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 |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
40d65a | comb_count_permutations_fixed_v1_1431428450_430 | Let $n = 6$. Let $s$ be the sum $\sum_{k=1}^{4} k$. Let $T$ be the set of all positive integers $p$ for which there exists a positive integer $q$ such that $pq = 216$, $\gcd(p,q) = 1$, and $p < q$. Let $c$ be the number of elements in $T$. Let $P$ be the set of all ordered pairs $(x,y)$ of positive integers such that $... | 240 | graphs = [
Graph(
let={
"_n": Const(6),
"n": Summation(var="k", start=Const(1), end=Const(4), expr=Var("k")),
"k": MaxOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), CountOverSet(set=SolutionsSet(var=Var("p"), condition=And(IsPositive(arg=Var(name='p'))... | NT | COMB | COUNT | sympy | COPRIME_PAIRS | [
"COPRIME_PAIRS/MAX_PRIME_BELOW",
"B1/MAX_PRIME_BELOW",
"SUM_ARITHMETIC"
] | 4a4632 | comb_count_permutations_fixed_v1 | null | 6 | 0 | [
"B1",
"COPRIME_PAIRS",
"MAX_PRIME_BELOW",
"SUM_ARITHMETIC"
] | 4 | 0.007 | 2026-02-08T13:27:27.074419Z | {
"verified": true,
"answer": 240,
"timestamp": "2026-02-08T13:27:27.081831Z"
} | a91954 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 232,
"completion_tokens": 1280
},
"timestamp": "2026-02-15T15:11:19.767Z",
"answer": 240
},
{
... | 1 | [
{
"lemma": "B1",
"status": "ok"
},
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok_l... | {
"lo": -8.26,
"mid": -5.01,
"hi": -1.76
} | ||
0a2637 | antilemma_k3_v1_48377204_2306 | Let $x = \sum_{d \mid 87676} \phi(d)$, where $\phi$ denotes Euler's totient function. Compute the remainder when
$$
x^2 + 7x + 200
$$
is divided by $53241$. | 13,954 | graphs = [
Graph(
let={
"x": SumOverDivisors(n=Const(value=87676), var='d', expr=EulerPhi(n=Var(name='d'))),
"_c": Const(200),
"Q": Mod(value=Sum(Pow(Ref("x"), Const(2)), Mul(Const(7), Ref("x")), Ref("_c")), modulus=Const(53241)),
},
goal=Ref("Q"),
)
] | NT | COMB | COMPUTE | sympy | K13 | [
"K3"
] | 54c41e | antilemma_k3_v1 | null | 3 | 0 | [
"K13",
"K3"
] | 2 | 0.003 | 2026-02-08T16:43:17.344610Z | {
"verified": true,
"answer": 13954,
"timestamp": "2026-02-08T16:43:17.347185Z"
} | bc220c | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 100,
"completion_tokens": 1753
},
"timestamp": "2026-02-17T10:14:24.007Z",
"answer": 13954
},
... | 1 | [
{
"lemma": "K3",
"status": "ok"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
973d42 | nt_min_coprime_above_v1_1520064083_7986 | Let $s$ be the sum of all real solutions to the equation $x^2 - 2x - 5475 = 0$. Let $t$ be the number of integers $\tau$ such that $37 \leq \tau \leq 1501$ and $\tau = 6a + 15b + 16$ for some positive integers $a \leq 195$ and $b \leq 21$. Let $m$ be the largest prime number $n$ satisfying $s \leq n \leq t$. Let $r$ be... | 35,181 | graphs = [
Graph(
let={
"_n": Const(44121),
"start": Const(14884),
"upper": Const(15373),
"modulus": MaxOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), SumOverSet(set=SolutionsSet(var=Var("x"), condition=Eq(Sum(Pow(Var("x"), Const(2)), Mul(C... | NT | null | EXTREMUM | sympy | VIETA_SUM | [
"VIETA_SUM/MAX_PRIME_BELOW",
"LIN_FORM/MAX_PRIME_BELOW"
] | b4b3ac | nt_min_coprime_above_v1 | null | 6 | 0 | [
"LIN_FORM",
"MAX_PRIME_BELOW",
"VIETA_SUM"
] | 3 | 0.123 | 2026-02-08T09:26:57.575303Z | {
"verified": true,
"answer": 35181,
"timestamp": "2026-02-08T09:26:57.698454Z"
} | 134790 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 212,
"completion_tokens": 3697
},
"timestamp": "2026-02-14T05:57:45.527Z",
"answer": 35181
},
... | 1 | [
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok_later"
},... | {
"lo": -5.49,
"mid": 0.22,
"hi": 6.51
} | ||
708867_n | sequence_fibonacci_compute_v1_601307018_11089 | A music app generates playlists based on a seed number $M = \sum_{k=1}^{5} \varphi(k) \cdot \left\lfloor \frac{5}{k} \right\rfloor$. A user selects a favorite number $n_1$ from $1$ to $37$ that is coprime to $M$. Let $n$ be how many such favorite numbers exist. The app then plays $F_n$ songs, where $F_n$ is the $n$-th ... | 6,765 | graphs = [
Graph(
let={
"_m": Const(5),
"_n": Summation(var="k", start=Const(1), end=Ref("_m"), expr=Mul(EulerPhi(n=Var("k")), Floor(Div(Const(5), Var("k"))))),
"n": CountOverSet(set=SolutionsSet(var=Var("n1"), condition=And(Geq(Var("n1"), Const(1)), Leq(Var("n1"), Const(... | NT | null | COMPUTE | sympy | K2 | [
"K2/C4"
] | 87860b | sequence_fibonacci_compute_v1 | null | 4 | null | [
"C4",
"K2"
] | 2 | 0.317 | 2026-03-10T11:31:57.720083Z | null | 256c8d | 708867 | narrative | CC BY 4.0 | [
{
"id": 36,
"model": "qwen2.5:3b-32k",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 176,
"completion_tokens": 1208
},
"timestamp": "2026-04-23T14:51:56.879Z",
"answer": 6765
}
] | 2 | [
{
"lemma": "C4",
"status": "ok_later"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "K2",
"status": "ok"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"l... | {
"lo": -10,
"mid": -5.89,
"hi": -1.79
} |
6f181d | nt_count_divisible_and_v1_1470522791_1915 | Let $S$ be the set of all ordered pairs of positive integers $(x, y)$ such that $x + y = 10$. Define $n_0$ to be the maximum value of $xy$ as $(x, y)$ ranges over $S$. Let $d_1$ be the minimum value of $x + y$ as $(x, y)$ ranges over all ordered pairs of positive integers such that $xy = n_0$. Let $d_2 = \sum_{k=1}^{5}... | 1,452 | graphs = [
Graph(
let={
"_m": Const(5),
"_n": MaxOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(Sum(Var("x"), Var("y")), Const(10)))), expr=Mul(Var("x"), Var("y")))),
... | NT | null | COUNT | sympy | B1 | [
"B1/B3",
"K2"
] | dd6f52 | nt_count_divisible_and_v1 | null | 6 | 0 | [
"B1",
"B3",
"K2"
] | 3 | 1.751 | 2026-02-08T14:06:32.741706Z | {
"verified": true,
"answer": 1452,
"timestamp": "2026-02-08T14:06:34.492212Z"
} | 25e785 | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 242,
"completion_tokens": 549
},
"timestamp": "2026-02-16T05:13:46.389Z",
"answer": 93
},
{
"id": 11,
... | 1 | [
{
"lemma": "B1",
"status": "ok"
},
{
"lemma": "B3",
"status": "ok_later"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "K2",
"status": "ok"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},... | {
"lo": -8.26,
"mid": -5.01,
"hi": -1.76
} | ||
cbcedd | sequence_fibonacci_compute_v1_601307018_10768 | Let $F_n$ denote the $n$-th Fibonacci number. Find $F_n$, where $n$ is the number of ordered pairs $(a, b)$ of positive integers with $1 \le a, b \le 25$ satisfying $5b^2 + 10ab + 5a^2 = 2645$. | 17,711 | graphs = [
Graph(
let={
"_n": Const(25),
"n": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("a"), Var("b")]), condition=And(Geq(Var("a"), Const(1)), Leq(Var("a"), Ref("_n")), Geq(Var("b"), Const(1)), Leq(Var("b"), Const(25)), Eq(Sum(Mul(Const(5), Pow(Var("b"), Const(2))), Mul... | ALG | null | COMPUTE | sympy | QF_PSD_COUNT | [
"QF_PSD_COUNT"
] | 09ce67 | sequence_fibonacci_compute_v1 | null | 3 | 0 | [
"QF_PSD_COUNT"
] | 1 | 0.002 | 2026-03-10T11:13:50.263456Z | {
"verified": true,
"answer": 17711,
"timestamp": "2026-03-10T11:13:50.265454Z"
} | 1a59d2 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 182,
"completion_tokens": 850
},
"timestamp": "2026-04-19T14:41:03.532Z",
"answer": 17711
},
{
"... | 1 | [
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "QF_PSD_COUNT",
"status": "ok"
}
] | {
"lo": -5.34,
"mid": 1.1,
"hi": 7.53
} | ||
1b8e0d | lin_form_endings_v1_677425708_3338 | Let $T$ be the set of all integers $t$ such that $59 \leq t \leq 1559$ and there exist positive integers $a$ and $b$ with $1 \leq a \leq 13$, $1 \leq b \leq 37$, and $t = 20a + 35b + 4$. Let $r$ be the number of elements in $T$. Compute the remainder when $19442 \cdot r$ is divided by $54798$. | 22,286 | graphs = [
Graph(
let={
"_inner_result": 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=13)), Geq(left=Var(name='b'), right=... | COMB | null | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | lin_form_endings_v1 | null | 5 | null | [
"LIN_FORM"
] | 1 | 0.002 | 2026-02-08T05:40:19.520632Z | {
"verified": true,
"answer": 22286,
"timestamp": "2026-02-08T05:40:19.522774Z"
} | de9849 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 222,
"completion_tokens": 4725
},
"timestamp": "2026-02-24T04:13:50.685Z",
"answer": 22286
},
{
"... | 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": "V7",
"st... | {
"lo": 3.43,
"mid": 5.73,
"hi": 8.84
} | ||
ffaddf | comb_count_partitions_v1_655260480_1326 | Let $n$ be the minimum value of $x + y$ over all ordered pairs $(x, y)$ of positive integers such that $xy = k$, where $k$ is the number of integers $t$ in the range $23 \leq t \leq 1478$ for which there exist positive integers $a \leq 215$ and $b \leq 20$ satisfying $t = 6a + 9b + 8$. Compute the number of integer par... | 75,175 | graphs = [
Graph(
let={
"_n": CountOverSet(set=SolutionsSet(var=Var("t"), condition=Exists(var=Var(name='a'), condition=Exists(var=Var(name='b'), condition=And(Geq(left=Var(name='a'), right=Const(value=1)), Leq(left=Var(name='a'), right=Const(value=215)), Geq(left=Var(name='b'), right=Const(valu... | COMB | null | COUNT | sympy | LIN_FORM | [
"LIN_FORM/B3"
] | 05313e | comb_count_partitions_v1 | null | 6 | 0 | [
"B3",
"LIN_FORM"
] | 2 | 0.003 | 2026-02-08T16:04:13.956924Z | {
"verified": true,
"answer": 75175,
"timestamp": "2026-02-08T16:04:13.960382Z"
} | 12279a | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 1,
"correct": {
"strict": false,
"boxed": false,
"relaxed": true
},
"usage": {
"prompt_tokens": 219,
"completion_tokens": 7125
},
"timestamp": "2026-02-24T19:46:27.118Z",
"answer": 1007460880
},
... | 1 | [
{
"lemma": "B3",
"status": "ok_later"
},
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "LIN_FORM",
"... | {
"lo": 1.98,
"mid": 5.23,
"hi": 8.52
} | ||
bea257 | diophantine_product_count_v1_349078426_1675 | Let $k = 180$ and let $\text{result}$ be the number of positive integers $x \leq 103$ such that $x$ divides $k$ and $\frac{k}{x} \leq 103$. Let $c$ be the number of positive integers $n \leq 54257$ such that $7$ divides $n$ and $\gcd(n, 12) = 1$. Define $Q = c - \text{result}$. Find the value of $Q$. | 2,568 | graphs = [
Graph(
let={
"k": Const(180),
"upper": Const(103),
"result": CountOverSet(set=SolutionsSet(var=Var("x"), condition=And(Geq(Var("x"), Const(1)), Leq(Var("x"), Ref("upper")), Divides(divisor=Var("x"), dividend=Ref("k")), Leq(Div(Ref("k"), Var("x")), Ref("upper"))... | NT | null | COUNT | sympy | C5 | [
"C5"
] | 92f7e3 | diophantine_product_count_v1 | negation_mod | 4 | 0 | [
"C5"
] | 1 | 0.007 | 2026-02-08T13:50:51.396983Z | {
"verified": true,
"answer": 2568,
"timestamp": "2026-02-08T13:50:51.403910Z"
} | 46e8ec | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 152,
"completion_tokens": 1989
},
"timestamp": "2026-02-15T20:51:00.983Z",
"answer": 2568
},
{... | 1 | [
{
"lemma": "C5",
"status": "ok"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "VAL_SUM_EQ",
"status": "no"
}
] | {
"lo": -5.49,
"mid": 0.22,
"hi": 6.51
} | ||
b88380 | modular_mod_compute_v1_784195855_5285 | Let $S$ be the set of all ordered pairs $(x, y)$ of positive integers such that $xy = 144$. Define $a$ to be the minimum value of $x + y$ over all such pairs. Compute the remainder when $a$ is divided by $1156$. | 24 | graphs = [
Graph(
let={
"a": MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(Mul(Var("x"), Var("y")), Const(144)))), expr=Sum(Var("x"), Var("y")))),
"m": Const(1156),
... | NT | null | COMPUTE | sympy | COUNT_COPRIME_GRID | [
"B3"
] | 0cd20d | modular_mod_compute_v1 | null | 4 | 0 | [
"B3",
"COUNT_COPRIME_GRID"
] | 2 | 0.005 | 2026-02-08T07:49:09.395477Z | {
"verified": true,
"answer": 24,
"timestamp": "2026-02-08T07:49:09.400582Z"
} | a62814 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 108,
"completion_tokens": 406
},
"timestamp": "2026-02-13T12:30:20.820Z",
"answer": 24
},
{
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no... | {
"lo": -7.01,
"mid": -4.68,
"hi": -2.15
} | ||
df5468 | algebra_quadratic_discriminant_v1_865884756_2852 | Let $a = 1$, $b = 7$, and let $c$ be the minimum value of $x + y$ over all ordered pairs $(x, y)$ of positive integers such that $xy = 36$. Define $\Delta = b^2 - 4ac$. Compute $64516 - \Delta$. | 64,515 | graphs = [
Graph(
let={
"a": Const(1),
"b": Const(7),
"c": MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(Mul(Var("x"), Var("y")), Const(36)))), expr=Sum(V... | NT | null | COMPUTE | sympy | B3 | [
"B3"
] | 0cd20d | algebra_quadratic_discriminant_v1 | null | 3 | 0 | [
"B3"
] | 1 | 0.004 | 2026-02-08T16:58:56.556237Z | {
"verified": true,
"answer": 64515,
"timestamp": "2026-02-08T16:58:56.559790Z"
} | 1871dc | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 115,
"completion_tokens": 408
},
"timestamp": "2026-02-17T16:15:45.089Z",
"answer": 64515
},
{... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "V7",
"status": "n... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
44ec83 | diophantine_fbi2_count_v1_717093673_2774 | Let $k = 1260$. Determine the number of integers $d$ such that $2 \leq d \leq 200$, $d$ divides $k$, and $2 \leq \frac{k}{d} \leq 200$. | 24 | graphs = [
Graph(
let={
"k": Const(1260),
"a": Const(1),
"b": Const(1),
"upper": Const(199),
"result": CountOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Const(2)), Leq(Var("d"), Const(200)), Divides(divisor=Var("d"), dividend=... | NT | null | COUNT | sympy | B3 | [
"LIN_FORM"
] | 7b2633 | diophantine_fbi2_count_v1 | null | 3 | 0 | [
"B3",
"LIN_FORM"
] | 2 | 0.101 | 2026-02-08T17:09:49.469240Z | {
"verified": true,
"answer": 24,
"timestamp": "2026-02-08T17:09:49.570336Z"
} | 9762cf | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 98,
"completion_tokens": 2516
},
"timestamp": "2026-02-17T21:48:12.448Z",
"answer": 24
},
{
... | 1 | [
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
252b06 | geo_visible_lattice_v1_168721529_276 | Let $n = 99$. Define $L$ to be the number of visible lattice points $(x,y)$ such that $1 \leq x, y \leq n$, where a point $(x,y)$ is visible if $\gcd(x,y) = 1$. Compute the remainder when $44121 \cdot L$ is divided by $53645$. | 28,547 | graphs = [
Graph(
let={
"n": Const(99),
"result": VisibleLatticePoints(n=Ref(name='n')),
"Q": Mod(value=Mul(Const(44121), Ref("result")), modulus=Const(53645)),
},
goal=Ref("Q"),
)
] | GEOM | null | COUNT | sympy | [] | geo_visible_lattice_v1 | null | 6 | 0 | null | null | 3.109 | 2026-02-08T12:56:37.240917Z | {
"verified": true,
"answer": 28547,
"timestamp": "2026-02-08T12:56:40.350198Z"
} | 844cec | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 187,
"completion_tokens": 7604
},
"timestamp": "2026-02-24T16:50:41.119Z",
"answer": 28547
},
{
"... | 1 | [] | {
"lo": -1.2,
"mid": 1.93,
"hi": 4.95
} | ||||
2da488 | comb_count_surjections_v1_1915831931_2209 | Let $n$ be the number of ordered pairs $(x_1, x_2)$ of positive odd integers such that $x_1 + x_2 = 10$. Let $k = 5$, and define $\text{result} = 5! \cdot S(n, 5)$, where $S(n, k)$ denotes the Stirling number of the second kind. Let $Q$ be the remainder when $44006 \cdot \text{result}$ is divided by $97895$. Compute $Q... | 92,285 | graphs = [
Graph(
let={
"_n": Const(10),
"n": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x1"), Var("x2")]), condition=And(IsPositive(arg=Var(name='x1')), IsPositive(arg=Var(name='x2')), IsOdd(arg=Var(name='x1')), IsOdd(arg=Var(name='x2')), Eq(Sum(Var("x1"), Var("x2")), Re... | COMB | null | COUNT | sympy | COMB1 | [
"COMB1"
] | 567f58 | comb_count_surjections_v1 | null | 4 | 0 | [
"COMB1"
] | 1 | 0.004 | 2026-02-08T16:40:29.825685Z | {
"verified": true,
"answer": 92285,
"timestamp": "2026-02-08T16:40:29.829899Z"
} | 071070 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 155,
"completion_tokens": 989
},
"timestamp": "2026-02-17T09:02:32.536Z",
"answer": 92285
},
{... | 1 | [
{
"lemma": "COMB1",
"status": "ok"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8_SUM",
"st... | {
"lo": -2.38,
"mid": 1.74,
"hi": 6.59
} | ||
0d19a8 | comb_count_derangements_v1_53965629_38 | Let $n$ be the largest prime number less than or equal to $7$. Define $!n$ to be the number of derangements of $n$ elements. Compute the smallest positive integer $d$ such that $2^d \equiv 1 \pmod{2 \cdot |!n| + 3}$. | 1,236 | graphs = [
Graph(
let={
"_n": Const(7),
"n": MaxOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(2)), Leq(Var("n"), Ref("_n")), IsPrime(Var("n"))))),
"result": Subfactorial(arg=Ref(name='n')),
"Q": MultiplicativeOrder(base=Const(value=2... | NT | COMB | COUNT | sympy | MAX_PRIME_BELOW | [
"MAX_PRIME_BELOW"
] | dc3ad3 | comb_count_derangements_v1 | null | 5 | 0 | [
"MAX_PRIME_BELOW"
] | 1 | 0.003 | 2026-02-08T11:13:55.231964Z | {
"verified": true,
"answer": 1236,
"timestamp": "2026-02-08T11:13:55.235324Z"
} | 7835fb | 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": 5062
},
"timestamp": "2026-02-09T11:11:30.367Z",
"answer": 1236
},
{
"i... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "VAL_SUM_EQ",
"status": "no"
}
] | {
"lo": -6.51,
"mid": -0.31,
"hi": 5.43
} | ||
c5ce46 | diophantine_fbi2_min_v1_1520064083_3164 | Let $k = 77$ and let the upper bound be $87$. Consider the set of all integers $d$ such that $6 \leq d \leq 87$, $d$ divides $k$, and $\frac{k}{d} \geq 6$. Compute the minimum value of $d$ in this set. | 7 | graphs = [
Graph(
let={
"k": Const(77),
"a": Const(5),
"b": Const(5),
"upper": Const(87),
"result": MinOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Const(6)), Leq(Var("d"), Ref("upper")), Divides(divisor=Var("d"), dividend=Ref... | NT | null | EXTREMUM | sympy | LIN_FORM | [
"LIN_FORM/LTE_SUM"
] | 9baae3 | diophantine_fbi2_min_v1 | null | 3 | 0 | [
"LIN_FORM",
"LTE_SUM"
] | 2 | 0.027 | 2026-02-08T05:29:49.804687Z | {
"verified": true,
"answer": 7,
"timestamp": "2026-02-08T05:29:49.831384Z"
} | ad39aa | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 129,
"completion_tokens": 390
},
"timestamp": "2026-02-11T22:50:20.372Z",
"answer": 7
},
{
"id": 11,
"... | 2 | [
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "ok_later"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"... | {
"lo": -10,
"mid": -7.73,
"hi": -5.46
} | ||
e433aa | modular_count_residue_v1_784195855_8267 | Let $r$ be the largest prime number $n$ such that $2 \leq n \leq 10$. Let $S$ be the set of all positive integers $n$ such that $1 \leq n \leq 63001$ and $n \equiv r \pmod{21}$. Compute the remainder when $44121$ times the number of elements in $S$ is divided by $82087$. | 38,756 | graphs = [
Graph(
let={
"_n": Const(82087),
"upper": Const(63001),
"m": Const(21),
"r": MaxOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(2)), Leq(Var("n"), Const(10)), IsPrime(Var("n"))))),
"result": CountOverSet(set=Solu... | NT | null | COUNT | sympy | MAX_PRIME_BELOW | [
"MAX_PRIME_BELOW"
] | dc3ad3 | modular_count_residue_v1 | null | 3 | 0 | [
"MAX_PRIME_BELOW"
] | 1 | 2.129 | 2026-02-08T15:58:59.809061Z | {
"verified": true,
"answer": 38756,
"timestamp": "2026-02-08T15:59:01.938255Z"
} | 48b0f2 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 134,
"completion_tokens": 1183
},
"timestamp": "2026-02-16T17:47:24.240Z",
"answer": 38756
},
... | 1 | [
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok"
},
{
"lemma": "MOD_ADD",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
acf675 | nt_num_divisors_compute_v1_1742523217_3263 | Let $T$ be the set of all integers $t$ such that $8 \le t \le 111$ and there exist positive integers $a \le 32$, $b \le 3$ satisfying $t = 3a + 5b$. Let $n$ be the maximum value of $xy$ over all ordered pairs $(x, y)$ of positive integers such that $x + y = |T|$. Compute $71631 - \tau(n)$, where $\tau(n)$ is the number... | 71,604 | graphs = [
Graph(
let={
"_n": Const(71631),
"n": MaxOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(Sum(Var("x"), Var("y")), CountOverSet(set=SolutionsSet(var=Var("t"), co... | NT | null | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM/B1"
] | b32639 | nt_num_divisors_compute_v1 | null | 7 | 0 | [
"B1",
"LIN_FORM"
] | 2 | 0.16 | 2026-02-08T05:45:11.329537Z | {
"verified": true,
"answer": 71604,
"timestamp": "2026-02-08T05:45:11.489261Z"
} | 3c9ab5 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 162,
"completion_tokens": 1553
},
"timestamp": "2026-02-12T13:33:31.900Z",
"answer": 71604
},
... | 1 | [
{
"lemma": "B1",
"status": "ok_later"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
... | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
95581f | alg_sym_quad_system_v1_1218484723_5752 | Let $N$ be the number of ordered pairs $(a_1, b_1)$ of positive integers with $1 \le a_1, b_1 \le 40$ such that
$$2b_1^{2} - 2a_1b_1 + 13a_1^{2} \le 877.$$
Let
$$R \equiv \sum_{(a, b, c)} \bigl(a^{4} + b^{4} + c^{4}\bigr) \pmod{5849},$$
where the sum is over all ordered triples $(a, b, c)$ of positive integers satisfyi... | 5,889 | graphs = [
Graph(
let={
"_n": Const(5849),
"result": Mod(value=SumOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("a"), Var("b"), Var("c")]), condition=And(Eq(Sum(Pow(Var("a"), Const(2)), Pow(Var("b"), Const(2)), Pow(Var("c"), Const(2))), Sum(Mul(Var("a"), Var("b")), ... | ALG | null | COMPUTE | sympy | QF_PSD_COUNT_LEQ | [
"QF_PSD_COUNT_LEQ"
] | e34ff7 | alg_sym_quad_system_v1 | quadratic_mod | 7 | 0 | [
"QF_PSD_COUNT_LEQ"
] | 1 | 0.016 | 2026-02-25T07:19:16.275167Z | {
"verified": true,
"answer": 5889,
"timestamp": "2026-02-25T07:19:16.291006Z"
} | 625aab | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 337,
"completion_tokens": 3209
},
"timestamp": "2026-03-29T22:34:27.525Z",
"answer": 47208
},
{
... | 1 | [
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "QF_PSD_COUNT_LEQ",
"status": "ok"
}
] | {
"lo": 1.53,
"mid": 4.7,
"hi": 7.23
} | ||
86d8a8 | comb_factorial_compute_v1_601307018_2623 | Let $R = 2a^3 \bmod 97$, $S = 2R^3 \bmod 97$, $T = 2S^3 \bmod 97$, and let $K = 2T^3 \bmod m$, where $$m = \min\{ 256b^4 - 512a_1 b^3 - 128a_1^3 b + 97a_1^4 + 384a_1^2 b^2 \mid a_1, b \in \mathbb{Z},\, 1 \le a_1, b \le 5 \}.$$ Let $n$ be the number of non-negative integers $a$ with $0 \le a \le 96$ such that $K = a$, $... | 40,320 | graphs = [
Graph(
let={
"_m": Const(256),
"_n": Const(2),
"n": CountOverSet(set=SolutionsSet(var=Var("a"), condition=And(Geq(Var("a"), Const(0)), Leq(Var("a"), Const(96)), Eq(Ref("_po_p4"), Var("a")), Neq(Ref("_po_p1"), Var("a")), Neq(Ref("_po_p2"), Var("a")), Neq(Ref("_p... | COMB | null | COMPUTE | sympy | POLY4_MIN | [
"POLY4_MIN/POLY_ORBIT_COUNT"
] | 088e19 | comb_factorial_compute_v1 | null | 7 | 0 | [
"POLY4_MIN",
"POLY_ORBIT_COUNT"
] | 2 | 0.008 | 2026-03-10T03:18:14.010562Z | {
"verified": true,
"answer": 40320,
"timestamp": "2026-03-10T03:18:14.019023Z"
} | cba2fd | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 306,
"completion_tokens": 10712
},
"timestamp": "2026-03-29T05:56:02.352Z",
"answer": 40320
},
{
... | 1 | [
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "POLY4_MIN",
"status": "ok"
},
{
"lemma": "POLY_ORBIT_COUNT",
"status": "ok_later"
},
{
"l... | {
"lo": 1.23,
"mid": 4.27,
"hi": 6.7
} | ||
7ba18b | antilemma_cartesian_v1_717093673_861 | Let $x$ be the number of ordered pairs $(a, b)$ such that $1 \le a \le 12$ and $1 \le b \le 19$. Compute $16384 - x$. | 16,156 | graphs = [
Graph(
let={
"x": CountOverSet(set=CartesianProduct(left=IntegerRange(start=Const(1), end=Const(12)), right=IntegerRange(start=Const(1), end=Const(19)))),
"Q": Sub(Const(16384), Ref("x")),
},
goal=Ref("Q"),
)
] | COMB | GEOM | COMPUTE | sympy | COUNT_CARTESIAN | [
"COUNT_CARTESIAN"
] | 409d7d | antilemma_cartesian_v1 | null | 2 | 0 | [
"COUNT_CARTESIAN"
] | 1 | 0.002 | 2026-02-08T15:43:56.524455Z | {
"verified": true,
"answer": 16156,
"timestamp": "2026-02-08T15:43:56.526020Z"
} | 6de541 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 155,
"completion_tokens": 237
},
"timestamp": "2026-02-24T18:25:59.244Z",
"answer": 16156
},
{
"... | 2 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "ok"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8_SUM",
"statu... | {
"lo": -10,
"mid": -7.42,
"hi": -4.85
} | ||
c28102 | nt_count_primes_v1_865884756_5069 | Let $m$ be the number of positive integers $p$ for which there exists a positive integer $q$ such that $p \cdot q = 72$, $\gcd(p, q) = 1$, and $p < q$. Compute the number of prime numbers $n$ such that $m \leq n \leq 10139$. | 1,244 | graphs = [
Graph(
let={
"upper": Const(10139),
"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 | 3 | 0 | [
"COPRIME_PAIRS"
] | 1 | 0.229 | 2026-02-08T18:22:05.106952Z | {
"verified": true,
"answer": 1244,
"timestamp": "2026-02-08T18:22:05.336403Z"
} | c0f9e3 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 119,
"completion_tokens": 3668
},
"timestamp": "2026-02-18T16:32:59.910Z",
"answer": 1244
},
{... | 1 | [
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
cd8cb4 | nt_min_crt_v1_458359167_3969 | Let $a = 5$, $m = 8$, $k = 9$, and $n_0 = 2$. Define $b = \sum_{j=1}^{2} \phi(j) \left\lfloor \frac{2}{j} \right\rfloor$, where $\phi$ denotes Euler's totient function. Let $r$ be the smallest positive integer $n \leq 72$ such that $n \equiv 5 \pmod{8}$ and $n \equiv b \pmod{9}$. Compute $r + \phi(|r| + 1) + \tau(|r| +... | 35 | graphs = [
Graph(
let={
"_n": Const(2),
"m": Const(8),
"k": Const(9),
"a": Const(5),
"b": Summation(var="k", start=Const(1), end=Const(2), expr=Mul(EulerPhi(n=Var("k")), Floor(Div(Ref("_n"), Var("k"))))),
"upper": Const(72),
... | NT | null | EXTREMUM | sympy | B3 | [
"K2"
] | 6897ab | nt_min_crt_v1 | null | 7 | 0 | [
"B3",
"K2"
] | 2 | 0.139 | 2026-02-08T11:27:32.953531Z | {
"verified": true,
"answer": 35,
"timestamp": "2026-02-08T11:27:33.092693Z"
} | eaf54d | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 198,
"completion_tokens": 907
},
"timestamp": "2026-02-14T14:25:19.903Z",
"answer": 35
},
{
... | 1 | [
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "K2",
"status": "ok"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
}
] | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
bf44aa | sequence_count_fib_divisible_v1_601307018_14 | Let $F_n$ denote the $n$-th Fibonacci number, and let $N$ be the minimum value of $|x - y|$ over all ordered pairs $(x, y)$ of positive integers with $xy = 237695$. Let $M$ be the number of positive integers $n$ with $1 \le n \le N$ such that $5 \mid F_n$. Compute $19321 - M$. | 19,254 | 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(237695)))), expr=Abs(arg=Sub(left=Var(name='x'), right=Var(name='y')... | NT | null | COUNT | sympy | B3_DIFF | [
"B3_DIFF"
] | b47ea7 | sequence_count_fib_divisible_v1 | null | 6 | 0 | [
"B3_DIFF"
] | 1 | 0.011 | 2026-03-10T00:41:06.942660Z | {
"verified": true,
"answer": 19254,
"timestamp": "2026-03-10T00:41:06.953751Z"
} | 4922d8 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 201,
"completion_tokens": 2679
},
"timestamp": "2026-03-28T22:18:47.238Z",
"answer": 19254
},
{
"... | 1 | [
{
"lemma": "B3_DIFF",
"status": "ok"
},
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "V8",
... | {
"lo": -0.92,
"mid": 2.07,
"hi": 4.67
} | ||
a40ac1 | comb_sum_binomial_row_v1_784195855_8739 | Let $h = \sum_{k=0}^{2} (-1)^k \binom{2}{k}$ and $e = \sum_{k=0}^{1} (-1)^k \binom{1}{k}$. Let $n = 11 + h + e$. Compute $2^n$. | 2,048 | graphs = [
Graph(
let={
"n2": Const(2),
"h": 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(1),
"e": Summation(var="k", start=Const(0), end=Ref("n1"), expr=Mul(Pow(Const(-1), V... | COMB | null | SUM | sympy | BINOMIAL_ALTERNATING | [
"BINOMIAL_ALTERNATING"
] | c21569 | comb_sum_binomial_row_v1 | null | 3 | 2 | [
"BINOMIAL_ALTERNATING"
] | 1 | 0.001 | 2026-02-08T16:17:46.516602Z | {
"verified": true,
"answer": 2048,
"timestamp": "2026-02-08T16:17:46.517420Z"
} | bbbb4e | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 178,
"completion_tokens": 300
},
"timestamp": "2026-02-24T20:37:01.539Z",
"answer": 2048
},
{
"i... | 2 | [
{
"lemma": "BINOMIAL_ALTERNATING",
"status": "ok"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8"... | {
"lo": -10,
"mid": -7.42,
"hi": -4.85
} | ||
a619b0 | comb_sum_binomial_row_v1_601307018_7034 | Let $n$ be the number of ordered pairs $(a, b)$ of positive integers with $1 \le a, b \le 30$ satisfying
$$
17a^4 + 68a^3b + 102a^2b^2 + 68ab^3 + 17b^4 = 82954577.
$$
Let $R = 2^n$. Find the remainder when $85816 \cdot R$ is divided by $69457$. | 60,750 | graphs = [
Graph(
let={
"_n": Const(68),
"n": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("a"), Var("b")]), condition=And(Geq(Var("a"), Const(1)), Leq(Var("a"), Const(30)), Geq(Var("b"), Const(1)), Leq(Var("b"), Const(30)), Eq(Sum(Mul(Const(17), Pow(Var("a"), Const(4))), Mu... | COMB | null | SUM | sympy | POLY4_COUNT | [
"POLY4_COUNT"
] | 861d91 | comb_sum_binomial_row_v1 | null | 7 | 0 | [
"POLY4_COUNT"
] | 1 | 0.004 | 2026-03-10T07:40:59.849000Z | {
"verified": true,
"answer": 60750,
"timestamp": "2026-03-10T07:40:59.852843Z"
} | d91773 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 213,
"completion_tokens": 1975
},
"timestamp": "2026-04-19T05:49:45.192Z",
"answer": 60750
},
{
... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "POLY4_COUNT",
"status": "ok"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no... | {
"lo": -5.34,
"mid": 1.1,
"hi": 7.53
} | ||
d03bb3 | antilemma_k3_v1_2051736721_1599 | Compute the sum of Euler's totient function $\phi(d)$ over all positive divisors $d$ of $78531$. | 78,531 | graphs = [
Graph(
let={
"x": SumOverDivisors(n=Const(value=78531), var='d', expr=EulerPhi(n=Var(name='d'))),
},
goal=Ref("x"),
)
] | NT | COMB | COMPUTE | sympy | K3 | [
"K3"
] | 54c41e | antilemma_k3_v1 | null | 3 | 0 | [
"K3"
] | 1 | 0 | 2026-02-08T16:07:15.554664Z | {
"verified": true,
"answer": 78531,
"timestamp": "2026-02-08T16:07:15.555071Z"
} | bad36d | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 71,
"completion_tokens": 2415
},
"timestamp": "2026-02-16T21:15:56.292Z",
"answer": 78531
},
{... | 1 | [
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "K3",
"status": "ok"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
98e1f0 | nt_euler_phi_compute_v1_1742523217_2646 | Let $n = 62500$ and let $\phi(n)$ denote Euler's totient function evaluated at $n$. Let $c$ be the number of integers $t$ in the range $7 \le t \le 42$ for which there exist positive integers $a \in [1,6]$ and $b \in [1,6]$ such that $t = 4a + 3b$. Compute the remainder when $c - \phi(n)$ is divided by 72303. | 47,333 | graphs = [
Graph(
let={
"n": Const(62500),
"result": EulerPhi(n=Ref("n")),
"_c": CountOverSet(set=SolutionsSet(var=Var("t"), condition=Exists(var=Var(name='a'), condition=Exists(var=Var(name='b'), condition=And(Geq(left=Var(name='a'), right=Const(value=1)), Leq(left=Var(n... | NT | null | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM"
] | 324ba4 | nt_euler_phi_compute_v1 | negation_mod | 5 | 0 | [
"LIN_FORM"
] | 1 | 0.002 | 2026-02-08T04:53:38.127522Z | {
"verified": true,
"answer": 47333,
"timestamp": "2026-02-08T04:53:38.129321Z"
} | a750c3 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 218,
"completion_tokens": 2415
},
"timestamp": "2026-02-11T22:20:28.918Z",
"answer": 47333
},
{
... | 1 | [
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
... | {
"lo": -3.42,
"mid": 1.86,
"hi": 7.55
} | ||
1c5358 | comb_count_permutations_fixed_v1_717093673_2734 | Let $m = 3$ and $n_0 = 2$. Define $n$ to be the largest prime number $n_1$ such that $n_0 \leq n_1 \leq \sum_{k=1}^{m} k$. Let $k = 2$. Compute $\binom{n}{k} \cdot !(n - k)$, where $!d$ denotes the number of derangements of $d$ elements. | 20 | graphs = [
Graph(
let={
"_m": Const(3),
"_n": Const(2),
"n": MaxOverSet(set=SolutionsSet(var=Var("n1"), condition=And(Geq(Var("n1"), Ref("_n")), Leq(Var("n1"), Summation(var="k1", start=Const(1), end=Ref("_m"), expr=Var("k1"))), IsPrime(Var("n1"))))),
"k": Con... | NT | COMB | COUNT | sympy | SUM_ARITHMETIC | [
"SUM_ARITHMETIC/MAX_PRIME_BELOW"
] | bde608 | comb_count_permutations_fixed_v1 | null | 4 | 0 | [
"MAX_PRIME_BELOW",
"SUM_ARITHMETIC"
] | 2 | 0.003 | 2026-02-08T17:08:31.435217Z | {
"verified": true,
"answer": 20,
"timestamp": "2026-02-08T17:08:31.438651Z"
} | 186f14 | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 151,
"completion_tokens": 679
},
"timestamp": "2026-02-16T09:04:08.334Z",
"answer": 20
},
{
"id": 11,
... | 2 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok_later"
},
{
"lemma": "SUM_ARITHMETIC",
"status": "ok"
},
{
"lemma": "V7",
"status": "no"
... | {
"lo": -10,
"mid": -7.27,
"hi": -4.54
} | ||
a46af1 | modular_count_residue_v1_2051736721_4461 | Let $x$ be a real number satisfying $x^2 - 2x - 7920 = 0$. Define $\_n$ to be the sum of all such solutions $x$. Let $t$ be a positive integer between 7 and 6135, inclusive, for which there exist positive integers $a \leq 765$ and $b \leq 921$ such that $t = 2a + 5b$. Let $D$ be the set of positive divisors $d$ of the ... | 2,358 | graphs = [
Graph(
let={
"_m": Const(2),
"_n": SumOverSet(set=SolutionsSet(var=Var("x"), condition=Eq(Sum(Pow(Var("x"), Ref("_m")), Mul(Const(-2), Var("x")), Const(-7920)), Const(0)))),
"upper": Const(42436),
"m": Const(18),
"r": MinOverSet(set=Solu... | NT | null | COUNT | sympy | VIETA_SUM | [
"VIETA_SUM/LIN_FORM/MIN_PRIME_FACTOR"
] | 81bc64 | modular_count_residue_v1 | null | 7 | 0 | [
"LIN_FORM",
"MIN_PRIME_FACTOR",
"VIETA_SUM"
] | 3 | 1.48 | 2026-02-08T17:59:48.884611Z | {
"verified": true,
"answer": 2358,
"timestamp": "2026-02-08T17:59:50.364204Z"
} | 108ea1 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 212,
"completion_tokens": 4781
},
"timestamp": "2026-02-18T11:33:00.693Z",
"answer": 2358
},
{... | 1 | [
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok_later"
},
{
"lemma": "MIN_PRIME_FACTOR",
"status": "ok_later"
},
{
"lemma": "MOD_ADD",
... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
ab50ec | algebra_vieta_sum_v1_1742523217_727 | Let $a$ be the smallest positive integer $n$ for which $2^k$ divides $n!$ for some $k \geq 1$. Define $f(x) = x^3 + 7x^a - 70x - 400$. Let $s$ be the sum of all real roots of $f(x) = 0$. Compute $40000 - s$. | 40,007 | graphs = [
Graph(
let={
"_n": Const(7),
"result": SumOverSet(set=SolutionsSet(var=Var("x"), condition=Eq(Sum(Pow(Var("x"), Const(3)), Mul(Ref("_n"), Pow(Var("x"), MinOverSet(set=SolutionsSet(var=Var("n"), condition=Geq(MaxKDivides(target=Factorial(Var("n")), base=Const(2)), Const(1))... | NT | null | COMPUTE | sympy | BINOMIAL_ALTERNATING | [
"V5"
] | 79df37 | algebra_vieta_sum_v1 | null | 7 | 0 | [
"BINOMIAL_ALTERNATING",
"V5"
] | 2 | 0.025 | 2026-02-08T03:11:51.654161Z | {
"verified": true,
"answer": 40007,
"timestamp": "2026-02-08T03:11:51.679485Z"
} | 019cbb | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 194,
"completion_tokens": 1344
},
"timestamp": "2026-02-09T21:54:05.358Z",
"answer": 40007
},
{
"... | 1 | [
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "V1",
"status": "no"
},
{
"lemma": "V5",
"status": "ok"
}
] | {
"lo": -6.51,
"mid": -0.31,
"hi": 5.43
} | ||
c35c6d | comb_catalan_compute_v1_168721529_155 | Let $S$ be the set of all ordered pairs of positive odd integers $(x_1, x_2)$ such that $x_1 + x_2 = 22$. Let $c$ be the number of elements in $S$. Define $m_0 = \sum_{k=0}^{0} (-1)^k \binom{0}{k}$. Let $n = c \cdot m_0$. Compute the $n$-th Catalan number. | 58,786 | graphs = [
Graph(
let={
"_n": Const(22),
"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": Const(0),
"m": Summation(var="k", start=Const(0), end=Ref("n1... | COMB | null | COMPUTE | sympy | COMB1 | [
"COMB1/BINOMIAL_ALTERNATING"
] | e72f96 | comb_catalan_compute_v1 | null | 4 | 2 | [
"BINOMIAL_ALTERNATING",
"COMB1"
] | 2 | 0.004 | 2026-02-08T12:52:04.730369Z | {
"verified": true,
"answer": 58786,
"timestamp": "2026-02-08T12:52:04.734266Z"
} | 48e835 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 216,
"completion_tokens": 861
},
"timestamp": "2026-02-08T21:06:41.774Z",
"answer": 58786
},
{
"i... | 1 | [
{
"lemma": "BINOMIAL_ALTERNATING",
"status": "ok_later"
},
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COMB1",
"status": "ok"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "V7",
... | {
"lo": -3.91,
"mid": -1.87,
"hi": 0.46
} | ||
04ec18 | antilemma_cartesian_v1_124444284_2441 | Compute the number of ordered pairs $(a,b)$ such that $a$ is an integer satisfying $1 \leq a \leq 19$ and $b$ is an integer satisfying $1 \leq b \leq 34$. | 646 | graphs = [
Graph(
let={
"x": CountOverSet(set=CartesianProduct(left=IntegerRange(start=Const(1), end=Const(19)), right=IntegerRange(start=Const(1), end=Const(34)))),
},
goal=Ref("x"),
)
] | COMB | GEOM | COMPUTE | sympy | COUNT_CARTESIAN | [
"COUNT_CARTESIAN"
] | 409d7d | antilemma_cartesian_v1 | null | 2 | 0 | [
"COUNT_CARTESIAN"
] | 1 | 0.001 | 2026-02-08T04:40:41.192608Z | {
"verified": true,
"answer": 646,
"timestamp": "2026-02-08T04:40:41.193136Z"
} | 8c5cbf | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 161,
"completion_tokens": 137
},
"timestamp": "2026-02-24T01:25:31.603Z",
"answer": 646
},
{
"id"... | 2 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "ok"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8",
"status": ... | {
"lo": -9.23,
"mid": -6.18,
"hi": -4.06
} | ||
5af600_n | sequence_lucas_compute_v1_601307018_3390 | A game designer assigns power levels to character builds using a formula based on stats $a$ and $b$, each ranging from 1 to 25. The total power is given by $102 a^{R} b^{2} + 17 b^{m} + 17 a^{4} + 68a b^{3} + 68 a^{3} b$, where $R$ is the largest divisor of 6 whose square is at most 6, and $m$ is the maximum product of... | 75,536 | ALG | null | COMPUTE | sympy | B3_CLOSEST | [
"B3_CLOSEST/POLY4_COUNT",
"B1/POLY4_COUNT"
] | 038850 | sequence_lucas_compute_v1 | null | 7 | null | [
"B1",
"B3_CLOSEST",
"POLY4_COUNT"
] | 3 | 0.018 | 2026-03-10T03:57:29.196546Z | null | 01d26e | 5af600 | narrative | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 274,
"completion_tokens": 4318
},
"timestamp": "2026-03-29T17:30:26.149Z",
"answer": 75536
},
{
"... | 1 | [
{
"lemma": "B1",
"status": "ok"
},
{
"lemma": "B3_CLOSEST",
"status": "ok"
},
{
"lemma": "POLY4_COUNT",
"status": "ok_later"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
}
] | {
"lo": -5.36,
"mid": 0.27,
"hi": 5.45
} | |
25f56e | sequence_fibonacci_compute_v1_1125832087_180 | Let $m = 400$. Define $s$ to be the minimum value of $x + y$ over all ordered pairs $(x, y)$ of positive integers such that $xy = 400$. Let $n$ be the number of ordered pairs $(x_1, x_2)$ of positive odd integers such that $x_1 + x_2 = s$. Compute the $n$-th Fibonacci number. | 6,765 | graphs = [
Graph(
let={
"_m": Const(400),
"_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 | COMPUTE | sympy | B3 | [
"B3/COMB1"
] | e26f7e | sequence_fibonacci_compute_v1 | null | 4 | 0 | [
"B3",
"COMB1"
] | 2 | 0.003 | 2026-02-08T02:55:26.185589Z | {
"verified": true,
"answer": 6765,
"timestamp": "2026-02-08T02:55:26.188494Z"
} | 2d7d59 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 198,
"completion_tokens": 1147
},
"timestamp": "2026-02-10T11:48:01.151Z",
"answer": 6765
},
{
"i... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "COMB1",
"status": "ok_later"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"l... | {
"lo": -2.25,
"mid": 0,
"hi": 1.85
} | ||
266547 | antilemma_k2_v1_2051736721_610 | Compute $\sum_{k=1}^{s} \phi(k) \left\lfloor \frac{329}{k} \right\rfloor$, where $s = \sum_{d \mid 329} \phi(d)$ and the sum is over all positive divisors $d$ of $329$. | 54,285 | graphs = [
Graph(
let={
"_n": Const(329),
"x": Summation(var="k", start=Const(1), end=SumOverDivisors(n=Const(value=329), var='d', expr=EulerPhi(n=Var(name='d'))), expr=Mul(EulerPhi(n=Var("k")), Floor(Div(Ref("_n"), Var("k"))))),
},
goal=Ref("x"),
)
] | NT | COMB | COMPUTE | sympy | K13 | [
"K3/K2",
"K2"
] | c7f244 | antilemma_k2_v1 | null | 5 | 0 | [
"K13",
"K2",
"K3"
] | 3 | 0.003 | 2026-02-08T15:33:48.434168Z | {
"verified": true,
"answer": 54285,
"timestamp": "2026-02-08T15:33:48.436740Z"
} | 9664b1 | 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": 772
},
"timestamp": "2026-02-16T09:06:27.349Z",
"answer": 54285
},
{... | 1 | [
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "K2",
"status": "ok"
},
{
"lemma": "K3",
"status": "ok"
},
{
"lemma": "K5",
"status": "no"
},
... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
737c09 | sequence_fibonacci_compute_v1_655260480_4964 | Let $n$ be the number of integers $t$ such that $35 \leq t \leq 116$ and there exist integers $a$ and $b$ with $1 \leq a \leq 12$, $1 \leq b \leq 2$, and $t = 6a + 15b + 14$. 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 $k \geq 3$. Compute the remainder when... | 57,350 | graphs = [
Graph(
let={
"_n": Const(75254),
"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=12)), Geq(left=V... | NT | null | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | sequence_fibonacci_compute_v1 | null | 5 | 0 | [
"LIN_FORM"
] | 1 | 0.002 | 2026-02-08T18:13:42.440946Z | {
"verified": true,
"answer": 57350,
"timestamp": "2026-02-08T18:13:42.443212Z"
} | 09ead6 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 194,
"completion_tokens": 3830
},
"timestamp": "2026-02-18T15:25:52.900Z",
"answer": 57350
},
... | 1 | [
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "V3",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
a34b78 | comb_bell_compute_v1_1978505735_6734 | Let $n$ be the number of integers $t$ in the interval $[5, 15]$ that can be expressed as $3a + 2b$ for positive integers $a$ and $b$ with $1 \leq a \leq 3$ and $1 \leq b \leq 3$. Let $B_n$ denote the $n$-th Bell number, which counts the number of partitions of a set of $n$ elements. Compute the value of $31329 - B_n$. | 10,182 | graphs = [
Graph(
let={
"n": CountOverSet(set=SolutionsSet(var=Var("t"), condition=Exists(var=Var(name='a'), condition=Exists(var=Var(name='b'), condition=And(Geq(left=Var(name='a'), right=Const(value=1)), Leq(left=Var(name='a'), right=Const(value=3)), Geq(left=Var(name='b'), right=Const(value=1... | COMB | null | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | comb_bell_compute_v1 | null | 4 | 0 | [
"LIN_FORM"
] | 1 | 0.002 | 2026-02-08T19:46:05.346074Z | {
"verified": true,
"answer": 10182,
"timestamp": "2026-02-08T19:46:05.347941Z"
} | eac8a7 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 154,
"completion_tokens": 1118
},
"timestamp": "2026-02-18T23:27:43.381Z",
"answer": 10182
},
... | 1 | [
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "V8",
"status": "no"
},
{
"lemma": "V8_SUM",
... | {
"lo": -5.39,
"mid": -2.64,
"hi": 0.63
} | ||
282461 | nt_min_coprime_above_v1_1918700295_1263 | Let $S$ be the set of all integers $t$ such that $8 \leq t \leq 5344$ and $t = 5a + 3b$ for some positive integers $a$, $b$ with $1 \leq a \leq 353$ and $1 \leq b \leq 1193$. Let $s = |S|$. Compute the smallest integer $n$ such that $n > s$, $n \leq 5719$, and $\gcd(n, 380) = 1$. | 5,331 | graphs = [
Graph(
let={
"start": 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=353)), Geq(left=Var(name='b'), right=Const(v... | NT | null | EXTREMUM | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | nt_min_coprime_above_v1 | null | 7 | 0 | [
"LIN_FORM"
] | 1 | 0.063 | 2026-02-08T05:45:01.488359Z | {
"verified": true,
"answer": 5331,
"timestamp": "2026-02-08T05:45:01.551309Z"
} | b5f4cd | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 160,
"completion_tokens": 4688
},
"timestamp": "2026-02-12T13:28:46.820Z",
"answer": 5331
},
{... | 1 | [
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "V3",
"status":... | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
df8ba6 | antilemma_sum_equals_v1_124444284_487 | Compute the number of ordered pairs $(i, j)$ of integers such that $1 \leq i \leq 17$, $1 \leq j \leq 17$, and $i + j = 19$. | 16 | graphs = [
Graph(
let={
"x": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("i"), Var("j")]), condition=Eq(Sum(Var("i"), Var("j")), Const(19)), domain=CartesianProduct(left=IntegerRange(start=Const(1), end=Const(17)), right=IntegerRange(start=Const(1), end=Const(17))))),
},
... | COMB | GEOM | COMPUTE | sympy | COUNT_SUM_EQUALS | [
"COUNT_SUM_EQUALS"
] | 75ab0f | antilemma_sum_equals_v1 | null | 2 | 0 | [
"COUNT_SUM_EQUALS"
] | 1 | 0.01 | 2026-02-08T03:19:40.428562Z | {
"verified": true,
"answer": 16,
"timestamp": "2026-02-08T03:19:40.438679Z"
} | c8afe5 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 158,
"completion_tokens": 254
},
"timestamp": "2026-02-09T18:17:26.550Z",
"answer": 16
},
{
"id":... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "ok"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8",
"status": "no... | {
"lo": -5.97,
"mid": -3.96,
"hi": -1.93
} | ||
7ce648 | algebra_poly_eval_v1_1470522791_1772 | Let $z$ be the smallest integer $d \geq 2$ that divides $7429$. Define $r = 9z^2 + 5z + 9$. Compute the smallest positive integer $k$ such that the $k$-th Fibonacci number is divisible by $|r| + 2$. | 420 | graphs = [
Graph(
let={
"_n": Const(2),
"z": MinOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Ref("_n")), Divides(divisor=Var("d"), dividend=Const(7429))))),
"result": Sum(Mul(Const(9), Pow(Ref("z"), Const(2))), Mul(Const(5), Ref("z")), Const(9)),
... | NT | null | COMPUTE | sympy | MIN_PRIME_FACTOR | [
"MIN_PRIME_FACTOR"
] | bc3776 | algebra_poly_eval_v1 | null | 3 | 0 | [
"MIN_PRIME_FACTOR"
] | 1 | 0.003 | 2026-02-08T13:57:45.067984Z | {
"verified": true,
"answer": 420,
"timestamp": "2026-02-08T13:57:45.070735Z"
} | d23601 | 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": 2054
},
"timestamp": "2026-02-15T22:30:28.286Z",
"answer": 420
},
{
... | 1 | [
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "MIN_PRIME_FACTOR",
"status": "ok"
},
{
"lemma": "MOD_ADD",
"st... | {
"lo": -5.49,
"mid": 0.22,
"hi": 6.51
} | ||
d9636f | lin_form_endings_v1_151522320_1821 | Let $a = 56$ and $b = 40$. Define $g$ to be the greatest common divisor of $a$ and $b$. Let $a' = \left\lfloor \frac{a}{g} \right\rfloor$ and $b' = \left\lfloor \frac{b}{g} \right\rfloor$. Compute the remainder when $9563 \cdot (a' \cdot 34 + b' \cdot 19 - a' \cdot b')$ is divided by $92269$. | 81,704 | graphs = [
Graph(
let={
"a_coeff": Const(56),
"b_coeff": Const(40),
"A_val": Const(34),
"B_val": Const(19),
"g_step": GCD(a=Ref("a_coeff"), b=Ref("b_coeff")),
"ap_node": Floor(Div(Ref("a_coeff"), Ref("g_step"))),
"bp_node": ... | COMB | NT | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | lin_form_endings_v1 | null | 3 | null | [
"LIN_FORM"
] | 1 | 0.001 | 2026-02-08T04:23:50.206003Z | {
"verified": true,
"answer": 81704,
"timestamp": "2026-02-08T04:23:50.207070Z"
} | cc7f61 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 230,
"completion_tokens": 852
},
"timestamp": "2026-02-10T16:33:33.460Z",
"answer": 81704
},
{
"... | 1 | [
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
... | {
"lo": -3.42,
"mid": 1.86,
"hi": 7.55
} | ||
e7442c | comb_count_surjections_v1_1978505735_5156 | Let $n = 7$. Let $k$ be the number of ordered pairs $(i,j)$ of positive integers such that $i \leq 3$, $j \leq 4$, and $i + j = 4$. Compute $10946 - k! \cdot S(n, k)$, where $S(n, k)$ denotes the Stirling number of the second kind. Find the value of this expression. | 9,140 | graphs = [
Graph(
let={
"_n": CountOverSet(set=CartesianProduct(left=IntegerRange(start=Const(1), end=Const(2)), right=IntegerRange(start=Const(1), end=Const(2)))),
"n": Const(7),
"k": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("i"), Var("j")]), condition=Eq(Su... | COMB | null | COUNT | sympy | COUNT_CARTESIAN | [
"COUNT_CARTESIAN/COUNT_SUM_EQUALS"
] | 1e820b | comb_count_surjections_v1 | null | 4 | 0 | [
"COUNT_CARTESIAN",
"COUNT_SUM_EQUALS"
] | 2 | 0.011 | 2026-02-08T18:48:18.897906Z | {
"verified": true,
"answer": 9140,
"timestamp": "2026-02-08T18:48:18.909048Z"
} | db9eaf | 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": 1464
},
"timestamp": "2026-02-18T19:49:23.784Z",
"answer": 9140
},
{... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "ok"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "ok_later"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8",
"statu... | {
"lo": -3.12,
"mid": 1.47,
"hi": 6.57
} | ||
343023 | diophantine_fbi2_min_v1_1742523217_4021 | Let $k = 36$, $a = 5$, and $b = 1$. Define the set $S$ as the set of all integers $d$ such that $6 \leq d \leq 46$, $d$ divides $k$, and $\frac{k}{d} \geq 2$. Compute the minimum value of $d$ in $S$. | 6 | graphs = [
Graph(
let={
"k": Const(36),
"a": Const(5),
"b": Const(1),
"upper": Const(46),
"result": MinOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Const(6)), Leq(Var("d"), Ref("upper")), Divides(divisor=Var("d"), dividend=Ref... | NT | null | EXTREMUM | sympy | K14 | [
"K14/C3",
"ONE_PHI_1"
] | 6f8797 | diophantine_fbi2_min_v1 | null | 4 | 0 | [
"C3",
"K14",
"ONE_PHI_1"
] | 3 | 0.393 | 2026-02-08T06:11:01.596942Z | {
"verified": true,
"answer": 6,
"timestamp": "2026-02-08T06:11:01.989895Z"
} | e59f8b | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 138,
"completion_tokens": 515
},
"timestamp": "2026-02-15T18:47:39.438Z",
"answer": 6
},
{
"id": 11,
"... | 2 | [
{
"lemma": "C3",
"status": "ok_later"
},
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K14",
"status": "ok"
},
{
"lemma": "K15",
"sta... | {
"lo": -10,
"mid": -7.73,
"hi": -5.46
} | ||
a175ee | algebra_poly_eval_v1_1520064083_1194 | Compute $5 \cdot 9^k - 2 \cdot 9^2 + 4 \cdot 9 + 4$, where $k$ is the largest prime number between $2$ and $4$, inclusive. | 3,523 | graphs = [
Graph(
let={
"_n": Const(4),
"y": Const(9),
"result": Sum(Mul(Const(5), Pow(Ref("y"), MaxOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(2)), Leq(Var("n"), Const(4)), IsPrime(Var("n"))))))), Mul(Const(-2), Pow(Ref("y"), Const(2))), Mul(... | NT | null | COMPUTE | sympy | MAX_PRIME_BELOW | [
"MAX_PRIME_BELOW"
] | dc3ad3 | algebra_poly_eval_v1 | null | 3 | 0 | [
"MAX_PRIME_BELOW"
] | 1 | 0.003 | 2026-02-08T03:50:02.676418Z | {
"verified": true,
"answer": 3523,
"timestamp": "2026-02-08T03:50:02.678923Z"
} | 6ec53f | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 161,
"completion_tokens": 290
},
"timestamp": "2026-02-10T16:02:55.788Z",
"answer": 3523
},
{
"id... | 2 | [
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
}
] | {
"lo": -10,
"mid": -7.73,
"hi": -5.46
} | ||
f0b40c | comb_count_surjections_v1_1820931509_43 | Let $n$ be the number of ordered pairs $(x_1, x_2)$ of positive odd integers such that $x_1 + x_2 = 14$. Let $k$ be the number of integers $t$ with $5 \leq t \leq 12$ for which there exist integers $a$ and $b$ such that $1 \leq a \leq 3$, $1 \leq b \leq 2$, and $t = 2a + 3b$. Compute $k! \cdot S(n, k)$, where $S(n, k)$... | 15,120 | graphs = [
Graph(
let={
"_n": Const(14),
"n": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x1"), Var("x2")]), condition=And(IsPositive(arg=Var(name='x1')), IsPositive(arg=Var(name='x2')), IsOdd(arg=Var(name='x1')), IsOdd(arg=Var(name='x2')), Eq(Sum(Var("x1"), Var("x2")), Re... | COMB | null | COUNT | sympy | LIN_FORM | [
"LIN_FORM",
"COMB1"
] | 3d1461 | comb_count_surjections_v1 | null | 6 | 0 | [
"COMB1",
"LIN_FORM"
] | 2 | 0.003 | 2026-02-08T11:19:07.287032Z | {
"verified": true,
"answer": 15120,
"timestamp": "2026-02-08T11:19:07.289638Z"
} | d815f3 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 252,
"completion_tokens": 968
},
"timestamp": "2026-02-24T13:27:05.404Z",
"answer": 15120
},
{
"i... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COMB1",
"status": "ok"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "V7",
"status": "no"
},
... | {
"lo": -3.84,
"mid": -1.67,
"hi": 1.32
} | ||
dbf22c | alg_poly3_min_v1_1218484723_6220 | Let $F_n$ denote the $n$-th Fibonacci number. Let $P$ be the largest prime $n$ with $2 \leq n \leq S$ such that $11 \mid F_n$, where $S$ is the number of positive integers $n_1 \leq 1250$ for which $11$ divides $F_{n_1}$. Let $T$ be the number of positive integers $n_2 \leq 19795$ that are coprime to $14$. Find the min... | 36,764 | graphs = [
Graph(
let={
"_c": Const(1250),
"_m": Const(14),
"_n": Const(19795),
"result": MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("a"), Var("b")]), condition=And(Geq(Var("a"), Const(1)), Leq(Var("a"), MaxOverSet(set=SolutionsSet(var=... | NT | null | COMPUTE | sympy | COUNT_FIB_DIVISIBLE | [
"COUNT_FIB_DIVISIBLE/MAX_PRIME_BELOW",
"C4"
] | 0511e6 | alg_poly3_min_v1 | null | 6 | 0 | [
"C4",
"COUNT_FIB_DIVISIBLE",
"MAX_PRIME_BELOW"
] | 3 | 0.044 | 2026-02-25T07:48:33.470219Z | {
"verified": true,
"answer": 36764,
"timestamp": "2026-02-25T07:48:33.513953Z"
} | 8994bd | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 268,
"completion_tokens": 32768
},
"timestamp": "2026-03-30T00:47:18.799Z",
"answer": 36764
},
{
... | 1 | [
{
"lemma": "C4",
"status": "ok"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "ok"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok_later"
... | {
"lo": -3.33,
"mid": 1.03,
"hi": 5.26
} | ||
58a08b_n | alg_poly3_min_v1_1419126231_517 | A drone flies along a path parameterized by integer coordinates $(a, b)$ with $1 \le a, b \le 220$. Its energy consumption for a move is given by $-16a^3 + 12a^2b - 150ab^2 + 37b^3$ joules. The drone seeks the path with minimal energy use (which may be negative). What is the remainder when this minimum energy value is ... | 41,791 | ALG | null | COMPUTE | sympy | QF_PSD_ORBIT | [
"QF_PSD_ORBIT/QF_PSD_DISTINCT",
"ABS_INEQ"
] | 2ae48a | alg_poly3_min_v1 | null | 3 | null | [
"ABS_INEQ",
"QF_PSD_DISTINCT",
"QF_PSD_ORBIT"
] | 3 | 0.148 | 2026-02-25T10:03:02.112247Z | null | 64e4ba | 58a08b | narrative | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 209,
"completion_tokens": 25900
},
"timestamp": "2026-03-31T03:47:54.321Z",
"answer": 41791
},
{
... | 1 | [
{
"lemma": "ABS_INEQ",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "QF_PSD_DISTINCT",
"status": "ok_later"
},
{
"lemma": "QF_PSD_ORBIT",
"status": "ok"
}
] | {
"lo": 1.5,
"mid": 4.69,
"hi": 7.23
} | |
2be8ac | geo_count_lattice_rect_v1_1520064083_5482 | Let $a = 41$ and $b = 47$. Define $r$ to be the number of lattice points in the rectangle $[0, a] \times [0, b]$, including the boundaries. Compute the remainder when $4159 \cdot r$ is divided by $66193$. | 44,226 | graphs = [
Graph(
let={
"a": Const(41),
"b": Const(47),
"result": LatticePointsRect(a=Ref(name='a'), b=Ref(name='b')),
"Q": Mod(value=Mul(Const(4159), Ref("result")), modulus=Const(66193)),
},
goal=Ref("Q"),
)
] | GEOM | null | COUNT | sympy | [] | geo_count_lattice_rect_v1 | null | 4 | 0 | null | null | 0.001 | 2026-02-08T06:49:05.265975Z | {
"verified": true,
"answer": 44226,
"timestamp": "2026-02-08T06:49:05.266534Z"
} | fd1865 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 175,
"completion_tokens": 1569
},
"timestamp": "2026-02-24T07:56:23.910Z",
"answer": 44226
},
{
"... | 1 | [] | {
"lo": -2.35,
"mid": 1.22,
"hi": 4.84
} | ||||
9f9b54 | antilemma_k3_v1_153355830_442 | Let $n = 73721$. Define $x$ to be the sum of Euler's totient function $\phi(d)$ over all positive divisors $d$ of $n$. Compute $x$. | 73,721 | graphs = [
Graph(
let={
"_n": Const(73721),
"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 | 4 | 0 | [
"K3"
] | 1 | 0 | 2026-02-08T03:06:05.795677Z | {
"verified": true,
"answer": 73721,
"timestamp": "2026-02-08T03:06:05.795976Z"
} | 0f2905 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 152,
"completion_tokens": 237
},
"timestamp": "2026-02-10T12:39:21.115Z",
"answer": 73721
},
{
"... | 1 | [
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "K3",
"status": "ok"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
... | {
"lo": -5.92,
"mid": -3.15,
"hi": 0.25
} | ||
089584 | comb_sum_binomial_row_v1_1353956133_344 | Let $n_2 = 0$. Define $v = \sum_{k=0}^{n_2} (-1)^k \binom{n_2}{k}$. Let $u = 10$ and $n_1 = u + 1$. Define $h = \sum_{k=0}^{n_1} (-1)^k \binom{n_1}{k}$. Let $n = 11 \cdot v$. Compute $ (2 + h)^n $. | 2,048 | graphs = [
Graph(
let={
"n2": Const(0),
"v": Summation(var="k", start=Const(0), end=Ref("n2"), expr=Mul(Pow(Const(-1), Var("k")), Binom(n=Ref("n2"), k=Var("k")))),
"u": Const(10),
"n1": Sum(Ref("u"), Const(1)),
"h": Summation(var="k", start=Const(0... | COMB | null | SUM | sympy | BINOMIAL_ALTERNATING | [
"BINOMIAL_ALTERNATING"
] | c21569 | comb_sum_binomial_row_v1 | null | 3 | 2 | [
"BINOMIAL_ALTERNATING"
] | 1 | 0.001 | 2026-02-08T11:25:26.522494Z | {
"verified": true,
"answer": 2048,
"timestamp": "2026-02-08T11:25:26.523623Z"
} | 301f7b | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 217,
"completion_tokens": 406
},
"timestamp": "2026-02-24T13:41:21.407Z",
"answer": 2048
},
{
"id... | 1 | [
{
"lemma": "BINOMIAL_ALTERNATING",
"status": "ok"
},
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
},
{
"lemma": "V8_SUM",
"stat... | {
"lo": -7.18,
"mid": -5,
"hi": -3.01
} | ||
e59f4c | diophantine_sum_product_min_v1_1978505735_7765 | Let $S = 35$ and $P = 286$. Let $m$ be the minimum value of $x + y$ over all ordered pairs $(x, y)$ of positive integers such that $x \cdot y = 289$. Let $r$ be the smallest positive integer $x_1$ such that $1 \leq x_1 \leq m$ and $x_1(S - x_1) = P$. Let $c$ be the maximum value of $x_2 \cdot y_1$ over all ordered pair... | 3,012 | 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(289)))), expr=Sum(Var("x"), Var("y")))),
"S": Const(35),
... | NT | null | EXTREMUM | sympy | B1 | [
"B1",
"B3/B1"
] | 06725c | diophantine_sum_product_min_v1 | negation_mod | 5 | 0 | [
"B1",
"B3"
] | 2 | 0.006 | 2026-02-08T20:25:43.164563Z | {
"verified": true,
"answer": 3012,
"timestamp": "2026-02-08T20:25:43.170518Z"
} | 9d9053 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 194,
"completion_tokens": 1092
},
"timestamp": "2026-02-19T00:34:00.092Z",
"answer": 3012
},
{... | 1 | [
{
"lemma": "B1",
"status": "ok"
},
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "V3",
"status": "no"
},
{
"lemma": "V5",
"... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
4fc5f2 | antilemma_cartesian_v1_1918700295_1228 | Let $x$ be the number of ordered pairs $(i, j)$ such that $1 \leq i \leq 18$ and $1 \leq j \leq 23$. Find the remainder when $44121 \cdot x$ is divided by $55852$. | 2,490 | graphs = [
Graph(
let={
"x": CountOverSet(set=CartesianProduct(left=IntegerRange(start=Const(1), end=Const(18)), right=IntegerRange(start=Const(1), end=Const(23)))),
"Q": Mod(value=Mul(Const(44121), Ref("x")), modulus=Const(55852)),
},
goal=Ref("Q"),
)
] | COMB | GEOM | COMPUTE | sympy | COUNT_CARTESIAN | [
"COUNT_CARTESIAN"
] | 409d7d | antilemma_cartesian_v1 | null | 2 | 0 | [
"COUNT_CARTESIAN"
] | 1 | 0.001 | 2026-02-08T05:40:30.698790Z | {
"verified": true,
"answer": 2490,
"timestamp": "2026-02-08T05:40:30.699537Z"
} | 085615 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 1,
"correct": {
"strict": false,
"boxed": false,
"relaxed": true
},
"usage": {
"prompt_tokens": 171,
"completion_tokens": 32768
},
"timestamp": "2026-02-24T04:27:03.177Z",
"answer": null
},
{
... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "ok"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
},
{
"lemma": "V8_SUM",
"statu... | {
"lo": 1.97,
"mid": 4.36,
"hi": 6.69
} | ||
af0805 | sequence_lucas_compute_v1_1742523217_5174 | Let $ n $ be the smallest possible value of $ x + y $, where $ x $ and $ y $ are positive integers such that $ x \cdot y = 100 $. 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 $ 44121 \cdot L_n $ is divided by... | 7,545 | graphs = [
Graph(
let={
"_n": Const(100),
"n": MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(Mul(Var("x"), Var("y")), Ref("_n")))), expr=Sum(Var("x"), Var("y")))),
... | NT | null | COMPUTE | sympy | B3 | [
"B3"
] | 0cd20d | sequence_lucas_compute_v1 | null | 6 | 0 | [
"B3"
] | 1 | 0.001 | 2026-02-08T10:50:55.936654Z | {
"verified": true,
"answer": 7545,
"timestamp": "2026-02-08T10:50:55.937520Z"
} | b5c245 | 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": 1216
},
"timestamp": "2026-02-14T09:01:16.529Z",
"answer": 7545
},
{... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
}
] | {
"lo": -5.49,
"mid": 0.22,
"hi": 6.51
} | ||
81b139 | antilemma_product_of_sums_v1_1248542787_220 | Let $S_1 = \sum_{k=1}^{19} k$. Let $\mu(d)$ denote the Möbius function. Define $L = \sum_{d \mid 30} \mu(d)$. Let $S_2$ be the sum of all integers $j$ such that $L \leq j \leq 31$ and $\binom{31}{j}$ is odd. Let $x = S_1 \cdot S_2$. Compute the remainder when $44121 \cdot x$ is divided by $90973$. | 42,075 | graphs = [
Graph(
let={
"_n": Const(19),
"S1": Summation(var="k", start=Const(1), end=Ref("_n"), expr=Var("k")),
"S2": SumOverSet(set=SolutionsSet(var=Var("j"), condition=And(Geq(Var("j"), SumOverDivisors(n=Const(value=30), var='d', expr=MoebiusMu(n=Var(name='d')))), Leq(... | NT | null | COMPUTE | sympy | MOBIUS_SUM | [
"MOBIUS_SUM",
"PRODUCT_OF_SUMS"
] | 6f05e1 | antilemma_product_of_sums_v1 | null | 5 | 0 | [
"MOBIUS_SUM",
"PRODUCT_OF_SUMS"
] | 2 | 0.002 | 2026-02-08T03:01:17.584236Z | {
"verified": true,
"answer": 42075,
"timestamp": "2026-02-08T03:01:17.586702Z"
} | 79ceb0 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 235,
"completion_tokens": 5171
},
"timestamp": "2026-02-09T01:30:32.273Z",
"answer": 42075
},
{
"... | 1 | [
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "MOBIUS_SUM",
"status": "ok"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
... | {
"lo": -6.51,
"mid": -0.32,
"hi": 5.36
} | ||
c3cde6 | modular_sum_quadratic_residues_v1_601307018_7037 | Let $B_n$ denote the $n$-th Bell number. For an integer $a$ with $0 \le a \le 12166$, define the sequence $M = a^2 + 5249 \bmod 12167$, $R = R(M) = M^2 + 5249 \bmod 12167$, $S = R(R) \bmod 12167$, and $T = R(S) \bmod 12167$. Let $p = 673$. Define $K = \frac{p(p-1)}{\left|\{ a \in [0, 12166] : T = a,\ M \ne a,\ R \ne a,... | 203 | graphs = [
Graph(
let={
"_n": Const(5249),
"p": Const(673),
"result": Div(Mul(Ref("p"), Sub(Ref("p"), Const(1))), CountOverSet(set=SolutionsSet(var=Var("a"), condition=And(Geq(Var("a"), Const(0)), Leq(Var("a"), Const(12166)), Eq(Ref("_po_p4"), Var("a")), Neq(Ref("_po_p1")... | NT | COMB | SUM | sympy | POLY_ORBIT_HENSEL | [
"POLY_ORBIT_HENSEL"
] | 53b6eb | modular_sum_quadratic_residues_v1 | null | 7 | 0 | [
"POLY_ORBIT_HENSEL"
] | 1 | 0.004 | 2026-03-10T07:41:00.011021Z | {
"verified": true,
"answer": 203,
"timestamp": "2026-03-10T07:41:00.014719Z"
} | a6a11e | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 283,
"completion_tokens": 7497
},
"timestamp": "2026-04-19T05:50:29.586Z",
"answer": 203
},
{
"i... | 1 | [
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "POLY_ORBIT_HENSEL",
"status": "ok"
},
{
"lemma": "V3... | {
"lo": -5.34,
"mid": 1.1,
"hi": 7.53
} | ||
5aeb07 | antilemma_product_of_sums_v1_1116507919_459 | Let $A$ be the set of all ordered pairs $(i,j)$ of integers with $1 \le i \le 10$ and $1 \le j \le 6$. For each $(i,j)$ in $A$, consider the product $ij$. Let
\[S = \sum_{(i,j) \in A} ij.
\]
Let
\[T = \sum_{k=1}^{8} k,
\]
and define
\[x = S \cdot T.
\]
Let $B$ be the set of all ordered pairs $(x,y)$ of positive intege... | 27,709 | graphs = [
Graph(
let={
"_n": Const(8),
"x": Mul(SumOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("i"), Var("j")]), condition=Const(1), domain=CartesianProduct(left=IntegerRange(start=Const(1), end=Const(10)), right=IntegerRange(start=Const(1), end=Const(6)))), expr... | NT | null | COMPUTE | sympy | B3 | [
"B3/C2",
"PRODUCT_OF_SUMS"
] | 820b7a | antilemma_product_of_sums_v1 | negation_mod | 5 | 0 | [
"B3",
"C2",
"PRODUCT_OF_SUMS"
] | 3 | 0.002 | 2026-02-08T02:34:39.366078Z | {
"verified": true,
"answer": 27709,
"timestamp": "2026-02-08T02:34:39.368291Z"
} | da51c5 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 365,
"completion_tokens": 913
},
"timestamp": "2026-02-08T19:34:51.227Z",
"answer": 27709
},
{
"i... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "C2",
"status": "ok_later"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "PROD... | {
"lo": -7.44,
"mid": -4.14,
"hi": -0.84
} | ||
9f37f9 | modular_mod_compute_v1_48377204_2896 | Let $P$ be the set of all positive integers $p$ for which there exists a positive integer $q$ such that $p < q$, $pq = 72$, and $\gcd(p, q) = 1$. Let $k$ be the number of elements in $P$. Let $m$ be the smallest divisor of $2637367$ that is at least $k$. Compute the remainder when $361$ is divided by $m$. | 361 | graphs = [
Graph(
let={
"a": Const(361),
"m": 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(name='q'), condition=And(Eq(left=Mul(Var(name='p'), Var(name='q'... | NT | null | COMPUTE | sympy | COPRIME_PAIRS | [
"COPRIME_PAIRS/MIN_PRIME_FACTOR"
] | 52cee2 | modular_mod_compute_v1 | null | 4 | 0 | [
"COPRIME_PAIRS",
"MIN_PRIME_FACTOR"
] | 2 | 0.004 | 2026-02-08T17:03:32.810511Z | {
"verified": true,
"answer": 361,
"timestamp": "2026-02-08T17:03:32.814222Z"
} | 8a6daf | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 142,
"completion_tokens": 2374
},
"timestamp": "2026-02-17T18:47:26.409Z",
"answer": 361
},
{
... | 1 | [
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "MIN_PRIME_FACTOR",
"status": "ok_later"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "V3",
"status": "no"
}... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
11a20f | alg_poly4_min_v1_1218484723_3967 | Let $S$ be the set of integers $t$ in $[18, 5280]$ that can be written as $t = 8a + 10b$ for integers $a, b$ with $1 \le a \le 375$, $1 \le b \le 228$. Let $|S|$ denote the size of $S$. Find the minimum value of the expression $$|S| \cdot a^4 - 10480a^3b - 136240ab^3 + 107420b^4 + 78600a^2b^2$$ over all ordered pairs $... | 41,920 | graphs = [
Graph(
let={
"_n": Const(78600),
"result": MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("a"), Var("b")]), condition=And(Geq(Var("a"), Const(1)), Leq(Var("a"), Const(69)), Geq(Var("b"), Const(1)), Leq(Var("b"), Const(69)))), expr=Sum(Mul(CountOverSet(s... | ALG | null | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | alg_poly4_min_v1 | null | 6 | 0 | [
"LIN_FORM"
] | 1 | 0.024 | 2026-02-25T05:34:48.955686Z | {
"verified": true,
"answer": 41920,
"timestamp": "2026-02-25T05:34:48.979372Z"
} | 6fd408 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 1,
"correct": {
"strict": false,
"boxed": false,
"relaxed": true
},
"usage": {
"prompt_tokens": 264,
"completion_tokens": 32768
},
"timestamp": "2026-03-29T13:12:40.033Z",
"answer": 41926
},
{
... | 1 | [
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
}
] | {
"lo": 3.81,
"mid": 6.33,
"hi": 9.49
} | ||
5a37e4 | diophantine_fbi2_count_v1_898971024_2617 | Determine the number of positive integers $d$ such that $4 \leq d \leq 154$, $d$ divides $180$, and the quotient $180/d$ is between $5$ and $155$, inclusive. Multiply this count by $44121$, and compute the remainder when the result is divided by $72728$. Find the value of this remainder. | 48,963 | graphs = [
Graph(
let={
"k": Const(180),
"result": CountOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Const(4)), Leq(Var("d"), Const(154)), Divides(divisor=Var("d"), dividend=Ref("k")), Geq(Div(Ref("k"), Var("d")), Const(5)), Leq(Div(Ref("k"), Var("d")), Const(15... | NT | null | COUNT | sympy | MIN_PRIME_FACTOR | [
"MIN_PRIME_FACTOR"
] | bc3776 | diophantine_fbi2_count_v1 | null | 3 | 0 | [
"MIN_PRIME_FACTOR"
] | 1 | 0.016 | 2026-02-08T16:53:01.006922Z | {
"verified": true,
"answer": 48963,
"timestamp": "2026-02-08T16:53:01.022742Z"
} | 09651c | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 122,
"completion_tokens": 1446
},
"timestamp": "2026-02-17T14:13:01.815Z",
"answer": 48963
},
... | 1 | [
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "MIN_PRIME_FACTOR",
"status": "ok"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
},
{
"lemma": "VAL_SUM_EQ",
"status": "no"
}... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
979a8b | comb_count_derangements_v1_1742523217_1349 | Let $n$ be the largest prime number such that $2 \leq n \leq 9$. Define $d_n$ to be the number of derangements of $n$ elements. Compute the remainder when $44121 \cdot d_n$ is divided by $62240$. | 16,974 | graphs = [
Graph(
let={
"_n": Const(9),
"n": MaxOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(2)), Leq(Var("n"), Ref("_n")), IsPrime(Var("n"))))),
"result": Subfactorial(arg=Ref(name='n')),
"Q": Mod(value=Mul(Const(44121), Ref("resul... | NT | COMB | COUNT | sympy | MAX_PRIME_BELOW | [
"MAX_PRIME_BELOW"
] | dc3ad3 | comb_count_derangements_v1 | null | 4 | 0 | [
"MAX_PRIME_BELOW"
] | 1 | 0.001 | 2026-02-08T03:41:21.425514Z | {
"verified": true,
"answer": 16974,
"timestamp": "2026-02-08T03:41:21.426271Z"
} | a04234 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 171,
"completion_tokens": 2268
},
"timestamp": "2026-02-10T15:20:13.457Z",
"answer": 16974
},
{
"... | 1 | [
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok"... | {
"lo": -3.53,
"mid": 1.02,
"hi": 5.49
} | ||
5176c4 | nt_max_prime_below_v1_124444284_6853 | Let $T$ be the number of ordered pairs $(p, q)$ of positive integers such that $p \cdot q = 54$, $\gcd(p, q) = 1$, and $p < q$. Let $\text{result}$ be the largest prime number $n$ satisfying $T \leq n \leq 56169$. Determine the value of $\text{result}$. | 56,167 | graphs = [
Graph(
let={
"upper": Const(56169),
"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 | 3.069 | 2026-02-08T08:40:11.442576Z | {
"verified": true,
"answer": 56167,
"timestamp": "2026-02-08T08:40:14.511151Z"
} | b9fa88 | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 142,
"completion_tokens": 323
},
"timestamp": "2026-02-15T20:19:08.670Z",
"answer": 56167
},
{
"id": 11,
... | 2 | [
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
}
] | {
"lo": -9.14,
"mid": -6.05,
"hi": -3.73
} | ||
750c85 | antilemma_sum_equals_v1_153355830_792 | Let $n = 7 \times 7$. Let $x$ be the number of ordered pairs $(i, j)$ of positive integers such that $i \leq 48$, $j \leq 49$, and $i + j = n$. Let $c = 20813$ and $m = 79639$. Find the remainder when $c \cdot x$ is divided by $m$. | 43,356 | graphs = [
Graph(
let={
"_m": Const(79639),
"_n": CountOverSet(set=CartesianProduct(left=IntegerRange(start=Const(1), end=Const(7)), right=IntegerRange(start=Const(1), end=Const(7)))),
"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 | 0.013 | 2026-02-08T04:10:43.710321Z | {
"verified": true,
"answer": 43356,
"timestamp": "2026-02-08T04:10:43.723562Z"
} | 969b81 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 198,
"completion_tokens": 778
},
"timestamp": "2026-02-23T23:40:28.810Z",
"answer": 43356
},
{
"i... | 1 | [
{
"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",
"status": "no"
},
{
"lemma": "V8",
... | {
"lo": -4.92,
"mid": -2.9,
"hi": -0.7
} | ||
39781a | geo_count_lattice_rect_v1_1978505735_2371 | Compute the number of lattice points in the rectangle $[0, 377] \times [0, 103]$. | 39,312 | graphs = [
Graph(
let={
"a": Const(377),
"b": Const(103),
"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 | 2026-02-08T16:51:16.560033Z | {
"verified": true,
"answer": 39312,
"timestamp": "2026-02-08T16:51:16.561471Z"
} | c11b80 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 72,
"completion_tokens": 446
},
"timestamp": "2026-02-24T21:59:13.059Z",
"answer": 39312
},
{
... | 1 | [] | {
"lo": -8.52,
"mid": -5.43,
"hi": -3.2
} | ||||
43ca1f | nt_count_divisible_and_v1_349078426_5 | Let $d_1$ be the maximum value of $xy$ over all pairs of positive integers $(x, y)$ such that $x + y = 6$. Let $\mathcal{T}$ be the set of all positive integers $n$ such that $1 \leq n \leq 117612$, $n$ is divisible by $d_1$, and $n$ is divisible by $12$. Let $c = 88853$. Compute the remainder when $c$ times the number... | 47,795 | graphs = [
Graph(
let={
"upper": Const(117612),
"d1": MaxOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(Sum(Var("x"), Var("y")), Const(6)))), expr=Mul(Var("x"), Var("y"))... | NT | null | COUNT | sympy | B1 | [
"B1"
] | 5b950e | nt_count_divisible_and_v1 | null | 3 | 0 | [
"B1"
] | 1 | 5.048 | 2026-02-08T12:46:13.838076Z | {
"verified": true,
"answer": 47795,
"timestamp": "2026-02-08T12:46:18.886569Z"
} | 3f2c84 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 163,
"completion_tokens": 1321
},
"timestamp": "2026-02-15T05:22:58.771Z",
"answer": 47795
},
... | 1 | [
{
"lemma": "B1",
"status": "ok"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "VAL_SUM_EQ",
"status": "no"
}
] | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
ba523d | nt_num_divisors_compute_v1_865884756_5710 | Let $T$ be the set of all ordered pairs $(x_1, y_1)$ of positive integers such that $x_1 y_1 = 640000$. For each such pair, compute $x_1 + y_1$, and let $m$ be the minimum value among all such sums. Now, let $S$ be the set of all ordered pairs $(x, y)$ of positive integers such that $xy = m$. For each such pair, comput... | 70,550 | graphs = [
Graph(
let={
"_n": Const(99530),
"n": MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(Mul(Var("x"), Var("y")), MinOverSet(set=MapOverSet(set=SolutionsSet(var... | NT | null | COMPUTE | sympy | B3 | [
"B3/B3"
] | 8ffef9 | nt_num_divisors_compute_v1 | null | 6 | 0 | [
"B3"
] | 1 | 0.002 | 2026-02-08T18:45:40.050151Z | {
"verified": true,
"answer": 70550,
"timestamp": "2026-02-08T18:45:40.052129Z"
} | c2959a | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 194,
"completion_tokens": 1994
},
"timestamp": "2026-02-18T19:23:41.590Z",
"answer": 70550
},
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "VAL_SUM_EQ",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
4a7061 | nt_sum_gcd_range_mod_v1_655260480_3085 | Let $N$ be the maximum value of $xy$ over all ordered pairs $(x, y)$ of positive integers such that $x + y = 178$. Let $k = 84$ and $M = 11689$. Define
$$
\text{sum} = \sum_{n=1}^{N} \gcd(n, k).
$$
Let $r$ be the remainder when $\text{sum}$ is divided by $M$. Compute the remainder when $2048 - r$ is divided by $70584$.... | 70,391 | graphs = [
Graph(
let={
"_n": Const(178),
"N": MaxOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(Sum(Var("x"), Var("y")), Ref("_n")))), expr=Mul(Var("x"), Var("y")))),
... | NT | null | COMPUTE | sympy | B1 | [
"B1"
] | 5b950e | nt_sum_gcd_range_mod_v1 | null | 5 | 0 | [
"B1"
] | 1 | 1.815 | 2026-02-08T17:10:36.288173Z | {
"verified": true,
"answer": 70391,
"timestamp": "2026-02-08T17:10:38.103486Z"
} | 9cd9bb | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 163,
"completion_tokens": 1908
},
"timestamp": "2026-02-17T21:04:34.830Z",
"answer": 70391
},
... | 1 | [
{
"lemma": "B1",
"status": "ok"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "VAL_SUM_EQ",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
4ac804_n | comb_factorial_compute_v1_1218484723_7587 | A designer is choosing rectangular tiles for a mosaic. Each tile type is labeled by a pair of positive integers $(a, b)$ with $1 \le a \le 35$ and $1 \le b \le 35$, representing its length and width in arbitrary units. A certain compatibility constant $C$ is defined as the number of pairs of positive integers $(a_1, b_... | 5,040 | COMB | null | COMPUTE | sympy | B3 | [
"B3/QF_PSD_ORBIT/QF_PSD_COUNT"
] | 50966c | comb_factorial_compute_v1 | null | 7 | null | [
"B3",
"QF_PSD_COUNT",
"QF_PSD_ORBIT"
] | 3 | 0.018 | 2026-02-25T09:01:26.662076Z | null | 8e72a0 | 4ac804 | narrative | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 368,
"completion_tokens": 2055
},
"timestamp": "2026-03-31T02:35:34.534Z",
"answer": 5040
},
{
"i... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "QF_PSD_COUNT",
"status": "ok_later"
},
{
"lemma": "QF_PSD_ORBIT",
"status": "ok_later"
},
{
"lemma": "V7",
... | {
"lo": -5.37,
"mid": 0.23,
"hi": 5.22
} | |
b15606 | comb_count_surjections_v1_655260480_4201 | Let $a$ be the number of ordered pairs $(x_1, x_2)$ of positive odd integers such that $x_1 + x_2 = 5000$. Let $b = 5! \cdot S(7, 5)$, where $S(7, 5)$ denotes the Stirling number of the second kind. Compute the remainder when $a - b$ is divided by $68779$. | 54,479 | graphs = [
Graph(
let={
"n": Const(7),
"k": Const(5),
"result": Mul(Factorial(Ref("k")), Stirling2(n=Ref(name='n'), k=Ref(name='k'))),
"Q": Mod(value=Sub(CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x1"), Var("x2")]), condition=And(IsPositive(arg=Var... | COMB | null | COUNT | sympy | COMB1 | [
"COMB1"
] | 9f12f1 | comb_count_surjections_v1 | negation_mod | 5 | 0 | [
"COMB1"
] | 1 | 0.003 | 2026-02-08T17:48:04.561406Z | {
"verified": true,
"answer": 54479,
"timestamp": "2026-02-08T17:48:04.564672Z"
} | 2a68a8 | 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": 1127
},
"timestamp": "2026-02-18T08:42:23.857Z",
"answer": 54479
},
... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COMB1",
"status": "ok"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
}
] | {
"lo": -4.1,
"mid": -1.76,
"hi": 1.32
} | ||
9e06bf | diophantine_fbi2_min_v1_1520064083_1119 | Let $k = 10$ and let $u = 20$. Define $d$ to be an integer such that $4 \leq d \leq u$, $d$ divides $k$, and $\frac{k}{d}$ is at least the number of ordered pairs $(p, q)$ of positive integers satisfying $pq = 36$, $\gcd(p, q) = 1$, and $p < q$. Let $r$ be the smallest such $d$. Let $S$ be the set of all ordered pairs ... | 26 | graphs = [
Graph(
let={
"k": Const(10),
"upper": Const(20),
"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"), Var("d")), CountOverSet(set=... | NT | null | EXTREMUM | sympy | L3B | [
"COUNT_COPRIME_GRID",
"COPRIME_PAIRS"
] | 37e5b2 | diophantine_fbi2_min_v1 | negation_mod | 5 | 0 | [
"COPRIME_PAIRS",
"COUNT_COPRIME_GRID",
"L3B"
] | 3 | 0.045 | 2026-02-08T03:48:08.404288Z | {
"verified": true,
"answer": 26,
"timestamp": "2026-02-08T03:48:08.449618Z"
} | 34c16b | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 274,
"completion_tokens": 1597
},
"timestamp": "2026-02-10T15:45:37.400Z",
"answer": 26
},
{
"id"... | 1 | [
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "ok"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status":... | {
"lo": -5.55,
"mid": -3.02,
"hi": 0.31
} | ||
8b686f | modular_count_residue_v1_168721529_1390 | Let $m$ be the number of ordered pairs $(a,b)$ where $a$ is an integer with $1 \leq a \leq 3$ and $b$ is an integer with $1 \leq b \leq 4$. Let $r = 2$ and let $N$ be the number of positive integers $n$ such that $1 \leq n \leq 86436$ and $n \equiv r \pmod{m}$. Compute the remainder when $78793 \cdot N$ is divided by $... | 32,635 | graphs = [
Graph(
let={
"upper": Const(86436),
"m": CountOverSet(set=CartesianProduct(left=IntegerRange(start=Const(1), end=Const(3)), right=IntegerRange(start=Const(1), end=Const(4)))),
"r": Const(2),
"result": CountOverSet(set=SolutionsSet(var=Var("n"), cond... | NT | null | COUNT | sympy | COUNT_CARTESIAN | [
"COUNT_CARTESIAN"
] | 409d7d | modular_count_residue_v1 | null | 3 | 0 | [
"COUNT_CARTESIAN"
] | 1 | 5.593 | 2026-02-08T13:40:39.299476Z | {
"verified": true,
"answer": 32635,
"timestamp": "2026-02-08T13:40:44.892630Z"
} | 5f8b87 | 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": 2471
},
"timestamp": "2026-02-09T16:26:28.184Z",
"answer": 32635
},
{
"... | 1 | [
{
"lemma": "COUNT_CARTESIAN",
"status": "ok"
},
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "V7",... | {
"lo": -1.95,
"mid": 2.14,
"hi": 6.33
} | ||
8bcde6 | algebra_vieta_sum_v1_1353956133_69 | Let $a$ be the number of ordered pairs $(p,q)$ of positive integers such that $p < q$, $pq = 12$, and $\gcd(p,q) = 1$. Define $f(x) = x^a - 2x - 24$. Let $R$ be the set of real roots of $f(x) = 0$. Compute the product of all elements in $R$, and subtract this product from $66666$. Find the value of the result. | 66,690 | graphs = [
Graph(
let={
"_n": Const(66666),
"result": ProductOverSet(set=SolutionsSet(var=Var(name='x'), condition=Eq(left=Sum(Pow(base=Var(name='x'), exp=CountOverSet(set=SolutionsSet(var=Var(name='p'), condition=And(IsPositive(arg=Var(name='p')), Exists(var=Var(name='q'), condition... | NT | null | COMPUTE | sympy | COPRIME_PAIRS | [
"COPRIME_PAIRS"
] | 2bb3aa | algebra_vieta_sum_v1 | null | 4 | 0 | [
"COPRIME_PAIRS"
] | 1 | 0.007 | 2026-02-08T11:17:17.510999Z | {
"verified": true,
"answer": 66690,
"timestamp": "2026-02-08T11:17:17.517587Z"
} | 381733 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 149,
"completion_tokens": 529
},
"timestamp": "2026-02-14T11:28:10.321Z",
"answer": 66690
},
{... | 1 | [
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
... | {
"lo": -6.96,
"mid": -4.56,
"hi": -1.46
} | ||
78c477 | modular_sum_quadratic_residues_v1_397696148_2532 | Let $p$ be the smallest prime divisor of 183247919. Compute $\frac{p(p-1)}{4}$. | 3,164 | 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(183247919))))),
"result": Div(Mul(Ref("p"), Sub(Ref("p"), Const(1))), Const(4)),
},
goal... | NT | null | SUM | sympy | MIN_PRIME_FACTOR | [
"MIN_PRIME_FACTOR"
] | bc3776 | modular_sum_quadratic_residues_v1 | null | 4 | 0 | [
"MIN_PRIME_FACTOR"
] | 1 | 0.003 | 2026-02-08T13:24:03.659378Z | {
"verified": true,
"answer": 3164,
"timestamp": "2026-02-08T13:24:03.662187Z"
} | b4c7ef | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 72,
"completion_tokens": 1920
},
"timestamp": "2026-02-15T14:40:18.426Z",
"answer": 3164
},
{
... | 1 | [
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MIN_PRIME_FACTOR",
"status": "ok"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "VAL_SUM_EQ",
... | {
"lo": -5.49,
"mid": 0.22,
"hi": 6.51
} | ||
503aef | nt_max_prime_below_v1_1915831931_1311 | Let $S$ be the set of all positive integers $p$ for which there exists a positive integer $q$ such that $p \cdot q = 18$, $\gcd(p, q) = 1$, and $p < q$. Let $T$ be the set of all prime numbers $n$ such that $n \ge |S|$ and $n \le 48841$. Determine the value of the largest element in $T$. | 48,823 | graphs = [
Graph(
let={
"upper": Const(48841),
"result": MaxOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), CountOverSet(set=SolutionsSet(var=Var("p"), condition=And(IsPositive(arg=Var(name='p')), Exists(var=Var(name='q'), condition=And(Eq(left=Mul(Var(name='p'), V... | NT | null | EXTREMUM | sympy | COPRIME_PAIRS | [
"COPRIME_PAIRS"
] | 2bb3aa | nt_max_prime_below_v1 | null | 3 | 0 | [
"COPRIME_PAIRS"
] | 1 | 1.398 | 2026-02-08T15:59:47.251967Z | {
"verified": true,
"answer": 48823,
"timestamp": "2026-02-08T15:59:48.650424Z"
} | 80344f | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 142,
"completion_tokens": 3975
},
"timestamp": "2026-02-16T19:31:02.028Z",
"answer": 48823
},
... | 1 | [
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
b7a5c8 | comb_count_surjections_v1_1820931509_240 | Let $n$ be the number of ordered pairs $(i, j)$ of positive integers such that $i + j = 8$, $1 \le i \le 6$, and $1 \le j \le 7$. Let $k = 3$. Compute $k! \cdot S(n, k)$, where $S(n, k)$ denotes the Stirling number of the second kind. Find the remainder when this result is multiplied by $53011$ and then divided by $842... | 51,969 | graphs = [
Graph(
let={
"_n": Const(8),
"n": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("i"), Var("j")]), condition=Eq(Sum(Var("i"), Var("j")), Ref("_n")), domain=CartesianProduct(left=IntegerRange(start=Const(1), end=Const(6)), right=IntegerRange(start=Const(1), end=Const... | COMB | null | COUNT | sympy | COUNT_SUM_EQUALS | [
"COUNT_SUM_EQUALS"
] | 75ab0f | comb_count_surjections_v1 | null | 5 | 0 | [
"COUNT_SUM_EQUALS"
] | 1 | 0.011 | 2026-02-08T11:27:34.152713Z | {
"verified": true,
"answer": 51969,
"timestamp": "2026-02-08T11:27:34.163895Z"
} | 700e47 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 217,
"completion_tokens": 1657
},
"timestamp": "2026-02-24T13:57:37.394Z",
"answer": 51969
},
{
"... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "ok"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8_SUM",
"stat... | {
"lo": -2.35,
"mid": 1.22,
"hi": 4.84
} | ||
1def89 | nt_num_divisors_compute_v1_2051736721_5038 | Let $S$ be the set of all ordered pairs $(x_1, x_2)$ of positive odd integers such that $x_1 + x_2 = 20000$. Let $n$ be the number of elements in $S$. Define $\text{result} = \tau(n)$, where $\tau(m)$ denotes the number of positive divisors of $m$. Compute the remainder when $44121 \cdot \text{result}$ is divided by 60... | 9,651 | graphs = [
Graph(
let={
"_n": Const(44121),
"n": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x1"), Var("x2")]), condition=And(IsPositive(arg=Var(name='x1')), IsPositive(arg=Var(name='x2')), IsOdd(arg=Var(name='x1')), IsOdd(arg=Var(name='x2')), Eq(Sum(Var("x1"), Var("x2")),... | NT | null | COMPUTE | sympy | COMB1 | [
"COMB1"
] | 567f58 | nt_num_divisors_compute_v1 | null | 3 | 0 | [
"COMB1"
] | 1 | 0.002 | 2026-02-08T18:21:06.658985Z | {
"verified": true,
"answer": 9651,
"timestamp": "2026-02-08T18:21:06.661249Z"
} | f7da2a | 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": 957
},
"timestamp": "2026-02-18T16:18:48.364Z",
"answer": 9651
},
{
... | 1 | [
{
"lemma": "COMB1",
"status": "ok"
},
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
716cdf | lin_form_endings_v1_601307018_130 | Let $K = \gcd(70, 98)$ and $T = 61$. Define $L = \left\lfloor \frac{T}{\gcd(T, K)} \right\rfloor$ and $P = 17409 \cdot L$. Find the remainder when $P$ is divided by $56870$. | 38,289 | graphs = [
Graph(
let={
"a_coeff": Const(70),
"b_coeff": Const(98),
"k_val": Const(61),
"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... | NT | COMB | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | lin_form_endings_v1 | null | 3 | null | [
"LIN_FORM"
] | 1 | 0.001 | 2026-03-10T00:46:01.837858Z | {
"verified": true,
"answer": 38289,
"timestamp": "2026-03-10T00:46:01.839304Z"
} | 31f79b | CC BY 4.0 | null | null | [
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "V5",
"s... | {
"lo": -10,
"mid": 0,
"hi": 10
} | ||
9bb2a6 | algebra_poly_eval_v1_898971024_2525 | Compute the value of
\[
4 \cdot 25^{\sum_{k=1}^{2} \varphi(k) \left\lfloor \frac{2}{k} \right\rfloor} + 3 \cdot 25^2 - 4 \cdot 25 + s,
\]
where $s$ is the number of positive integers $p$ for which there exists a positive integer $q$ such that $p < q$, $\gcd(p, q) = 1$, and $p \cdot q = 370440$. | 64,283 | graphs = [
Graph(
let={
"_m": Const(4),
"_n": Const(2),
"z": Const(25),
"result": Sum(Mul(Ref("_m"), Pow(Ref("z"), Summation(var="k", start=Const(1), end=Const(2), expr=Mul(EulerPhi(n=Var("k")), Floor(Div(Const(2), Var("k"))))))), Mul(Const(3), Pow(Ref("z"), R... | NT | null | COMPUTE | sympy | COPRIME_PAIRS | [
"COPRIME_PAIRS",
"K2"
] | 5d07bf | algebra_poly_eval_v1 | null | 5 | 0 | [
"COPRIME_PAIRS",
"K2"
] | 2 | 0.022 | 2026-02-08T16:47:51.500457Z | {
"verified": true,
"answer": 64283,
"timestamp": "2026-02-08T16:47:51.522058Z"
} | 450f1e | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 160,
"completion_tokens": 2199
},
"timestamp": "2026-02-17T13:00:56.178Z",
"answer": 64283
},
... | 1 | [
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "K2",
"status": "ok"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": ... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
4955f8 | comb_binomial_compute_v1_1520064083_2011 | Let $n$ be the number of integers $j$ with $0 \leq j \leq 1360$ such that $\binom{1360}{j}$ is odd. Let $k$ be the number of integers $t$ with $15 \leq t \leq 45$ for which there exist positive integers $a \leq 3$ and $b \leq 3$ such that $t = 9a + 6b$. Let $c = 44589$ and $m = 52343$. Compute the remainder when $c \cd... | 15,625 | graphs = [
Graph(
let={
"_n": Const(52343),
"n": CountOverSet(set=SolutionsSet(var=Var("j"), condition=And(Geq(Var("j"), Const(0)), Leq(Var("j"), Const(1360)), Eq(Mod(value=Binom(n=Const(1360), k=Var("j")), modulus=Const(2)), Const(1))), domain='nonnegative_integers')),
"... | ALG | COMB | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM",
"V8"
] | a2d4b4 | comb_binomial_compute_v1 | null | 7 | 0 | [
"LIN_FORM",
"V8"
] | 2 | 0.004 | 2026-02-08T04:27:15.834566Z | {
"verified": true,
"answer": 15625,
"timestamp": "2026-02-08T04:27:15.838401Z"
} | 2e0da5 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 250,
"completion_tokens": 1829
},
"timestamp": "2026-02-24T00:40:12.513Z",
"answer": 15625
},
{
"... | 1 | [
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "V8",
"status": "ok"
},
{
"lemma... | {
"lo": -2.46,
"mid": 0.47,
"hi": 3.59
} | ||
54c31f | comb_binomial_compute_v1_1874849503_1091 | Let $m = 25200$ and $n = 13013$. Let $S$ be the set of all positive integers $p$ such that there exists a positive integer $q$ with $p < q$, $pq = 108$, and $\gcd(p, q) = 1$. Let $d_0$ be the number of elements in $S$. Define $k$ to be the smallest positive divisor of $n$ that is at least $d_0$. Compute $\binom{15}{k}$... | 18,765 | graphs = [
Graph(
let={
"_m": Const(25200),
"_n": Const(13013),
"n": Const(15),
"k": 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(n... | NT | null | COMPUTE | sympy | COPRIME_PAIRS | [
"COPRIME_PAIRS/MIN_PRIME_FACTOR"
] | 52cee2 | comb_binomial_compute_v1 | null | 6 | 0 | [
"COPRIME_PAIRS",
"MIN_PRIME_FACTOR"
] | 2 | 0.003 | 2026-02-08T13:34:11.355988Z | {
"verified": true,
"answer": 18765,
"timestamp": "2026-02-08T13:34:11.359053Z"
} | 720dff | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 239,
"completion_tokens": 1502
},
"timestamp": "2026-02-10T00:58:34.864Z",
"answer": 18765
},
{
"... | 1 | [
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "MIN_PRIME_FACTOR",
"status": "ok_later"
},
{
"lemma": "MOD_MUL",
"s... | {
"lo": -8.26,
"mid": -5.01,
"hi": -1.76
} | ||
cfc5c4 | antilemma_sum_equals_v1_655260480_3542 | Let $n$ be the number of ordered pairs $(i, j)$ where $i \in \{1, 2\}$ and $j \in \{1, 2, \dots, 29\}$. Let $x$ be the number of ordered pairs $(i, j)$ of positive integers such that $i + j = n$ and $1 \leq i, j \leq 58$. Compute the remainder when $16332 \cdot x$ is divided by $54041$. | 12,227 | graphs = [
Graph(
let={
"_n": CountOverSet(set=CartesianProduct(left=IntegerRange(start=Const(1), end=Const(2)), right=IntegerRange(start=Const(1), end=Const(29)))),
"x": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("i"), Var("j")]), condition=Eq(Sum(Var("i"), Var("j")), Ref... | COMB | GEOM | COMPUTE | sympy | COUNT_CARTESIAN | [
"COUNT_CARTESIAN/COUNT_SUM_EQUALS",
"COUNT_SUM_EQUALS"
] | 8bee9e | antilemma_sum_equals_v1 | null | 4 | 0 | [
"COUNT_CARTESIAN",
"COUNT_SUM_EQUALS"
] | 2 | 0.009 | 2026-02-08T17:25:26.695965Z | {
"verified": true,
"answer": 12227,
"timestamp": "2026-02-08T17:25:26.704658Z"
} | 3a9bfa | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 150,
"completion_tokens": 725
},
"timestamp": "2026-02-18T01:41:00.048Z",
"answer": 12227
},
{... | 1 | [
{
"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",
"status": "no"
},
{
"lemma": "V8",
... | {
"lo": -2.38,
"mid": 1.74,
"hi": 6.59
} | ||
daec4e | alg_qf_psd_count_v1_601307018_8838 | Find the number of ordered pairs $(a, b)$ of positive integers with $1 \le a, b \le 433$ such that
$$
10a^2 + 8b^2 - 8ab = 1308320.
$$ | 15 | graphs = [
Graph(
let={
"result": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("a"), Var("b")]), condition=And(Geq(Var("a"), Const(1)), Leq(Var("a"), Const(433)), Geq(Var("b"), Const(1)), Leq(Var("b"), Const(433)), Eq(Sum(Mul(Const(10), Pow(Var("a"), Const(2))), Mul(Const(8), Pow(Var("b... | ALG | null | COUNT | sympy | QF_PSD_MIN | [
"QF_PSD_COUNT_LEQ",
"POLY4_COUNT"
] | c72518 | alg_qf_psd_count_v1 | null | 5 | null | [
"POLY4_COUNT",
"QF_PSD_COUNT_LEQ",
"QF_PSD_MIN"
] | 3 | 16.161 | 2026-03-10T09:17:03.321540Z | {
"verified": true,
"answer": 15,
"timestamp": "2026-03-10T09:17:19.482642Z"
} | 1f5f7b | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 163,
"completion_tokens": 14190
},
"timestamp": "2026-04-19T09:56:54.067Z",
"answer": 15
},
{
"i... | 1 | [
{
"lemma": "POLY4_COUNT",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "QF_PSD_COUNT_LEQ",
"status": "ok"
}
] | {
"lo": -5.34,
"mid": 1.1,
"hi": 7.53
} | ||
405545 | nt_count_coprime_v1_153355830_1390 | Let $k$ be the number of positive integers $p$ for which there exists a positive integer $q$ such that $pq = 600$, $\gcd(p, q) = 1$, and $p < q$. Determine the number of positive integers $n$ such that $1 \le n \le 59536$ and $\gcd(n, k) = 1$. | 29,768 | graphs = [
Graph(
let={
"upper": Const(59536),
"k": CountOverSet(set=SolutionsSet(var=Var("p"), condition=And(IsPositive(arg=Var(name='p')), Exists(var=Var(name='q'), condition=And(Eq(left=Mul(Var(name='p'), Var(name='q')), right=Const(value=600)), Eq(left=GCD(a=Var(name='p'), b=Var(... | NT | null | COUNT | sympy | COPRIME_PAIRS | [
"COPRIME_PAIRS"
] | 2bb3aa | nt_count_coprime_v1 | null | 4 | 0 | [
"COPRIME_PAIRS"
] | 1 | 4.778 | 2026-02-08T06:22:31.444129Z | {
"verified": true,
"answer": 29768,
"timestamp": "2026-02-08T06:22:36.222514Z"
} | 552071 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 127,
"completion_tokens": 1311
},
"timestamp": "2026-02-12T23:08:19.883Z",
"answer": 29768
},
... | 1 | [
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
}
] | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
a640cf | comb_count_surjections_v1_48377204_2586 | Let $n = 7$ and let $k$ be the number of ordered pairs $(i, j)$ of positive integers such that $i + j = 6$ and $1 \leq i, j \leq 4$. Compute $k! \cdot S(n, k)$, where $S(n, k)$ denotes the Stirling number of the second kind.
Find the value of this expression. | 1,806 | graphs = [
Graph(
let={
"_n": Const(6),
"n": Const(7),
"k": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("i"), Var("j")]), condition=Eq(Sum(Var("i"), Var("j")), Ref("_n")), domain=CartesianProduct(left=IntegerRange(start=Const(1), end=Const(4)), right=IntegerRang... | COMB | null | COUNT | sympy | COUNT_SUM_EQUALS | [
"COUNT_SUM_EQUALS"
] | 75ab0f | comb_count_surjections_v1 | null | 4 | 0 | [
"COUNT_SUM_EQUALS"
] | 1 | 0.021 | 2026-02-08T16:49:54.591257Z | {
"verified": true,
"answer": 1806,
"timestamp": "2026-02-08T16:49:54.612288Z"
} | 43546a | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 130,
"completion_tokens": 1303
},
"timestamp": "2026-02-17T14:28:28.651Z",
"answer": 1806
},
{... | 1 | [
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "ok"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
},
{
"lemma": "V8_SUM",
"status"... | {
"lo": -4.1,
"mid": -1.76,
"hi": 1.32
} | ||
3b67df | antilemma_sum_equals_v1_798873815_404 | Let $S$ be the set of all integers $t$ with $18 \leq t \leq 110$ for which there exist positive integers $a \leq 17$ and $b \leq 3$ such that $t = 4a + 14b$. Let $n = |S|$. Compute the number of ordered pairs $(i, j)$ of positive integers with $1 \leq i, j \leq 41$ such that $i + j = n$. | 40 | 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=17)), 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 | 4 | 0 | [
"COUNT_SUM_EQUALS",
"LIN_FORM"
] | 2 | 0.1 | 2026-02-08T02:38:04.898326Z | {
"verified": true,
"answer": 40,
"timestamp": "2026-02-08T02:38:04.998767Z"
} | 909c7c | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 222,
"completion_tokens": 3459
},
"timestamp": "2026-02-08T19:28:38.934Z",
"answer": 40
},
{
"id"... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "ok"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "V8",
"statu... | {
"lo": -0.81,
"mid": 1.02,
"hi": 2.61
} | ||
67b98f | antilemma_v8_lucas_865884756_298 | Let $m=36$. Consider all ordered pairs $(x,y)$ of positive integers such that $xy=m$. Let $S$ be the set of all possible values of $x+y$ for such pairs, and let $n$ be the smallest element of $S$.
Let $X$ be the number of integers $j$ with $0\le j\le 98991$ for which the binomial coefficient $\binom{98991}{j}$ is odd.... | 203 | graphs = [
Graph(
let={
"_m": Const(36),
"_n": MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x1"), Var("y")]), condition=And(IsPositive(arg=Var(name='x1')), IsPositive(arg=Var(name='y')), Eq(Mul(Var("x1"), Var("y")), Ref("_m")))), expr=Sum(Var("x1"), Var("y"))))... | NT | COMB | COMPUTE | sympy | B3 | [
"B3/MAX_PRIME_BELOW",
"V8"
] | 7e2e3b | antilemma_v8_lucas | bell_mod | 6 | 0 | [
"B3",
"MAX_PRIME_BELOW",
"V8"
] | 3 | 0.004 | 2026-02-08T15:18:32.724901Z | {
"verified": true,
"answer": 203,
"timestamp": "2026-02-08T15:18:32.728720Z"
} | 326664 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 285,
"completion_tokens": 1003
},
"timestamp": "2026-02-10T06:47:18.186Z",
"answer": 203
}
] | 2 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok_later"
},
{
"lemma": "MOD_MUL",
"status": "no"
... | {
"lo": -10,
"mid": -1.96,
"hi": 6.09
} | ||
357533 | nt_sum_phi_v1_548369836_323 | Let $S$ be the set of all positive integers $n$ such that $1 \leq n \leq 500$. For each $n$, let $\phi(n)$ denote Euler's totient function. Compute the sum of $\phi(n)$ over all $n \in S$. | 76,116 | graphs = [
Graph(
let={
"upper": Const(500),
"result": SumOverSet(set=MapOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Ref("upper")))), expr=EulerPhi(n=Var("n")))),
},
goal=Ref("result"),
)
] | NT | null | SUM | sympy | L3B | [
"B3"
] | 0cd20d | nt_sum_phi_v1 | null | 4 | 0 | [
"B3",
"L3B"
] | 2 | 0.144 | 2026-02-08T02:51:56.826001Z | {
"verified": true,
"answer": 76116,
"timestamp": "2026-02-08T02:51:56.970237Z"
} | bc7e38 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 171,
"completion_tokens": 17956
},
"timestamp": "2026-02-23T17:57:38.832Z",
"answer": 75990
},
{
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "V1",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
}
] | {
"lo": 3.92,
"mid": 5.59,
"hi": 7.61
} | ||
dcc760 | antilemma_k3_v1_655260480_2573 | Let $n = 82570$. Define $x = \sum_{d \mid n} \phi(d)$, where $\phi$ denotes Euler's totient function. Let $\mathcal{S}$ be the set of all real numbers $x_1$ such that
$$
x_1^2 - 7091x_1 + 678418 = 0.
$$
Compute the remainder when $x$ multiplied by the sum of all elements of $\mathcal{S}$ is divided by $76290$. | 54,410 | graphs = [
Graph(
let={
"_n": Const(82570),
"x": SumOverDivisors(n=Ref(name='_n'), var='d', expr=EulerPhi(n=Var(name='d'))),
"Q": Mod(value=Mul(SumOverSet(set=SolutionsSet(var=Var("x1"), condition=Eq(Sum(Pow(Var("x1"), Const(2)), Mul(Const(-7091), Var("x1")), Const(678418... | NT | COMB | COMPUTE | sympy | VIETA_SUM | [
"VIETA_SUM",
"IDENTITY_MUL_ZERO",
"K3"
] | 23907a | antilemma_k3_v1 | affine_mod | 4 | 0 | [
"IDENTITY_MUL_ZERO",
"K3",
"VIETA_SUM"
] | 3 | 0.002 | 2026-02-08T16:50:24.130846Z | {
"verified": true,
"answer": 54410,
"timestamp": "2026-02-08T16:50:24.133342Z"
} | 68ae22 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 149,
"completion_tokens": 1249
},
"timestamp": "2026-02-17T13:20:54.271Z",
"answer": 54410
},
... | 1 | [
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "IDENTITY_MUL_ZERO",
"status": "ok"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "K3",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"sta... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
7424f7 | diophantine_sum_product_min_v1_1820931509_726 | Let $P$ be the number of positive integers $k$ such that $1 \leq k \leq 516672$ and $144$ divides $k$. Let $S = 124$ and $n = 123$. Determine the smallest positive integer $x \leq 123$ such that
$$
x(S - x) = P.
$$
Find the value of this $x$. | 46 | graphs = [
Graph(
let={
"_n": Const(123),
"S": Const(124),
"P": CountOverSet(set=SolutionsSet(var=Var("k"), condition=And(Geq(Var("k"), Const(1)), Leq(Var("k"), Const(516672)), Divides(divisor=Const(144), dividend=Var("k"))), domain='positive_integers')),
"res... | ALG | NT | EXTREMUM | sympy | LIN_FORM | [
"C2"
] | 9685eb | diophantine_sum_product_min_v1 | null | 5 | 0 | [
"C2",
"LIN_FORM"
] | 2 | 0.072 | 2026-02-08T11:50:28.200851Z | {
"verified": true,
"answer": 46,
"timestamp": "2026-02-08T11:50:28.273323Z"
} | e8a332 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 128,
"completion_tokens": 742
},
"timestamp": "2026-02-14T19:30:44.173Z",
"answer": 46
},
{
... | 1 | [
{
"lemma": "C2",
"status": "ok"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "V1",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
}
] | {
"lo": -6.96,
"mid": -4.56,
"hi": -1.46
} | ||
9fd487 | diophantine_product_count_v1_1470522791_69 | Let $k$ be the minimum value of $x + y$ over all ordered pairs of positive integers $(x, y)$ such that $xy = 900$. Let $R$ be the number of positive integers $x$ such that $1 \leq x \leq 32$, $x$ divides $k$, and $\frac{k}{x} \leq 32$. Compute the remainder when $44121 \cdot R$ is divided by $62032$. | 6,986 | graphs = [
Graph(
let={
"k": MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(Mul(Var("x"), Var("y")), Const(900)))), expr=Sum(Var("x"), Var("y")))),
"upper": Const(32),... | NT | null | COUNT | sympy | B3 | [
"B3"
] | 0cd20d | diophantine_product_count_v1 | null | 4 | 0 | [
"B3"
] | 1 | 0.006 | 2026-02-08T12:48:41.968962Z | {
"verified": true,
"answer": 6986,
"timestamp": "2026-02-08T12:48:41.974724Z"
} | 44f359 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 143,
"completion_tokens": 1336
},
"timestamp": "2026-02-15T05:08:34.931Z",
"answer": 6986
},
{... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
}
... | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
caf277 | comb_count_permutations_fixed_v1_677425708_1831 | Let $n = 6$. Let $k$ be the number of ordered pairs $(i,j)$ of integers such that $1 \leq i \leq 4$, $1 \leq j \leq 4$, and $i + j = 4$. Define
$$
\text{result} = \binom{n}{k} \cdot !\left(n - k\right),
$$
where $!m$ denotes the number of derangements of $m$ elements. Let $Q$ be the remainder when $44121 \cdot \text{re... | 69,276 | graphs = [
Graph(
let={
"n": Const(6),
"k": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("i"), Var("j")]), condition=Eq(Sum(Var("i"), Var("j")), Const(4)), domain=CartesianProduct(left=IntegerRange(start=Const(1), end=Const(4)), right=IntegerRange(start=Const(1), end=Const(4... | COMB | null | COUNT | sympy | COUNT_SUM_EQUALS | [
"COUNT_SUM_EQUALS"
] | 75ab0f | comb_count_permutations_fixed_v1 | null | 4 | 0 | [
"COUNT_SUM_EQUALS"
] | 1 | 0.012 | 2026-02-08T04:29:16.427008Z | {
"verified": true,
"answer": 69276,
"timestamp": "2026-02-08T04:29:16.439239Z"
} | 897cf8 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 247,
"completion_tokens": 815
},
"timestamp": "2026-02-10T01:39:00.156Z",
"answer": 69276
},
{
"i... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "ok"
},
{
"lemma": "V8",
... | {
"lo": -2.46,
"mid": 0.47,
"hi": 3.59
} | ||
6e76d3 | diophantine_sum_product_min_v1_898971024_2067 | Let $n = 2116$. Let $S$ be the minimum value of $x + y$ where $x$ and $y$ are positive integers such that $xy = 2116$. Let $P = 2035$. Determine the smallest positive integer $x_1$ such that $1 \leq x_1 \leq 91$ and $x_1(S - x_1) = P$. Let $Q = 21321 - x_1$. Find the value of $Q$. | 21,284 | graphs = [
Graph(
let={
"_n": Const(2116),
"S": MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(Mul(Var("x"), Var("y")), Ref("_n")))), expr=Sum(Var("x"), Var("y")))),
... | NT | null | EXTREMUM | sympy | B3 | [
"B3"
] | 0cd20d | diophantine_sum_product_min_v1 | null | 7 | 0 | [
"B3"
] | 1 | 0.011 | 2026-02-08T16:31:30.223584Z | {
"verified": true,
"answer": 21284,
"timestamp": "2026-02-08T16:31:30.234758Z"
} | 1f6003 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 154,
"completion_tokens": 726
},
"timestamp": "2026-02-17T06:37:27.093Z",
"answer": 21284
},
{... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "V3",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
1b7eae | sequence_lucas_compute_v1_153355830_767 | Let $m = 2$ and $N = 97178$. Let $d_{\text{max}}$ be the largest positive divisor of 638 that is at most 22. Define $n$ to be the largest prime number $p$ such that $m \leq p \leq d_{\text{max}}$. Let $L_n$ denote the $n$th Lucas number. Compute the remainder when $44121 \cdot L_n$ is divided by $N$. | 63,797 | graphs = [
Graph(
let={
"_m": Const(2),
"_n": Const(97178),
"n": MaxOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Ref("_m")), Leq(Var("n"), MaxOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Const(1)), Leq(Var("d"), Const(22)), Divi... | NT | null | COMPUTE | sympy | MAX_DIVISOR | [
"MAX_DIVISOR/MAX_PRIME_BELOW"
] | 495f8b | sequence_lucas_compute_v1 | null | 4 | 0 | [
"MAX_DIVISOR",
"MAX_PRIME_BELOW"
] | 2 | 0.002 | 2026-02-08T04:09:53.386678Z | {
"verified": true,
"answer": 63797,
"timestamp": "2026-02-08T04:09:53.388188Z"
} | 4ae927 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 213,
"completion_tokens": 1197
},
"timestamp": "2026-02-10T15:39:02.349Z",
"answer": 63797
},
{
... | 1 | [
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "MAX_DIVISOR",
"status": "ok"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok_later"
},
{
"lemma": "V5",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
},
{
... | {
"lo": -3.42,
"mid": 1.86,
"hi": 7.55
} | ||
eac452 | comb_bell_compute_v1_865884756_3909 | Let $A$ be the set of all ordered pairs $(x, y)$ of positive integers such that $xy = 64$. Let $B$ be the set of all values of $x + y$ where $(x, y) \in A$. Let $m$ be the minimum element of $B$. Let $S$ be the set of all positive integers $n_1$ such that $1 \leq n_1 \leq m$ and the sum of the decimal digits of $n_1$ i... | 26,083 | graphs = [
Graph(
let={
"_n": Const(83984),
"n": CountOverSet(set=SolutionsSet(var=Var("n1"), condition=And(Geq(Var("n1"), Const(1)), Leq(Var("n1"), MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPos... | COMB | null | COMPUTE | sympy | B3 | [
"B3/L3B"
] | aaa20b | comb_bell_compute_v1 | null | 4 | 0 | [
"B3",
"L3B"
] | 2 | 0.002 | 2026-02-08T17:39:46.007357Z | {
"verified": true,
"answer": 26083,
"timestamp": "2026-02-08T17:39:46.009669Z"
} | 6532ec | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 201,
"completion_tokens": 1274
},
"timestamp": "2026-02-18T05:31:38.153Z",
"answer": 26083
},
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "L3B",
"status": "ok_later"
},
{
"lemma": "V7",
"status": "no"
}... | {
"lo": -2.38,
"mid": 1.74,
"hi": 6.59
} | ||
fbabac | comb_sum_binomial_row_v1_124444284_5214 | Let $n$ be the largest positive integer $k$ such that $2^k \leq 6121$. Compute $2^n$. | 4,096 | graphs = [
Graph(
let={
"_n": Const(2),
"n": MaxOverSet(set=SolutionsSet(var=Var("k"), condition=Leq(Pow(Ref("_n"), Var("k")), Const(6121)))),
"result": Pow(Const(2), Ref("n")),
},
goal=Ref("result"),
)
] | NT | null | SUM | sympy | MAX_VAL | [
"MAX_VAL"
] | 1da621 | comb_sum_binomial_row_v1 | null | 2 | 0 | [
"MAX_VAL"
] | 1 | 0.001 | 2026-02-08T06:27:05.783899Z | {
"verified": true,
"answer": 4096,
"timestamp": "2026-02-08T06:27:05.785263Z"
} | 251f54 | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 87,
"completion_tokens": 235
},
"timestamp": "2026-02-15T17:33:02.320Z",
"answer": 8192
},
{
"id": 11,
... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K16",
"status": "same_pattern_wrong"
},
{
"lemma": "MAX_VAL",
"status": "ok"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"... | {
"lo": -8.32,
"mid": -5.11,
"hi": -2.37
} | ||
063a7d | diophantine_fbi2_count_v1_124444284_9157 | Let $d$ be a positive integer. Define $k = 60$. Let $S$ be the set of all positive integers $k'$ such that $1 \leq k' \leq 4602$ and $78$ divides $k'$. Let $T$ be the set of all integers $d$ such that $5 \leq d \leq |S|$, $d$ divides $k$, and $4 \leq \frac{k}{d} \leq 58$. Compute the number of elements in $T$. | 5 | graphs = [
Graph(
let={
"_n": Const(58),
"k": Const(60),
"result": CountOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Const(5)), Leq(Var("d"), CountOverSet(set=SolutionsSet(var=Var("k"), condition=And(Geq(Var("k"), Const(1)), Leq(Var("k"), Const(4602)... | NT | null | COUNT | sympy | C5 | [
"C2"
] | 9685eb | diophantine_fbi2_count_v1 | null | 4 | 0 | [
"C2",
"C5"
] | 2 | 0.066 | 2026-02-08T12:15:07.892743Z | {
"verified": true,
"answer": 5,
"timestamp": "2026-02-08T12:15:07.958501Z"
} | 1d0c4c | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 159,
"completion_tokens": 944
},
"timestamp": "2026-02-14T23:28:51.068Z",
"answer": 5
},
{
... | 1 | [
{
"lemma": "C2",
"status": "ok"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
}
] | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
d93913 | nt_count_digit_sum_v1_168721529_1568 | Let $n = 7$. Define $u = \left( \sum_{d \mid n} \phi(d) \right) - n$, where $\phi$ is Euler's totient function. Let $p = 5 + u$. Define $w$ to be the remainder when $((p-1)! + 1)$ is divided by $p$. Let $\text{target\_sum} = 20 + w$. Determine the value of the number of positive integers $n$ such that $1 \leq n \leq 99... | 5,631 | graphs = [
Graph(
let={
"n": Const(7),
"u": Sub(SumOverDivisors(n=Ref(name='n'), var='d', expr=EulerPhi(n=Var(name='d'))), Ref("n")),
"p": Sum(Const(5), Ref("u")),
"w": Mod(value=Sum(Factorial(Sub(Ref("p"), Const(1))), Const(1)), modulus=Ref("p")),
... | NT | null | COUNT | sympy | EULER_TOTIENT_SUM | [
"EULER_TOTIENT_SUM",
"WILSON"
] | bd04a1 | nt_count_digit_sum_v1 | null | 4 | 2 | [
"EULER_TOTIENT_SUM",
"WILSON"
] | 2 | 3.852 | 2026-02-08T13:46:57.943027Z | {
"verified": true,
"answer": 5631,
"timestamp": "2026-02-08T13:47:01.794719Z"
} | cfb13d | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 249,
"completion_tokens": 1977
},
"timestamp": "2026-02-09T18:59:56.702Z",
"answer": 5631
},
{
"i... | 1 | [
{
"lemma": "EULER_TOTIENT_SUM",
"status": "ok"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
},
{
"lemma... | {
"lo": -6.5,
"mid": -0.2,
"hi": 6.11
} | ||
b6664f | diophantine_fbi2_min_v1_124444284_4441 | Let $m = 8$ and $n = 2$. Let $k = 26$. Define $u = \sum_{i=1}^{m} i$. Let $d$ be the smallest integer such that $d \geq 3$, $d \leq u$, $d$ divides $k$, and $\frac{k}{d} \geq n$. Compute $\sum_{j=1}^{|d|} \phi(j)$, where $\phi$ is Euler's totient function. | 58 | graphs = [
Graph(
let={
"_m": Const(8),
"_n": Const(2),
"k": Const(26),
"upper": Summation(var="k", start=Const(1), end=Ref("_m"), expr=Var("k")),
"result": MinOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Summation(var="k", st... | NT | null | EXTREMUM | sympy | SUM_ARITHMETIC | [
"SUM_ARITHMETIC",
"COPRIME_PAIRS"
] | ac053f | diophantine_fbi2_min_v1 | null | 4 | 0 | [
"COPRIME_PAIRS",
"SUM_ARITHMETIC"
] | 2 | 0.017 | 2026-02-08T06:01:36.351495Z | {
"verified": true,
"answer": 58,
"timestamp": "2026-02-08T06:01:36.368755Z"
} | dbbf7e | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 149,
"completion_tokens": 915
},
"timestamp": "2026-02-12T18:17:30.160Z",
"answer": 58
},
{
... | 1 | [
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
... | {
"lo": -7.01,
"mid": -4.68,
"hi": -2.15
} | ||
18f1b2 | nt_count_divisors_in_range_v1_784195855_1887 | Let $n = 25200$. Let $a = 16$ and let $b$ be the number of prime numbers $n$ such that $2 \leq n \leq 62861$. Compute the number of positive divisors $d$ of $n$ such that $a \leq d \leq b$, and call this count $\text{result}$. Find the remainder when $44121 \times \text{result}$ is divided by $64514$. | 39,254 | graphs = [
Graph(
let={
"_n": Const(44121),
"n": Const(25200),
"a": Const(16),
"b": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(2)), Leq(Var("n"), Const(62861)), IsPrime(Var("n"))))),
"result": CountOverSet(set=Sol... | NT | null | COUNT | sympy | COUNT_PRIMES | [
"COUNT_PRIMES"
] | 07c874 | nt_count_divisors_in_range_v1 | null | 4 | 0 | [
"COUNT_PRIMES"
] | 1 | 0.076 | 2026-02-08T05:22:58.738414Z | {
"verified": true,
"answer": 39254,
"timestamp": "2026-02-08T05:22:58.814236Z"
} | a3b022 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 143,
"completion_tokens": 4550
},
"timestamp": "2026-02-12T07:00:50.657Z",
"answer": 39254
},
... | 1 | [
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_PRIMES",
"status": "ok"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "V8",
... | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
1d453a | diophantine_product_count_v1_898971024_2603 | Let $A$ be the set of positive integers $n$ such that $1 \le n \le 771$ and $\gcd(n, 14) = 1$. Let $u$ denote the number of elements in $A$. Let $k = 720$. Determine the number of positive integers $x$ such that $1 \le x \le u$, $x$ divides $k$, and $k/x \le u$. | 26 | graphs = [
Graph(
let={
"_n": Const(771),
"k": Const(720),
"upper": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Ref("_n")), Eq(GCD(a=Var("n"), b=Const(14)), Const(1))))),
"result": CountOverSet(set=Solutions... | NT | null | COUNT | sympy | C4 | [
"C4"
] | 08d162 | diophantine_product_count_v1 | null | 5 | 0 | [
"C4"
] | 1 | 0.025 | 2026-02-08T16:52:39.081660Z | {
"verified": true,
"answer": 26,
"timestamp": "2026-02-08T16:52:39.106179Z"
} | d362e2 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 139,
"completion_tokens": 1593
},
"timestamp": "2026-02-17T14:07:25.427Z",
"answer": 26
},
{
... | 1 | [
{
"lemma": "C4",
"status": "ok"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "VAL_SUM_EQ",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} |
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