$. Define $L$ to be the number of ordered pairs $(x, y)$ of positive integers with $1 \le x, y \le 199$ such that $\gcd(x, y) = 1$. Let $k = |L| \bmod 11$. Compute the $k$-th Bell number, where the Bell numbers count the number of partitions of a set of size $k$. Find the value of this Bell number. | 15 | graphs = [
Graph(
let={
"n": Const(199),
"result": VisibleLatticePoints(n=Ref(name='n')),
"Q": Bell(Mod(value=Abs(arg=Ref(name='result')), modulus=Const(11))),
},
goal=Ref("Q"),
)
] | GEOM | COMB | COUNT | sympy | [] | geo_visible_lattice_v1 | null | 4 | 0 | null | null | 5.984 | 2026-02-08T15:55:25.201441Z | {
"verified": true,
"answer": 15,
"timestamp": "2026-02-08T15:55:31.185712Z"
} | f4ca5a | 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": 18740
},
"timestamp": "2026-02-24T19:22:04.667Z",
"answer": 15
},
{
"i... | 1 | [] | {
"lo": 1.98,
"mid": 5.23,
"hi": 8.52
} | ||||
264470 | nt_count_phi_equals_v1_1520064083_9190 | Let $P$ be the maximum value of $xy$ over all pairs of positive integers $(x, y)$ such that $x + y = 118$. Let $k = 592$. Determine the number of positive integers $n$ such that $1 \leq n \leq P$ and $\phi(n) = k$, where $\phi$ denotes Euler's totient function. | 6 | 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(118)))), expr=Mul(Var("x"), Var("y")))),
"k": Const(592)... | NT | null | COUNT | sympy | B3 | [
"B1"
] | 5b950e | nt_count_phi_equals_v1 | null | 7 | 0 | [
"B1",
"B3"
] | 2 | 2.881 | 2026-02-08T10:35:35.433484Z | {
"verified": true,
"answer": 6,
"timestamp": "2026-02-08T10:35:38.314511Z"
} | cca792 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 125,
"completion_tokens": 5177
},
"timestamp": "2026-02-14T07:52:35.209Z",
"answer": 6
},
{
... | 1 | [
{
"lemma": "B1",
"status": "ok"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "VAL_SUM_EQ",
"status"... | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
0ab97d | comb_count_permutations_fixed_v1_601307018_1099 | Let $D_n$ denote the number of derangements of $n$ elements. Compute $\binom{7}{k} \cdot D_{7 - k}$ where $k = \binom{12}{0} - 1$. | 1,854 | graphs = [
Graph(
let={
"n": Const(7),
"k": Sub(Binom(n=Const(12), k=Const(0)), Const(1)),
"result": Mul(Binom(n=Ref("n"), k=Ref("k")), Subfactorial(arg=Sub(left=Ref(name='n'), right=Ref(name='k')))),
},
goal=Ref("result"),
)
] | COMB | null | COUNT | sympy | POLY_ORBIT_LEGENDRE | [
"ZERO_BINOM_0"
] | fb90f6 | comb_count_permutations_fixed_v1 | null | 3 | 0 | [
"POLY_ORBIT_LEGENDRE",
"ZERO_BINOM_0"
] | 2 | 0.013 | 2026-03-10T01:40:37.846687Z | {
"verified": true,
"answer": 1854,
"timestamp": "2026-03-10T01:40:37.859942Z"
} | 0649f3 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 161,
"completion_tokens": 896
},
"timestamp": "2026-03-29T01:11:43.538Z",
"answer": 1854
},
{
"id... | 1 | [
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
},
{
"lemma": "ZERO_BINOM_0",
"st... | {
"lo": -4.31,
"mid": -1.92,
"hi": 0.62
} | ||
82ac52 | modular_sum_quadratic_residues_v1_153355830_336 | Let $ n = 4 $ and let $ p $ be the smallest prime divisor of $ 1342553 $. Compute the value of $ \frac{p(p-1)}{n} $. | 2,943 | graphs = [
Graph(
let={
"_n": Const(4),
"p": MinOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Const(2)), Divides(divisor=Var("d"), dividend=Const(1342553))))),
"result": Div(Mul(Ref("p"), Sub(Ref("p"), Const(1))), Ref("_n")),
},
goal=R... | NT | null | SUM | sympy | MIN_PRIME_FACTOR | [
"MIN_PRIME_FACTOR"
] | bc3776 | modular_sum_quadratic_residues_v1 | null | 3 | 0 | [
"MIN_PRIME_FACTOR"
] | 1 | 0.001 | 2026-02-08T03:02:47.618018Z | {
"verified": true,
"answer": 2943,
"timestamp": "2026-02-08T03:02:47.619112Z"
} | 99af7a | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 151,
"completion_tokens": 1686
},
"timestamp": "2026-02-10T12:38:21.623Z",
"answer": 2943
},
{
"i... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MIN_PRIME_FACTOR",
"status": "ok"
}... | {
"lo": 1.1,
"mid": 4.17,
"hi": 6.61
} | ||
24a40a | antilemma_k3_v1_784195855_5129 | Let $n = 36955$. Compute the sum $\sum_{d \mid n} \phi(d)$, where $\phi$ denotes Euler's totient function. | 36,955 | graphs = [
Graph(
let={
"_n": Const(36955),
"x": SumOverDivisors(n=Ref(name='_n'), var='d', expr=EulerPhi(n=Var(name='d'))),
},
goal=Ref("x"),
)
] | NT | COMB | COMPUTE | sympy | K3 | [
"K3"
] | 54c41e | antilemma_k3_v1 | null | 3 | 0 | [
"K3"
] | 1 | 0 | 2026-02-08T07:41:47.747324Z | {
"verified": true,
"answer": 36955,
"timestamp": "2026-02-08T07:41:47.747664Z"
} | a5cf94 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 80,
"completion_tokens": 638
},
"timestamp": "2026-02-13T11:42:45.221Z",
"answer": 36955
},
{
... | 1 | [
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "K3",
"status": "ok"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
}
] | {
"lo": -3.51,
"mid": 1.33,
"hi": 6.56
} | ||
222e42 | nt_count_divisors_in_range_v1_898971024_375 | Let $a$ be the number of positive integers $p$ for which there exists a positive integer $q$ such that $pq = 12$, $\gcd(p, q) = 1$, and $p < q$. Let $b$ be the minimum value of $x + y$ over all pairs of positive integers $(x, y)$ such that $xy = 131769$. Let $r$ be the number of positive divisors $d$ of $10080$ such th... | 65,476 | graphs = [
Graph(
let={
"n": Const(10080),
"a": CountOverSet(set=SolutionsSet(var=Var("p"), condition=And(IsPositive(arg=Var(name='p')), Exists(var=Var(name='q'), condition=And(Eq(left=Mul(Var(name='p'), Var(name='q')), right=Const(value=12)), Eq(left=GCD(a=Var(name='p'), b=Var(name=... | NT | null | COUNT | sympy | COPRIME_PAIRS | [
"COPRIME_PAIRS",
"B3"
] | 1999ea | nt_count_divisors_in_range_v1 | null | 6 | 0 | [
"B3",
"COPRIME_PAIRS"
] | 2 | 0.015 | 2026-02-08T15:25:09.916033Z | {
"verified": true,
"answer": 65476,
"timestamp": "2026-02-08T15:25:09.931340Z"
} | 42f9e2 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 164,
"completion_tokens": 2144
},
"timestamp": "2026-02-16T06:03:39.182Z",
"answer": 65476
},
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
ad0507 | nt_lcm_compute_v1_1978505735_980 | Let $A$ be the number of positive integers $n$ with $1 \leq n \leq 26773$ such that $n \equiv \left\lfloor \frac{n}{2} \right\rfloor \pmod{11}$. Let $B$ be the number of positive integers $n_1$ with $1 \leq n_1 \leq 8405$ such that $n_1 \equiv \left\lfloor \frac{n_1}{2} \right\rfloor \pmod{3}$. Compute the remainder wh... | 38,358 | graphs = [
Graph(
let={
"_m": Const(77841),
"_n": Const(79710),
"a": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Const(26773)), Congruent(a=Var(name='n'), b=Floor(arg=Div(left=Var(name='n'), right=Const(value=2))), modu... | NT | null | COMPUTE | sympy | L3C | [
"L3C"
] | 73f8b0 | nt_lcm_compute_v1 | null | 6 | 0 | [
"L3C"
] | 1 | 0.002 | 2026-02-08T15:43:30.374607Z | {
"verified": true,
"answer": 38358,
"timestamp": "2026-02-08T15:43:30.376937Z"
} | d7ae4b | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 181,
"completion_tokens": 2971
},
"timestamp": "2026-02-16T12:59:29.623Z",
"answer": 38358
},
... | 1 | [
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "L3C",
"status": "ok"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "V3",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
c9c2ce | comb_factorial_compute_v1_1520064083_10321 | Let $n$ be the number of positive integers $p$ for which there exists a positive integer $q$ such that $p \cdot q = 441000$, $\gcd(p, q) = 1$, and $p < q$. Let $r = n!$. Compute the remainder when $44121 \cdot r$ is divided by $80744$. | 6,912 | graphs = [
Graph(
let={
"_n": Const(80744),
"n": CountOverSet(set=SolutionsSet(var=Var("p"), condition=And(IsPositive(arg=Var(name='p')), Exists(var=Var(name='q'), condition=And(Eq(left=Mul(Var(name='p'), Var(name='q')), right=Const(value=441000)), Eq(left=GCD(a=Var(name='p'), b=Var(... | NT | null | COMPUTE | sympy | COPRIME_PAIRS | [
"COPRIME_PAIRS"
] | 2bb3aa | comb_factorial_compute_v1 | null | 6 | 0 | [
"COPRIME_PAIRS"
] | 1 | 0.001 | 2026-02-08T11:21:16.104234Z | {
"verified": true,
"answer": 6912,
"timestamp": "2026-02-08T11:21:16.105079Z"
} | 7ed7f2 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 123,
"completion_tokens": 3076
},
"timestamp": "2026-02-14T12:06:40.875Z",
"answer": 6912
},
{... | 1 | [
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "V3",
"status": "no"
}
] | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
2a7ddb | geo_visible_lattice_v1_1520064083_5463 | Let $n = 90$. Define $L$ to be the set of all ordered pairs of positive integers $(x, y)$ such that $1 \leq x, y \leq n$ and $\gcd(x, y) = 1$. Let $r$ be the number of elements in $L$. Compute the remainder when $2053 \cdot r$ is divided by $86253$. | 2,973 | graphs = [
Graph(
let={
"n": Const(90),
"result": VisibleLatticePoints(n=Ref(name='n')),
"_c": Const(2053),
"Q": Mod(value=Mul(Ref("_c"), Ref("result")), modulus=Const(86253)),
},
goal=Ref("Q"),
)
] | GEOM | null | COUNT | sympy | [] | geo_visible_lattice_v1 | null | 6 | 0 | null | null | 1.289 | 2026-02-08T06:48:12.686270Z | {
"verified": true,
"answer": 2973,
"timestamp": "2026-02-08T06:48:13.975723Z"
} | 3b0699 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 196,
"completion_tokens": 3027
},
"timestamp": "2026-02-24T07:55:58.497Z",
"answer": 2973
},
{
"i... | 1 | [] | {
"lo": 1.15,
"mid": 4.18,
"hi": 6.61
} | ||||
a2d227 | diophantine_fbi2_min_v1_677425708_3220 | Let $T$ be the set of all integers $t$ such that $8 \leq t \leq 46$ and there exist positive integers $a$ and $b$ with $1 \leq a \leq 5$, $1 \leq b \leq 7$, and $t = 5a + 3b$. Let $u$ be the number of elements in $T$. Let $d$ be the smallest divisor of $21$ such that $d \geq 3$, $d \leq u$, and $\frac{21}{d} \geq 5$. C... | 16 | graphs = [
Graph(
let={
"_n": Const(19),
"k": Const(21),
"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... | NT | null | EXTREMUM | sympy | MIN_PRIME_FACTOR | [
"LIN_FORM"
] | 7b2633 | diophantine_fbi2_min_v1 | null | 5 | 0 | [
"LIN_FORM",
"MIN_PRIME_FACTOR"
] | 2 | 0.018 | 2026-02-08T05:32:28.924618Z | {
"verified": true,
"answer": 16,
"timestamp": "2026-02-08T05:32:28.942832Z"
} | f80afe | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 183,
"completion_tokens": 1682
},
"timestamp": "2026-02-12T11:28:28.504Z",
"answer": 16
},
{
... | 1 | [
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
}
] | {
"lo": -8.32,
"mid": -5.11,
"hi": -2.37
} | ||
884d1b | nt_count_coprime_v1_260342960_95 | Let $k$ be the number of ordered pairs $(i,j)$ of positive integers with $1 \leq i \leq 3$ and $1 \leq j \leq 8$ such that $\gcd(i,j) = 1$. Let $\text{result}$ be the number of positive integers $n$ with $1 \leq n \leq 32761$ such that $\gcd(n, k) = 1$. Compute the value of $\text{result} + \phi(|\text{result}| + \phi(... | 16,221 | graphs = [
Graph(
let={
"_n": Const(2),
"upper": Const(32761),
"k": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("i"), Var("j")]), condition=Eq(GCD(a=Var("i"), b=Var("j")), Const(1)), domain=CartesianProduct(left=IntegerRange(start=Const(1), end=Const(3)), right=... | NT | null | COUNT | sympy | COUNT_COPRIME_GRID | [
"COUNT_COPRIME_GRID",
"ONE_PHI_2"
] | 98ffdc | nt_count_coprime_v1 | null | 4 | 0 | [
"COUNT_COPRIME_GRID",
"ONE_PHI_2"
] | 2 | 2.589 | 2026-02-08T11:13:47.985674Z | {
"verified": true,
"answer": 16221,
"timestamp": "2026-02-08T11:13:50.574655Z"
} | 7039db | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 275,
"completion_tokens": 1930
},
"timestamp": "2026-02-08T20:28:21.204Z",
"answer": 16221
},
{
"... | 1 | [
{
"lemma": "COUNT_COPRIME_GRID",
"status": "ok"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
... | {
"lo": -2.08,
"mid": 1.77,
"hi": 4.93
} | ||
dbc467 | alg_sym_quad_system_v1_601307018_9222 | Let $R$ be the number of ordered pairs $(a, b)$ of positive integers with $1 \le a, b \le 20$ satisfying $5b^2 + 34a^2 - 2ab = 1690$. Let $m = \min\{ x + y : x > 0, y > 0, xy = 8088336, x \le y \}$. Let $S$ be the set of positive integer triples $(a_1, b_1, c)$ such that $a_1^2 + b_1^2 + c^R = a_1b_1 + b_1c + ca_1$, $8... | 1,479 | graphs = [
Graph(
let={
"_c": Const(2),
"_m": Const(2),
"_n": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("a"), Var("b")]), condition=And(Geq(Var("a"), Const(1)), Leq(Var("a"), Const(20)), Geq(Var("b"), Const(1)), Leq(Var("b"), Const(20)), Eq(Sum(Mul(Const(5), P... | NT | null | COMPUTE | sympy | QF_PSD_COUNT | [
"QF_PSD_COUNT/B3",
"B3_CLOSEST"
] | a6df09 | alg_sym_quad_system_v1 | null | 7 | 0 | [
"B3",
"B3_CLOSEST",
"QF_PSD_COUNT"
] | 3 | 0.029 | 2026-03-10T09:36:08.739263Z | {
"verified": true,
"answer": 1479,
"timestamp": "2026-03-10T09:36:08.768309Z"
} | d2808b | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 360,
"completion_tokens": 7052
},
"timestamp": "2026-04-19T10:53:02.163Z",
"answer": 1479
},
{
"... | 1 | [
{
"lemma": "B3",
"status": "ok_later"
},
{
"lemma": "B3_CLOSEST",
"status": "ok"
},
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONS... | {
"lo": -5.34,
"mid": 1.1,
"hi": 7.53
} | ||
9e913f | comb_binomial_compute_v1_1248542787_106 | Let $T$ be the set of all integers $t$ such that $15 \le t \le 28$ and there exist positive integers $a$ and $b$ with $1 \le a \le 2$, $1 \le b \le 6$, and $t = 3a + 2b + 10$. Define $n$ to be the number of elements in $T$.
Let $\binom{n}{7}$ denote the binomial coefficient. Compute the remainder when $30841 \cdot \bi... | 47,862 | graphs = [
Graph(
let={
"_n": Const(30841),
"n": CountOverSet(set=SolutionsSet(var=Var("t"), condition=Exists(var=Var(name='a'), condition=Exists(var=Var(name='b'), condition=And(Geq(left=Var(name='a'), right=Const(value=1)), Leq(left=Var(name='a'), right=Const(value=2)), Geq(left=Va... | ALG | COMB | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | comb_binomial_compute_v1 | null | 5 | 0 | [
"LIN_FORM"
] | 1 | 0.002 | 2026-02-08T02:57:16.280371Z | {
"verified": true,
"answer": 47862,
"timestamp": "2026-02-08T02:57:16.282543Z"
} | 58c135 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 242,
"completion_tokens": 1411
},
"timestamp": "2026-02-09T00:21:19.348Z",
"answer": 47862
},
{
"... | 1 | [
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
}
] | {
"lo": 0.52,
"mid": 2,
"hi": 3.36
} | ||
654b4f | geo_count_lattice_rect_v1_1080341949_270 | Compute the number of lattice points $(x, y)$ such that $0 \leq x \leq 180$ and $0 \leq y \leq 202$. | 36,743 | graphs = [
Graph(
let={
"a": Const(180),
"b": Const(202),
"result": LatticePointsRect(a=Ref(name='a'), b=Ref(name='b')),
},
goal=Ref("result"),
)
] | GEOM | null | COUNT | sympy | [] | geo_count_lattice_rect_v1 | null | 4 | 0 | null | null | 0.001 | 2026-02-08T13:21:54.998274Z | {
"verified": true,
"answer": 36743,
"timestamp": "2026-02-08T13:21:54.998805Z"
} | bd88b1 | 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": 123
},
"timestamp": "2026-02-24T18:06:03.693Z",
"answer": 36743
},
{
"i... | 1 | [] | {
"lo": -5.97,
"mid": -3.97,
"hi": -1.93
} |
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