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 |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
ddffd8 | antilemma_k2_v1_1520064083_4302 | Let $m = 72$. Let $r$ and $s$ be the roots of the equation $x^2 - 72x + 272 = 0$, and let $n = r + s$. Compute
$$
\sum_{k=1}^{m} \phi(k) \left\lfloor \frac{n}{k} \right\rfloor,
$$
where $\phi$ denotes Euler's totient function. | 2,628 | graphs = [
Graph(
let={
"_m": Const(72),
"_n": SumOverSet(set=SolutionsSet(var=Var("x"), condition=Eq(Sum(Pow(Var("x"), Const(2)), Mul(Const(-72), Var("x")), Const(272)), Const(0)))),
"x": Summation(var="k", start=Const(1), end=Ref("_m"), expr=Mul(EulerPhi(n=Var("k")), Fl... | NT | COMB | COMPUTE | sympy | K13 | [
"VIETA_SUM/K2",
"K2"
] | 6be084 | antilemma_k2_v1 | null | 6 | 0 | [
"K13",
"K2",
"VIETA_SUM"
] | 3 | 0.003 | 2026-02-08T06:12:10.242539Z | {
"verified": true,
"answer": 2628,
"timestamp": "2026-02-08T06:12:10.245649Z"
} | fec6a3 | 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": 906
},
"timestamp": "2026-02-12T21:22:10.076Z",
"answer": 2628
},
{
... | 1 | [
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "K2",
"status": "ok"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "... | {
"lo": -3.51,
"mid": 1.33,
"hi": 6.56
} | ||
cc37d5_n | alg_poly4_count_v1_1218484723_3297 | A designer creates square tiles of size $a \times b$ where $a, b \in \{1,2,\ldots,20\}$, each having a stability score $17a^2 - 16ab + 17b^2$. Scores range from 18 to $M = 7200$, and $V$ is the number of distinct scores in that range. The system requires configurations where $b^4 = 10000$. Given $a$ can go up to 198, h... | 198 | ALG | null | COUNT | sympy | COUNT_CARTESIAN | [
"COUNT_CARTESIAN/QF_PSD_DISTINCT"
] | 6ed5a8 | alg_poly4_count_v1 | null | 6 | null | [
"COUNT_CARTESIAN",
"QF_PSD_DISTINCT"
] | 2 | 2.212 | 2026-02-25T04:59:41.604410Z | null | 820558 | cc37d5 | narrative | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 1,
"correct": {
"strict": false,
"boxed": false,
"relaxed": true
},
"usage": {
"prompt_tokens": 237,
"completion_tokens": 2165
},
"timestamp": "2026-03-30T19:56:37.825Z",
"answer": 23
},
{
"i... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "ok"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "Q... | {
"lo": 1.5,
"mid": 4.69,
"hi": 7.23
} | |
b6dda0_n | algebra_poly_eval_v1_1419126231_494 | A music composer uses a sequence generator defined by the value $M = 5^2 + 5 - 7$. To determine the length of a symphonic movement, they raise $M$ to the power of the minimum value of $41a^2 + 5b^2 - 28ab$ over integers $a, b$ from $1$ to $20$, then add $23$ times $M$ and the sum of the first five powers of two (starti... | 1,089 | ALG | null | COMPUTE | sympy | QF_PSD_MIN | [
"QF_PSD_MIN",
"SUM_GEOM"
] | f57523 | algebra_poly_eval_v1 | quadratic_mod | 3 | null | [
"QF_PSD_MIN",
"SUM_GEOM"
] | 2 | 0.005 | 2026-02-25T10:02:21.394935Z | null | 952202 | b6dda0 | narrative | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 226,
"completion_tokens": 2732
},
"timestamp": "2026-03-31T03:42:52.442Z",
"answer": 1089
},
{
"i... | 1 | [
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "QF_PSD_MIN",
"status": "ok"
},
{
"lemma": "SUM_GEOM",
"status": "ok"
}
] | {
"lo": -5.37,
"mid": 0.23,
"hi": 5.22
} | |
24dc9c | antilemma_cartesian_v1_2051736721_5292 | Let $x$ be the number of ordered pairs $(a,b)$ where $a$ is an integer from 1 to 24 and $b$ is an integer from 1 to 47. Let $S$ be the set of all integers $t$ such that $5 \leq t \leq 17$ and there exist positive integers $a$ and $b$ with $1 \leq a \leq 4$, $1 \leq b \leq 3$, and $t = 2a + 3b$. Compute the Bell number ... | 203 | graphs = [
Graph(
let={
"x": CountOverSet(set=CartesianProduct(left=IntegerRange(start=Const(1), end=Const(24)), right=IntegerRange(start=Const(1), end=Const(47)))),
"Q": Bell(Mod(value=Abs(arg=Ref(name='x')), modulus=CountOverSet(set=SolutionsSet(var=Var("t"), condition=Exists(var=V... | COMB | GEOM | COMPUTE | sympy | COUNT_SUM_EQUALS | [
"LIN_FORM",
"COUNT_CARTESIAN"
] | 6e491f | antilemma_cartesian_v1 | bell_mod | 5 | 0 | [
"COUNT_CARTESIAN",
"COUNT_SUM_EQUALS",
"LIN_FORM"
] | 3 | 0.017 | 2026-02-08T18:28:38.187510Z | {
"verified": true,
"answer": 203,
"timestamp": "2026-02-08T18:28:38.204958Z"
} | 77d4e0 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 190,
"completion_tokens": 1270
},
"timestamp": "2026-02-18T17:20:54.615Z",
"answer": 203
},
{
... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "ok"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "V7",
"sta... | {
"lo": -3.12,
"mid": 1.47,
"hi": 6.57
} | ||
1cd007 | nt_lcm_compute_v1_1918700295_72 | Let $n$ be a positive integer. Define $a = 2134$ and let $b$ be the number of positive integers $n \leq 18739$ such that the $n$-th Fibonacci number is divisible by 13. Let $\text{result} = \text{LCM}(a, b)$. Compute the smallest positive integer $Q$ such that the $Q$-th Fibonacci number is divisible by $|\text{result}... | 25,620 | graphs = [
Graph(
let={
"_n": Const(13),
"a": Const(2134),
"b": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Const(18739)), Divides(divisor=Ref("_n"), dividend=Fibonacci(arg=Var(name='n')))))),
"result": LCM(... | NT | null | COMPUTE | sympy | COUNT_FIB_DIVISIBLE | [
"COUNT_FIB_DIVISIBLE"
] | 66de3c | nt_lcm_compute_v1 | null | 7 | 0 | [
"COUNT_FIB_DIVISIBLE"
] | 1 | 0.003 | 2026-02-08T02:58:18.506172Z | {
"verified": true,
"answer": 25620,
"timestamp": "2026-02-08T02:58:18.508833Z"
} | 67a5e5 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 1,
"correct": {
"strict": false,
"boxed": false,
"relaxed": true
},
"usage": {
"prompt_tokens": 219,
"completion_tokens": 32768
},
"timestamp": "2026-02-23T20:49:31.108Z",
"answer": null
},
{
... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "ok"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
}
] | {
"lo": 3.11,
"mid": 4.79,
"hi": 6.55
} | ||
36cacf | alg_poly4_sum_v1_1419126231_509 | Let $S$ be the set of ordered pairs $(a_1, b_1)$ of positive integers with $1 \le a_1, b_1 \le 30$ such that $41a_1^2 - 12a_1b_1 + 20b_1^2 \le 7684$. Let $N = |S|$. Compute the remainder when $$\sum_{\substack{1 \le a \le N \\ 1 \le b \le 226}} \left(17a^4 + 24a^3b + 48a^2b^2 - 24ab^3 + 17b^4\right)$$ is divided by $98... | 63,460 | graphs = [
Graph(
let={
"_n": Const(98207),
"result": Mod(value=SumOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("a"), Var("b")]), condition=And(Geq(Var("a"), Const(1)), Leq(Var("a"), CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("a1"), Var("b1")]), conditio... | ALG | null | COMPUTE | sympy | QF_PSD_COUNT_LEQ | [
"QF_PSD_COUNT_LEQ"
] | 009d0f | alg_poly4_sum_v1 | null | 6 | 0 | [
"QF_PSD_COUNT_LEQ"
] | 1 | 0.76 | 2026-02-25T10:02:58.841326Z | {
"verified": true,
"answer": 63460,
"timestamp": "2026-02-25T10:02:59.601458Z"
} | 059646 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 264,
"completion_tokens": 21444
},
"timestamp": "2026-03-30T08:50:10.645Z",
"answer": 38060
},
{
... | 1 | [
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "QF_PSD_COUNT_LEQ",
"status": "ok"
}
] | {
"lo": 1.5,
"mid": 4.69,
"hi": 7.23
} | ||
94e378 | modular_sum_quadratic_residues_v1_397696148_146 | Let $p = 233$. Let $s$ be the number of positive integers $n \leq 40$ such that the $n$-th Fibonacci number is divisible by 11. Let $T$ be the set of all ordered pairs $(x, y)$ of positive integers such that $x + y = s$. Compute the value of
$$
\frac{p(p - 1)}{\max\{xy \mid (x, y) \in T\}}.
$$ | 13,514 | graphs = [
Graph(
let={
"_n": Const(11),
"p": Const(233),
"result": Div(Mul(Ref("p"), Sub(Ref("p"), Const(1))), MaxOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')),... | NT | null | SUM | sympy | COUNT_FIB_DIVISIBLE | [
"COUNT_FIB_DIVISIBLE/B1"
] | e7f15f | modular_sum_quadratic_residues_v1 | null | 7 | 0 | [
"B1",
"COUNT_FIB_DIVISIBLE"
] | 2 | 0.003 | 2026-02-08T11:18:24.060497Z | {
"verified": true,
"answer": 13514,
"timestamp": "2026-02-08T11:18:24.063360Z"
} | 7086a5 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 144,
"completion_tokens": 1031
},
"timestamp": "2026-02-14T12:17:51.895Z",
"answer": 13514
},
... | 1 | [
{
"lemma": "B1",
"status": "ok_later"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "ok"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "V3",
"status": "no"
},
{
"l... | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
13393e | nt_count_divisible_and_v1_865884756_6843 | Let $T$ be the set of all ordered pairs $(x, y)$ of positive integers such that $xy = 81$. Define $d_2$ to be the minimum value of $x + y$ as $(x, y)$ ranges over $T$. Let $N$ be the number of positive integers $n$ such that $1 \leq n \leq 35532$, $n$ is divisible by $12$, and $n$ is divisible by $d_2$. Compute the rem... | 14,403 | graphs = [
Graph(
let={
"_n": Const(81),
"upper": Const(35532),
"d1": Const(12),
"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("... | NT | null | COUNT | sympy | B3 | [
"B3"
] | 0cd20d | nt_count_divisible_and_v1 | null | 5 | 0 | [
"B3"
] | 1 | 1.081 | 2026-02-08T19:24:59.156560Z | {
"verified": true,
"answer": 14403,
"timestamp": "2026-02-08T19:25:00.237225Z"
} | f1d0b6 | 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": 7814
},
"timestamp": "2026-02-18T22:21:38.151Z",
"answer": 14403
},
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "VAL_SUM_EQ",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
53cd3a | sequence_lucas_compute_v1_1978505735_5570 | Let $n$ be the number of integers $t$ such that $7 \leq t \leq 29$ and $t = 5a + 2b$ for some integers $a$ and $b$ with $1 \leq a \leq 3$ and $1 \leq b \leq 7$. Let $\text{result}$ be the $n$-th Lucas number, where the Lucas sequence is defined by $L_1 = 1$, $L_2 = 3$, and $L_k = L_{k-1} + L_{k-2}$ for $k \geq 3$. Let ... | 51,431 | graphs = [
Graph(
let={
"_n": Const(74319),
"n": CountOverSet(set=SolutionsSet(var=Var("t"), condition=Exists(var=Var(name='a'), condition=Exists(var=Var(name='b'), condition=And(Geq(left=Var(name='a'), right=Const(value=1)), Leq(left=Var(name='a'), right=Const(value=3)), Geq(left=Va... | NT | null | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | sequence_lucas_compute_v1 | null | 4 | 0 | [
"LIN_FORM"
] | 1 | 0.002 | 2026-02-08T19:05:25.962979Z | {
"verified": true,
"answer": 51431,
"timestamp": "2026-02-08T19:05:25.964938Z"
} | 782361 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 208,
"completion_tokens": 3298
},
"timestamp": "2026-02-18T21:19:57.252Z",
"answer": 51431
},
... | 1 | [
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
71aaa0 | diophantine_sum_product_min_v1_809748730_925 | Let $S = 100$ and let $P$ be the number of positive integers $t$ such that $5 \leq t \leq 1606$ and there exist positive integers $a$ and $b$ with $1 \leq a \leq 155$, $1 \leq b \leq 432$, and $t = 2a + 3b$. Let $x$ be the smallest positive integer such that $1 \leq x \leq 99$ and $x(S - x) = P$. Compute the value of $... | 128 | graphs = [
Graph(
let={
"_n": Const(99),
"S": Const(100),
"P": CountOverSet(set=SolutionsSet(var=Var("t"), condition=Exists(var=Var(name='a'), condition=Exists(var=Var(name='b'), condition=And(Geq(left=Var(name='a'), right=Const(value=1)), Leq(left=Var(name='a'), right=Co... | NT | null | EXTREMUM | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | diophantine_sum_product_min_v1 | null | 7 | 0 | [
"LIN_FORM"
] | 1 | 0.01 | 2026-02-08T11:50:03.286624Z | {
"verified": true,
"answer": 128,
"timestamp": "2026-02-08T11:50:03.296247Z"
} | a8182e | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 187,
"completion_tokens": 4819
},
"timestamp": "2026-02-14T19:11:49.155Z",
"answer": 128
},
{
... | 1 | [
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
... | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
3b0930 | nt_min_coprime_above_v1_971394319_781 | Let $m = 33124$. Let $s$ be the minimum value of $x + y$ over all ordered pairs of positive integers $(x, y)$ such that $xy = m$. Let $p$ be the largest prime number that is at most $s$. Find the smallest integer $n$ such that $26569 < n \leq 26938$ and $\gcd(n, p) = 1$. | 26,570 | graphs = [
Graph(
let={
"_m": Const(33124),
"_n": MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(Mul(Var("x"), Var("y")), Ref("_m")))), expr=Sum(Var("x"), Var("y")))),... | NT | null | EXTREMUM | sympy | B3 | [
"B3/MAX_PRIME_BELOW"
] | f253c0 | nt_min_coprime_above_v1 | null | 6 | 0 | [
"B3",
"MAX_PRIME_BELOW"
] | 2 | 0.061 | 2026-02-08T13:18:06.950191Z | {
"verified": true,
"answer": 26570,
"timestamp": "2026-02-08T13:18:07.011060Z"
} | 43d070 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 135,
"completion_tokens": 1553
},
"timestamp": "2026-02-15T12:52:02.562Z",
"answer": 26570
},
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok_... | {
"lo": -6.96,
"mid": -4.56,
"hi": -1.46
} | ||
ab5c00 | comb_sum_binomial_row_v1_1520064083_1416 | Let $ n = 11 $ and $ r = 2^n $. Compute the Bell number $ B_{|r| \bmod 11} $. | 2 | graphs = [
Graph(
let={
"n": Const(11),
"result": Pow(Const(2), Ref("n")),
"Q": Bell(Mod(value=Abs(arg=Ref(name='result')), modulus=Const(11))),
},
goal=Ref("Q"),
)
] | COMB | null | SUM | sympy | LIN_FORM | [
"LIN_FORM"
] | 1ae498 | comb_sum_binomial_row_v1 | bell_mod | 3 | 0 | [
"LIN_FORM"
] | 1 | 0.01 | 2026-02-08T03:59:08.387271Z | {
"verified": true,
"answer": 2,
"timestamp": "2026-02-08T03:59:08.396856Z"
} | 009f45 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 143,
"completion_tokens": 242
},
"timestamp": "2026-02-10T16:31:07.193Z",
"answer": 2
},
{
"id": ... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
}
... | {
"lo": -7.18,
"mid": -4.99,
"hi": -3
} | ||
bf6b1b | comb_bell_compute_v1_1218484723_5246 | Let $B_n$ denote the $n$-th Bell number. Let $n$ be the number of integers $a$ with $0 \le a \le 5040$ such that
$$\Bigl(\bigl(a^{3} + 5a - 1 \bmod 5041\bigr)^{3} + 5\bigl(a^{3} + 5a - 1 \bmod 5041\bigr) - 1 \bmod 5041\Bigr)^{3} + 5\Bigl(\bigl(a^{3} + 5a - 1 \bmod 5041\bigr)^{3} + 5\bigl(a^{3} + 5a - 1 \bmod 5041\bigr)... | 21,147 | graphs = [
Graph(
let={
"_n": Const(5041),
"n": CountOverSet(set=SolutionsSet(var=Var("a"), condition=And(Geq(Var("a"), Const(0)), Leq(Var("a"), Const(5040)), Eq(Mod(value=Sum(Pow(Mod(value=Sum(Pow(Mod(value=Sum(Pow(Var("a"), Const(3)), Mul(Const(5), Var("a")), Const(-1)), modulus=Co... | COMB | null | COMPUTE | sympy | POLY_ORBIT_HENSEL | [
"POLY_ORBIT_HENSEL"
] | 53b6eb | comb_bell_compute_v1 | null | 7 | 0 | [
"POLY_ORBIT_HENSEL"
] | 1 | 0.003 | 2026-02-25T06:54:08.111924Z | {
"verified": true,
"answer": 21147,
"timestamp": "2026-02-25T06:54:08.114652Z"
} | 574612 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 416,
"completion_tokens": 32768
},
"timestamp": "2026-03-29T20:12:47.079Z",
"answer": null
},
{
... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "POLY_ORBIT_HENSEL",
"status": "ok"
},
{
"lemma": "V8_S... | {
"lo": 1.53,
"mid": 4.7,
"hi": 7.23
} | ||
50b6c1 | comb_sum_binomial_mod_v1_168721529_669 | Let $m$ be the minimum value of $x + y$ over all pairs of positive integers $(x, y)$ such that $xy = 1156$. Let $n$ be the number of integers $t$ such that $14 \leq t \leq 9948$ and there exist integers $a$ and $b$ with $1 \leq a \leq 1227$, $1 \leq b \leq 504$, and $t = 4a + 10b$. Let $s = \sum_{k=0}^{d_{\max}} \binom... | 364 | graphs = [
Graph(
let={
"_c": Const(10883),
"_m": 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(1156)))), expr=Sum(Var("x"), Var("y")))... | NT | null | COMPUTE | sympy | B3 | [
"B3/LIN_FORM/MAX_DIVISOR"
] | 62f3df | comb_sum_binomial_mod_v1 | null | 7 | 0 | [
"B3",
"LIN_FORM",
"MAX_DIVISOR"
] | 3 | 0.01 | 2026-02-08T13:11:17.564377Z | {
"verified": true,
"answer": 364,
"timestamp": "2026-02-08T13:11:17.573928Z"
} | 42de20 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 280,
"completion_tokens": 8103
},
"timestamp": "2026-02-11T07:38:12.135Z",
"answer": 364
},
{
"i... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok_later"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MAX_DIVISOR",
"status": "ok_later"
},
... | {
"lo": -1.83,
"mid": 2.85,
"hi": 7.63
} | ||
932081 | modular_min_linear_v1_397696148_1038 | Let $S$ be the set of all integers $t$ such that $7 \leq t \leq 8919$ and there exist positive integers $a$ and $b$ with $1 \leq a \leq 2892$, $1 \leq b \leq 627$, and $t = 2a + 5b$. Let $a$ be the number of elements in $S$. Let $m = 12923$ and $b = 934$. Determine the smallest positive integer $x$ such that $1 \leq x ... | 3,773 | graphs = [
Graph(
let={
"a": 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=2892)), Geq(left=Var(name='b'), right=Const(valu... | NT | null | EXTREMUM | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | modular_min_linear_v1 | null | 6 | 0 | [
"LIN_FORM"
] | 1 | 0.661 | 2026-02-08T12:18:40.603173Z | {
"verified": true,
"answer": 3773,
"timestamp": "2026-02-08T12:18:41.263680Z"
} | 51ba3c | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 182,
"completion_tokens": 4439
},
"timestamp": "2026-02-14T23:52:55.566Z",
"answer": 3773
},
{... | 1 | [
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "VAL_SUM_EQ",
"status": "no"
... | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
b61f2a | lin_form_endings_v1_971394319_304 | Let $a = 21$ and $b = 49$. Let $k = 74$. Define $d = \gcd(a, b)$ and $g = \gcd(k, d)$. Let $r = \left\lfloor \frac{k}{g} \right\rfloor$. Compute the remainder when $17887 \cdot r$ is divided by $51882$. | 26,588 | graphs = [
Graph(
let={
"a_coeff": Const(21),
"b_coeff": Const(49),
"k_val": Const(74),
"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(17... | COMB | NT | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | lin_form_endings_v1 | null | 3 | null | [
"LIN_FORM"
] | 1 | 0.001 | 2026-02-08T12:56:58.816003Z | {
"verified": true,
"answer": 26588,
"timestamp": "2026-02-08T12:56:58.817133Z"
} | 3b5c6e | 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": 644
},
"timestamp": "2026-02-15T08:08:45.647Z",
"answer": 26588
},
{... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "V8",
"st... | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
05dc22 | diophantine_fbi2_min_v1_1918700295_4511 | Let $S$ be the set of all positive integers $p$ for which there exists a positive integer $q$ such that $pq = 1350$, $\gcd(p, q) = 1$, and $p < q$. Let $t$ be the number of elements in $S$. Determine the smallest integer $d$ such that $d \geq t$, $d \leq 26$, $d$ divides $16$, and $\frac{16}{d} \geq 4$. | 4 | graphs = [
Graph(
let={
"_n": Const(4),
"k": Const(16),
"upper": Const(26),
"result": MinOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), CountOverSet(set=SolutionsSet(var=Var("p"), condition=And(IsPositive(arg=Var(name='p')), Exists(var=Var(... | NT | null | EXTREMUM | sympy | MAX_PRIME_BELOW | [
"COPRIME_PAIRS"
] | 2bb3aa | diophantine_fbi2_min_v1 | null | 4 | 0 | [
"COPRIME_PAIRS",
"MAX_PRIME_BELOW"
] | 2 | 0.03 | 2026-02-08T09:24:55.413232Z | {
"verified": true,
"answer": 4,
"timestamp": "2026-02-08T09:24:55.443609Z"
} | 7a76cb | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 151,
"completion_tokens": 1221
},
"timestamp": "2026-02-14T04:04:53.631Z",
"answer": 4
},
{
... | 1 | [
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
... | {
"lo": -6.96,
"mid": -4.56,
"hi": -1.46
} | ||
f3c624 | diophantine_product_count_v1_1520064083_2219 | Let $n = 1089$ and $k = 120$. Let $S$ be the set of all ordered pairs $(x,y)$ of positive integers such that $xy = n$. Define $u$ to be the minimum value of $x + y$ over all such pairs $(x,y) \in S$. Let $r$ be the number of positive integers $x$ with $1 \le x \le u$ such that $x$ divides $k$ and $\frac{k}{x} \le u$. C... | 67,256 | graphs = [
Graph(
let={
"_n": Const(1089),
"k": Const(120),
"upper": MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(Mul(Var("x"), Var("y")), Ref("_n")))), ... | NT | null | COUNT | sympy | B3 | [
"B3"
] | 0cd20d | diophantine_product_count_v1 | null | 5 | 0 | [
"B3"
] | 1 | 0.01 | 2026-02-08T04:35:14.436445Z | {
"verified": true,
"answer": 67256,
"timestamp": "2026-02-08T04:35:14.446547Z"
} | c10bc4 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 239,
"completion_tokens": 1528
},
"timestamp": "2026-02-10T17:08:46.610Z",
"answer": 67256
},
{
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
}
] | {
"lo": -3.42,
"mid": 1.86,
"hi": 7.55
} | ||
78b2c7 | v1_endings_v1_1125832087_50 | Let $n = 66971$ and $m = 106833$. Determine the exponent of the highest power of $2$ that divides $m!$, and subtract from it the exponent of the highest power of $2$ that divides $n!$. Compute the value of this difference. | 39,863 | graphs = [
Graph(
let={
"n_val": Const(66971),
"nm_val": Const(106833),
"p_val": Const(2),
"n_fact": Factorial(Ref("n_val")),
"nm_fact": Factorial(Ref("nm_val")),
"vp_n": MaxKDivides(target=Ref("n_fact"), base=Ref("p_val")),
... | NT | null | COMPUTE | sympy | V1 | [
"V1"
] | dae96f | v1_endings_v1 | null | 6 | null | [
"V1"
] | 1 | 0 | 2026-02-08T02:50:55.050856Z | {
"verified": true,
"answer": 39863,
"timestamp": "2026-02-08T02:50:55.051290Z"
} | eac339 | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 163,
"completion_tokens": 1215
},
"timestamp": "2026-02-17T14:51:14.380Z",
"answer": 33029
}
] | 0 | [
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "K5",
"status": "same_pattern_wrong"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "V1",
"status": "ok"
},
... | {
"lo": -6.48,
"mid": 1.54,
"hi": 9.56
} | ||
0b741a_n | alg_poly4_count_v1_1218484723_5302 | A digital lock uses a code based on two positive integers $a$ and $b$, each between 1 and 120. The lock opens only if the expression $82a^4 - 328a^3b + 492a^2b^2 - 328ab^3 + 82b^4$ equals 647019442. How many such valid $(a, b)$ pairs unlock the device? | 134 | ALG | null | COUNT | sympy | B3 | [
"B3/QF_PSD_COUNT_LEQ"
] | 0168fb | alg_poly4_count_v1 | null | 5 | null | [
"B3",
"QF_PSD_COUNT_LEQ"
] | 2 | 1.008 | 2026-02-25T06:56:04.413754Z | null | 486297 | 0b741a | narrative | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 197,
"completion_tokens": 1399
},
"timestamp": "2026-03-30T23:14:03.395Z",
"answer": 134
},
{
"id... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "QF_PSD_COUNT_LEQ",
"status": "ok_later"
}
] | {
"lo": -5.37,
"mid": 0.23,
"hi": 5.22
} | |
5573f3 | nt_count_divisors_in_range_v1_677425708_1432 | Let $n = 10080$, $a = 6$, and $b$ be the sum of $\phi(d)$ over all positive divisors $d$ of $287$, where $\phi$ is Euler's totient function. Compute the number of positive divisors $d$ of $n$ such that $a \leq d \leq b$. | 45 | graphs = [
Graph(
let={
"n": Const(10080),
"a": Const(6),
"b": SumOverDivisors(n=Const(value=287), var='d', expr=EulerPhi(n=Var(name='d'))),
"result": CountOverSet(set=SolutionsSet(var=Var("d"), condition=And(Divides(divisor=Var("d"), dividend=Ref("n")), Geq(V... | NT | null | COUNT | sympy | K13 | [
"K3"
] | 54c41e | nt_count_divisors_in_range_v1 | null | 3 | 0 | [
"K13",
"K3"
] | 2 | 0.027 | 2026-02-08T04:11:57.467462Z | {
"verified": true,
"answer": 45,
"timestamp": "2026-02-08T04:11:57.494764Z"
} | bd3b48 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 186,
"completion_tokens": 4739
},
"timestamp": "2026-02-09T19:53:20.754Z",
"answer": 45
},
{
"id"... | 1 | [
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "K3",
"status": "ok"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
... | {
"lo": -3.46,
"mid": 1.03,
"hi": 5.49
} | ||
4c07fe | comb_catalan_compute_v1_655260480_1617 | Let $n$ be the number of integers $t$ such that $14 \leq t \leq 40$ and there exist integers $a$ and $b$ with $1 \leq a \leq 2$, $1 \leq b \leq 5$, and $t = 10a + 4b$. Let $\text{result}$ be the $n$-th Catalan number, and let $Q$ be the remainder when $76871 \cdot \text{result}$ is divided by $71536$. Compute $Q$. | 43,588 | graphs = [
Graph(
let={
"_n": Const(71536),
"n": CountOverSet(set=SolutionsSet(var=Var("t"), condition=Exists(var=Var(name='a'), condition=Exists(var=Var(name='b'), condition=And(Geq(left=Var(name='a'), right=Const(value=1)), Leq(left=Var(name='a'), right=Const(value=2)), Geq(left=Va... | COMB | null | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | comb_catalan_compute_v1 | null | 4 | 0 | [
"LIN_FORM"
] | 1 | 0.004 | 2026-02-08T16:15:15.447405Z | {
"verified": true,
"answer": 43588,
"timestamp": "2026-02-08T16:15:15.451534Z"
} | f66fd8 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 232,
"completion_tokens": 2599
},
"timestamp": "2026-02-24T20:24:50.982Z",
"answer": 43588
},
{
... | 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",
"status... | {
"lo": -2.4,
"mid": 1.57,
"hi": 5.75
} | ||
7d87b6 | antilemma_sum_equals_v1_1520064083_8503 | Let $T$ be the set of integers $t$ such that $12 \leq t \leq 104$ and there exist positive integers $a$ and $b$ with $1 \leq a \leq 11$, $1 \leq b \leq 7$, and $t = 5a + 7b$. Let $n$ be the number of elements in $T$.
Let $S$ be the set of ordered pairs $(i, j)$ of positive integers such that $1 \leq i \leq 68$, $1 \le... | 68 | 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=11)), Geq(left=Var(name='b'), right=Const(value... | COMB | GEOM | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM/COUNT_SUM_EQUALS",
"COUNT_SUM_EQUALS"
] | ada383 | antilemma_sum_equals_v1 | null | 5 | 0 | [
"COUNT_SUM_EQUALS",
"LIN_FORM"
] | 2 | 0.005 | 2026-02-08T10:13:56.596158Z | {
"verified": true,
"answer": 68,
"timestamp": "2026-02-08T10:13:56.601461Z"
} | dd2a80 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 260,
"completion_tokens": 5354
},
"timestamp": "2026-02-24T11:53:21.882Z",
"answer": 68
},
{
"id"... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "ok"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
},
... | {
"lo": -2.35,
"mid": 1.22,
"hi": 4.84
} | ||
436c66 | nt_sum_divisors_range_v1_1978505735_7749 | Let $S$ be the set of all positive integers $n$ such that $1 \leq n \leq 5184$. For each $n \in S$, let $d(n)$ denote the number of positive divisors of $n$. Compute the sum of $d(n)$ over all $n \in S$. | 45,158 | graphs = [
Graph(
let={
"upper": Const(5184),
"result": SumOverSet(set=MapOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Ref("upper")))), expr=NumDivisors(n=Var("n")))),
},
goal=Ref("result"),
)
] | NT | null | SUM | sympy | ONE_PHI_2 | [
"ONE_PHI_2"
] | e19278 | nt_sum_divisors_range_v1 | null | 4 | 0 | [
"ONE_PHI_2"
] | 1 | 0.57 | 2026-02-08T20:25:12.203044Z | {
"verified": true,
"answer": 45158,
"timestamp": "2026-02-08T20:25:12.772736Z"
} | 7658bf | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 113,
"completion_tokens": 3581
},
"timestamp": "2026-02-19T00:35:55.363Z",
"answer": 45158
},
... | 1 | [
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "ONE_PHI_2",
"status": "ok"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
17ba61 | geo_count_lattice_triangle_v1_1874849503_6 | Let $ A $ be the area of the triangle with vertices at $ (0, 0) $, $ (109, 41) $, and $ (9, 121) $, multiplied by 2. Let $ b $ be the number of lattice points on the boundary of this triangle. Compute the remainder when $ 3828 - \frac{A + 2 - b}{2} $ is divided by $ 83502 $. | 80,930 | graphs = [
Graph(
let={
"_n": Const(41),
"area_2x": Abs(arg=Sum(Mul(Const(value=109), Const(value=121)), Mul(Const(value=9), Sub(left=Const(value=0), right=Const(value=41))))),
"boundary": Sum(GCD(a=Abs(arg=Const(value=109)), b=Abs(arg=Const(value=41))), GCD(a=Abs(arg=Sub... | NT | null | COUNT | sympy | MAX_PRIME_BELOW | [
"MAX_PRIME_BELOW"
] | dc3ad3 | geo_count_lattice_triangle_v1 | null | 7 | 0 | [
"MAX_PRIME_BELOW"
] | 1 | 0.005 | 2026-02-08T12:45:48.306600Z | {
"verified": true,
"answer": 80930,
"timestamp": "2026-02-08T12:45:48.311853Z"
} | 3c23cf | 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": 1516
},
"timestamp": "2026-02-09T12:39:20.468Z",
"answer": 80930
},
{
"... | 1 | [
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok"
},
{
"lemma": "V8",
"status": "no"... | {
"lo": -5.15,
"mid": 0.01,
"hi": 5.44
} | ||
56ef49 | alg_poly_orbit_count_v1_1419126231_1194 | For a non-negative integer $a$, define the sequence $N = (2a^3 - 5a) \bmod 37$, $M = (2N^3 - 5N) \bmod 37$, $R = (2M^3 - 5M) \bmod 37$, $S = (2R^3 - 5R) \bmod 37$, $T = (2S^3 - 5S) \bmod 37$, $K = (2T^3 - 5T) \bmod 37$. Find the number of integers $a$ with $0 \leq a \leq 32818$ such that $K = a$, but $N \ne a$, $M \ne ... | 5,322 | graphs = [
Graph(
let={
"p1": Mod(value=Sum(Mul(Const(2), Pow(Var("a"), Const(3))), Mul(Const(-5), Var("a"))), modulus=Const(37)),
"p2": Mod(value=Sum(Mul(Const(2), Pow(Ref("p1"), Const(3))), Mul(Const(-5), Ref("p1"))), modulus=Const(37)),
"p3": Mod(value=Sum(Mul(Const(2)... | ALG | null | COUNT | sympy | POLY_ORBIT_COUNT | [
"POLY_ORBIT_COUNT"
] | 4ad965 | alg_poly_orbit_count_v1 | null | 6 | null | [
"POLY_ORBIT_COUNT"
] | 1 | 0.036 | 2026-02-25T10:40:02.062763Z | {
"verified": true,
"answer": 5322,
"timestamp": "2026-02-25T10:40:02.099158Z"
} | 8276f5 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 296,
"completion_tokens": 10718
},
"timestamp": "2026-03-30T11:43:34.647Z",
"answer": 5322
},
{
"... | 1 | [
{
"lemma": "POLY_ORBIT_COUNT",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
}
] | {
"lo": -5.37,
"mid": 0.23,
"hi": 5.22
} | ||
2aac82 | diophantine_fbi2_count_v1_124444284_9998 | Let $k = 120$. Consider the set of all positive integers $d$ such that $3 \leq d \leq \sum_{k=1}^{13} k$, $d$ divides $k$, and $3 \leq \frac{k}{d} \leq 91$. Compute the number of such integers $d$. | 12 | graphs = [
Graph(
let={
"k": Const(120),
"result": CountOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Const(3)), Leq(Var("d"), Summation(var="k", start=Const(1), end=Const(13), expr=Var("k"))), Divides(divisor=Var("d"), dividend=Ref("k")), Geq(Div(Ref("k"), Var("... | NT | null | COUNT | sympy | B3 | [
"SUM_ARITHMETIC"
] | eb34f0 | diophantine_fbi2_count_v1 | null | 3 | 0 | [
"B3",
"SUM_ARITHMETIC"
] | 2 | 0.045 | 2026-02-08T12:46:08.638328Z | {
"verified": true,
"answer": 12,
"timestamp": "2026-02-08T12:46:08.683782Z"
} | 0e312c | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 116,
"completion_tokens": 1251
},
"timestamp": "2026-02-15T04:42:13.855Z",
"answer": 12
},
{
... | 1 | [
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "SUM_ARITHMETIC",
"status": "ok"
},
{
"lemma": "V5",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
... | {
"lo": -6.96,
"mid": -4.56,
"hi": -1.46
} | ||
e7da42 | modular_product_range_v1_548369836_179 | Let $m$ be the smallest value of $x + y$ over all pairs of positive integers $(x, y)$ such that $xy = 36864$. Let $P$ be the product of all integers from $128$ to $m$, inclusive. Find the remainder when $P$ is divided by $11813$. | 2,105 | graphs = [
Graph(
let={
"_n": Const(128),
"prod": MathProduct(expr=Var("i"), var="i", start=Ref("_n"), end=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"),... | NT | null | COMPUTE | sympy | B3 | [
"B3"
] | 0cd20d | modular_product_range_v1 | null | 6 | 0 | [
"B3"
] | 1 | 0.002 | 2026-02-08T02:47:55.010301Z | {
"verified": true,
"answer": 2105,
"timestamp": "2026-02-08T02:47:55.012445Z"
} | 492e3c | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 178,
"completion_tokens": 32768
},
"timestamp": "2026-02-23T16:18:26.723Z",
"answer": null
},
{
... | 0 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
}
] | {
"lo": 4.68,
"mid": 6.57,
"hi": 9.55
} | ||
ca8f86 | nt_sum_divisors_mod_v1_1470522791_1 | Let $S$ be the set of all ordered pairs $(x,y)$ of positive integers such that $xy = 705600$. For each such pair, compute $x + y$, and let $T$ be the set of all such sums. Let $n$ be the minimum value in $T$. Let $\sigma(n)$ denote the sum of all positive divisors of $n$. Let $r$ be the remainder when $\sigma(n)$ is di... | 18,516 | graphs = [
Graph(
let={
"n": MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(Mul(Var("x"), Var("y")), Const(705600)))), expr=Sum(Var("x"), Var("y")))),
"M": Const(11743... | NT | null | COMPUTE | sympy | B3 | [
"B3"
] | 0cd20d | nt_sum_divisors_mod_v1 | null | 4 | 0 | [
"B3"
] | 1 | 0.004 | 2026-02-08T12:47:17.092695Z | {
"verified": true,
"answer": 18516,
"timestamp": "2026-02-08T12:47:17.096401Z"
} | 6a7302 | 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": 3549
},
"timestamp": "2026-02-15T05:04:20.182Z",
"answer": 18516
},
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
}
] | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
585b80 | comb_count_derangements_v1_1470522791_200 | Let $n$ be the number of nonnegative integers $j$ such that $0 \leq j \leq 580$ and the binomial coefficient $\binom{580}{j}$ is odd. Compute the value of the subfactorial of $n$, denoted $!n$, which counts the number of derangements of $n$ elements. | 14,833 | graphs = [
Graph(
let={
"_n": Const(580),
"n": CountOverSet(set=SolutionsSet(var=Var("j"), condition=And(Geq(Var("j"), Const(0)), Leq(Var("j"), Ref("_n")), Eq(Mod(value=Binom(n=Const(580), k=Var("j")), modulus=Const(2)), Const(1))), domain='nonnegative_integers')),
"resul... | COMB | null | COUNT | sympy | V8 | [
"V8"
] | 86348e | comb_count_derangements_v1 | null | 7 | 0 | [
"V8"
] | 1 | 0.002 | 2026-02-08T12:54:28.859518Z | {
"verified": true,
"answer": 14833,
"timestamp": "2026-02-08T12:54:28.861504Z"
} | 7dcf72 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 185,
"completion_tokens": 1115
},
"timestamp": "2026-02-24T16:36:17.650Z",
"answer": 14833
},
{
"... | 1 | [
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "V8",
"status": "ok"
... | {
"lo": -2.35,
"mid": 1.22,
"hi": 4.84
} | ||
cba8f1 | geo_count_lattice_triangle_v1_784195855_5383 | Let $A = (0,0)$, $B = (120,34)$, and $C = (153,137)$. The area of triangle $ABC$ is $\frac{1}{2} \cdot |120 \cdot 137 - 153 \cdot 34|$. Compute twice this area, denoted $A_{2x}$. Let $B$ be the number of lattice points on the boundary of triangle $ABC$, which is given by $\gcd(120,34) + \gcd(153-120,137-34) + \gcd(153,... | 5,618 | graphs = [
Graph(
let={
"_n": Const(153),
"area_2x": Abs(arg=Sum(Mul(Const(value=120), Const(value=137)), Mul(Ref(name='_n'), Sub(left=SumOverDivisors(n=Const(value=7), var='d', expr=MoebiusMu(n=Var(name='d'))), right=Const(value=34))))),
"boundary": Sum(GCD(a=Abs(arg=Con... | NT | null | COUNT | sympy | MOBIUS_SUM | [
"MOBIUS_SUM",
"B3"
] | 6945d1 | geo_count_lattice_triangle_v1 | null | 6 | 0 | [
"B3",
"MOBIUS_SUM"
] | 2 | 0.018 | 2026-02-08T07:51:07.991666Z | {
"verified": true,
"answer": 5618,
"timestamp": "2026-02-08T07:51:08.009257Z"
} | bd2eb0 | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 301,
"completion_tokens": 958
},
"timestamp": "2026-02-20T07:14:03.432Z",
"answer": 5618
}
] | 2 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MOBIUS_SUM",
"status": "ok"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
... | {
"lo": -10,
"mid": -6.47,
"hi": -2.95
} | ||
d41ccc | nt_num_divisors_compute_v1_865884756_1711 | Let $n = 3$. Define $d(n)$ as the number of positive divisors of $n$. Let $a = d(n)$. Compute the value of
$$
d(n) + \varphi(a + 1) + d(a + 1),
$$
where $\varphi(k)$ denotes the number of positive integers less than or equal to $k$ that are relatively prime to $k$, and $d(k)$ denotes the number of positive divisors of ... | 6 | graphs = [
Graph(
let={
"n": Const(3),
"result": NumDivisors(n=Ref("n")),
"Q": Sum(Ref("result"), EulerPhi(n=Sum(Abs(arg=Ref(name='result')), Const(1))), NumDivisors(n=Sum(Abs(arg=Ref(name='result')), Const(1)))),
},
goal=Ref("Q"),
)
] | NT | null | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | nt_num_divisors_compute_v1 | null | 2 | 0 | [
"LIN_FORM"
] | 1 | 0.033 | 2026-02-08T16:14:26.548344Z | {
"verified": true,
"answer": 6,
"timestamp": "2026-02-08T16:14:26.581683Z"
} | 8b3ed7 | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 164,
"completion_tokens": 401
},
"timestamp": "2026-02-16T07:14:37.729Z",
"answer": 6
},
{
"id": 11,
"... | 2 | [
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "V1",
"status": "no"
},
{
"lemma": "VAL_SUM_EQ",
"status": "no"
}
] | {
"lo": -10,
"mid": -7.27,
"hi": -4.54
} | ||
04b54b | nt_count_gcd_equals_v1_1520064083_3810 | Let $n$ be a positive integer. Define $\text{upper}$ to be the number of integers $n$ such that $1 \leq n \leq 23329$ and $\gcd(n, 6) = 1$. Let $k = 377$ and $d = 29$. Define $\text{result}$ to be the number of integers $n$ such that $1 \leq n \leq \text{upper}$ and $\gcd(n, k) = d$. Compute the remainder when $44121 \... | 25,713 | graphs = [
Graph(
let={
"_n": Const(98345),
"upper": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Const(23329)), Eq(GCD(a=Var("n"), b=Const(6)), Const(1))))),
"k": Const(377),
"d": Const(29),
"res... | NT | null | COUNT | sympy | C4 | [
"C4"
] | 08d162 | nt_count_gcd_equals_v1 | null | 5 | 0 | [
"C4"
] | 1 | 0.587 | 2026-02-08T05:55:20.160917Z | {
"verified": true,
"answer": 25713,
"timestamp": "2026-02-08T05:55:20.748322Z"
} | 8da7d5 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 170,
"completion_tokens": 1598
},
"timestamp": "2026-02-12T16:21:26.910Z",
"answer": 25713
},
... | 1 | [
{
"lemma": "C4",
"status": "ok"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "V3",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
}
] | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
c54971 | alg_qf_psd_orbit_v1_1218484723_3452 | Let $A$ be the number of ordered pairs $(a_1, b_1)$ with $1 \leq a_1, b_1 \leq 25$ such that $-18a_1b_1 + 10a_1^2 + 25b_1^2 \leq 2500$. Let $B$ be the number of ordered pairs $(a_2, b_2)$ with $1 \leq a_2, b_2 \leq 20$ such that $13a_2^2 + 2b_2^2 - 2a_2b_2 \leq 1513$. Find the number of ordered triples $(a, b, c)$ of p... | 118 | graphs = [
Graph(
let={
"_m": Const(2),
"_n": Const(2),
"result": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("a"), Var("b"), Var("c")]), condition=And(Geq(Var("a"), Const(1)), Leq(Var("a"), Const(70)), Geq(Var("b"), Const(1)), Leq(Var("b"), Const(70)), Geq(Var(... | ALG | null | COUNT | sympy | LIN_FORM | [
"QF_PSD_COUNT_LEQ"
] | 009d0f | alg_qf_psd_orbit_v1 | null | 6 | 0 | [
"LIN_FORM",
"QF_PSD_COUNT_LEQ"
] | 2 | 1.854 | 2026-02-25T05:08:32.436374Z | {
"verified": true,
"answer": 118,
"timestamp": "2026-02-25T05:08:34.290521Z"
} | 5a0ff9 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 1,
"correct": {
"strict": false,
"boxed": false,
"relaxed": true
},
"usage": {
"prompt_tokens": 321,
"completion_tokens": 25249
},
"timestamp": "2026-03-29T10:19:34.017Z",
"answer": 0
},
{
"i... | 1 | [
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "QF_PSD_COUNT_LEQ",
"status": "ok"
}
] | {
"lo": 1.55,
"mid": 4.7,
"hi": 7.23
} | ||
95a5cf_n | alg_poly_orbit_legendre_v1_1218484723_6364 | A cryptographic function maps each non-negative integer $a$ to a value $M$ modulo $31$ using the formula $3a^3 - a^2 - 4a + 1$. This value is then reprocessed through the same function to yield $T$. For inputs $a$ from $0$ to $39400$, count how many satisfy $T = a$, the sum $a^{15} + M^{15} \bmod 31$ is divisible by $3... | 2,542 | ALG | null | COUNT | sympy | POLY_ORBIT_LEGENDRE_COUNT | [
"POLY_ORBIT_LEGENDRE_COUNT"
] | b47831 | alg_poly_orbit_legendre_v1 | null | 6 | null | [
"POLY_ORBIT_LEGENDRE_COUNT"
] | 1 | 0.019 | 2026-02-25T07:54:26.288840Z | null | 604d06 | 95a5cf | narrative | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 237,
"completion_tokens": 7924
},
"timestamp": "2026-03-31T01:16:07.940Z",
"answer": 2542
},
{
"i... | 1 | [
{
"lemma": "POLY_ORBIT_LEGENDRE_COUNT",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
}
] | {
"lo": 1.5,
"mid": 4.69,
"hi": 7.23
} | |
e133fe_l | comb_factorial_compute_v1_798873815_55 | Let $T$ be the set of all integers $t$ such that $5 \leq t \leq 14$ and there exist positive integers $a$ and $b$ with $1 \leq a \leq 4$, $1 \leq b \leq 2$, and $t = 2a + 3b$. Let $n$ be the number of elements in $T$. Compute $n!$. | 5,040 | ALG | COMB | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | comb_factorial_compute_v1 | null | 3 | 0 | [
"LIN_FORM"
] | 1 | 0.001 | 2026-02-08T02:25:33.659775Z | {
"verified": false,
"answer": 40320,
"timestamp": "2026-02-08T02:25:33.661102Z"
} | 52f2a2 | e133fe | legacy_text | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 208,
"completion_tokens": 444
},
"timestamp": "2026-02-08T18:32:06.603Z",
"answer": 40320
},
{
"i... | 1 | [
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
}
] | {
"lo": -6.29,
"mid": -4.58,
"hi": -2.79
} | |
d7d35a | nt_count_intersection_v1_1918700295_4553 | Let $ d_0 $ be the smallest divisor of $ 6125 $ that is at least $ 2 $. Let $ b $ be the sum of all positive integers from $ 1 $ to $ d_0 $. Compute the number of positive integers $ n \leq 100000 $ such that $ 11 $ divides $ n $ and $ \gcd(n, b) = 1 $. | 4,848 | graphs = [
Graph(
let={
"_n": MinOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Const(2)), Divides(divisor=Var("d"), dividend=Const(6125))))),
"N": Const(100000),
"a": Const(11),
"b": Summation(var="k", start=Const(1), end=Ref("_n"), expr=V... | NT | null | COUNT | sympy | MIN_PRIME_FACTOR | [
"MIN_PRIME_FACTOR/SUM_ARITHMETIC"
] | 487060 | nt_count_intersection_v1 | null | 5 | 0 | [
"MIN_PRIME_FACTOR",
"SUM_ARITHMETIC"
] | 2 | 4 | 2026-02-08T09:27:35.056379Z | {
"verified": true,
"answer": 4848,
"timestamp": "2026-02-08T09:27:39.056378Z"
} | 5ee1de | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 129,
"completion_tokens": 1237
},
"timestamp": "2026-02-14T04:10:17.170Z",
"answer": 4848
},
{... | 1 | [
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MIN_PRIME_FACTOR",
"status": "ok"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "SUM_ARITHMETIC",
"status": "ok_later"
},
{
"lemma": "V1",
"status": "no"... | {
"lo": -5.49,
"mid": 0.22,
"hi": 6.51
} | ||
bfec56 | lin_form_endings_v1_784195855_4467 | Compute the remainder when $19479 \times \gcd(8, 28)$ is divided by $57039$. | 20,877 | graphs = [
Graph(
let={
"a_coeff": Const(8),
"b_coeff": Const(28),
"_inner_result": GCD(a=Ref("a_coeff"), b=Ref("b_coeff")),
"_scale_k": Const(19479),
"_scaled": Mul(Ref("_scale_k"), Ref("_inner_result")),
"_mod_M": Const(57039),
... | COMB | NT | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | lin_form_endings_v1 | null | 2 | null | [
"LIN_FORM"
] | 1 | 0 | 2026-02-08T07:07:54.972086Z | {
"verified": true,
"answer": 20877,
"timestamp": "2026-02-08T07:07:54.972519Z"
} | 6a6428 | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 87,
"completion_tokens": 298
},
"timestamp": "2026-02-15T18:52:33.957Z",
"answer": 20877
},
{
"id": 11,
... | 2 | [
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
... | {
"lo": -9.14,
"mid": -6.05,
"hi": -3.73
} | ||
932489 | comb_factorial_compute_v1_124444284_4897 | Let $p$ and $q$ be positive integers such that $pq = 14700$, $\gcd(p, q) = 1$, and $p < q$. Let $n$ be the number of such integers $p$. Compute $n!$. | 40,320 | 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=14700)), Eq(left=GCD(a=Var(name='p'), b=Var(name='q')), right=Const(value=1))... | NT | null | COMPUTE | sympy | COPRIME_PAIRS | [
"COPRIME_PAIRS"
] | 2bb3aa | comb_factorial_compute_v1 | null | 6 | 0 | [
"COPRIME_PAIRS"
] | 1 | 0.001 | 2026-02-08T06:16:56.677780Z | {
"verified": true,
"answer": 40320,
"timestamp": "2026-02-08T06:16:56.679058Z"
} | bf5105 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 101,
"completion_tokens": 761
},
"timestamp": "2026-02-12T22:31:24.602Z",
"answer": 40320
},
{... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
},
{
"lemma": "VAL_SUM_EQ",
"status": "no"
}
] | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
2821cf | nt_count_gcd_equals_v1_717093673_1064 | Let $\text{result}$ be the number of positive integers $n \leq 12100$ such that $\gcd(n, 425) = 85$. Let $s$ be the minimum value of $x + y$ over all ordered pairs $(x, y)$ of positive integers such that $x \cdot y = 90000$. Compute $\text{result}^2 + 7 \cdot \text{result} + s$. | 14,394 | graphs = [
Graph(
let={
"_n": Const(90000),
"upper": Const(12100),
"k": Const(425),
"d": Const(85),
"result": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Ref("upper")), Eq(GCD(a=Var("n"), b=Ref("... | NT | null | COUNT | sympy | B3 | [
"B3"
] | d720b5 | nt_count_gcd_equals_v1 | quadratic_mod | 5 | 0 | [
"B3"
] | 1 | 1.242 | 2026-02-08T15:50:06.702484Z | {
"verified": true,
"answer": 14394,
"timestamp": "2026-02-08T15:50:07.944652Z"
} | 6da8a1 | 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": 1390
},
"timestamp": "2026-02-16T15:16:25.142Z",
"answer": 14394
},
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
1159c3 | comb_catalan_compute_v1_1915831931_2139 | Let $v = \sum_{k=0}^{2} (-1)^k \binom{2}{k}$. Let $e = \sum_{k_1=0}^{9} (-1)^{k_1} \binom{9}{k_1}$, where the summation starts at $k_1 = \binom{20}{0} - 1 = 0$. Let $n = 10 + v + e$. Compute the $n$-th Catalan number. | 16,796 | graphs = [
Graph(
let={
"n2": Const(2),
"v": 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(9),
"e": Summation(var="k1", start=Sub(Binom(n=Const(20), k=Const(0)), Const(1)), en... | COMB | null | COMPUTE | sympy | BINOMIAL_ALTERNATING | [
"BINOMIAL_ALTERNATING",
"ZERO_BINOM_0"
] | 38a409 | comb_catalan_compute_v1 | null | 4 | 2 | [
"BINOMIAL_ALTERNATING",
"ZERO_BINOM_0"
] | 2 | 0.003 | 2026-02-08T16:38:59.301649Z | {
"verified": true,
"answer": 16796,
"timestamp": "2026-02-08T16:38:59.304621Z"
} | d0bcac | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 146,
"completion_tokens": 604
},
"timestamp": "2026-02-17T08:57:37.403Z",
"answer": 16796
},
{... | 1 | [
{
"lemma": "BINOMIAL_ALTERNATING",
"status": "ok"
},
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "V... | {
"lo": -8,
"mid": -4.75,
"hi": -2.28
} | ||
b3bf7d | antilemma_k2_v1_1439011603_2545 | Compute the value of
$$
\sum_{k=1}^{46} \phi(k) \left\lfloor \frac{46}{k} \right\rfloor.
$$ | 1,081 | graphs = [
Graph(
let={
"x": Summation(var="k", start=Div(Const(95), Const(95)), end=Const(46), expr=Mul(EulerPhi(n=Var("k")), Floor(Div(Const(46), Var("k"))))),
},
goal=Ref("x"),
)
] | NT | COMB | COMPUTE | sympy | IDENTITY_DIV_SELF | [
"IDENTITY_DIV_SELF",
"K2"
] | 39e678 | antilemma_k2_v1 | null | 3 | 0 | [
"IDENTITY_DIV_SELF",
"K2"
] | 2 | 0.001 | 2026-02-08T16:51:27.297593Z | {
"verified": true,
"answer": 1081,
"timestamp": "2026-02-08T16:51:27.298553Z"
} | a1ae3f | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 82,
"completion_tokens": 796
},
"timestamp": "2026-02-17T13:36:46.812Z",
"answer": 1081
},
{
... | 1 | [
{
"lemma": "IDENTITY_DIV_SELF",
"status": "ok"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "K2",
"status": "ok"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
},
{
"lemma": "V... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
0904ee | nt_count_primes_v1_1918700295_2662 | Let $T$ be the set of all positive integers $p$ for which there exists a positive integer $q$ such that $pq = 18$, $\gcd(p, q) = 1$, and $p < q$. Let $m$ be the number of elements in $T$. Let $S$ be the set of all prime numbers $n$ such that $m \leq n \leq 30276$. Compute the number of elements in $S$. | 3,274 | graphs = [
Graph(
let={
"upper": Const(30276),
"result": CountOverSet(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'),... | NT | null | COUNT | sympy | COPRIME_PAIRS | [
"COPRIME_PAIRS"
] | 2bb3aa | nt_count_primes_v1 | null | 4 | 0 | [
"COPRIME_PAIRS"
] | 1 | 0.928 | 2026-02-08T08:09:26.430233Z | {
"verified": true,
"answer": 3274,
"timestamp": "2026-02-08T08:09:27.358211Z"
} | 94f115 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 144,
"completion_tokens": 1599
},
"timestamp": "2026-02-13T14:58:53.070Z",
"answer": 3274
},
{... | 1 | [
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "V1",
"status": "no"
}
] | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
f8b66d | antilemma_sum_equals_v1_48377204_2433 | Let $m = 76702$. Let $n$ be the number of ordered pairs $(i, j)$ such that $1 \leq i \leq 6$ and $1 \leq j \leq 9$. Let $x$ be the number of ordered pairs $(i, j)$ of integers with $1 \leq i \leq 52$ and $1 \leq j \leq 52$ such that $i + j = n$. Compute the remainder when $44121x$ is divided by $m$. | 25,813 | graphs = [
Graph(
let={
"_m": Const(76702),
"_n": CountOverSet(set=CartesianProduct(left=IntegerRange(start=Const(1), end=Const(6)), right=IntegerRange(start=Const(1), end=Const(9)))),
"x": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("i"), Var("j")]), condition=... | COMB | GEOM | COMPUTE | sympy | COUNT_CARTESIAN | [
"COUNT_CARTESIAN/COUNT_SUM_EQUALS",
"COUNT_SUM_EQUALS"
] | 8bee9e | antilemma_sum_equals_v1 | null | 3 | 0 | [
"COUNT_CARTESIAN",
"COUNT_SUM_EQUALS"
] | 2 | 0.01 | 2026-02-08T16:46:24.087994Z | {
"verified": true,
"answer": 25813,
"timestamp": "2026-02-08T16:46:24.097514Z"
} | bec241 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 156,
"completion_tokens": 787
},
"timestamp": "2026-02-17T10:43:49.118Z",
"answer": 25813
},
{... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "ok"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "ok"
},
{
"lemma": "V7",
... | {
"lo": -2.38,
"mid": 1.74,
"hi": 6.59
} | ||
f260e6 | antilemma_k2_v1_784195855_6609 | Compute the value of
$$
\sum_{k=1}^{417} \phi(k) \left\lfloor \frac{417}{k} \right\rfloor,
$$
where $\phi(k)$ denotes Euler's totient function. | 87,153 | graphs = [
Graph(
let={
"x": Summation(var="k", start=Const(1), end=Const(417), expr=Mul(EulerPhi(n=Var("k")), Floor(Div(Const(417), Var("k"))))),
},
goal=Ref("x"),
)
] | NT | COMB | COMPUTE | sympy | K2 | [
"K2"
] | 6897ab | antilemma_k2_v1 | null | 6 | 0 | [
"K2"
] | 1 | 0 | 2026-02-08T08:45:11.468878Z | {
"verified": true,
"answer": 87153,
"timestamp": "2026-02-08T08:45:11.469168Z"
} | 6f1633 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 93,
"completion_tokens": 582
},
"timestamp": "2026-02-13T21:02:04.950Z",
"answer": 87153
},
{
... | 1 | [
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "K2",
"status": "ok"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "V1",
"status": "no"
}
] | {
"lo": -3.51,
"mid": 1.33,
"hi": 6.56
} | ||
d210c3 | sequence_fibonacci_compute_v1_1353956133_225 | Let $n = 21$ and let $F_n$ denote the $n$th Fibonacci number, where $F_1 = 1$, $F_2 = 1$, and $F_k = F_{k-1} + F_{k-2}$ for $k \geq 3$. Let $S$ be the set of all positive divisors of 2989 that are at most 49. Compute the remainder when
$$
F_n^2 + \left(\max(S)\right) \cdot F_n + 99
$$
is divided by 96769.
Find the v... | 67,502 | graphs = [
Graph(
let={
"_n": Const(49),
"n": Const(21),
"result": Fibonacci(arg=Ref(name='n')),
"Q": Mod(value=Sum(Pow(Ref("result"), Const(2)), Mul(MaxOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Const(1)), Leq(Var("d"), Ref("_n")), Div... | NT | null | COMPUTE | sympy | MAX_DIVISOR | [
"MAX_DIVISOR"
] | d27307 | sequence_fibonacci_compute_v1 | quadratic_mod | 4 | 0 | [
"MAX_DIVISOR"
] | 1 | 0.003 | 2026-02-08T11:21:01.528648Z | {
"verified": true,
"answer": 67502,
"timestamp": "2026-02-08T11:21:01.531473Z"
} | e0f663 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 176,
"completion_tokens": 1470
},
"timestamp": "2026-02-14T13:15:15.099Z",
"answer": 67502
},
... | 1 | [
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "MAX_DIVISOR",
"status": "ok"
},
{
"lemma": "MAX_PRIME_BELOW",
"stat... | {
"lo": -5.49,
"mid": 0.22,
"hi": 6.51
} | ||
e9ad1b | nt_count_divisors_in_range_v1_1080341949_384 | Let $n = 166320$, $a = 83$, and $b$ be the largest prime number less than or equal to 3698. Compute the number of positive divisors $d$ of $n$ such that $a \leq d \leq b$. Let this count be $C$. Compute $36856 - C$. | 36,766 | graphs = [
Graph(
let={
"n": Const(166320),
"a": Const(83),
"b": MaxOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(2)), Leq(Var("n"), Const(3698)), IsPrime(Var("n"))))),
"result": CountOverSet(set=SolutionsSet(var=Var("d"), condition=... | NT | null | COUNT | sympy | MAX_PRIME_BELOW | [
"MAX_PRIME_BELOW"
] | dc3ad3 | nt_count_divisors_in_range_v1 | null | 4 | 0 | [
"MAX_PRIME_BELOW"
] | 1 | 0.072 | 2026-02-08T13:28:18.613903Z | {
"verified": true,
"answer": 36766,
"timestamp": "2026-02-08T13:28:18.686116Z"
} | 63ac33 | 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": 3372
},
"timestamp": "2026-02-15T16:13:19.011Z",
"answer": 36766
},
... | 1 | [
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok"
},
{
"lemma": "MOD_ADD",
"status": "no"
}
] | {
"lo": -5.49,
"mid": 0.22,
"hi": 6.51
} | ||
8ebf6a | modular_modexp_compute_v1_1978505735_3310 | Let $a$ be the number of integers $n$ with $1 \leq n \leq 10$ such that $n \equiv \left\lfloor \frac{n}{2} \right\rfloor \pmod{5}$.
Let $e$ be the number of ordered pairs $(x_1, x_2)$ of positive odd integers such that $x_1 + x_2 = 14792$.
Compute the remainder when $a^e$ is divided by 84100. | 8,136 | graphs = [
Graph(
let={
"_n": Const(14792),
"a": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Const(10)), Congruent(a=Var(name='n'), b=Floor(arg=Div(left=Var(name='n'), right=Const(value=2))), modulus=Const(value=5))))),
... | NT | null | COMPUTE | sympy | COMB1 | [
"COMB1",
"L3C"
] | 942b13 | modular_modexp_compute_v1 | null | 4 | 0 | [
"COMB1",
"L3C"
] | 2 | 0.004 | 2026-02-08T17:33:03.635871Z | {
"verified": true,
"answer": 8136,
"timestamp": "2026-02-08T17:33:03.639507Z"
} | 50f015 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 151,
"completion_tokens": 4748
},
"timestamp": "2026-02-18T03:51:31.805Z",
"answer": 8136
},
{... | 1 | [
{
"lemma": "COMB1",
"status": "ok"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "L3C",
"status": "ok"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lem... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
9ee36c | nt_min_coprime_above_v1_1125832087_212 | Let $p = 2$, and define $m = ( (p-1)! + 1 ) \bmod p$. Let $a = 54$ and $b = 175 + m$. Define $u = \sum_{d \mid \gcd(a,b)} \mu(d)$, where $\mu(d)$ is the M\"obius function. Let $T$ be the set of all integers $n$ such that $14641 < n \le 14970$ and $\gcd(n, 319) = 1$. Let $r$ be the smallest element of $T$. Compute the r... | 65,097 | graphs = [
Graph(
let={
"p": Const(2),
"m": Mod(value=Sum(Factorial(Sub(Ref("p"), Const(1))), Const(1)), modulus=Ref("p")),
"a": Const(54),
"b": Sum(Const(175), Ref("m")),
"u": SumOverDivisors(n=GCD(a=Ref(name='a'), b=Ref(name='b')), var='d', expr=... | NT | null | EXTREMUM | sympy | MOBIUS_COPRIME | [
"MOBIUS_COPRIME",
"WILSON"
] | 9e4f5c | nt_min_coprime_above_v1 | null | 6 | 2 | [
"MOBIUS_COPRIME",
"WILSON"
] | 2 | 0.037 | 2026-02-08T02:56:30.201448Z | {
"verified": true,
"answer": 65097,
"timestamp": "2026-02-08T02:56:30.238328Z"
} | 531a7e | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 264,
"completion_tokens": 549
},
"timestamp": "2026-02-17T15:51:19.460Z",
"answer": 40874
}
] | 0 | [
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "MOBIUS_COPRIME",
"status": "ok"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "V3",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
},
... | {
"lo": -6.48,
"mid": 1.54,
"hi": 9.56
} | ||
8a997a | nt_sum_gcd_range_mod_v1_677425708_2157 | Let $S$ be the set of all ordered pairs of positive integers $(x, y)$ such that $xy = 20250000$. Let $c$ be the minimum value of $x + y$ over all $(x, y) \in S$. Let $s = \sum_{n=1}^{3000} \gcd(n, 600)$, and let $r$ be the remainder when $s$ is divided by $10253$. Compute the remainder when $r^2 + 25r + c$ is divided b... | 43,694 | graphs = [
Graph(
let={
"_n": Const(2),
"N": Const(3000),
"k": Const(600),
"M": Const(10253),
"sum": Summation(var="n", start=Const(1), end=Ref("N"), expr=GCD(a=Var("n"), b=Ref("k"))),
"result": Mod(value=Ref("sum"), modulus=Ref("M")),
... | NT | null | COMPUTE | sympy | B3 | [
"B3"
] | d720b5 | nt_sum_gcd_range_mod_v1 | quadratic_mod | 6 | 0 | [
"B3"
] | 1 | 0.266 | 2026-02-08T04:49:04.584572Z | {
"verified": true,
"answer": 43694,
"timestamp": "2026-02-08T04:49:04.850995Z"
} | 898812 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 228,
"completion_tokens": 6546
},
"timestamp": "2026-02-10T06:37:53.127Z",
"answer": 43694
},
{
"... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "V1",
"status": "no"
}
] | {
"lo": -3.45,
"mid": 1.15,
"hi": 6.18
} | ||
3061e2 | geo_count_lattice_rect_v1_124444284_751 | Compute the number of lattice points in the rectangle $[0, 196] \times [0, 84]$. | 16,745 | graphs = [
Graph(
let={
"a": Const(196),
"b": Const(84),
"result": LatticePointsRect(a=Ref(name='a'), b=Ref(name='b')),
},
goal=Ref("result"),
)
] | GEOM | null | COUNT | sympy | [] | geo_count_lattice_rect_v1 | null | 3 | 0 | null | null | 0.001 | 2026-02-08T03:29:38.045292Z | {
"verified": true,
"answer": 16745,
"timestamp": "2026-02-08T03:29:38.045807Z"
} | 7de06f | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 135,
"completion_tokens": 167
},
"timestamp": "2026-02-09T21:29:38.353Z",
"answer": 16745
},
{
"i... | 1 | [] | {
"lo": -7.18,
"mid": -4.99,
"hi": -3
} | ||||
8c89f9 | alg_sum_ap_v1_1218484723_2060 | Let $F_n$ denote the $n$-th Fibonacci number. Let $M$ be the number of positive integers $n$ with $1 \le n \le 7758$ such that $8 \mid F_n$. Find the remainder when $\sum_{k=0}^{M} (10k + 84)$ is divided by $\left|\{ t : \text{there exist integers } a, b \text{ with } 1 \leq a \leq 315, 1 \leq b \leq 1282 \text{ such t... | 649 | graphs = [
Graph(
let={
"_m": Const(10),
"_n": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Const(7758)), Divides(divisor=Const(8), dividend=Fibonacci(arg=Var(name='n')))))),
"result": Mod(value=Summation(var="k", start=... | ALG | NT | COMPUTE | sympy | COUNT_FIB_DIVISIBLE | [
"COUNT_FIB_DIVISIBLE/LIN_FORM"
] | c6b73c | alg_sum_ap_v1 | null | 4 | 0 | [
"COUNT_FIB_DIVISIBLE",
"LIN_FORM"
] | 2 | 0.019 | 2026-02-25T03:45:11.051234Z | {
"verified": true,
"answer": 649,
"timestamp": "2026-02-25T03:45:11.069986Z"
} | affccb | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 260,
"completion_tokens": 10578
},
"timestamp": "2026-03-29T02:47:03.066Z",
"answer": 649
},
{
"i... | 1 | [
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "ok"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok_later"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "V3",
"status... | {
"lo": 1.14,
"mid": 4.13,
"hi": 6.32
} | ||
ab936f | nt_count_primes_v1_1978505735_6752 | Let $a$ be the number of positive integers $p$ such that there exists an integer $q > p$ with $pq = 216$ and $\gcd(p, q) = 1$. Let $N$ be the number of prime numbers $n$ such that $a \leq n \leq 28224$. Compute the remainder when $84119 \cdot N$ is divided by $93745$. | 13,844 | graphs = [
Graph(
let={
"_n": Const(93745),
"upper": Const(28224),
"result": CountOverSet(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'), conditio... | NT | null | COUNT | sympy | COPRIME_PAIRS | [
"COPRIME_PAIRS"
] | 2bb3aa | nt_count_primes_v1 | null | 5 | 0 | [
"COPRIME_PAIRS"
] | 1 | 0.605 | 2026-02-08T19:46:59.293474Z | {
"verified": true,
"answer": 13844,
"timestamp": "2026-02-08T19:46:59.898530Z"
} | da5439 | 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": 4087
},
"timestamp": "2026-02-18T23:29:06.382Z",
"answer": 13844
},
... | 1 | [
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "POLY_PADIC_... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
be1cb5 | antilemma_k3_v1_1520064083_8284 | Let $n = 85225$ and $c = 1009$. Define $x$ to be the sum of $\phi(d)$ over all positive divisors $d$ of $n$. Compute the value of $(x \bmod 199) + c \cdot (x \bmod 499)$, and let $Q$ be the remainder when this sum is divided by $65829$. Find the value of $Q$. | 3,634 | graphs = [
Graph(
let={
"_n": Const(85225),
"x": SumOverDivisors(n=Ref(name='_n'), var='d', expr=EulerPhi(n=Var(name='d'))),
"_c": Const(1009),
"Q": Mod(value=Sum(Mod(value=Ref("x"), modulus=Const(199)), Mul(Ref("_c"), Mod(value=Ref("x"), modulus=Const(499))))... | NT | COMB | COMPUTE | sympy | K3 | [
"K3"
] | 54c41e | antilemma_k3_v1 | null | 4 | 0 | [
"K3"
] | 1 | 0 | 2026-02-08T10:07:07.096660Z | {
"verified": true,
"answer": 3634,
"timestamp": "2026-02-08T10:07:07.097127Z"
} | c5d21f | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 136,
"completion_tokens": 521
},
"timestamp": "2026-02-14T06:26:22.979Z",
"answer": 3634
},
{
... | 1 | [
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "K3",
"status": "ok"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
}
] | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
149c6b | nt_count_intersection_v1_1439011603_1347 | Let $a$ be the largest prime number $n$ such that $2 \leq n \leq 5$. Let $S$ be the set of all ordered pairs $(x, y)$ of positive integers such that $xy = 36$. Define $b$ to be the minimum value of $x + y$ as $(x, y)$ ranges over $S$. Let $N = 50000$. Determine the number of positive integers $n_1$ such that $1 \leq n_... | 3,333 | graphs = [
Graph(
let={
"_m": Const(5),
"_n": Const(2),
"N": Const(50000),
"a": MaxOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Ref("_n")), Leq(Var("n"), Ref("_m")), IsPrime(Var("n"))))),
"b": MinOverSet(set=MapOverSet(set=Sol... | NT | null | COUNT | sympy | MAX_PRIME_BELOW | [
"MAX_PRIME_BELOW",
"B3"
] | 78ed98 | nt_count_intersection_v1 | null | 5 | 0 | [
"B3",
"MAX_PRIME_BELOW"
] | 2 | 2.508 | 2026-02-08T16:02:35.864856Z | {
"verified": true,
"answer": 3333,
"timestamp": "2026-02-08T16:02:38.372861Z"
} | acc5b7 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 178,
"completion_tokens": 1201
},
"timestamp": "2026-02-16T19:23:19.840Z",
"answer": 3333
},
{... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
a15ad2 | geo_count_lattice_rect_v1_784195855_4048 | Let $a = 30$ and $b = 52$. Compute the number of lattice points $(x, y)$ such that $0 \leq x \leq a$ and $0 \leq y \leq b$. | 1,643 | graphs = [
Graph(
let={
"a": Const(30),
"b": Const(52),
"result": LatticePointsRect(a=Ref(name='a'), b=Ref(name='b')),
},
goal=Ref("result"),
)
] | GEOM | null | COUNT | sympy | [] | geo_count_lattice_rect_v1 | null | 3 | 0 | null | null | 0.002 | 2026-02-08T06:47:33.296885Z | {
"verified": true,
"answer": 1643,
"timestamp": "2026-02-08T06:47:33.299346Z"
} | 71d5b4 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 160,
"completion_tokens": 248
},
"timestamp": "2026-02-24T07:05:30.163Z",
"answer": 1643
},
{
"id... | 2 | [] | {
"lo": -10,
"mid": -7.79,
"hi": -5.57
} | ||||
c2869e | algebra_poly_eval_v1_124444284_5164 | Let $b = 27$. Let $S$ be the set of prime numbers $n$ such that $2 \leq n \leq 8753$. Let $k$ be the number of elements $n$ in $S$ such that $n \equiv \left\lfloor \frac{n}{2} \right\rfloor \pmod{7}$. Compute the value of
\[
\frac{32b^5 + 164b^4 - 200b^3 - 260b^2 + k \cdot b + 84}{23408}.
\] | 23,163 | graphs = [
Graph(
let={
"_n": Const(23408),
"b": Const(27),
"result": Div(Sum(Mul(Const(32), Pow(Ref("b"), Const(5))), Mul(Const(164), Pow(Ref("b"), Const(4))), Mul(Const(-200), Pow(Ref("b"), Const(3))), Mul(Const(-260), Pow(Ref("b"), Const(2))), Mul(CountOverSet(set=Solu... | NT | null | COMPUTE | sympy | COUNT_PRIMES | [
"COUNT_PRIMES/L3C"
] | a11314 | algebra_poly_eval_v1 | null | 7 | 0 | [
"COUNT_PRIMES",
"L3C"
] | 2 | 0.013 | 2026-02-08T06:25:54.835354Z | {
"verified": true,
"answer": 23163,
"timestamp": "2026-02-08T06:25:54.848753Z"
} | 765545 | 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": 5987
},
"timestamp": "2026-02-12T23:47:43.902Z",
"answer": 23163
},
... | 1 | [
{
"lemma": "COUNT_PRIMES",
"status": "ok"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "L3C",
"status": "ok_later"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"le... | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
10876f | nt_euler_phi_compute_v1_349078426_542 | Let $N = 38400$ and $n = 66666$. Let $r = \phi(n)$, where $\phi$ denotes Euler's totient function. Let $c$ be the number of positive integers $k$ such that $1 \leq k \leq N$ and the $k$-th Fibonacci number is divisible by 4. Compute the remainder when $c - r$ is divided by 74799. | 59,599 | graphs = [
Graph(
let={
"_n": Const(38400),
"n": Const(66666),
"result": EulerPhi(n=Ref("n")),
"Q": Mod(value=Sub(CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Ref("_n")), Divides(divisor=Const(4), dividend=Fi... | NT | null | COMPUTE | sympy | COUNT_FIB_DIVISIBLE | [
"COUNT_FIB_DIVISIBLE"
] | 222f73 | nt_euler_phi_compute_v1 | negation_mod | 7 | 0 | [
"COUNT_FIB_DIVISIBLE"
] | 1 | 0.001 | 2026-02-08T13:07:24.058135Z | {
"verified": true,
"answer": 59599,
"timestamp": "2026-02-08T13:07:24.059610Z"
} | e1bfe4 | 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": 1421
},
"timestamp": "2026-02-15T10:20:24.759Z",
"answer": 59599
},
... | 1 | [
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "ok"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "VAL_SUM_EQ",
"status": "no"
}... | {
"lo": -5.49,
"mid": 0.22,
"hi": 6.51
} | ||
9c0872 | nt_count_coprime_and_v1_1520064083_922 | Let $S$ be the set of all ordered pairs $(x, y)$ of positive integers such that $xy = 23931664$. For each such pair, compute $x + y$. Let $U$ be the set of all such sums. Define $u$ to be the minimum value in $U$. Let $T$ be the set of all positive integers $n$ such that $1 \leq n \leq u$, $\gcd(n, 5) = 1$, and $\gcd(n... | 7,116 | graphs = [
Graph(
let={
"upper": MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(Mul(Var("x"), Var("y")), Const(23931664)))), expr=Sum(Var("x"), Var("y")))),
"k1": Cons... | NT | null | COUNT | sympy | B3 | [
"B3"
] | 0cd20d | nt_count_coprime_and_v1 | null | 6 | 0 | [
"B3"
] | 1 | 1.753 | 2026-02-08T03:40:10.767777Z | {
"verified": true,
"answer": 7116,
"timestamp": "2026-02-08T03:40:12.520708Z"
} | f57c9d | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 236,
"completion_tokens": 1700
},
"timestamp": "2026-02-23T21:07:53.553Z",
"answer": 7116
},
{
"... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
}
] | {
"lo": -3.45,
"mid": 1.18,
"hi": 5.72
} | ||
7bd70a | comb_count_surjections_v1_1218484723_3217 | Let $B_n$ denote the $n$-th Bell number. Let $k$ be the number of integers $a$ with $0 \leq a \leq 2208$ such that \[
2x^5 - 5x^4 - 4x^3 + 5x^2 + 3x + 1 \equiv a \pmod{2209}
\] where $x \equiv 2a^5 - 5a^4 - 4a^3 + 5a^2 + 3a + 1 \pmod{2209}$, and $x \not\equiv a \pmod{2209}$. Let $n = \sum_{k1=0}^{2} 2^{k1}$. Define $R ... | 877 | graphs = [
Graph(
let={
"_m": Const(5),
"_n": Const(2),
"n": Summation(var="k1", start=Const(0), end=Const(2), expr=Pow(Ref("_n"), Var("k1"))),
"k": CountOverSet(set=SolutionsSet(var=Var("a"), condition=And(Geq(Var("a"), Const(0)), Leq(Var("a"), Const(2208)), ... | COMB | null | COUNT | sympy | K2 | [
"POLY_ORBIT_HENSEL",
"SUM_GEOM"
] | 67249c | comb_count_surjections_v1 | null | 5 | 0 | [
"K2",
"POLY_ORBIT_HENSEL",
"SUM_GEOM"
] | 3 | 0.011 | 2026-02-25T04:54:43.671615Z | {
"verified": true,
"answer": 877,
"timestamp": "2026-02-25T04:54:43.682972Z"
} | 54dd05 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 313,
"completion_tokens": 32768
},
"timestamp": "2026-03-29T09:05:03.256Z",
"answer": null
},
{
... | 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": "SUM_GEOM",
"status": "ok"
},
{
"lemma": "V... | {
"lo": 3.81,
"mid": 6.33,
"hi": 9.49
} | ||
bbd906 | antilemma_sum_equals_v1_1742523217_4080 | Let $m = 50$. Let $n$ be the number of ordered pairs of integers $(i, j)$ such that $1 \le i \le 48$, $1 \le j \le 48$, and $i + j = m$. Compute the number of ordered pairs of integers $(i, j)$ such that $1 \le i \le 45$, $1 \le j \le 45$, and $i + j = n$. | 44 | graphs = [
Graph(
let={
"_m": Const(50),
"_n": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("i"), Var("j")]), condition=Eq(Sum(Var("i"), Var("j")), Ref("_m")), domain=CartesianProduct(left=IntegerRange(start=Const(1), end=Const(48)), 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 | 3 | 0 | [
"COUNT_SUM_EQUALS",
"LIN_FORM"
] | 2 | 0.097 | 2026-02-08T06:59:23.696994Z | {
"verified": true,
"answer": 44,
"timestamp": "2026-02-08T06:59:23.793812Z"
} | 6ab0a9 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 207,
"completion_tokens": 762
},
"timestamp": "2026-02-24T07:24:57.313Z",
"answer": 44
},
{
"id":... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "ok"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
}
] | {
"lo": -3.84,
"mid": -1.67,
"hi": 1.32
} | ||
63f50b | alg_qf_psd_sum_v1_1218484723_6665 | Find the remainder when
$$
\sum_{\substack{1 \le a \le 200 \\ 1 \le b \le 200}} \left( -6ab + 5a^{m} + 5b^2 \right)
$$
is divided by $58206$, where
$$
m = \min\left\{ -96a_1 b_1^2 + 24a_1^2 b_1 + 98b_1^3 \mid 1 \le a_1, b_1 \le 20 \right\}.
$$ | 41,980 | graphs = [
Graph(
let={
"_n": Const(58206),
"result": Mod(value=SumOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("a"), Var("b")]), condition=And(Geq(Var("a"), Const(1)), Leq(Var("a"), Const(200)), Geq(Var("b"), Const(1)), Leq(Var("b"), Const(200)))), expr=Sum(Mul(Co... | ALG | null | COMPUTE | sympy | POLY3_MIN | [
"POLY3_MIN"
] | e2e279 | alg_qf_psd_sum_v1 | null | 6 | 0 | [
"POLY3_MIN"
] | 1 | 0.069 | 2026-02-25T08:11:21.315265Z | {
"verified": true,
"answer": 41980,
"timestamp": "2026-02-25T08:11:21.384072Z"
} | 667426 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 236,
"completion_tokens": 6527
},
"timestamp": "2026-03-30T02:32:26.298Z",
"answer": 41980
},
{
"... | 1 | [
{
"lemma": "POLY3_MIN",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
}
] | {
"lo": -3.33,
"mid": 1.03,
"hi": 5.26
} | ||
ca8f85 | diophantine_fbi2_min_v1_238844314_932 | Let $d$ be the smallest integer such that $5 \leq d \leq 70$, $d$ divides $60$, and $\frac{60}{d} \geq 2$. Compute the smallest positive integer $k$ such that the $k$-th Fibonacci number is divisible by $|d| + 2$. | 8 | graphs = [
Graph(
let={
"k": Const(60),
"a": Const(4),
"b": Const(1),
"upper": Const(70),
"result": MinOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Const(5)), Leq(Var("d"), Ref("upper")), Divides(divisor=Var("d"), dividend=Ref... | NT | null | EXTREMUM | sympy | C4 | [
"C4",
"B3"
] | 8d18b3 | diophantine_fbi2_min_v1 | null | 3 | 0 | [
"B3",
"C4"
] | 2 | 0.025 | 2026-02-08T13:46:25.418119Z | {
"verified": true,
"answer": 8,
"timestamp": "2026-02-08T13:46:25.443051Z"
} | 42d3e2 | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 1,
"correct": {
"strict": false,
"boxed": false,
"relaxed": true
},
"usage": {
"prompt_tokens": 167,
"completion_tokens": 1379
},
"timestamp": "2026-02-25T21:42:10.791Z",
"answer": 7
},
{
"id": 11,
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "C4",
"status": "ok"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
... | {
"lo": -8.26,
"mid": -5.01,
"hi": -1.76
} | ||
d8ae64 | antilemma_k3_v1_1978505735_3899 | Compute the value of $$\sum_{d \mid 91063} \phi(d),$$ where $\phi$ denotes Euler's totient function and the sum is taken over all positive divisors $d$ of $91063$. | 91,063 | graphs = [
Graph(
let={
"_n": Const(91063),
"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 | 2 | 0 | [
"K3"
] | 1 | 0.001 | 2026-02-08T17:55:22.662612Z | {
"verified": true,
"answer": 91063,
"timestamp": "2026-02-08T17:55:22.663423Z"
} | ea20be | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 1,
"correct": {
"strict": false,
"boxed": false,
"relaxed": true
},
"usage": {
"prompt_tokens": 111,
"completion_tokens": 569
},
"timestamp": "2026-02-16T11:45:51.370Z",
"answer": 4109
},
{
"id": 11,
... | 1 | [
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K3",
"status": "ok"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
}
] | {
"lo": -8.26,
"mid": -5.01,
"hi": -1.76
} | ||
bb7b3f | nt_max_prime_below_v1_397696148_1028 | Let $C$ be the number of positive integers $p$ for which there exists a positive integer $q$ such that $p \cdot q = 6$, $\gcd(p, q) = 1$, and $p < q$. Compute the largest prime number $n$ such that $C \leq n \leq 26244$. | 26,237 | graphs = [
Graph(
let={
"upper": Const(26244),
"result": MaxOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), CountOverSet(set=SolutionsSet(var=Var("p"), condition=And(IsPositive(arg=Var(name='p')), Exists(var=Var(name='q'), condition=And(Eq(left=Mul(Var(name='p'), V... | NT | null | EXTREMUM | sympy | COPRIME_PAIRS | [
"COPRIME_PAIRS"
] | 2bb3aa | nt_max_prime_below_v1 | null | 3 | 0 | [
"COPRIME_PAIRS"
] | 1 | 3.081 | 2026-02-08T12:18:35.892704Z | {
"verified": true,
"answer": 26237,
"timestamp": "2026-02-08T12:18:38.973388Z"
} | bf9cbb | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 118,
"completion_tokens": 2273
},
"timestamp": "2026-02-14T23:52:43.929Z",
"answer": 26237
},
... | 1 | [
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
}... | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
3f96a0 | nt_count_divisible_and_v1_153355830_1450 | Let $n = 12$. Define $d_2 = \sum_{d \mid n} \phi(d)$, where $\phi$ denotes Euler's totient function. Determine the number of positive integers $n$ such that $1 \leq n \leq 285300$, $n$ is divisible by 10, and the remainder when $n$ is divided by $d_2$ equals
$$
\sum_{k=0}^{5} (-1)^k \binom{5}{k}.
$$ | 4,755 | graphs = [
Graph(
let={
"_n": Const(12),
"upper": Const(285300),
"d1": Const(10),
"d2": SumOverDivisors(n=Ref(name='_n'), var='d', expr=EulerPhi(n=Var(name='d'))),
"result": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Co... | COMB | NT | COUNT | sympy | BINOMIAL_ALTERNATING | [
"BINOMIAL_ALTERNATING",
"K3"
] | e8b60b | nt_count_divisible_and_v1 | null | 6 | 0 | [
"BINOMIAL_ALTERNATING",
"K3"
] | 2 | 16.978 | 2026-02-08T06:24:46.297028Z | {
"verified": true,
"answer": 4755,
"timestamp": "2026-02-08T06:25:03.275501Z"
} | 04eb67 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 151,
"completion_tokens": 853
},
"timestamp": "2026-02-13T00:10:29.152Z",
"answer": 4755
},
{
... | 1 | [
{
"lemma": "BINOMIAL_ALTERNATING",
"status": "ok"
},
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "K3",
"status": "ok"
},
{
"lemma": "V7",
"status... | {
"lo": -9.14,
"mid": -6.05,
"hi": -3.73
} | ||
919e9c | comb_sum_binomial_row_v1_784195855_3206 | Let $n$ be the number of positive integers $p$ for which there exists a positive integer $q$ such that $p < q$, $\gcd(p, q) = 1$, and $p \cdot q = 1778700$. Let $s$ be the number of positive integers $p$ for which there exists a positive integer $q$ such that $p < q$, $\gcd(p, q) = 1$, and $p \cdot q = 6$. Define $r = ... | 39,616 | graphs = [
Graph(
let={
"_n": Const(86014),
"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=1778700)), Eq(left=GCD(a=Var(name='p'), b=Var... | NT | null | SUM | sympy | COPRIME_PAIRS | [
"COPRIME_PAIRS"
] | 2bb3aa | comb_sum_binomial_row_v1 | null | 5 | 0 | [
"COPRIME_PAIRS"
] | 1 | 0.003 | 2026-02-08T06:17:47.382057Z | {
"verified": true,
"answer": 39616,
"timestamp": "2026-02-08T06:17:47.384672Z"
} | 1a52e0 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 174,
"completion_tokens": 2727
},
"timestamp": "2026-02-12T22:24:03.083Z",
"answer": 39616
},
... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "MOD_SUB",
"s... | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
4e77fa | comb_sum_binomial_row_v1_677425708_1533 | Let $S$ be the set of prime numbers $n$ such that $2 \leq n \leq 5$. Define $$n = \sum_{k=1}^{\max(S)} \phi(k) \left\lfloor \frac{5}{k} \right\rfloor,$$ where $\phi(k)$ is the number of positive integers less than or equal to $k$ that are relatively prime to $k$. Compute the value of $2^n$. | 32,768 | graphs = [
Graph(
let={
"_m": Const(2),
"_n": Const(2),
"n": Summation(var="k", start=Const(1), end=MaxOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Ref("_m")), Leq(Var("n"), Const(5)), IsPrime(Var("n"))))), expr=Mul(EulerPhi(n=Var("k")), Floor(Div(Co... | NT | null | SUM | sympy | MAX_PRIME_BELOW | [
"MAX_PRIME_BELOW/K2"
] | 7eb1ee | comb_sum_binomial_row_v1 | null | 5 | 0 | [
"K2",
"MAX_PRIME_BELOW"
] | 2 | 0.001 | 2026-02-08T04:14:41.194080Z | {
"verified": true,
"answer": 32768,
"timestamp": "2026-02-08T04:14:41.195364Z"
} | 639be6 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 211,
"completion_tokens": 638
},
"timestamp": "2026-02-09T21:07:50.063Z",
"answer": 32768
},
{
"i... | 1 | [
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "K2",
"status": "ok_later"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok"
},
{
"lemma": "MOD_FACTORIAL",
"status... | {
"lo": -7.01,
"mid": -4.68,
"hi": -2.15
} | ||
a8bd20 | nt_count_divisible_and_v1_168721529_1322 | Let $a$ and $b$ be positive integers such that $\gcd(4, 9) = d$. Define $S$ to be the set of all positive integers $n$ such that $n \geq \sum_{d \mid \gcd(4,9)} \mu(d)$, $n \leq 210240$, $n \equiv 0 \pmod{10}$, and $n \equiv 0 \pmod{12}$. Compute the number of elements in $S$. | 3,504 | graphs = [
Graph(
let={
"upper": Const(210240),
"d1": Const(10),
"d2": Const(12),
"result": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), SumOverDivisors(n=GCD(a=Const(value=4), b=Const(value=9)), var='d', expr=MoebiusMu(n=Var(name='d... | NT | null | COUNT | sympy | MOBIUS_COPRIME | [
"MOBIUS_COPRIME"
] | ac54ac | nt_count_divisible_and_v1 | null | 3 | 0 | [
"MOBIUS_COPRIME"
] | 1 | 12.151 | 2026-02-08T13:35:50.053819Z | {
"verified": true,
"answer": 3504,
"timestamp": "2026-02-08T13:36:02.204639Z"
} | 7194b6 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 223,
"completion_tokens": 755
},
"timestamp": "2026-02-09T15:39:30.024Z",
"answer": 3504
},
{
"id... | 2 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "MOBIUS_COPRIME",
"status": "ok"
},
{
"lemma": "MOD_MUL",
"status": "no"
... | {
"lo": -10,
"mid": -6.5,
"hi": -3.01
} | ||
5b30ad | antilemma_sum_equals_v1_1742523217_3285 | Let $c=228$. Let $m$ be the number of ordered pairs $(x_1,x_2)$ of positive odd integers such that
$$x_1+x_2=c.$$Let $n$ be the number of ordered pairs $(x_1,x_2)$ of positive odd integers such that
$$x_1+x_2=m.$$
Let $x$ be the number of ordered pairs $(i,j)$ of integers with $1\le i\le 57$, $1\le j\le 57$, and
$$i+j... | 1,624 | graphs = [
Graph(
let={
"_c": Const(228),
"_m": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x1"), Var("x2")]), condition=And(IsPositive(arg=Var(name='x1')), IsPositive(arg=Var(name='x2')), IsOdd(arg=Var(name='x1')), IsOdd(arg=Var(name='x2')), Eq(Sum(Var("x1"), Var("x2")), ... | COMB | GEOM | COMPUTE | sympy | COMB1 | [
"COMB1/COMB1/COUNT_SUM_EQUALS",
"LIN_FORM",
"COUNT_SUM_EQUALS"
] | 05e921 | antilemma_sum_equals_v1 | negation_mod | 4 | 0 | [
"COMB1",
"COUNT_SUM_EQUALS",
"LIN_FORM"
] | 3 | 0.008 | 2026-02-08T05:45:48.573328Z | {
"verified": true,
"answer": 1624,
"timestamp": "2026-02-08T05:45:48.581432Z"
} | fc4e15 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 328,
"completion_tokens": 13886
},
"timestamp": "2026-02-24T04:27:16.005Z",
"answer": 1624
},
{
"... | 1 | [
{
"lemma": "COMB1",
"status": "ok"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "ok"
},
{
"lemma": "LI... | {
"lo": 1.97,
"mid": 4.36,
"hi": 6.69
} | ||
3e9a1f | diophantine_fbi2_min_v1_865884756_1714 | Let $k = 240$. Define $\mathcal{D}$ as the set of all integers $d$ such that $4 \leq d \leq 250$, $d$ divides $k$, and $\frac{k}{d} \geq 3$. Let $d_{\min}$ be the minimum element of $\mathcal{D}$. Let $S$ be the set of all positive integers $n$ such that $1 \leq n \leq 101$ and $n \equiv 0 \pmod{101}$. Compute the rema... | 35,823 | graphs = [
Graph(
let={
"_n": Const(97),
"k": Const(240),
"upper": Const(250),
"result": MinOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Const(4)), Leq(Var("d"), Ref("upper")), Divides(divisor=Var("d"), dividend=Ref("k")), Geq(Div(Ref("k"... | NT | null | EXTREMUM | sympy | SUM_DIVISIBLE | [
"SUM_DIVISIBLE"
] | 9168ce | diophantine_fbi2_min_v1 | crt_mix_3 | 4 | 0 | [
"SUM_DIVISIBLE"
] | 1 | 0.029 | 2026-02-08T16:14:26.618337Z | {
"verified": true,
"answer": 35823,
"timestamp": "2026-02-08T16:14:26.647021Z"
} | 7866b9 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 262,
"completion_tokens": 1401
},
"timestamp": "2026-02-17T00:16:16.463Z",
"answer": 35823
},
... | 1 | [
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "SUM_DIVISIBLE",
"status": "ok"
},
{
"lemma": "V3",
"status": "no"
},
{
"lemma": "V8",
"status... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
bd81a9 | modular_count_residue_v1_898971024_1846 | Let $S$ be the set of all ordered pairs $(x, y)$ of positive integers such that $xy = 36$. Let $m$ be the minimum value of $x + y$ over all such pairs. Determine the number of positive integers $n$ such that $1 \leq n \leq 31907$ and the remainder when $n$ is divided by $m$ is 8. Compute this number. | 2,659 | graphs = [
Graph(
let={
"_n": Const(36),
"upper": Const(31907),
"m": MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(Mul(Var("x"), Var("y")), Ref("_n")))), ... | NT | null | COUNT | sympy | B3 | [
"B3"
] | 0cd20d | modular_count_residue_v1 | null | 4 | 0 | [
"B3"
] | 1 | 3.449 | 2026-02-08T16:23:20.927521Z | {
"verified": true,
"answer": 2659,
"timestamp": "2026-02-08T16:23:24.376091Z"
} | aa08d3 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 136,
"completion_tokens": 804
},
"timestamp": "2026-02-17T02:42:29.358Z",
"answer": 2659
},
{
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
67c5cf | algebra_poly_eval_v1_971394319_900 | Let $n = 7602$. Define $a = 5$ and compute the value of $3a^2 - 2a$. Let $S$ be the set of all positive integers $j$ such that $1 \le j \le n$ and $j^4 \le 3339730794483216$. Compute the number of elements in $S$, multiply it by $3a^2 - 2a$, and then find the remainder when this product is divided by $71305$. Determine... | 66,300 | graphs = [
Graph(
let={
"_n": Const(7602),
"a": Const(5),
"result": Sum(Mul(Const(3), Pow(Ref("a"), Const(2))), Mul(Const(-2), Ref("a"))),
"Q": Mod(value=Mul(CountOverSet(set=SolutionsSet(var=Var("j"), condition=And(Geq(Var("j"), Const(1)), Leq(Var("j"), Ref("... | NT | null | COMPUTE | sympy | C3 | [
"C3"
] | 887000 | algebra_poly_eval_v1 | affine_mod | 3 | 0 | [
"C3"
] | 1 | 0.003 | 2026-02-08T13:22:38.252049Z | {
"verified": true,
"answer": 66300,
"timestamp": "2026-02-08T13:22:38.254618Z"
} | b6c33b | 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": 2203
},
"timestamp": "2026-02-15T14:17:03.074Z",
"answer": 66300
},
... | 1 | [
{
"lemma": "C3",
"status": "ok"
},
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
}
] | {
"lo": -5.49,
"mid": 0.22,
"hi": 6.51
} | ||
66e2a8 | diophantine_sum_product_min_v1_1978505735_4474 | Let $ S = 17 $ and $ P = 70 $. Define $ x $ to be the smallest positive integer such that $ 1 \leq x \leq 16 $ and $ x(S - x) = P $. Let $ c = 37 $. For each digit position $ i $ (starting from 0 at the units place), let the digit of $ x $ at position $ i $ be multiplied by $ (i+1)^k $, where $ k $ is the number of ord... | 44 | graphs = [
Graph(
let={
"S": Const(17),
"P": Const(70),
"result": MinOverSet(set=SolutionsSet(var=Var("x"), condition=And(Geq(Var("x"), Const(1)), Leq(Var("x"), Const(16)), Eq(Mul(Var("x"), Sub(Ref("S"), Var("x"))), Ref("P"))))),
"_c": Const(37),
"... | NT | null | EXTREMUM | sympy | COPRIME_PAIRS | [
"COPRIME_PAIRS"
] | a9a663 | diophantine_sum_product_min_v1 | digits_weighted_mod | 5 | 0 | [
"COPRIME_PAIRS"
] | 1 | 0.02 | 2026-02-08T18:15:56.221774Z | {
"verified": true,
"answer": 44,
"timestamp": "2026-02-08T18:15:56.241363Z"
} | 5bc448 | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 225,
"completion_tokens": 917
},
"timestamp": "2026-02-16T12:14:15.301Z",
"answer": 156
},
{
"id": 11,
... | 1 | [
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "V1",
"status": "no"
}
] | {
"lo": -8.26,
"mid": -5.01,
"hi": -1.76
} | ||
b6647b | comb_binomial_compute_v1_1820931509_477 | Let $N=4736$. Let
$$S=\sum_{k=0}^{6}(-1)^k\binom{6}{k}.$$
Let $A$ be the set of all nonnegative integers $j$ such that $j\ge S$, $j\le N$, and
$$\binom{M}{j}\equiv 1\pmod{2},$$
where $M$ is the number of integers $n$ with $1\le n\le 33152$ such that
$$n\equiv \left\lfloor\frac{n}{2}\right\rfloor \pmod{7}.$$
Let $n$ be... | 6,435 | graphs = [
Graph(
let={
"_n": Const(4736),
"n": Sum(CountOverSet(set=SolutionsSet(var=Var("j"), condition=And(Geq(Var("j"), Summation(var="k", start=Const(0), end=Const(6), expr=Mul(Pow(Const(-1), Var("k")), Binom(n=Const(6), k=Var("k"))))), Leq(Var("j"), Ref("_n")), Eq(Mod(value=Bin... | COMB | NT | COMPUTE | sympy | BINOMIAL_ALTERNATING | [
"BINOMIAL_ALTERNATING",
"L3C/V8"
] | abf110 | comb_binomial_compute_v1 | null | 8 | 0 | [
"BINOMIAL_ALTERNATING",
"L3C",
"V8"
] | 3 | 0.004 | 2026-02-08T11:39:15.654364Z | {
"verified": true,
"answer": 6435,
"timestamp": "2026-02-08T11:39:15.658624Z"
} | 208006 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 218,
"completion_tokens": 2194
},
"timestamp": "2026-02-14T17:58:08.967Z",
"answer": 6435
},
{... | 1 | [
{
"lemma": "BINOMIAL_ALTERNATING",
"status": "ok"
},
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "L3C",
"status": "ok"
},
{
"lemma": "V7",
"sta... | {
"lo": -5.49,
"mid": 0.22,
"hi": 6.51
} | ||
753e94 | alg_poly_orbit_count_v1_601307018_3125 | Let $N \equiv a^3 + a \pmod{43}$ and $M \equiv N^3 + N \pmod{43}$. Find the number of non-negative integers $a$ with $0 \le a \le 36721$ such that $M = a$ and $N \ne a$. | 5,124 | graphs = [
Graph(
let={
"p1": Mod(value=Sum(Pow(Var("a"), Const(3)), Var("a")), modulus=Const(43)),
"p2": Mod(value=Sum(Pow(Ref("p1"), Const(3)), Ref("p1")), modulus=Const(43)),
"result": CountOverSet(set=SolutionsSet(var=Var("a"), condition=And(Geq(Var("a"), Const(0)), L... | ALG | null | COUNT | sympy | POLY_ORBIT_COUNT | [
"POLY_ORBIT_COUNT"
] | 4ad965 | alg_poly_orbit_count_v1 | null | 6 | null | [
"POLY_ORBIT_COUNT"
] | 1 | 0.01 | 2026-03-10T03:42:19.326646Z | {
"verified": true,
"answer": 5124,
"timestamp": "2026-03-10T03:42:19.336815Z"
} | aa4f9c | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 181,
"completion_tokens": 11990
},
"timestamp": "2026-03-29T07:35:08.771Z",
"answer": 1708
},
{
... | 1 | [
{
"lemma": "POLY_ORBIT_COUNT",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
}
] | {
"lo": 3.34,
"mid": 5.77,
"hi": 8.89
} | ||
20f0c4 | comb_count_derangements_v1_1520064083_7792 | Let $s = \sum_{k=0}^{0} (-1)^k \binom{0}{k}$, and define $n_1 = 10s$. Let $e = \sum_{k=0}^{n_1} (-1)^k \binom{n_1}{k}$, and let $n = 8 + e$. Determine the value of the subfactorial of $n$, denoted $!n$, which counts the number of derangements of $n$ elements. | 14,833 | graphs = [
Graph(
let={
"n2": Const(0),
"s": Summation(var="k", start=Const(0), end=Ref("n2"), expr=Mul(Pow(Const(-1), Var("k")), Binom(n=Ref("n2"), k=Var("k")))),
"n1": Mul(Const(10), Ref("s")),
"e": Summation(var="k", start=Const(0), end=Ref("n1"), expr=Mul(... | COMB | null | COUNT | sympy | BINOMIAL_ALTERNATING | [
"BINOMIAL_ALTERNATING"
] | c21569 | comb_count_derangements_v1 | null | 3 | 2 | [
"BINOMIAL_ALTERNATING"
] | 1 | 0.001 | 2026-02-08T09:18:30.734416Z | {
"verified": true,
"answer": 14833,
"timestamp": "2026-02-08T09:18:30.735405Z"
} | d44f0b | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 218,
"completion_tokens": 1188
},
"timestamp": "2026-02-24T11:06:55.416Z",
"answer": 14833
},
{
"... | 1 | [
{
"lemma": "BINOMIAL_ALTERNATING",
"status": "ok"
},
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "V8_... | {
"lo": -5.97,
"mid": -3.97,
"hi": -1.93
} | ||
8363fc | nt_sum_divisors_mod_v1_1978505735_475 | Let $S$ be the set of all ordered pairs $(x, y)$ of positive integers such that $xy = 705600$. Define $n$ to be the minimum value of $x + y$ as $(x, y)$ ranges over $S$. Let $\sigma$ be the sum of all positive divisors of $n$. Compute the value of
$$
Q = (59192 \cdot (\sigma \bmod 10891)) \bmod 86267.
$$ | 82,623 | graphs = [
Graph(
let={
"_n": Const(59192),
"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(705600)))), expr=Sum(Var("x"), Var("y"))... | NT | null | COMPUTE | sympy | B3 | [
"B3"
] | 0cd20d | nt_sum_divisors_mod_v1 | null | 4 | 0 | [
"B3"
] | 1 | 0.003 | 2026-02-08T15:24:15.150439Z | {
"verified": true,
"answer": 82623,
"timestamp": "2026-02-08T15:24:15.153028Z"
} | 8ec4af | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 146,
"completion_tokens": 1824
},
"timestamp": "2026-02-16T05:41:33.289Z",
"answer": 82623
},
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
b52f6d | geo_visible_lattice_v1_458359167_51 | A lattice point $(x,y)$ is called visible from the origin if $\gcd(x,y) = 1$. Compute the number of visible lattice points $(x,y)$ with $1 \leq x, y \leq 121$. | 8,991 | graphs = [
Graph(
let={
"n": Const(121),
"result": VisibleLatticePoints(n=Ref(name='n')),
},
goal=Ref("result"),
)
] | GEOM | null | COUNT | sympy | [] | geo_visible_lattice_v1 | null | 6 | 0 | null | null | 0.318 | 2026-02-08T02:58:10.222118Z | {
"verified": true,
"answer": 8991,
"timestamp": "2026-02-08T02:58:10.539629Z"
} | aeca13 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 160,
"completion_tokens": 4152
},
"timestamp": "2026-02-23T20:33:06.220Z",
"answer": 8991
},
{
"i... | 1 | [] | {
"lo": 2.55,
"mid": 3.99,
"hi": 5.3
} | ||||
1e88a7 | lte_diff_endings_v1_1520064083_444 | Let $a = 9$, $b = 5$, $p = 2$, $K = 3$, and $N = 391809$. Let $d_1$ be the largest integer $k$ such that $p^k$ divides $a - b$, and let $d_2$ be the largest integer $k$ such that $p^k$ divides $a + b$. Let $t = (K + 1) - d_1 - d_2$, $p^t = 2^t$, and $p^{t+1} = 2 \cdot p^t$. Let $c_1$ be the number of positive integers ... | 97,952 | graphs = [
Graph(
let={
"a_val": Const(9),
"b_val": Const(5),
"p_val": Const(2),
"K_val": Const(3),
"N_val": Const(391809),
"ab_diff": Sub(Ref("a_val"), Ref("b_val")),
"vp_diff": MaxKDivides(target=Ref("ab_diff"), base=Ref("... | NT | null | COMPUTE | sympy | LTE_DIFF | [
"LTE_DIFF"
] | cf8260 | lte_diff_endings_v1 | null | 6 | null | [
"LTE_DIFF"
] | 1 | 0.001 | 2026-02-08T03:21:35.409256Z | {
"verified": true,
"answer": 97952,
"timestamp": "2026-02-08T03:21:35.409822Z"
} | 777495 | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 297,
"completion_tokens": 380
},
"timestamp": "2026-02-18T00:19:33.567Z",
"answer": 97952
}
] | 2 | [
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "ok"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "V3",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
}
] | {
"lo": -10,
"mid": -6.47,
"hi": -2.95
} | ||
7d11f7 | comb_count_derangements_v1_1431428450_1479 | Let $n$ be the number of positive integers $p$ for which there exists a positive integer $q$ such that $pq = 26460$, $\gcd(p, q) = 1$, and $p < q$. Let $d = !n$, the number of derangements of $n$ elements. Find the smallest positive integer $k$ such that the $k$-th Fibonacci number is divisible by $|d| + 2$. | 1,320 | 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=26460)), Eq(left=GCD(a=Var(name='p'), b=Var(name='q')), right=Const(value=1))... | NT | COMB | COUNT | sympy | COPRIME_PAIRS | [
"COPRIME_PAIRS"
] | 2bb3aa | comb_count_derangements_v1 | null | 5 | 0 | [
"COPRIME_PAIRS"
] | 1 | 0.004 | 2026-02-08T14:07:17.320613Z | {
"verified": true,
"answer": 1320,
"timestamp": "2026-02-08T14:07:17.324355Z"
} | dc5bed | 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": 2611
},
"timestamp": "2026-02-15T23:59:33.568Z",
"answer": 1320
},
{... | 1 | [
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
},
{
"lemma": "VAL_SUM_EQ",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
a87c5b | comb_catalan_compute_v1_601307018_657 | Let $C_n$ denote the $n$-th Catalan number. Let $n$ be the number of distinct values of $t = 3a + 2b$ where $a, b$ are integers with $1 \leq a \leq 3$, $1 \leq b \leq 4$, and $5 \leq t \leq 17$. Let $R = C_n$. Find the remainder when $38489 \cdot R$ is divided by $67794$. | 57,398 | graphs = [
Graph(
let={
"_n": Const(67794),
"n": CountOverSet(set=SolutionsSet(var=Var("t"), condition=Exists(var=Var(name='a'), condition=Exists(var=Var(name='b'), condition=And(Geq(left=Var(name='a'), right=Const(value=1)), Leq(left=Var(name='a'), right=Const(value=3)), Geq(left=Va... | COMB | null | COMPUTE | sympy | POLY_ORBIT_HENSEL | [
"LIN_FORM"
] | 7b2633 | comb_catalan_compute_v1 | null | 4 | 0 | [
"LIN_FORM",
"POLY_ORBIT_HENSEL"
] | 2 | 0.014 | 2026-03-10T01:12:01.553087Z | {
"verified": true,
"answer": 57398,
"timestamp": "2026-03-10T01:12:01.567244Z"
} | 040ad3 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 1,
"correct": {
"strict": false,
"boxed": false,
"relaxed": true
},
"usage": {
"prompt_tokens": 220,
"completion_tokens": 32768
},
"timestamp": "2026-03-28T23:46:03.472Z",
"answer": null
},
{
... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
... | {
"lo": 1.27,
"mid": 3.84,
"hi": 5.91
} | ||
c57dae | nt_count_coprime_v1_1520064083_6931 | Let $N = 51671$ and $k = 39$. Let $r$ be the number of positive integers $n \leq 24964$ such that $\gcd(n, k) = 1$. Let $p_{\max}$ be the largest prime number at most $1012$. Compute the remainder when
$$
(r \bmod 293) + p_{\max} \cdot (r \bmod 337)
$$
is divided by $N$. | 44,896 | graphs = [
Graph(
let={
"_n": Const(51671),
"upper": Const(24964),
"k": Const(39),
"result": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Ref("upper")), Eq(GCD(a=Var("n"), b=Ref("k")), Const(1))))),
... | NT | null | COUNT | sympy | MAX_PRIME_BELOW | [
"MAX_PRIME_BELOW"
] | 08a653 | nt_count_coprime_v1 | two_moduli | 6 | 0 | [
"MAX_PRIME_BELOW"
] | 1 | 2.273 | 2026-02-08T08:25:37.922063Z | {
"verified": true,
"answer": 44896,
"timestamp": "2026-02-08T08:25:40.194788Z"
} | ba1df4 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 144,
"completion_tokens": 1086
},
"timestamp": "2026-02-13T18:12:58.963Z",
"answer": 44896
},
... | 1 | [
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok"
},
{
"lemma": "V5",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
}
] | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
d61ce9 | geo_count_lattice_rect_v1_1874849503_211 | Compute the number of lattice points in the rectangle defined by $0 \leq x \leq 333$ and $0 \leq y \leq 164$, including the boundary. | 55,110 | graphs = [
Graph(
let={
"a": Const(333),
"b": Const(164),
"result": LatticePointsRect(a=Ref(name='a'), b=Ref(name='b')),
},
goal=Ref("result"),
)
] | GEOM | null | COUNT | sympy | [] | geo_count_lattice_rect_v1 | null | 3 | 0 | null | null | 0.001 | 2026-02-08T12:53:10.741720Z | {
"verified": true,
"answer": 55110,
"timestamp": "2026-02-08T12:53:10.742467Z"
} | 337afd | 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": 354
},
"timestamp": "2026-02-09T14:39:26.268Z",
"answer": 55110
},
{
"i... | 1 | [] | {
"lo": -4.92,
"mid": -2.91,
"hi": -0.68
} | ||||
fdf2c6 | lin_form_endings_v1_1915831931_3381 | Let $a = 24$ and $b = 32$. Define
$$
x = \left\lfloor \frac{24}{\gcd(24, 32)} \right\rfloor.
$$
Compute the remainder when $15833 \cdot x$ is divided by $52103$. | 47,499 | graphs = [
Graph(
let={
"a_coeff": Const(24),
"b_coeff": Const(32),
"_inner_result": Floor(Div(Const(24), GCD(a=Ref("a_coeff"), b=Ref("b_coeff")))),
"_scale_k": Const(15833),
"_scaled": Mul(Ref("_scale_k"), Ref("_inner_result")),
"_mod_... | COMB | NT | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | lin_form_endings_v1 | null | 2 | null | [
"LIN_FORM"
] | 1 | 0.001 | 2026-02-08T17:36:47.460855Z | {
"verified": true,
"answer": 47499,
"timestamp": "2026-02-08T17:36:47.461627Z"
} | 0212db | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 130,
"completion_tokens": 402
},
"timestamp": "2026-02-16T11:27:33.197Z",
"answer": 47499
},
{
"id": 11,
... | 2 | [
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "V8",
"status": "no"
},
{
"lemma": "V8_SUM",
"s... | {
"lo": -10,
"mid": -7.27,
"hi": -4.54
} | ||
f1bdce | nt_count_divisible_v1_865884756_5176 | Let $n$ be a positive integer such that $1 \leq n \leq 47524$. Let $d = 1 + 2 + 3 + 4 = 10$. Determine the number of such integers $n$ for which $n$ is divisible by $d$. Compute this number. | 4,752 | graphs = [
Graph(
let={
"_n": Const(4),
"upper": Const(47524),
"divisor": Summation(var="k", start=Const(1), end=Ref("_n"), expr=Var("k")),
"result": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Ref("upper"))... | NT | null | COUNT | sympy | SUM_ARITHMETIC | [
"SUM_ARITHMETIC"
] | eb34f0 | nt_count_divisible_v1 | null | 3 | 0 | [
"SUM_ARITHMETIC"
] | 1 | 1.404 | 2026-02-08T18:25:15.953675Z | {
"verified": true,
"answer": 4752,
"timestamp": "2026-02-08T18:25:17.358023Z"
} | 30602d | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 126,
"completion_tokens": 301
},
"timestamp": "2026-02-16T12:22:26.184Z",
"answer": 4752
},
{
"id": 11,
... | 2 | [
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "SUM_ARITHMETIC",
"status": "ok"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "VAL_SUM_EQ",
"status": "no"
}
] | {
"lo": -10,
"mid": -7.27,
"hi": -4.54
} | ||
0d6e89 | modular_sum_quadratic_residues_v1_784195855_8556 | Let $\_n = 2$. Let $p$ be the smallest divisor of $181451$ that is at least $\_n$. Compute $\frac{p(p-1)}{4}$. | 44,205 | graphs = [
Graph(
let={
"_n": Const(2),
"p": MinOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Ref("_n")), Divides(divisor=Var("d"), dividend=Const(181451))))),
"result": Div(Mul(Ref("p"), Sub(Ref("p"), Const(1))), Const(4)),
},
goal=Re... | NT | null | SUM | sympy | MIN_PRIME_FACTOR | [
"MIN_PRIME_FACTOR"
] | bc3776 | modular_sum_quadratic_residues_v1 | null | 2 | 0 | [
"MIN_PRIME_FACTOR"
] | 1 | 0.001 | 2026-02-08T16:11:27.420806Z | {
"verified": true,
"answer": 44205,
"timestamp": "2026-02-08T16:11:27.422283Z"
} | 21d5cd | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 86,
"completion_tokens": 3531
},
"timestamp": "2026-02-16T22:25:27.674Z",
"answer": 44205
},
{... | 1 | [
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MIN_PRIME_FACTOR",
"status": "ok"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
4ae691 | diophantine_fbi2_min_v1_151522320_2547 | Let $ d $ be an integer such that $ 7 \leq d \leq 24 $, $ d $ divides $ 14 $, and $ \frac{14}{d} \geq 2 $. Determine the value of the smallest such $ d $. | 7 | graphs = [
Graph(
let={
"_n": Const(2),
"k": Const(14),
"upper": Const(24),
"result": MinOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Const(7)), Leq(Var("d"), Ref("upper")), Divides(divisor=Var("d"), dividend=Ref("k")), Geq(Div(Ref("k"), ... | NT | null | EXTREMUM | sympy | B3 | [
"B3"
] | 0cd20d | diophantine_fbi2_min_v1 | null | 2 | 0 | [
"B3"
] | 1 | 0.014 | 2026-02-08T04:52:30.792996Z | {
"verified": true,
"answer": 7,
"timestamp": "2026-02-08T04:52:30.807431Z"
} | f75fcc | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 165,
"completion_tokens": 364
},
"timestamp": "2026-02-11T22:21:35.154Z",
"answer": 7
},
{
"id":... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "V1",
"status": "no"
},
{
"lemma": "V3",
"status": "no"
}
] | {
"lo": -9.14,
"mid": -6.05,
"hi": -3.73
} | ||
4f9625 | nt_sum_divisors_mod_v1_865884756_1439 | Let $n$ be the minimum value of $x + y$ where $x$ and $y$ are positive integers such that $xy = 8100$. Let $\sigma$ be the sum of all positive divisors of $n$. Compute the remainder when $\sigma$ is divided by $11491$. | 546 | graphs = [
Graph(
let={
"n": MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(Mul(Var("x"), Var("y")), Const(8100)))), expr=Sum(Var("x"), Var("y")))),
"M": Const(11491),... | NT | null | COMPUTE | sympy | B3 | [
"B3"
] | 0cd20d | nt_sum_divisors_mod_v1 | null | 4 | 0 | [
"B3"
] | 1 | 0.004 | 2026-02-08T16:04:16.307911Z | {
"verified": true,
"answer": 546,
"timestamp": "2026-02-08T16:04:16.311688Z"
} | e8e56c | 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": 784
},
"timestamp": "2026-02-16T20:05:38.429Z",
"answer": 546
},
{
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "V3",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
03c8b1 | sequence_lucas_compute_v1_153355830_1966 | Let $n$ be the smallest divisor of $19343$ that is at least $2$. Compute the $n$-th Lucas number. | 64,079 | graphs = [
Graph(
let={
"_n": Const(19343),
"n": MinOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Const(2)), Divides(divisor=Var("d"), dividend=Ref("_n"))))),
"result": Lucas(arg=Ref(name='n')),
},
goal=Ref("result"),
)
] | NT | null | COMPUTE | sympy | MIN_PRIME_FACTOR | [
"MIN_PRIME_FACTOR"
] | bc3776 | sequence_lucas_compute_v1 | null | 3 | 0 | [
"MIN_PRIME_FACTOR"
] | 1 | 0.001 | 2026-02-08T06:49:53.075315Z | {
"verified": true,
"answer": 64079,
"timestamp": "2026-02-08T06:49:53.076291Z"
} | bdc070 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 76,
"completion_tokens": 1028
},
"timestamp": "2026-02-13T05:16:45.474Z",
"answer": 64079
},
{... | 1 | [
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "MIN_PRIME_FACTOR",
"status": "ok"
},
{
"lemma": "MOD_ADD",
"status": "no"
}
] | {
"lo": -3.51,
"mid": 1.33,
"hi": 6.56
} | ||
92e90e | lin_form_endings_v1_898971024_676 | Let $a = 60$ and $b = 24$. Compute $\ell = \text{lcm}(a, b)$, and let $s = 10829$. Then define $m = 55239$.
Compute the remainder when $s \cdot \ell$ is divided by $m$. | 28,983 | graphs = [
Graph(
let={
"a_coeff": Const(60),
"b_coeff": Const(24),
"_inner_result": LCM(a=Ref("a_coeff"), b=Ref("b_coeff")),
"_scale_k": Const(10829),
"_scaled": Mul(Ref("_scale_k"), Ref("_inner_result")),
"_mod_M": Const(55239),
... | COMB | NT | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | lin_form_endings_v1 | null | 2 | null | [
"LIN_FORM"
] | 1 | 0.001 | 2026-02-08T15:35:37.825204Z | {
"verified": true,
"answer": 28983,
"timestamp": "2026-02-08T15:35:37.825710Z"
} | 532ba9 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 109,
"completion_tokens": 707
},
"timestamp": "2026-02-16T09:11:50.703Z",
"answer": 28983
},
{... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
0e363e | nt_num_divisors_compute_v1_151522320_2004 | Let $n = 33124$. Compute the number of positive divisors of $n$. | 27 | graphs = [
Graph(
let={
"n": Const(33124),
"result": NumDivisors(n=Ref("n")),
},
goal=Ref("result"),
)
] | NT | null | COMPUTE | sympy | V5 | [
"B3/K2"
] | 9f3175 | nt_num_divisors_compute_v1 | null | 2 | 0 | [
"B3",
"K2",
"V5"
] | 3 | 0.028 | 2026-02-08T04:31:02.556709Z | {
"verified": true,
"answer": 27,
"timestamp": "2026-02-08T04:31:02.584339Z"
} | 3f6ea4 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 129,
"completion_tokens": 438
},
"timestamp": "2026-02-10T16:49:50.584Z",
"answer": 27
},
{
"id"... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K2",
"status": "ok_later"
},
{
"lem... | {
"lo": -5.55,
"mid": -3.01,
"hi": 0.33
} | ||
77fb8f_n | comb_count_permutations_fixed_v1_1218484723_713 | A theater has 7 performers, each assigned a unique costume. After a mix-up, the costumes are redistributed so that some may get their own, but we are interested in ways where a subset of size $k$ keeps their costumes and the rest do not. Here, $k = \binom{12}{12} - \binom{10}{0}$. The number of such arrangements is $M ... | 39,517 | COMB | null | COUNT | sympy | ZERO_BINOM_N | [
"ZERO_BINOM_N",
"ONE_BINOM_0"
] | 1c72d2 | comb_count_permutations_fixed_v1 | null | 3 | null | [
"ONE_BINOM_0",
"ZERO_BINOM_N"
] | 2 | 0.002 | 2026-02-25T02:27:19.653627Z | null | 54f3aa | 77fb8f | narrative | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 233,
"completion_tokens": 1086
},
"timestamp": "2026-03-30T15:48:31.768Z",
"answer": 39517
},
{
"... | 2 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "ONE_B... | {
"lo": -10,
"mid": -5.89,
"hi": -1.79
} | |
99cd6d | comb_catalan_compute_v1_153355830_540 | Let $n$ be the number of integers $t$ such that $5 \leq t \leq 16$ and there exist positive integers $a$ and $b$ with $1 \leq a \leq 5$, $1 \leq b \leq 2$, and $t = 2a + 3b$. Compute the $n$-th Catalan number. | 16,796 | 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=5)), Geq(left=Var(name='b'), right=Const(value=1... | COMB | null | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | comb_catalan_compute_v1 | null | 4 | 0 | [
"LIN_FORM"
] | 1 | 0.002 | 2026-02-08T03:09:32.224769Z | {
"verified": true,
"answer": 16796,
"timestamp": "2026-02-08T03:09:32.226751Z"
} | 36b896 | 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": 703
},
"timestamp": "2026-02-23T23:12:38.630Z",
"answer": 16796
},
{
"i... | 1 | [
{
"lemma": "COUNT_CARTESIAN",
"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": -7.18,
"mid": -4.99,
"hi": -3
} | ||
a2d3da | algebra_poly_eval_v1_124444284_5677 | Let $m = 7$ and $c = 2$. Let $j_0$ be the number of positive integers $j \le 2$ such that $j^4$ is less than or equal to the number of unordered pairs $(p, q)$ of positive integers satisfying $pq = 273919800$, $\gcd(p, q) = 1$, and $p < q$. Let $n = \sum_{k=1}^{m} k$. Compute $c \cdot n^{j_0} - 4n - 2$. | 1,454 | graphs = [
Graph(
let={
"_c": Const(2),
"_m": Const(7),
"_n": CountOverSet(set=SolutionsSet(var=Var("j"), condition=And(Geq(Var("j"), Const(1)), Leq(Var("j"), Const(2)), Leq(Pow(Var("j"), Const(4)), CountOverSet(set=SolutionsSet(var=Var("p"), condition=And(IsPositive(arg=... | NT | null | COMPUTE | sympy | COPRIME_PAIRS | [
"COPRIME_PAIRS/C3/SUM_ARITHMETIC"
] | 565378 | algebra_poly_eval_v1 | null | 5 | 0 | [
"C3",
"COPRIME_PAIRS",
"SUM_ARITHMETIC"
] | 3 | 0.006 | 2026-02-08T06:46:09.674479Z | {
"verified": true,
"answer": 1454,
"timestamp": "2026-02-08T06:46:09.680313Z"
} | ca87e1 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 165,
"completion_tokens": 1254
},
"timestamp": "2026-02-13T04:25:12.084Z",
"answer": 1454
},
{... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "C3",
"status": "ok_later"
},
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma":... | {
"lo": -7.01,
"mid": -4.68,
"hi": -2.15
} | ||
a1816d | sequence_lucas_compute_v1_1470522791_943 | Let $n = \sum_{k=1}^{6} \phi(k) \left\lfloor \frac{6}{k} \right\rfloor$, where $\phi$ denotes Euler's totient function. Let $L_n$ denote the $n$-th Lucas number, defined by $L_1 = 1$, $L_2 = 3$, and $L_k = L_{k-1} + L_{k-2}$ for $k \geq 3$. Find the remainder when $49085 \cdot L_n$ is divided by $67308$. | 23,968 | graphs = [
Graph(
let={
"_n": Const(67308),
"n": Summation(var="k", start=Const(1), end=Const(6), expr=Mul(EulerPhi(n=Var("k")), Floor(Div(Const(6), Var("k"))))),
"result": Lucas(arg=Ref(name='n')),
"Q": Mod(value=Mul(Const(49085), Ref("result")), modulus=Ref(... | NT | null | COMPUTE | sympy | K2 | [
"K2"
] | 6897ab | sequence_lucas_compute_v1 | null | 4 | 0 | [
"K2"
] | 1 | 0.002 | 2026-02-08T13:20:26.272440Z | {
"verified": true,
"answer": 23968,
"timestamp": "2026-02-08T13:20:26.273979Z"
} | 593083 | 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": 2750
},
"timestamp": "2026-02-15T13:14:19.490Z",
"answer": 23968
},
... | 1 | [
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "K2",
"status": "ok"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "V8_SUM",
"status"... | {
"lo": -5.49,
"mid": 0.22,
"hi": 6.51
} | ||
b23799 | nt_sum_divisors_mod_v1_865884756_1114 | Let $n$ be the minimum value of $x + y$ over all ordered pairs $(x, y)$ of positive integers such that $xy = 176400$. Let $\sigma(n)$ denote the sum of all positive divisors of $n$. Compute the remainder when $44121 \cdot (\sigma(n) \bmod 10067)$ is divided by $71363$. | 42,340 | graphs = [
Graph(
let={
"n": MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(Mul(Var("x"), Var("y")), Const(176400)))), expr=Sum(Var("x"), Var("y")))),
"M": Const(10067... | NT | null | COMPUTE | sympy | B3 | [
"B3"
] | 0cd20d | nt_sum_divisors_mod_v1 | null | 4 | 0 | [
"B3"
] | 1 | 0.01 | 2026-02-08T15:47:47.482894Z | {
"verified": true,
"answer": 42340,
"timestamp": "2026-02-08T15:47:47.493103Z"
} | f6bcd3 | 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": 2032
},
"timestamp": "2026-02-16T13:36:19.020Z",
"answer": 42340
},
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "V3",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
3eca11 | nt_lcm_compute_v1_548369836_399 | Let $a = 1421$. Let $S$ be the set of all ordered pairs $(x, y)$ of positive integers such that $xy = 430336$. Define $b$ to be the minimum value of $x + y$ as $(x, y)$ ranges over $S$. Let $c = 65523$ and let $L = \text{lcm}(a, b)$. Compute the remainder when $c \cdot L$ is divided by $80521$. | 10,122 | graphs = [
Graph(
let={
"a": Const(1421),
"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(430336)))), expr=Sum(Var("x"), Var("y"))))... | NT | null | COMPUTE | sympy | B3 | [
"B3"
] | 0cd20d | nt_lcm_compute_v1 | null | 5 | 0 | [
"B3"
] | 1 | 0.001 | 2026-02-08T02:53:49.793648Z | {
"verified": true,
"answer": 10122,
"timestamp": "2026-02-08T02:53:49.794763Z"
} | d607ef | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 218,
"completion_tokens": 3037
},
"timestamp": "2026-02-08T20:26:26.550Z",
"answer": 10122
},
{
"... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "V1",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
}
] | {
"lo": 1.12,
"mid": 2.83,
"hi": 4.45
} | ||
8ec117 | nt_min_phi_inverse_v1_458359167_2221 | Let $S$ be the set of all positive integers $n$ such that $1 \leq n \leq 19$ and the sum of the decimal digits of $n$ is odd. Let $T$ be the set of all positive integers $n$ such that $1 \leq n \leq |S|$ and $\phi(n) = 1$. Determine the value of the smallest element in $T$. | 1 | graphs = [
Graph(
let={
"_n": Const(2),
"upper": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Const(19)), Eq(Mod(value=DigitSum(Var("n")), modulus=Ref("_n")), Const(1))))),
"k": Const(1),
"result": MinOverSet... | NT | null | EXTREMUM | sympy | B3 | [
"L3B"
] | cc148f | nt_min_phi_inverse_v1 | null | 4 | 0 | [
"B3",
"L3B"
] | 2 | 0.043 | 2026-02-08T05:12:17.011280Z | {
"verified": true,
"answer": 1,
"timestamp": "2026-02-08T05:12:17.054340Z"
} | 0995d3 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 201,
"completion_tokens": 614
},
"timestamp": "2026-02-11T23:01:46.034Z",
"answer": 1
},
{
"id":... | 1 | [
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "L3B",
"status": "ok"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
}... | {
"lo": -7.01,
"mid": -4.68,
"hi": -2.15
} | ||
c18f55 | geo_count_lattice_triangle_v1_458359167_1566 | Let $A$ be the area of the triangle with vertices at $(121, 256)$, $(180, 360)$, and $(0, 0)$, multiplied by 2. Let $B$ be the number of lattice points on the boundary of this triangle. Compute $\frac{A + 2 - B}{2}$. | 1,170 | graphs = [
Graph(
let={
"area_2x": Abs(arg=Sum(Mul(Const(value=121), Const(value=360)), Mul(Const(value=180), Sub(left=Const(value=0), right=Const(value=256))))),
"boundary": Sum(GCD(a=Abs(arg=Const(value=121)), b=Abs(arg=Const(value=256))), GCD(a=Abs(arg=Sub(left=Const(value=180), r... | ALG | NT | COUNT | sympy | [] | geo_count_lattice_triangle_v1 | null | 6 | 0 | null | null | 0.008 | 2026-02-08T04:45:26.347323Z | {
"verified": true,
"answer": 1170,
"timestamp": "2026-02-08T04:45:26.354958Z"
} | d89284 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 181,
"completion_tokens": 1834
},
"timestamp": "2026-02-11T21:53:02.369Z",
"answer": 1170
},
{
"i... | 1 | [] | {
"lo": -3.45,
"mid": 1.15,
"hi": 6.18
} |
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