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 |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
f5e8f6 | geo_visible_lattice_v1_1431428450_1059 | Let $n = 64$. Define $V$ as the number of ordered pairs $(x, y)$ of positive integers such that $1 \leq x, y \leq n$ and $\gcd(x, y) = 1$. Compute the remainder when $48596 \cdot V$ is divided by $51257$. | 11,608 | graphs = [
Graph(
let={
"n": Const(64),
"result": VisibleLatticePoints(n=Ref(name='n')),
"_c": Const(48596),
"Q": Mod(value=Mul(Ref("_c"), Ref("result")), modulus=Const(51257)),
},
goal=Ref("Q"),
)
] | GEOM | null | COUNT | sympy | [] | geo_visible_lattice_v1 | null | 4 | 0 | null | null | 0.752 | 2026-02-08T13:52:54.732606Z | {
"verified": true,
"answer": 11608,
"timestamp": "2026-02-08T13:52:55.484919Z"
} | 99440f | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 181,
"completion_tokens": 4999
},
"timestamp": "2026-02-24T19:17:11.837Z",
"answer": 11608
},
{
"... | 1 | [] | {
"lo": -2.37,
"mid": 1.22,
"hi": 4.84
} | ||||
2d0f1c | sequence_fibonacci_compute_v1_1742523217_1308 | Let $T$ be the set of all integers $t$ such that $24 \leq t \leq 66$ and $t = 6a + 9b + 9$ for some positive integers $a,b$ with $1 \leq a \leq 5$ and $1 \leq b \leq 3$. Let $n$ be the number of ordered triples $(x_1, x_2, x_3)$ of positive odd integers such that $x_1 + x_2 + x_3 = |T|$. Let $F_n$ denote the $n$-th Fib... | 47,266 | graphs = [
Graph(
let={
"_n": CountOverSet(set=SolutionsSet(var=Var("t"), condition=Exists(var=Var(name='a'), condition=Exists(var=Var(name='b'), condition=And(Geq(left=Var(name='a'), right=Const(value=1)), Leq(left=Var(name='a'), right=Const(value=5)), Geq(left=Var(name='b'), right=Const(value=... | NT | null | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM/COMB1"
] | 268a62 | sequence_fibonacci_compute_v1 | null | 6 | 0 | [
"COMB1",
"LIN_FORM"
] | 2 | 0.004 | 2026-02-08T03:36:02.299228Z | {
"verified": true,
"answer": 47266,
"timestamp": "2026-02-08T03:36:02.302819Z"
} | 823bf4 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 280,
"completion_tokens": 4448
},
"timestamp": "2026-02-10T06:33:25.089Z",
"answer": 47266
},
{
"... | 1 | [
{
"lemma": "COMB1",
"status": "ok_later"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "V3",
"status": "no"
},... | {
"lo": -3.46,
"mid": 1.03,
"hi": 5.49
} | ||
118ead | sequence_count_fib_divisible_v1_1248542787_406 | Let $S$ be the set of all integers $t$ such that $11 \leq t \leq 752$ and there exist positive integers $a$ and $b$ with $1 \leq a \leq 160$, $1 \leq b \leq 16$, and $t = 4a + 7b$. Let $N$ be the number of elements in $S$. Compute the number of positive integers $n$ such that $1 \leq n \leq N$ and the $n$th Fibonacci n... | 120 | graphs = [
Graph(
let={
"upper": CountOverSet(set=SolutionsSet(var=Var("t"), condition=Exists(var=Var(name='a'), condition=Exists(var=Var(name='b'), condition=And(Geq(left=Var(name='a'), right=Const(value=1)), Leq(left=Var(name='a'), right=Const(value=160)), Geq(left=Var(name='b'), right=Const(v... | NT | null | COUNT | sympy | MOBIUS_COPRIME | [
"LIN_FORM"
] | 7b2633 | sequence_count_fib_divisible_v1 | null | 5 | 0 | [
"LIN_FORM",
"MOBIUS_COPRIME"
] | 2 | 0.202 | 2026-02-08T03:06:54.712174Z | {
"verified": true,
"answer": 120,
"timestamp": "2026-02-08T03:06:54.914245Z"
} | 477c37 | 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": 6804
},
"timestamp": "2026-02-09T03:47:53.535Z",
"answer": 120
},
{
"id... | 1 | [
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "V8_SUM",
"status": "no"
},
{
"lemma": "VAL_SUM_EQ",
"status": "no"
}
... | {
"lo": 1.1,
"mid": 4.17,
"hi": 6.61
} | ||
282439 | nt_count_with_divisor_count_v1_397696148_2251 | Let $S$ be the set of all nonnegative integers $j$ such that $0 \leq j \leq 200$ and $\binom{200}{j}$ is odd. Let $d$ be the largest prime number satisfying $2 \leq d \leq |S|$. Let $U$ be the set of all positive integers $n$ such that $1 \leq n \leq 32400$ and the number of positive divisors of $n$ is equal to $d$. Co... | 28,350 | graphs = [
Graph(
let={
"_n": Const(88349),
"upper": Const(32400),
"div_count": MaxOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(2)), Leq(Var("n"), CountOverSet(set=SolutionsSet(var=Var("j"), condition=And(Geq(Var("j"), Const(0)), Leq(Var("j"), ... | NT | null | COUNT | sympy | V8 | [
"V8/MAX_PRIME_BELOW"
] | 3b83f5 | nt_count_with_divisor_count_v1 | null | 7 | 0 | [
"MAX_PRIME_BELOW",
"V8"
] | 2 | 1.466 | 2026-02-08T13:03:01.582649Z | {
"verified": true,
"answer": 28350,
"timestamp": "2026-02-08T13:03:03.048471Z"
} | 6afc28 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 176,
"completion_tokens": 1046
},
"timestamp": "2026-02-15T09:09:23.147Z",
"answer": 28350
},
... | 1 | [
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok_later"
},
{
"lemma": "MAX_VAL",
"status... | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
1f8007 | modular_inverse_v1_865884756_2635 | Let $a = 969$ and $m = 1117$. Let $u$ be the number of integers $t$ such that $9 \leq t \leq 1136$ and there exist positive integers $a'$ and $b'$ with $1 \leq a' \leq 159$, $1 \leq b' \leq 100$, and $t = 4a' + 5b'$. Find the smallest positive integer $x$ such that $1 \leq x \leq u$ and $ax \equiv 1 \pmod{m}$. | 400 | graphs = [
Graph(
let={
"a": Const(969),
"m": Const(1117),
"upper": CountOverSet(set=SolutionsSet(var=Var("t"), condition=Exists(var=Var(name='a'), condition=Exists(var=Var(name='b'), condition=And(Geq(left=Var(name='a'), right=Const(value=1)), Leq(left=Var(name='a'), rig... | NT | null | EXTREMUM | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | modular_inverse_v1 | null | 5 | 0 | [
"LIN_FORM"
] | 1 | 0.098 | 2026-02-08T16:51:44.941978Z | {
"verified": true,
"answer": 400,
"timestamp": "2026-02-08T16:51:45.039525Z"
} | a624ae | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 169,
"completion_tokens": 4821
},
"timestamp": "2026-02-17T12:53:53.194Z",
"answer": 400
},
{
... | 1 | [
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
1d3087 | nt_count_intersection_v1_1353956133_55 | Let $N$ be the number of positive integers $n$ such that $1 \leq n \leq 18749$ and $\gcd(n, 15) = 1$. Let $T$ be the set of all positive integers $n$ such that $1 \leq n \leq N$, $n$ is divisible by 9, and $\gcd(n, 22) = 1$. Compute the number of elements in $T$. | 505 | graphs = [
Graph(
let={
"_n": Const(15),
"N": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Const(18749)), Eq(GCD(a=Var("n"), b=Ref("_n")), Const(1))))),
"a": Const(9),
"b": Const(22),
"result": Co... | NT | null | COUNT | sympy | C4 | [
"C4"
] | 08d162 | nt_count_intersection_v1 | null | 4 | 0 | [
"C4"
] | 1 | 0.571 | 2026-02-08T11:17:10.167801Z | {
"verified": true,
"answer": 505,
"timestamp": "2026-02-08T11:17:10.739188Z"
} | 512d6f | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 140,
"completion_tokens": 1125
},
"timestamp": "2026-02-14T11:26:44.359Z",
"answer": 505
},
{
... | 1 | [
{
"lemma": "C4",
"status": "ok"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "V1",
"status": "no"
}
] | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
33b516 | antilemma_cartesian_v1_1439011603_1879 | Let $x$ be the number of ordered pairs $(a, b)$ such that $1 \leq a \leq 17$ and $1 \leq b \leq 20$. Find the remainder when $x^2 + 4x + 225$ is divided by 73115. | 44,070 | graphs = [
Graph(
let={
"x": CountOverSet(set=CartesianProduct(left=IntegerRange(start=Const(1), end=Const(17)), right=IntegerRange(start=Const(1), end=Const(20)))),
"Q": Mod(value=Sum(Pow(Ref("x"), Const(2)), Mul(Const(4), Ref("x")), Const(225)), modulus=Const(73115)),
},
... | COMB | GEOM | COMPUTE | sympy | COUNT_CARTESIAN | [
"COUNT_CARTESIAN"
] | 409d7d | antilemma_cartesian_v1 | null | 2 | 0 | [
"COUNT_CARTESIAN"
] | 1 | 0.001 | 2026-02-08T16:20:37.980417Z | {
"verified": true,
"answer": 44070,
"timestamp": "2026-02-08T16:20:37.981325Z"
} | 10a838 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 175,
"completion_tokens": 395
},
"timestamp": "2026-02-24T20:43:18.274Z",
"answer": 44070
},
{
"... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "ok"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
}
] | {
"lo": -8.52,
"mid": -5.43,
"hi": -3.2
} | ||
c7eab6 | antilemma_v7_kummer_168721529_1577 | Let $n = 4898$. Compute the largest integer $k$ such that $2^k$ divides $\binom{n}{1959}$. | 12 | graphs = [
Graph(
let={
"_n": Const(4898),
"x": MaxKDivides(target=Binom(n=Ref("_n"), k=Const(1959)), base=Const(2)),
},
goal=Ref("x"),
)
] | NT | null | COMPUTE | sympy | B3 | [
"V7"
] | 0672d4 | antilemma_v7_kummer | null | 6 | 0 | [
"B3",
"V7"
] | 2 | 0.013 | 2026-02-08T13:47:19.713652Z | {
"verified": true,
"answer": 12,
"timestamp": "2026-02-08T13:47:19.726219Z"
} | 13456c | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 143,
"completion_tokens": 1034
},
"timestamp": "2026-02-09T19:03:50.008Z",
"answer": 12
},
{
"id"... | 1 | [
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "V3",
"status": "no"
},
{
"lemma": "V7",
"status": "ok"
}
] | {
"lo": -6.5,
"mid": -0.2,
"hi": 6.11
} | ||
7d917f | comb_count_surjections_v1_655260480_2308 | Let $T$ be the set of all integers $t$ with $10 \leq t \leq 28$ such that $t = 4a + 6b$ for some integers $a, b$ with $1 \leq a \leq 4$ and $1 \leq b \leq 2$. Let $s$ be the number of such integers $t$. Let $n$ be the number of ordered pairs of positive odd integers $(x_1, x_2)$ such that $x_1 + x_2 = s$. Let $k$ be th... | 23,256 | graphs = [
Graph(
let={
"n": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x1"), Var("x2")]), condition=And(IsPositive(arg=Var(name='x1')), IsPositive(arg=Var(name='x2')), IsOdd(arg=Var(name='x1')), IsOdd(arg=Var(name='x2')), Eq(Sum(Var("x1"), Var("x2")), CountOverSet(set=SolutionsSet(v... | COMB | null | COUNT | sympy | LIN_FORM | [
"LIN_FORM/COMB1"
] | 268a62 | comb_count_surjections_v1 | null | 7 | 0 | [
"COMB1",
"LIN_FORM"
] | 2 | 0.006 | 2026-02-08T16:39:57.438283Z | {
"verified": true,
"answer": 23256,
"timestamp": "2026-02-08T16:39:57.444643Z"
} | 13d5e3 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 250,
"completion_tokens": 1591
},
"timestamp": "2026-02-17T08:30:18.703Z",
"answer": 23256
},
... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COMB1",
"status": "ok_later"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "V7",
"status": "... | {
"lo": -2.38,
"mid": 1.74,
"hi": 6.59
} | ||
e3bf8d | algebra_quadratic_discriminant_v1_1915831931_2099 | Let $S$ be the set of all ordered pairs $(x,y)$ of positive integers such that $xy = 4$. Let $s_{\text{min}}$ be the minimum value of $x + y$ over all such pairs. Compute $40320 - ( (-20)^2 - (-1) \cdot (-100) \cdot s_{\text{min}} )$. | 40,320 | graphs = [
Graph(
let={
"_n": Const(2),
"a": Const(-1),
"b": Const(-20),
"c": Const(-100),
"result": Sub(Pow(Ref("b"), Ref("_n")), Mul(MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg... | NT | null | COMPUTE | sympy | B3 | [
"B3"
] | 0cd20d | algebra_quadratic_discriminant_v1 | null | 3 | 0 | [
"B3"
] | 1 | 0.003 | 2026-02-08T16:36:36.387147Z | {
"verified": true,
"answer": 40320,
"timestamp": "2026-02-08T16:36:36.389676Z"
} | d11213 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 125,
"completion_tokens": 376
},
"timestamp": "2026-02-17T07:40:07.485Z",
"answer": 40320
},
{... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
b54229 | comb_factorial_compute_v1_124444284_1021 | Let $n$ be the smallest divisor of $3773$ that is at least $2$. Compute $n!$, and then compute $87025 - n!$. Find the value of $87025 - n!$. | 81,985 | graphs = [
Graph(
let={
"_n": Const(2),
"n": MinOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Ref("_n")), Divides(divisor=Var("d"), dividend=Const(3773))))),
"result": Factorial(Ref("n")),
"Q": Sub(Const(87025), Ref("result")),
},
... | NT | null | COMPUTE | sympy | MIN_PRIME_FACTOR | [
"MIN_PRIME_FACTOR"
] | bc3776 | comb_factorial_compute_v1 | null | 3 | 0 | [
"MIN_PRIME_FACTOR"
] | 1 | 0.001 | 2026-02-08T03:39:09.417537Z | {
"verified": true,
"answer": 81985,
"timestamp": "2026-02-08T03:39:09.418954Z"
} | 65e733 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 156,
"completion_tokens": 297
},
"timestamp": "2026-02-10T01:29:29.453Z",
"answer": 81985
},
{
"i... | 1 | [
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MIN_PRIME_FACTOR",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status... | {
"lo": -3.46,
"mid": 1.03,
"hi": 5.49
} | ||
1d6b24 | nt_count_with_divisor_count_v1_809748730_1895 | Let $d$ be the number of prime numbers $n$ such that $2 \leq n \leq 43$. Determine the number of positive integers $n$ such that $1 \leq n \leq 72361$ and the number of positive divisors of $n$ is exactly $d$. Compute this value. | 215 | graphs = [
Graph(
let={
"_n": Const(2),
"upper": Const(72361),
"div_count": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Ref("_n")), Leq(Var("n"), Const(43)), IsPrime(Var("n"))))),
"result": CountOverSet(set=SolutionsSet(var=Var("n")... | NT | null | COUNT | sympy | COUNT_PRIMES | [
"COUNT_PRIMES"
] | 07c874 | nt_count_with_divisor_count_v1 | null | 5 | 0 | [
"COUNT_PRIMES"
] | 1 | 3.788 | 2026-02-08T12:44:59.995412Z | {
"verified": true,
"answer": 215,
"timestamp": "2026-02-08T12:45:03.783839Z"
} | dce0ce | 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": 2212
},
"timestamp": "2026-02-15T04:28:32.906Z",
"answer": 215
},
{
... | 1 | [
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "COUNT_PRIMES",
"status": "ok"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
}
... | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
733faa | nt_min_with_divisor_count_v1_798873815_261 | Let $n = 3$. Define $T$ as the set of all integers $t$ such that $18 \leq t \leq 1140$ and there exist positive integers $a \leq 199$ and $b \leq 67$ satisfying $t = 4a + 5b + 9$. Let $\text{upper}$ be the number of elements in $T$. Let $s = \sum_{k=1}^{n} k$. Determine the value of the smallest positive integer $n'$ s... | 12 | graphs = [
Graph(
let={
"_n": Const(3),
"upper": CountOverSet(set=SolutionsSet(var=Var("t"), condition=Exists(var=Var(name='a'), condition=Exists(var=Var(name='b'), condition=And(Geq(left=Var(name='a'), right=Const(value=1)), Leq(left=Var(name='a'), right=Const(value=199)), Geq(left=... | NT | null | EXTREMUM | sympy | MAX_PRIME_BELOW | [
"SUM_ARITHMETIC",
"LIN_FORM"
] | 7209d0 | nt_min_with_divisor_count_v1 | null | 6 | 0 | [
"LIN_FORM",
"MAX_PRIME_BELOW",
"SUM_ARITHMETIC"
] | 3 | 0.586 | 2026-02-08T02:31:57.320547Z | {
"verified": true,
"answer": 12,
"timestamp": "2026-02-08T02:31:57.906455Z"
} | 9234cd | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 251,
"completion_tokens": 19709
},
"timestamp": "2026-02-23T14:27:58.917Z",
"answer": 12
},
{
"id... | 1 | [
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "SUM_ARITHMETIC",
"status": "ok"
},
{
"lemma": "V1",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
},
... | {
"lo": -6.29,
"mid": -4.59,
"hi": -2.79
} | ||
44202a | antilemma_k2_v1_865884756_7178 | Let $x = \sum_{k=1}^{104} \phi(k) \left\lfloor \frac{104}{k} \right\rfloor$, where $\phi(k)$ denotes Euler's totient function. Compute the remainder when $95847 \cdot x$ is divided by $72172$. | 5,448 | graphs = [
Graph(
let={
"_n": Const(104),
"x": Summation(var="k", start=Const(1), end=Const(104), expr=Mul(EulerPhi(n=Var("k")), Floor(Div(Ref("_n"), Var("k"))))),
"_c": Const(95847),
"Q": Mod(value=Mul(Ref("_c"), Ref("x")), modulus=Const(72172)),
},
... | NT | COMB | COMPUTE | sympy | K2 | [
"K2"
] | 6897ab | antilemma_k2_v1 | null | 5 | 0 | [
"K2"
] | 1 | 0.001 | 2026-02-08T19:39:22.725886Z | {
"verified": true,
"answer": 5448,
"timestamp": "2026-02-08T19:39:22.726627Z"
} | 13274e | 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": 1891
},
"timestamp": "2026-02-18T23:03:24.595Z",
"answer": 5448
},
{... | 1 | [
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "K2",
"status": "ok"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
2d1861 | nt_gcd_compute_v1_677425708_1215 | Let $p = 5$, and define $e = ( (p-1)! + 1 ) \bmod p$. Let $n = \phi(2)$, where $\phi$ is Euler's totient function, and let $h$ be the number of prime factors of $n$ counted with multiplicity. Let $a = 210222$ and $b = 490518 + e + h$. Compute $\gcd(a, b)$, then multiply the result by $64335$ and take the remainder when... | 86,840 | graphs = [
Graph(
let={
"p": Const(5),
"e": Mod(value=Sum(Factorial(Sub(Ref("p"), Const(1))), Const(1)), modulus=Ref("p")),
"n": EulerPhi(n=Const(2)),
"h": BigOmega(n=Ref(name='n')),
"a": Const(210222),
"b": Sum(Const(490518), Ref("e"),... | NT | null | COMPUTE | sympy | BIG_OMEGA_ZERO | [
"BIG_OMEGA_ZERO",
"WILSON",
"ONE_PHI_2"
] | d1c2a4 | nt_gcd_compute_v1 | null | 4 | 2 | [
"BIG_OMEGA_ZERO",
"ONE_PHI_2",
"WILSON"
] | 3 | 0.004 | 2026-02-08T04:02:15.526074Z | {
"verified": true,
"answer": 86840,
"timestamp": "2026-02-08T04:02:15.530518Z"
} | d488b6 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 234,
"completion_tokens": 2200
},
"timestamp": "2026-02-09T17:09:36.681Z",
"answer": 86840
},
{
"... | 1 | [
{
"lemma": "BIG_OMEGA_ZERO",
"status": "ok"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "... | {
"lo": -6.5,
"mid": -0.2,
"hi": 6.11
} | ||
ddce1d | nt_num_divisors_compute_v1_397696148_2375 | Compute the number of positive divisors of the number of elements in the Cartesian product of the sets $\{1, 2, 3, 4, 5\}$ and $\{1, 2, \dots, 10\}$. | 6 | graphs = [
Graph(
let={
"n": CountOverSet(set=CartesianProduct(left=IntegerRange(start=Const(1), end=Const(5)), right=IntegerRange(start=Const(1), end=Const(10)))),
"result": NumDivisors(n=Ref("n")),
},
goal=Ref("result"),
)
] | NT | null | COMPUTE | sympy | COUNT_CARTESIAN | [
"COUNT_CARTESIAN"
] | 409d7d | nt_num_divisors_compute_v1 | null | 2 | 0 | [
"COUNT_CARTESIAN"
] | 1 | 0.003 | 2026-02-08T13:08:03.345619Z | {
"verified": true,
"answer": 6,
"timestamp": "2026-02-08T13:08:03.348146Z"
} | 80b538 | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 105,
"completion_tokens": 347
},
"timestamp": "2026-02-16T04:30:47.855Z",
"answer": 6
},
{
"id": 11,
"... | 2 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "ok"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"sta... | {
"lo": -9.12,
"mid": -6.02,
"hi": -3.62
} | ||
19e7ba | modular_count_residue_v1_1439011603_2116 | Let $r = \sum_{k=0}^{7} (-1)^k \binom{7}{k}$, where the lower limit of summation is interpreted as the value of $\sum_{k_1=0}^{8} (-1)^{k_1} \binom{8}{k_1}$. Let $m = 5$ and $U = 66564$. Compute the number of positive integers $n \leq U$ such that $n \equiv r \pmod{m}$. | 13,312 | graphs = [
Graph(
let={
"upper": Const(66564),
"m": Const(5),
"r": Summation(var="k", start=Summation(var="k1", start=Const(0), end=Const(8), expr=Mul(Pow(Const(-1), Var("k1")), Binom(n=Const(8), k=Var("k1")))), end=Const(7), expr=Mul(Pow(Const(-1), Var("k")), Binom(n=Con... | COMB | null | COUNT | sympy | BINOMIAL_ALTERNATING | [
"BINOMIAL_ALTERNATING"
] | c21569 | modular_count_residue_v1 | null | 4 | 0 | [
"BINOMIAL_ALTERNATING"
] | 1 | 3.964 | 2026-02-08T16:31:07.666017Z | {
"verified": true,
"answer": 13312,
"timestamp": "2026-02-08T16:31:11.629609Z"
} | 0c4b70 | 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": 1051
},
"timestamp": "2026-02-24T21:43:06.610Z",
"answer": 13312
},
... | 1 | [
{
"lemma": "BINOMIAL_ALTERNATING",
"status": "ok"
},
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8",
"status":... | {
"lo": -8.52,
"mid": -5.43,
"hi": -3.2
} | ||
9219f0 | comb_count_partitions_v1_153355830_2595 | Let $n$ be the minimum value of $x + y$ over all pairs of positive integers $(x, y)$ such that $xy = 361$. Let $p(n)$ denote the number of integer partitions of $n$. Compute the remainder when $44121 \cdot p(n)$ is divided by $90038$. | 3,391 | graphs = [
Graph(
let={
"_n": Const(90038),
"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(361)))), expr=Sum(Var("x"), Var("y")))),... | COMB | null | COUNT | sympy | B3 | [
"B3"
] | 0cd20d | comb_count_partitions_v1 | null | 6 | 0 | [
"B3"
] | 1 | 0.001 | 2026-02-08T07:14:23.893152Z | {
"verified": true,
"answer": 3391,
"timestamp": "2026-02-08T07:14:23.894202Z"
} | b8309d | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 178,
"completion_tokens": 4020
},
"timestamp": "2026-02-24T07:46:45.705Z",
"answer": 3391
},
{
"i... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
}
] | {
"lo": 1.15,
"mid": 4.18,
"hi": 6.61
} | ||
d0d4c7 | alg_linear_system_2x2_v1_601307018_8799 | Let $\det = 8 \cdot (-16) - (-12) \cdot (-9)$, $M = 14406 \cdot (-16) - (-7980) \cdot (-9)$, and $R = \left|\{ (a, b) : a \geq 1, a \leq 30, b \geq 1, b \leq 30, a \leq b, 2b^2 - 4ab + 2a^2 = 968 \}\right| \cdot (-7980) - (-12) \cdot 14406$. Compute $\frac{M}{\det} + \frac{R}{\det}$. | 819 | graphs = [
Graph(
let={
"_n": Const(30),
"num_x": Sub(Mul(Const(14406), Const(-16)), Mul(Const(-7980), Const(-9))),
"num_y": Sub(Mul(CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("a"), Var("b")]), condition=And(Geq(Var("a"), Const(1)), Leq(Var("a"), Const(30)), Ge... | ALG | null | COMPUTE | sympy | QF_PSD_ORBIT | [
"QF_PSD_ORBIT"
] | 1d37f3 | alg_linear_system_2x2_v1 | null | 6 | 0 | [
"QF_PSD_ORBIT"
] | 1 | 0.007 | 2026-03-10T09:15:40.388505Z | {
"verified": true,
"answer": 819,
"timestamp": "2026-03-10T09:15:40.395123Z"
} | 6c21ef | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 264,
"completion_tokens": 1440
},
"timestamp": "2026-04-19T09:48:46.085Z",
"answer": 819
},
{
"i... | 2 | [
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "QF_PSD_ORBIT",
"status": "ok"
}
] | {
"lo": -10,
"mid": -5.89,
"hi": -1.79
} | ||
a5e834 | nt_euler_phi_compute_v1_151522320_299 | Let $n = 40320$. Compute $\varphi(n)$, the number of positive integers less than or equal to $n$ that are relatively prime to $n$. Let $d_{\text{min}}$ be the smallest divisor of $1859$ that is at least $2$. Define $Q$ to be the Bell number $B_k$, where $k$ is the remainder when $|\varphi(n)|$ is divided by $d_{\text{m... | 21,147 | graphs = [
Graph(
let={
"_n": Const(1859),
"n": Const(40320),
"result": EulerPhi(n=Ref("n")),
"Q": Bell(Mod(value=Abs(arg=Ref(name='result')), modulus=MinOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Const(2)), Divides(divisor=Var("d"), di... | NT | COMB | COMPUTE | sympy | MIN_PRIME_FACTOR | [
"MIN_PRIME_FACTOR"
] | 58d7e9 | nt_euler_phi_compute_v1 | bell_mod | 6 | 0 | [
"MIN_PRIME_FACTOR"
] | 1 | 0.001 | 2026-02-08T03:08:52.980157Z | {
"verified": true,
"answer": 21147,
"timestamp": "2026-02-08T03:08:52.981352Z"
} | afe667 | 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": 2287
},
"timestamp": "2026-02-10T13:08:18.403Z",
"answer": 21147
},
{
"... | 1 | [
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "MIN_PRIME_FACTOR",
"status": "ok"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
}
] | {
"lo": -3.47,
"mid": 0.81,
"hi": 4.81
} | ||
e68655 | modular_count_residue_v1_1439011603_1224 | Let $n = 17956$ and $m = 20$. Let $d$ be a positive integer at most $14$ such that $d$ divides the number of integers $t$ with $5 \leq t \leq 272$ for which there exist positive integers $a$ and $b$ satisfying $1 \leq a \leq 40$, $1 \leq b \leq 64$, and $t = 2a + 3b$. Let $r$ be the largest such $d$. Let $\text{result}... | 14,392 | graphs = [
Graph(
let={
"_n": Const(17956),
"upper": Const(71289),
"m": Const(20),
"r": MaxOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Const(1)), Leq(Var("d"), Const(14)), Divides(divisor=Var("d"), dividend=CountOverSet(set=SolutionsSet(... | NT | null | COUNT | sympy | LIN_FORM | [
"LIN_FORM/MAX_DIVISOR"
] | 8c55ae | modular_count_residue_v1 | null | 6 | 0 | [
"LIN_FORM",
"MAX_DIVISOR"
] | 2 | 2.773 | 2026-02-08T15:58:46.731781Z | {
"verified": true,
"answer": 14392,
"timestamp": "2026-02-08T15:58:49.504846Z"
} | 91bb6f | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 208,
"completion_tokens": 2978
},
"timestamp": "2026-02-16T18:33:40.585Z",
"answer": 14392
},
... | 1 | [
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "MAX_DIVISOR",
"status": "ok_later"
},
{
"lemma": "V3",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
},
{
"lemm... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
7c7539 | nt_count_gcd_equals_v1_784195855_6688 | Let $S$ be the set of all ordered pairs $(x,y)$ of positive integers such that $xy = 25281$. Define $k$ to be the minimum value of $x + y$ as $(x,y)$ ranges over $S$. Let $d$ be the largest prime number less than or equal to 57. Let $T$ be the set of all positive integers $n$ such that $1 \le n \le 10816$ and $\gcd(n, ... | 64,193 | graphs = [
Graph(
let={
"_n": Const(2),
"upper": Const(10816),
"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(25281))))... | NT | null | COUNT | sympy | MAX_PRIME_BELOW | [
"MAX_PRIME_BELOW",
"B3"
] | 78ed98 | nt_count_gcd_equals_v1 | null | 6 | 0 | [
"B3",
"MAX_PRIME_BELOW"
] | 2 | 0.849 | 2026-02-08T08:47:07.350990Z | {
"verified": true,
"answer": 64193,
"timestamp": "2026-02-08T08:47:08.200079Z"
} | bfcb6f | 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": 1403
},
"timestamp": "2026-02-13T21:51:54.942Z",
"answer": 64193
},
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok"
},
{
"lemma": "V5",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
},
{
... | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
064bfa | diophantine_product_count_v1_655260480_1685 | Let
$$
m = \sum_{k=1}^{5} \phi(k) \left\lfloor \frac{5}{k} \right\rfloor
$$
and
$$
k = \sum_{k=1}^{m} \phi(k) \left\lfloor \frac{15}{k} \right\rfloor.
$$
Let $S$ be the set of all positive integers $x$ such that $1 \leq x \leq 17$, $x$ divides $k$, and $\frac{k}{x} \leq 17$.
Compute the number of elements in $S$. | 4 | graphs = [
Graph(
let={
"_m": Const(15),
"_n": Summation(var="k1", start=Const(1), end=Const(5), expr=Mul(EulerPhi(n=Var("k1")), Floor(Div(Const(5), Var("k1"))))),
"k": Summation(var="k2", start=Const(1), end=Ref("_n"), expr=Mul(EulerPhi(n=Var("k2")), Floor(Div(Ref("_m"),... | NT | null | COUNT | sympy | K2 | [
"K2/K2"
] | ddede2 | diophantine_product_count_v1 | null | 6 | 0 | [
"K2"
] | 1 | 0.008 | 2026-02-08T16:17:30.505486Z | {
"verified": true,
"answer": 4,
"timestamp": "2026-02-08T16:17:30.513957Z"
} | 5b43d3 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 171,
"completion_tokens": 1569
},
"timestamp": "2026-02-17T00:08:43.814Z",
"answer": 4
},
{
... | 1 | [
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "K2",
"status": "ok"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "V1",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
a6724d | antilemma_v7_kummer_798873815_395 | Let $x$ be the largest integer $k$ such that $2^k$ divides $\binom{190}{76}$. Let $A$ be the set of all integers $n$ such that $1 \le n \le 5021$ and $\gcd(n,20)=1$, and let $B$ be the set of all integers $n$ such that $2 \le n \le |A|$ and $n$ is prime. Let $M$ be the maximum element of $B$.
Define
$$Q = \left(x \bmo... | 2,004 | graphs = [
Graph(
let={
"_c": Const(190),
"_m": Const(2),
"_n": Const(2),
"x": MaxKDivides(target=Binom(n=Ref("_c"), k=Const(76)), base=Ref("_n")),
"Q": Sum(Mod(value=Ref("x"), modulus=Const(251)), Mul(MaxOverSet(set=SolutionsSet(var=Var("n"), cond... | NT | null | COMPUTE | sympy | C4 | [
"C4/MAX_PRIME_BELOW",
"V7"
] | c9c4f2 | antilemma_v7_kummer | two_moduli | 6 | 0 | [
"C4",
"MAX_PRIME_BELOW",
"V7"
] | 3 | 0.002 | 2026-02-08T02:37:44.418931Z | {
"verified": true,
"answer": 2004,
"timestamp": "2026-02-08T02:37:44.421022Z"
} | 3029d3 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 263,
"completion_tokens": 2040
},
"timestamp": "2026-02-08T19:28:00.710Z",
"answer": 2004
},
{
"i... | 1 | [
{
"lemma": "C4",
"status": "ok"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok_later"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "V3",
"status": "no"
},
{
... | {
"lo": -1.89,
"mid": 1.79,
"hi": 4.93
} | ||
b3d95b | algebra_vieta_sum_v1_458359167_16 | Let $n = 30012$. Define $S$ as the set of all integers $x$ such that
$$
x^4 - 7x^3 - 58x^2 + \left(\sum_{y \in T} y\right)x - 384 = 0,
$$
where $T$ is the set of all integers $y$ satisfying $y^2 - 448y + n = 0$.
Compute the sum of all elements in $S$. | 7 | graphs = [
Graph(
let={
"_n": Const(30012),
"result": SumOverSet(set=SolutionsSet(var=Var("x"), condition=Eq(Sum(Pow(Var("x"), Const(4)), Mul(Const(-7), Pow(Var("x"), Const(3))), Mul(Const(-58), Pow(Var("x"), Const(2))), Mul(SumOverSet(set=SolutionsSet(var=Var("x"), condition=Eq(Sum(... | NT | null | COMPUTE | sympy | VIETA_SUM | [
"VIETA_SUM"
] | b33a7a | algebra_vieta_sum_v1 | null | 6 | 0 | [
"VIETA_SUM"
] | 1 | 0.167 | 2026-02-08T02:57:04.720855Z | {
"verified": true,
"answer": 7,
"timestamp": "2026-02-08T02:57:04.887535Z"
} | 0f4d71 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 218,
"completion_tokens": 2740
},
"timestamp": "2026-02-08T20:13:12.510Z",
"answer": 7
},
{
"id":... | 1 | [
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "V1",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
},
{
"lemma": "VIETA_SUM",
"status": "ok"
}
] | {
"lo": -2.11,
"mid": 0.26,
"hi": 2.32
} | ||
9c7e79 | nt_count_coprime_v1_124444284_8197 | Let $S$ be the set of all ordered pairs $(k, j)$ of positive integers such that $1 \leq k \leq 5$ and $1 \leq j \leq 6$. Define $k_0 = \frac{8}{48} \sum_{(k,j) \in S} k$. Let $N = 65536$. Determine the number of positive integers $n$ such that $1 \leq n \leq N$ and $\gcd(n, k_0) = 1$. | 34,953 | graphs = [
Graph(
let={
"upper": Const(65536),
"k": Div(Mul(Const(8), SumOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("k"), Var("_j")]), condition=Const(1), domain=CartesianProduct(left=IntegerRange(start=Const(1), end=Const(5)), right=IntegerRange(start=Const(1), ... | NT | null | COUNT | sympy | SUM_INDEPENDENT | [
"SUM_INDEPENDENT",
"SUM_ARITHMETIC"
] | 9f7183 | nt_count_coprime_v1 | null | 5 | 0 | [
"SUM_ARITHMETIC",
"SUM_INDEPENDENT"
] | 2 | 5.511 | 2026-02-08T09:35:47.236361Z | {
"verified": true,
"answer": 34953,
"timestamp": "2026-02-08T09:35:52.747650Z"
} | 1e8d2c | 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": 956
},
"timestamp": "2026-02-14T05:05:59.228Z",
"answer": 34953
},
{... | 1 | [
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "SUM_ARITHMETIC",
"status": "ok"
},
{
"lemma": "SUM_INDEPENDENT",
"status": "ok"
},
{
"lemma": "V3",
... | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
537a03 | alg_telescope_v1_1218484723_6668 | Let $T$ be the number of ordered pairs $(a, b)$ of positive integers with $1 \le a, b \le 25$ such that
$$
10a^2 - 18ab + 25b^2 \le 10858.
$$
Let $p$ be the largest prime number less than or equal to $3666$. Compute the remainder when
$$
\sum_{k=0}^{T} (4k^3 + 6k^2 + 4k + 1)
$$
is divided by $p$, and then compute $16... | 13,110 | graphs = [
Graph(
let={
"_m": Const(3),
"_n": Const(25),
"result": Mod(value=Summation(var="k", start=Const(0), end=CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("a"), Var("b")]), condition=And(Geq(Var("a"), Const(1)), Leq(Var("a"), Const(25)), Geq(Var("b"), Const... | NT | null | COMPUTE | sympy | QF_PSD_COUNT_LEQ | [
"QF_PSD_COUNT_LEQ",
"MAX_PRIME_BELOW"
] | db0606 | alg_telescope_v1 | null | 5 | 0 | [
"MAX_PRIME_BELOW",
"QF_PSD_COUNT_LEQ"
] | 2 | 0.057 | 2026-02-25T08:11:21.526263Z | {
"verified": true,
"answer": 13110,
"timestamp": "2026-02-25T08:11:21.583438Z"
} | c373d8 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 240,
"completion_tokens": 9125
},
"timestamp": "2026-03-30T02:32:47.801Z",
"answer": 13110
},
{
"... | 1 | [
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok"
},
{
"lemma": "Q... | {
"lo": -3.33,
"mid": 1.03,
"hi": 5.26
} | ||
e53cd5 | nt_sum_gcd_range_mod_v1_349078426_1714 | Let $N$ be the maximum value of $x \cdot y$ over all ordered pairs $(x, y)$ of positive integers such that $x + y = 86$. Let $k = 120$. Compute the sum $\sum_{n=1}^{N} \gcd(n, k)$, and let $s$ be the remainder when this sum is divided by $11597$. Then compute $\sum_{n=1}^{s} \tau(n)$, where $\tau(n)$ is the number of p... | 17,459 | graphs = [
Graph(
let={
"N": MaxOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(Sum(Var("x"), Var("y")), Const(86)))), expr=Mul(Var("x"), Var("y")))),
"k": Const(120),
... | NT | null | COMPUTE | sympy | B1 | [
"B1"
] | 5b950e | nt_sum_gcd_range_mod_v1 | null | 5 | 0 | [
"B1"
] | 1 | 0.325 | 2026-02-08T13:51:17.291070Z | {
"verified": true,
"answer": 17459,
"timestamp": "2026-02-08T13:51:17.616397Z"
} | 11207f | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 165,
"completion_tokens": 3488
},
"timestamp": "2026-02-15T21:57:33.388Z",
"answer": 17459
},
... | 1 | [
{
"lemma": "B1",
"status": "ok"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
}
] | {
"lo": -5.49,
"mid": 0.22,
"hi": 6.51
} | ||
18b7fe | antilemma_sum_equals_v1_1978505735_2138 | Let $m$ be the number of ordered pairs $(i, j)$ with $1 \leq i \leq 8$ and $1 \leq j \leq 17$. Let $n$ be the number of ordered pairs $(x_1, x_2)$ of positive odd integers such that $x_1 + x_2 = m$. Determine the number of ordered pairs $(i, j)$ with $1 \leq i, j \leq 66$ such that $i + j = n$. | 65 | graphs = [
Graph(
let={
"_m": CountOverSet(set=CartesianProduct(left=IntegerRange(start=Const(1), end=Const(8)), right=IntegerRange(start=Const(1), end=Const(17)))),
"_n": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x1"), Var("x2")]), condition=And(IsPositive(arg=Var(name=... | COMB | GEOM | COMPUTE | sympy | LIN_FORM | [
"COUNT_CARTESIAN/COMB1/COUNT_SUM_EQUALS",
"COUNT_SUM_EQUALS"
] | 9b4db5 | antilemma_sum_equals_v1 | null | 4 | 0 | [
"COMB1",
"COUNT_CARTESIAN",
"COUNT_SUM_EQUALS",
"LIN_FORM"
] | 4 | 0.113 | 2026-02-08T16:40:33.592876Z | {
"verified": true,
"answer": 65,
"timestamp": "2026-02-08T16:40:33.705384Z"
} | c3dbbc | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 153,
"completion_tokens": 934
},
"timestamp": "2026-02-17T11:07:56.594Z",
"answer": 65
},
{
... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COMB1",
"status": "ok_later"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "ok"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_... | {
"lo": -5.64,
"mid": -3.17,
"hi": -0.81
} | ||
94d54b | nt_count_divisors_in_range_v1_124444284_2132 | Let $n = 166320$ and $a = 139$. Let $b$ be the minimum value of $x + y$ over all ordered pairs $(x, y)$ of positive integers such that $x \cdot y = 1592644$. Let $\text{result}$ be the number of positive divisors $d$ of $n$ such that $a \leq d \leq b$. Compute the remainder when $36905 \cdot \text{result}$ is divided b... | 27,499 | graphs = [
Graph(
let={
"n": Const(166320),
"a": Const(139),
"b": MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(Mul(Var("x"), Var("y")), Const(1592644))))... | NT | null | COUNT | sympy | B3 | [
"B3"
] | 0cd20d | nt_count_divisors_in_range_v1 | null | 6 | 0 | [
"B3"
] | 1 | 0.024 | 2026-02-08T04:19:40.055272Z | {
"verified": true,
"answer": 27499,
"timestamp": "2026-02-08T04:19:40.079419Z"
} | 22cf1f | 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": 5527
},
"timestamp": "2026-02-12T00:25:33.870Z",
"answer": 27499
},
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
},
{
"lemma": "VAL_SUM_EQ",
"status": "no"
}
] | {
"lo": -3.51,
"mid": 1.33,
"hi": 6.56
} | ||
54341b | nt_min_coprime_above_v1_48377204_2816 | Let $A$ be the set of all ordered pairs $(x,y)$ of positive integers such that $xy=3610000$. Let $M$ be the minimum element of the set of all values of $x+y$ as $(x,y)$ ranges over $A$.
Let $B$ be the set of all integers $n$ such that
\begin{itemize}
\item $1\le n\le M$, and
\item $n \equiv \left\lfloor \dfrac{n}{2} \... | 13,691 | graphs = [
Graph(
let={
"start": Const(13689),
"upper": Const(14079),
"modulus": 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=Va... | NT | null | EXTREMUM | sympy | B3 | [
"B3/L3C/COMB1"
] | 981f9e | nt_min_coprime_above_v1 | null | 8 | 0 | [
"B3",
"COMB1",
"L3C"
] | 3 | 0.054 | 2026-02-08T16:59:55.418847Z | {
"verified": true,
"answer": 13691,
"timestamp": "2026-02-08T16:59:55.472582Z"
} | 8d5f33 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 305,
"completion_tokens": 1556
},
"timestamp": "2026-02-17T17:55:12.733Z",
"answer": 13691
},
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "COMB1",
"status": "ok_later"
},
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "L3C",
"status": "ok_later"
},
{
"lemma": "V3",
"status": "no"
},
... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
ef938a | nt_sum_divisors_compute_v1_548369836_80 | Let $A$ be the set of all integers $t$ such that $21 \leq t \leq 35$ and there exist positive integers $a$ and $b$ with $1 \leq a \leq 3$, $1 \leq b \leq 5$, and $t = 3a + 2b + 16$. Let $B$ be the set of all integers $t$ such that $5 \leq t \leq 23$ and there exist positive integers $a$ and $b$ with $1 \leq a \leq 5$, ... | 51,516 | graphs = [
Graph(
let={
"n": Const(64009),
"result": SumDivisors(n=Ref("n")),
"Q": Mod(value=Summation(var="n", start=SumOverDivisors(n=GCD(a=CountOverSet(set=SolutionsSet(var=Var(name='t'), condition=Exists(var=Var(name='a'), condition=Exists(var=Var(name='b'), condition... | NT | null | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM/MOBIUS_COPRIME"
] | e7194c | nt_sum_divisors_compute_v1 | sum_totient | 7 | 0 | [
"LIN_FORM",
"MOBIUS_COPRIME"
] | 2 | 3.58 | 2026-02-08T02:44:54.507100Z | {
"verified": true,
"answer": 51516,
"timestamp": "2026-02-08T02:44:58.087427Z"
} | 22ce42 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 377,
"completion_tokens": 5522
},
"timestamp": "2026-02-09T19:26:08.756Z",
"answer": 0
},
{
"... | 0 | [
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "MOBIUS_COPRIME",
"status": "ok_later"
},
{
"lemma": "MOD_SUB... | {
"lo": 4.29,
"mid": 7.01,
"hi": 10
} | ||
6c48a1 | nt_count_divisible_v1_153355830_1743 | Let $n = 75829$ and let $u = 68644$. Consider the set of all ordered pairs $(x, y)$ of positive integers such that $xy = 4$. Let $s$ be the sum $x + y$ for each such pair. Define $d$ to be the minimum value of $s$ over all such pairs.
Let $S$ be the set of all positive integers $k$ such that $1 \leq k \leq u$ and $k$ ... | 7,916 | graphs = [
Graph(
let={
"_n": Const(75829),
"upper": Const(68644),
"divisor": MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(Mul(Var("x"), Var("y")), Const... | NT | null | COUNT | sympy | B3 | [
"B3"
] | 0cd20d | nt_count_divisible_v1 | null | 3 | 0 | [
"B3"
] | 1 | 7.368 | 2026-02-08T06:35:32.980045Z | {
"verified": true,
"answer": 7916,
"timestamp": "2026-02-08T06:35:40.347895Z"
} | 1dcae0 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 187,
"completion_tokens": 1323
},
"timestamp": "2026-02-13T02:27:07.979Z",
"answer": 7916
},
{... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "V1",
"status": "no"
},
{
"lemma": "V3",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
}
] | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
92eece | nt_num_divisors_compute_v1_1520064083_3044 | Let $N = 10000$ and $n = 465$. Let $r$ be the number of positive divisors of $n$. Define $s$ to be the minimum value of $x + y$ over all pairs of positive integers $(x, y)$ such that $xy = N$. Compute $s - r$. | 192 | graphs = [
Graph(
let={
"_n": Const(10000),
"n": Const(465),
"result": NumDivisors(n=Ref("n")),
"Q": Sub(MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='... | NT | null | COMPUTE | sympy | B3 | [
"B3"
] | fc629c | nt_num_divisors_compute_v1 | negation_mod | 4 | 0 | [
"B3"
] | 1 | 0.001 | 2026-02-08T05:25:56.864607Z | {
"verified": true,
"answer": 192,
"timestamp": "2026-02-08T05:25:56.866001Z"
} | e2f879 | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 130,
"completion_tokens": 320
},
"timestamp": "2026-02-11T22:48:28.448Z",
"answer": 192
},
{
"id": 11,
... | 2 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
}
] | {
"lo": -9.14,
"mid": -6.05,
"hi": -3.73
} | ||
db4a75 | nt_count_divisible_v1_1874849503_253 | Let $A$ be the set of all positive integers $n$ such that $1 \leq n \leq 60516$ and $n$ is divisible by 12. Let $a$ be the number of elements in $A$. Let $B$ be the set of all integers $t$ such that $14 \leq t \leq 68$ and $t = 10a + 4b$ for some integers $a \in \{1,2\}$ and $b \in \{1,2,\dots,12\}$. Let $b$ be the num... | 49,901 | graphs = [
Graph(
let={
"upper": Const(60516),
"divisor": Const(12),
"result": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Ref("upper")), Eq(Mod(value=Var("n"), modulus=Ref("divisor")), Const(0))))),
"_c": S... | NT | null | COUNT | sympy | LIN_FORM | [
"LIN_FORM/SUM_ARITHMETIC"
] | 1c5c0a | nt_count_divisible_v1 | negation_mod | 4 | 0 | [
"LIN_FORM",
"SUM_ARITHMETIC"
] | 2 | 3.88 | 2026-02-08T12:53:35.910871Z | {
"verified": true,
"answer": 49901,
"timestamp": "2026-02-08T12:53:39.790623Z"
} | 3a8f68 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 280,
"completion_tokens": 2106
},
"timestamp": "2026-02-09T15:03:14.463Z",
"answer": 49901
},
{
"... | 1 | [
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "SUM_ARITHMETIC",
"stat... | {
"lo": -5.15,
"mid": 0.01,
"hi": 5.44
} | ||
de03c7 | comb_count_partitions_v1_1353956133_217 | Let $n$ be the number of integers $t$ such that $14 \leq t \leq 108$ and there exist positive integers $a$ and $b$ with $1 \leq a \leq 4$, $1 \leq b \leq 17$, and $t = 10a + 4b$. Compute the number of integer partitions of $n$. | 75,175 | graphs = [
Graph(
let={
"n": CountOverSet(set=SolutionsSet(var=Var("t"), condition=Exists(var=Var(name='a'), condition=Exists(var=Var(name='b'), condition=And(Geq(left=Var(name='a'), right=Const(value=1)), Leq(left=Var(name='a'), right=Const(value=4)), Geq(left=Var(name='b'), right=Const(value=1... | COMB | null | COUNT | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | comb_count_partitions_v1 | null | 5 | 0 | [
"LIN_FORM"
] | 1 | 0.002 | 2026-02-08T11:20:49.695689Z | {
"verified": true,
"answer": 75175,
"timestamp": "2026-02-08T11:20:49.697808Z"
} | 1efefc | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 195,
"completion_tokens": 6989
},
"timestamp": "2026-02-24T13:22:56.928Z",
"answer": 74784
},
{
... | 1 | [
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8",
"sta... | {
"lo": 1.15,
"mid": 4.18,
"hi": 6.61
} | ||
f5f968_n | alg_sum_powers_v1_1218484723_1898 | A game board consists of squares labeled by positive integers from 1 to 35 in both rows and columns. A square $(a,b)$ is *active* if $41a^2 - 12ab + 20b^2 \le 20961$. Let $M$ be the number of active squares. Players earn points equal to the cube of their turn number over $M$ turns. What is the remainder when the total ... | 2,773 | ALG | null | COMPUTE | sympy | QF_PSD_COUNT_LEQ | [
"QF_PSD_COUNT_LEQ/ABS_INEQ"
] | ed242b | alg_sum_powers_v1 | null | 5 | null | [
"ABS_INEQ",
"QF_PSD_COUNT_LEQ"
] | 2 | 0.031 | 2026-02-25T03:38:07.701754Z | null | 4f97a6 | f5f968 | narrative | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 237,
"completion_tokens": 8310
},
"timestamp": "2026-03-30T17:30:54.817Z",
"answer": 3922
},
{
... | 1 | [
{
"lemma": "ABS_INEQ",
"status": "ok_later"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "QF_PSD_COUNT_LEQ",
"status": "ok"
}
] | {
"lo": 1.5,
"mid": 4.69,
"hi": 7.23
} | |
cc892a | diophantine_product_count_v1_153355830_2563 | Let $S$ be the set of all ordered pairs $(x, y)$ of positive integers such that $xy = 129600$. Let $k$ be the minimum value of $x + y$ as $(x, y)$ ranges over $S$. Let $T$ be the set of all positive integers $x$ such that $1 \leq x \leq 430$, $x$ divides $k$, and $\frac{k}{x} \leq 430$. Let $r$ be the number of element... | 242 | 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(129600)))), expr=Sum(Var("x"), Var("y")))),
"upper": Const(4... | NT | null | COUNT | sympy | B3 | [
"B3"
] | 0cd20d | diophantine_product_count_v1 | null | 6 | 0 | [
"B3"
] | 1 | 0.016 | 2026-02-08T07:13:48.813254Z | {
"verified": true,
"answer": 242,
"timestamp": "2026-02-08T07:13:48.829456Z"
} | b725f1 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 183,
"completion_tokens": 2657
},
"timestamp": "2026-02-13T09:00:47.746Z",
"answer": 242
},
{
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
}
] | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
b5fe11 | modular_count_residue_v1_865884756_2868 | Let $r$ be the minimum value of $x + y$ over all ordered pairs $(x,y)$ of positive integers such that $xy = 49$. Let $S$ be the set of all positive integers $n$ such that $1 \leq n \leq 74529$ and $n \equiv r \pmod{23}$. Compute the number of elements in $S$. | 3,240 | graphs = [
Graph(
let={
"upper": Const(74529),
"m": Const(23),
"r": 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(49)))), e... | NT | null | COUNT | sympy | B3 | [
"B3"
] | 0cd20d | modular_count_residue_v1 | null | 3 | 0 | [
"B3"
] | 1 | 4.326 | 2026-02-08T16:59:05.457037Z | {
"verified": true,
"answer": 3240,
"timestamp": "2026-02-08T16:59:09.782831Z"
} | 2e89b5 | 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": 748
},
"timestamp": "2026-02-17T17:18:37.451Z",
"answer": 3240
},
{
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
be5afe | sequence_count_fib_divisible_v1_784195855_5490 | Let $n = 305$. Compute the sum
$$
\sum_{d \mid n} \phi(d),
$$
where $\phi$ is Euler's totient function. Let $S$ be the set of all positive integers $k$ from $1$ to this sum such that $8$ divides the $k$-th Fibonacci number. Compute the number of elements in $S$. | 50 | graphs = [
Graph(
let={
"_n": Const(305),
"upper": SumOverDivisors(n=Ref(name='_n'), var='d', expr=EulerPhi(n=Var(name='d'))),
"d": Const(8),
"result": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Ref("upper"... | NT | null | COUNT | sympy | B3 | [
"K3"
] | 54c41e | sequence_count_fib_divisible_v1 | null | 5 | 0 | [
"B3",
"K3"
] | 2 | 0.081 | 2026-02-08T07:55:45.040096Z | {
"verified": true,
"answer": 50,
"timestamp": "2026-02-08T07:55:45.121208Z"
} | 1dd525 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 125,
"completion_tokens": 1788
},
"timestamp": "2026-02-13T13:29:38.911Z",
"answer": 50
},
{
... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "K3",
"status": "ok"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
}
] | {
"lo": -5.55,
"mid": -3.01,
"hi": 0.32
} | ||
6f9e11 | comb_binomial_compute_v1_898971024_1083 | Let $m = 5$ and $n_0 = 2$. Define $n$ to be the largest prime number satisfying $n_0 \leq n \leq \sum_{k=1}^{5} \phi(k) \left\lfloor \frac{m}{k} \right\rfloor$, where $\phi$ denotes Euler's totient function. Let $k$ be the smallest divisor of $539$ that is at least $2$. Compute $\binom{n}{k}$. Find the remainder when $... | 51,112 | graphs = [
Graph(
let={
"_m": Const(5),
"_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=Const(5), expr=Mul(EulerPhi(n=Var("k1")), Floor(Div(Ref("_m"), Var("k1")... | NT | null | COMPUTE | sympy | K2 | [
"K2/MAX_PRIME_BELOW",
"MIN_PRIME_FACTOR"
] | d952d1 | comb_binomial_compute_v1 | null | 5 | 0 | [
"K2",
"MAX_PRIME_BELOW",
"MIN_PRIME_FACTOR"
] | 3 | 0.007 | 2026-02-08T15:55:25.700910Z | {
"verified": true,
"answer": 51112,
"timestamp": "2026-02-08T15:55:25.707664Z"
} | b21cb6 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 166,
"completion_tokens": 3065
},
"timestamp": "2026-02-16T17:29:02.858Z",
"answer": 51112
},
... | 1 | [
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K2",
"status": "ok"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok_later"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "MIN_PRIME_FACTOR",
"status": "ok"
},
{
"lemma": "MOD_ADD",
"status": "n... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
918ffe | nt_min_coprime_above_v1_655260480_1738 | Let $A$ be the smallest integer $n$ such that $65536 < n \leq 65576$ and $\gcd(n, 30) = 1$.
Compute the remainder when the Bell number $B_{|A| \bmod 11}$ is divided by $96728$. | 19,247 | graphs = [
Graph(
let={
"start": Const(65536),
"upper": Const(65576),
"modulus": Const(30),
"result": MinOverSet(set=SolutionsSet(var=Var("n"), condition=And(Gt(Var("n"), Ref("start")), Leq(Var("n"), Ref("upper")), Eq(GCD(a=Var("n"), b=Ref("modulus")), Const(1... | NT | COMB | EXTREMUM | sympy | C5 | [
"B1"
] | 5b950e | nt_min_coprime_above_v1 | null | 4 | 0 | [
"B1",
"C5"
] | 2 | 0.164 | 2026-02-08T16:19:09.145441Z | {
"verified": true,
"answer": 19247,
"timestamp": "2026-02-08T16:19:09.309065Z"
} | 804c67 | 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": 860
},
"timestamp": "2026-02-17T01:13:19.890Z",
"answer": 19247
},
{... | 1 | [
{
"lemma": "B1",
"status": "ok"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
3ec4a0 | modular_min_linear_v1_1125832087_1157 | Let $S$ be the set of all ordered pairs $(x, y)$ of positive integers such that $xy = 625$. Define $a$ to be the minimum value of $x + y$ as $(x, y)$ ranges over $S$. Let $m = 38189$ and $b = 23940$. Determine the value of the smallest positive integer $x$ such that $1 \leq x \leq m$ and $ax \equiv b \pmod{m}$. | 31,030 | 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(625)))), expr=Sum(Var("x"), Var("y")))),
"b": Const(23940),
... | NT | null | EXTREMUM | sympy | B3 | [
"B3"
] | 0cd20d | modular_min_linear_v1 | null | 6 | 0 | [
"B3"
] | 1 | 1.868 | 2026-02-08T03:33:53.220134Z | {
"verified": true,
"answer": 31030,
"timestamp": "2026-02-08T03:33:55.087841Z"
} | c82b38 | 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": 2278
},
"timestamp": "2026-02-10T14:55:25.720Z",
"answer": 31030
},
{
"... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
}
] | {
"lo": -3.46,
"mid": 1.03,
"hi": 5.49
} | ||
a72676 | nt_count_phi_equals_v1_717093673_2826 | Let $k = 162$. Determine the number of positive integers $n$ such that $1 \leq n \leq 3364$ and $\phi(n) = k$. Let this number be $t$.
Compute $\sum_{n=1}^{t} \phi(n)$. | 6 | graphs = [
Graph(
let={
"upper": Const(3364),
"k": Const(162),
"result": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Ref("upper")), Eq(EulerPhi(n=Var("n")), Ref("k"))))),
"Q": Summation(var="n1", start=Const... | NT | null | COUNT | sympy | COUNT_PRIMES | [
"L3B"
] | cc148f | nt_count_phi_equals_v1 | null | 5 | 0 | [
"COUNT_PRIMES",
"L3B"
] | 2 | 2.412 | 2026-02-08T17:13:09.975591Z | {
"verified": true,
"answer": 6,
"timestamp": "2026-02-08T17:13:12.387404Z"
} | 4a697a | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 105,
"completion_tokens": 3646
},
"timestamp": "2026-02-17T21:55:41.999Z",
"answer": 6
},
{
... | 1 | [
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "L3B",
"status": "ok"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
c9990a | comb_count_permutations_fixed_v1_1125832087_1190 | Let $n$ be the largest prime number such that $2 \leq n \leq 11$.
Compute the value of $\binom{n}{6} \cdot !(n - 6)$, where $!k$ denotes the number of derangements of $k$ elements. | 20,328 | graphs = [
Graph(
let={
"_n": Const(2),
"n": MaxOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Ref("_n")), Leq(Var("n"), Const(11)), IsPrime(Var("n"))))),
"k": Const(6),
"result": Mul(Binom(n=Ref("n"), k=Ref("k")), Subfactorial(arg=Sub(left... | NT | COMB | COUNT | sympy | COPRIME_PAIRS | [
"MAX_PRIME_BELOW"
] | dc3ad3 | comb_count_permutations_fixed_v1 | null | 5 | 0 | [
"COPRIME_PAIRS",
"MAX_PRIME_BELOW"
] | 2 | 0.02 | 2026-02-08T03:36:42.329131Z | {
"verified": true,
"answer": 20328,
"timestamp": "2026-02-08T03:36:42.348958Z"
} | 9cba76 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 173,
"completion_tokens": 621
},
"timestamp": "2026-02-10T15:08:58.683Z",
"answer": 20328
},
{
"i... | 1 | [
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "VAL_SUM_EQ",
... | {
"lo": -5.55,
"mid": -3.02,
"hi": 0.31
} | ||
311e8e | algebra_quadratic_discriminant_v1_655260480_4336 | Let $S$ be the set of all positive integers $p$ for which there exists a positive integer $q$ such that $p \cdot q = 6750$, $\gcd(p, q) = 1$, and $p < q$. Let $T$ be the number of elements in $S$. Define $D = b^2 - 4ac$, where $a = -1$, $b = -9$, $c = 9$, and the coefficient of $c$ is $T$. Let $\alpha = 1$ if $D > 0$, ... | 79,550 | graphs = [
Graph(
let={
"_n": Const(39775),
"a": Const(-1),
"b": Const(-9),
"c": Const(9),
"D": Sub(Pow(Ref("b"), Const(2)), Mul(CountOverSet(set=SolutionsSet(var=Var("p"), condition=And(IsPositive(arg=Var(name='p')), Exists(var=Var(name='q'), cond... | NT | null | COMPUTE | sympy | COPRIME_PAIRS | [
"COPRIME_PAIRS"
] | 2bb3aa | algebra_quadratic_discriminant_v1 | null | 5 | 0 | [
"COPRIME_PAIRS"
] | 1 | 0.003 | 2026-02-08T17:53:21.625565Z | {
"verified": true,
"answer": 79550,
"timestamp": "2026-02-08T17:53:21.628397Z"
} | 75cf38 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 229,
"completion_tokens": 1728
},
"timestamp": "2026-02-18T09:38:47.399Z",
"answer": 79550
},
... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "VAL_SUM_EQ",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
03bf53 | lin_form_endings_v1_1125832087_2177 | Let $a = 75$ and $b = 60$. Compute the greatest common divisor of $a$ and $b$, then multiply the result by $14990$. Find the remainder when this product is divided by $51035$. Compute this remainder. | 20,710 | graphs = [
Graph(
let={
"a_coeff": Const(75),
"b_coeff": Const(60),
"_inner_result": GCD(a=Ref("a_coeff"), b=Ref("b_coeff")),
"_scale_k": Const(14990),
"_scaled": Mul(Ref("_scale_k"), Ref("_inner_result")),
"_mod_M": Const(51035),
... | COMB | NT | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | lin_form_endings_v1 | null | 2 | null | [
"LIN_FORM"
] | 1 | 0.001 | 2026-02-08T04:23:45.157675Z | {
"verified": true,
"answer": 20710,
"timestamp": "2026-02-08T04:23:45.158209Z"
} | 3f3fcf | 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": 368
},
"timestamp": "2026-02-10T16:23:42.822Z",
"answer": 20710
},
{
"... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
}
] | {
"lo": -5.55,
"mid": -3.01,
"hi": 0.33
} | ||
747b83 | geo_count_lattice_triangle_v1_1470522791_1003 | Consider the triangle with vertices at $(0,0)$, $(100,33)$, and $(99,225)$. Let $\text{area}_{2x}$ be twice the area of this triangle. Let $\text{boundary}$ be the sum of the greatest common divisors of the absolute differences in coordinates along each side: $\gcd(100,33) + \gcd(|99-100|, |225-33|) + \gcd(|0-99|, |0 -... | 41,893 | graphs = [
Graph(
let={
"_n": Const(2),
"area_2x": Abs(arg=Sum(Mul(Const(value=100), Const(value=225)), Mul(Const(value=99), Sub(left=Const(value=0), right=Const(value=33))))),
"boundary": Sum(GCD(a=Abs(arg=Const(value=100)), b=Abs(arg=Const(value=33))), GCD(a=Abs(arg=Sub... | ALG | NT | COUNT | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | geo_count_lattice_triangle_v1 | null | 6 | 0 | [
"LIN_FORM"
] | 1 | 0.012 | 2026-02-08T13:22:36.076881Z | {
"verified": true,
"answer": 41893,
"timestamp": "2026-02-08T13:22:36.088444Z"
} | 8937ef | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 269,
"completion_tokens": 3895
},
"timestamp": "2026-02-15T14:05:30.390Z",
"answer": 41893
},
... | 1 | [
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
}
] | {
"lo": -5.49,
"mid": 0.22,
"hi": 6.51
} | ||
7d77a3 | comb_factorial_compute_v1_124444284_3409 | Let $a = 2$ and $b = 1$. Define $n_2 = a + b$. Let
$$
e = \sum_{k=0}^{n_2} (-1)^k \binom{n_2}{k}.
$$
Set $n_1 = e$, and define
$$
v = \sum_{k=0}^{n_1} (-1)^k \binom{n_1}{k}.
$$
Let $S$ be the set of all ordered pairs $(i, j)$ of integers with $1 \leq i \leq 8$ and $1 \leq j \leq 9$ such that $i + j = 9$. Let $n = |... | 40,320 | graphs = [
Graph(
let={
"a": Const(2),
"b": Const(1),
"n2": Sum(Ref("a"), Ref("b")),
"e": Summation(var="k", start=Const(0), end=Ref("n2"), expr=Mul(Pow(Const(-1), Var("k")), Binom(n=Ref("n2"), k=Var("k")))),
"n1": Ref("e"),
"v": Summat... | COMB | null | COMPUTE | sympy | COUNT_SUM_EQUALS | [
"COUNT_SUM_EQUALS/BINOMIAL_ALTERNATING"
] | ab0fe8 | comb_factorial_compute_v1 | null | 5 | 2 | [
"BINOMIAL_ALTERNATING",
"COUNT_SUM_EQUALS"
] | 2 | 0.011 | 2026-02-08T05:23:35.001478Z | {
"verified": true,
"answer": 40320,
"timestamp": "2026-02-08T05:23:35.012762Z"
} | f3a6bf | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 296,
"completion_tokens": 632
},
"timestamp": "2026-02-24T03:22:39.403Z",
"answer": 40320
},
{
"i... | 1 | [
{
"lemma": "BINOMIAL_ALTERNATING",
"status": "ok_later"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "ok"
},... | {
"lo": -7.18,
"mid": -5,
"hi": -3.01
} | ||
1172d1 | geo_count_lattice_triangle_v1_971394319_1561 | Let $A = (0, 0)$, $B = (100, 128)$, and $C = (49, 169)$. The area of triangle $ABC$ is half of the absolute value of $100 \cdot 169 - 49 \cdot 128$. Let $P$ be the number of lattice points on the boundary of triangle $ABC$, which is given by
$$
\gcd(100, 128) + \gcd(|49 - 100|, |169 - 128|) + \gcd(|0 - 49|, |0 - 169|)... | 46,424 | graphs = [
Graph(
let={
"_c": Const(49),
"_m": Const(100),
"_n": Const(169),
"area_2x": Abs(arg=Sum(Mul(Ref(name='_m'), Const(value=169)), Mul(Ref(name='_c'), Sub(left=Const(value=0), right=Const(value=128))))),
"boundary": Sum(GCD(a=Abs(arg=Const(... | ALG | NT | COUNT | sympy | LIN_FORM | [
"LIN_FORM/C5",
"L3C/C5"
] | ada9eb | geo_count_lattice_triangle_v1 | null | 5 | 0 | [
"C5",
"L3C",
"LIN_FORM"
] | 3 | 0.03 | 2026-02-08T13:44:37.057000Z | {
"verified": true,
"answer": 46424,
"timestamp": "2026-02-08T13:44:37.087386Z"
} | aa4ffe | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 260,
"completion_tokens": 1988
},
"timestamp": "2026-02-15T20:21:53.663Z",
"answer": 46424
},
... | 1 | [
{
"lemma": "C5",
"status": "ok_later"
},
{
"lemma": "L3C",
"status": "ok"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
}
] | {
"lo": -5.49,
"mid": 0.22,
"hi": 6.51
} | ||
13b411 | comb_sum_binomial_row_v1_655260480_4111 | Let $m = 4$. Let $S$ be the set of all ordered pairs $(x, y)$ of positive integers such that $xy = 4$. Define $n_0$ to be the minimum value of $x + y$ over all such pairs. Let $n = \sum_{k=1}^{n_0} \phi(k) \left\lfloor \frac{m}{k} \right\rfloor$.
Let $T$ be the set of all positive integers $p$ for which there exists a... | 1,024 | graphs = [
Graph(
let={
"_m": Const(4),
"_n": MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(Mul(Var("x"), Var("y")), Const(4)))), expr=Sum(Var("x"), Var("y")))),
... | NT | null | SUM | sympy | COPRIME_PAIRS | [
"COPRIME_PAIRS",
"B3/K2"
] | 4916a0 | comb_sum_binomial_row_v1 | null | 4 | 0 | [
"B3",
"COPRIME_PAIRS",
"K2"
] | 3 | 0.006 | 2026-02-08T17:43:35.401640Z | {
"verified": true,
"answer": 1024,
"timestamp": "2026-02-08T17:43:35.407305Z"
} | 98f485 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 193,
"completion_tokens": 970
},
"timestamp": "2026-02-18T07:44:15.862Z",
"answer": 1024
},
{
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "K2",
"status": "ok_later"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
240c6d | sequence_count_fib_divisible_v1_1470522791_1455 | Let $u$ be the largest prime number $n$ such that $2 \leq n \leq 383$. Determine the number of positive integers $n$ with $1 \leq n \leq u$ such that the $n$th Fibonacci number is divisible by $10$. | 25 | graphs = [
Graph(
let={
"_n": Const(2),
"upper": MaxOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Ref("_n")), Leq(Var("n"), Const(383)), IsPrime(Var("n"))))),
"d": Const(10),
"result": CountOverSet(set=SolutionsSet(var=Var("n"), condition=... | NT | null | COUNT | sympy | V5 | [
"MAX_PRIME_BELOW"
] | dc3ad3 | sequence_count_fib_divisible_v1 | null | 5 | 0 | [
"MAX_PRIME_BELOW",
"V5"
] | 2 | 0.063 | 2026-02-08T13:39:39.535936Z | {
"verified": true,
"answer": 25,
"timestamp": "2026-02-08T13:39:39.598917Z"
} | 0ea672 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 105,
"completion_tokens": 1065
},
"timestamp": "2026-02-15T19:25:27.123Z",
"answer": 25
},
{
... | 1 | [
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "V8",
... | {
"lo": -5.49,
"mid": 0.22,
"hi": 6.51
} | ||
2fb397 | comb_count_partitions_v1_677425708_4101 | Let $n$ be the number of integers $t$ with $30 \leq t \leq 195$ for which there exist positive integers $a \leq 5$ and $b \leq 10$ such that $t = 21a + 9b$. Compute the number of partitions of $n$. | 75,175 | graphs = [
Graph(
let={
"n": CountOverSet(set=SolutionsSet(var=Var("t"), condition=Exists(var=Var(name='a'), condition=Exists(var=Var(name='b'), condition=And(Geq(left=Var(name='a'), right=Const(value=1)), Leq(left=Var(name='a'), right=Const(value=5)), Geq(left=Var(name='b'), right=Const(value=1... | COMB | null | COUNT | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | comb_count_partitions_v1 | null | 5 | 0 | [
"LIN_FORM"
] | 1 | 0.002 | 2026-02-08T06:25:53.969187Z | {
"verified": true,
"answer": 75175,
"timestamp": "2026-02-08T06:25:53.970975Z"
} | e23c2c | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 180,
"completion_tokens": 32768
},
"timestamp": "2026-02-24T06:12:09.826Z",
"answer": 74627
},
{
... | 1 | [
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8_SUM",
... | {
"lo": 3.43,
"mid": 5.73,
"hi": 8.84
} | ||
87f860 | diophantine_fbi2_min_v1_865884756_2323 | Let $k = 72$. Determine the smallest integer $d$ such that $4 \leq d \leq 82$, $d$ divides $k$, and $\frac{k}{d} \geq 2$. | 4 | graphs = [
Graph(
let={
"k": Const(72),
"a": Const(3),
"b": Const(1),
"upper": Const(82),
"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... | NT | null | EXTREMUM | sympy | COPRIME_PAIRS | [
"MIN_PRIME_FACTOR/C4"
] | bf3815 | diophantine_fbi2_min_v1 | null | 3 | 0 | [
"C4",
"COPRIME_PAIRS",
"MIN_PRIME_FACTOR"
] | 3 | 0.044 | 2026-02-08T16:41:37.279647Z | {
"verified": true,
"answer": 4,
"timestamp": "2026-02-08T16:41:37.323395Z"
} | 0e7703 | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 104,
"completion_tokens": 546
},
"timestamp": "2026-02-16T07:43:07.991Z",
"answer": 4
},
{
"id": 11,
"... | 2 | [
{
"lemma": "C4",
"status": "ok_later"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "MIN_PRIME_FACTOR",
"status": "ok"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma... | {
"lo": -10,
"mid": -7.27,
"hi": -4.54
} | ||
d18c44 | nt_num_divisors_compute_v1_1470522791_1237 | Compute the number of positive divisors of $77777$. | 8 | graphs = [
Graph(
let={
"n": Const(77777),
"result": NumDivisors(n=Ref("n")),
},
goal=Ref("result"),
)
] | NT | null | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | nt_num_divisors_compute_v1 | null | 2 | 0 | [
"LIN_FORM"
] | 1 | 0.08 | 2026-02-08T13:32:05.140846Z | {
"verified": true,
"answer": 8,
"timestamp": "2026-02-08T13:32:05.220373Z"
} | 1207b1 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 58,
"completion_tokens": 1272
},
"timestamp": "2026-02-15T17:01:36.852Z",
"answer": 8
},
{
... | 1 | [
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "V1",
"status": "no"
}
] | {
"lo": -5.49,
"mid": 0.22,
"hi": 6.51
} | ||
5ff43f | sequence_lucas_compute_v1_1520064083_6474 | Let $A$ be the set of all positive integers $n$ such that $1 \leq n \leq 17363$ and $\gcd(n, 15) = 1$. Let $m = |A|$. Now let $B$ be the set of all positive integers $j$ such that $1 \leq j \leq 21$ and $j^3 \leq m$. Let $n = |B|$. Compute the $n$-th Lucas number, where the Lucas sequence is defined by $L_1 = 1$, $L_2 ... | 24,476 | graphs = [
Graph(
let={
"_m": Const(17363),
"_n": Const(21),
"n": CountOverSet(set=SolutionsSet(var=Var("j"), condition=And(Geq(Var("j"), Const(1)), Leq(Var("j"), Ref("_n")), Leq(Pow(Var("j"), Const(3)), CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n... | NT | null | COMPUTE | sympy | C4 | [
"C4/C3"
] | 56c6e0 | sequence_lucas_compute_v1 | null | 5 | 0 | [
"C3",
"C4"
] | 2 | 0.002 | 2026-02-08T08:06:40.432439Z | {
"verified": true,
"answer": 24476,
"timestamp": "2026-02-08T08:06:40.434206Z"
} | 432a60 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 196,
"completion_tokens": 1177
},
"timestamp": "2026-02-13T15:05:17.632Z",
"answer": 24476
},
... | 1 | [
{
"lemma": "C3",
"status": "ok_later"
},
{
"lemma": "C4",
"status": "ok"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
... | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
f4680c | algebra_quadratic_discriminant_v1_1080341949_151 | Let $a = 1$, $b = 4$, and $c = -21$. Compute $b^2 - 4ac$. | 100 | graphs = [
Graph(
let={
"a": Const(1),
"b": Const(4),
"c": Const(-21),
"result": Sub(Pow(Ref("b"), Const(2)), Mul(Const(4), Ref("a"), Ref("c"))),
},
goal=Ref("result"),
)
] | NT | null | COMPUTE | sympy | COPRIME_PAIRS | [
"MOBIUS_COPRIME",
"COPRIME_PAIRS",
"MOBIUS_SUM"
] | f3abc5 | algebra_quadratic_discriminant_v1 | null | 2 | 0 | [
"COPRIME_PAIRS",
"MOBIUS_COPRIME",
"MOBIUS_SUM"
] | 3 | 0.057 | 2026-02-08T13:15:41.958542Z | {
"verified": true,
"answer": 100,
"timestamp": "2026-02-08T13:15:42.015706Z"
} | 64a671 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 77,
"completion_tokens": 168
},
"timestamp": "2026-02-15T12:08:28.543Z",
"answer": 100
},
{
... | 1 | [
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "MOBIUS_COPRIME",
"status": ... | {
"lo": -9.12,
"mid": -6.02,
"hi": -3.62
} | ||
84f79b | nt_count_coprime_and_v1_1431428450_364 | Let $k_2$ be the maximum value of $xy$ over all pairs of positive integers $(x, y)$ such that $x + y = 6$. Compute the number of positive integers $n$ such that $1 \leq n \leq 14364$, $\gcd(n, 5) = 1$, and $\gcd(n, k_2) = 1$. | 7,661 | graphs = [
Graph(
let={
"_n": Const(6),
"upper": Const(14364),
"k1": Const(5),
"k2": MaxOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(Sum(Var("x"... | NT | null | COUNT | sympy | B1 | [
"B1"
] | 5b950e | nt_count_coprime_and_v1 | null | 5 | 0 | [
"B1"
] | 1 | 1.637 | 2026-02-08T13:25:20.836486Z | {
"verified": true,
"answer": 7661,
"timestamp": "2026-02-08T13:25:22.473933Z"
} | 31e217 | 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": 813
},
"timestamp": "2026-02-15T15:05:31.422Z",
"answer": 7661
},
{
... | 1 | [
{
"lemma": "B1",
"status": "ok"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"
}
] | {
"lo": -5.49,
"mid": 0.22,
"hi": 6.51
} | ||
f94818 | nt_sum_divisors_compute_v1_798873815_378 | Let $a_1 = 4$ and $b_1 = 17$. Define $n_2 = a_1 b_1 + 1$. Let $c$ be the remainder when the number of positive divisors of $n_2$ is divided by 2. Let $g = 14$, $m = 1$, and $n_1 = 15$. Define $a = g \cdot m$ and $b = g \cdot n_1$. Let $h$ be the sum of $\mu(d)$ over all positive divisors $d$ of $\gcd(a, b)$, where $\mu... | 37,473 | graphs = [
Graph(
let={
"a1": Const(4),
"b1": Const(17),
"n2": Sum(Mul(Ref("a1"), Ref("b1")), Const(1)),
"c": Mod(value=NumDivisors(n=Ref("n2")), modulus=Const(2)),
"g": Const(14),
"m": Const(1),
"n1": Const(15),
... | NT | null | COMPUTE | sympy | MOBIUS_COPRIME | [
"MOBIUS_COPRIME",
"DIVISOR_PARITY"
] | 69075e | nt_sum_divisors_compute_v1 | null | 3 | 2 | [
"DIVISOR_PARITY",
"MOBIUS_COPRIME"
] | 2 | 0.001 | 2026-02-08T02:37:08.053393Z | {
"verified": true,
"answer": 37473,
"timestamp": "2026-02-08T02:37:08.054739Z"
} | c22f65 | 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": 3078
},
"timestamp": "2026-02-08T19:26:21.939Z",
"answer": 37473
},
{
"... | 1 | [
{
"lemma": "DIVISOR_PARITY",
"status": "ok"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "MOBIUS_COPRIME",
"status": "o... | {
"lo": -4.84,
"mid": -1.65,
"hi": 1.93
} | ||
394250 | modular_count_residue_v1_898971024_625 | Let $m = 9$. Define $n$ to be the number of positive integers $p$ for which there exists a positive integer $q$ such that $pq = 18$, $\gcd(p, q) = 1$, and $p < q$. Let $m'$ be the largest prime number $n$ satisfying $n \geq n$ and $n \leq m$. Compute the number of positive integers $n_1$ at most $31237$ such that $n_1 ... | 4,463 | graphs = [
Graph(
let={
"_m": Const(9),
"_n": CountOverSet(set=SolutionsSet(var=Var("p"), condition=And(IsPositive(arg=Var(name='p')), Exists(var=Var(name='q'), condition=And(Eq(left=Mul(Var(name='p'), Var(name='q')), right=Const(value=18)), Eq(left=GCD(a=Var(name='p'), b=Var(name='q... | NT | null | COUNT | sympy | COPRIME_PAIRS | [
"COPRIME_PAIRS/MAX_PRIME_BELOW"
] | 2248fc | modular_count_residue_v1 | null | 3 | 0 | [
"COPRIME_PAIRS",
"MAX_PRIME_BELOW"
] | 2 | 1.754 | 2026-02-08T15:34:09.448544Z | {
"verified": true,
"answer": 4463,
"timestamp": "2026-02-08T15:34:11.202302Z"
} | cc323c | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 179,
"completion_tokens": 434
},
"timestamp": "2026-02-16T06:07:09.146Z",
"answer": 4462
},
{
"id": 11,... | 1 | [
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok_later"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "V8_SU... | {
"lo": -8.26,
"mid": -5.01,
"hi": -1.76
} | ||
e54bd6 | diophantine_fbi2_min_v1_1978505735_8212 | Let $n = 3$, $k = 8$, and define the upper bound as $18$. Let $d$ be an integer such that $2 \le d \le 18$, $d$ divides $k$, and $\frac{k}{d} \ge n$. Let $r$ be the smallest such $d$. Let $c$ be the maximum value of $xy$ over all ordered pairs $(x, y)$ of positive integers such that $x + y = 66$. Compute $r^2 + 32r + c... | 1,157 | graphs = [
Graph(
let={
"_n": Const(3),
"k": Const(8),
"upper": Const(18),
"result": MinOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Const(2)), Leq(Var("d"), Ref("upper")), Divides(divisor=Var("d"), dividend=Ref("k")), Geq(Div(Ref("k"), V... | NT | null | EXTREMUM | sympy | B1 | [
"B1"
] | bf138c | diophantine_fbi2_min_v1 | quadratic_mod | 4 | 0 | [
"B1"
] | 1 | 0.004 | 2026-02-08T20:43:55.225510Z | {
"verified": true,
"answer": 1157,
"timestamp": "2026-02-08T20:43:55.229909Z"
} | 1ded3e | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 178,
"completion_tokens": 332
},
"timestamp": "2026-02-16T18:53:00.728Z",
"answer": 1157
},
{
"id": 11,
... | 2 | [
{
"lemma": "B1",
"status": "ok"
},
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
}
] | {
"lo": -10,
"mid": -7.27,
"hi": -4.54
} | ||
ad9350 | nt_count_coprime_v1_784195855_9320 | Let $S$ be the set of all ordered pairs $(x,y)$ of positive integers such that $xy$ equals the number of integers $t$ in the interval $[5, 447]$ for which there exist integers $a$ and $b$ satisfying $1 \leq a \leq 141$, $1 \leq b \leq 12$, and $t = 3a + 2b$. Let $k$ be the minimum value of $x + y$ over all pairs $(x,y)... | 6,349 | graphs = [
Graph(
let={
"upper": Const(22222),
"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")), CountOverSet(set=SolutionsSet(var=Var("t"),... | NT | null | COUNT | sympy | LIN_FORM | [
"LIN_FORM/B3"
] | 05313e | nt_count_coprime_v1 | null | 6 | 0 | [
"B3",
"LIN_FORM"
] | 2 | 1.938 | 2026-02-08T16:42:08.996445Z | {
"verified": true,
"answer": 6349,
"timestamp": "2026-02-08T16:42:10.934765Z"
} | 5cf823 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 190,
"completion_tokens": 2728
},
"timestamp": "2026-02-17T11:29:16.209Z",
"answer": 6349
},
{... | 1 | [
{
"lemma": "B3",
"status": "ok_later"
},
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "V3",
"status": "no"
},
{
... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
448a45 | nt_count_divisible_v1_397696148_961 | Let $ A $ be the set of positive integers $ n \leq 44521 $ that are divisible by 4. Let $ s = |A| $. Let $ t = \min\{x + y \mid x, y \in \mathbb{Z}^+,\ xy = 49\} $. Compute $ s + 2^{s \bmod t} \bmod 77282 $. | 11,131 | graphs = [
Graph(
let={
"_n": Const(77282),
"upper": Const(44521),
"divisor": Const(4),
"result": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Ref("upper")), Eq(Mod(value=Var("n"), modulus=Ref("divisor")), Co... | NT | null | COUNT | sympy | B3 | [
"B3"
] | 385411 | nt_count_divisible_v1 | mod_exp | 5 | 0 | [
"B3"
] | 1 | 1.712 | 2026-02-08T11:58:13.584648Z | {
"verified": true,
"answer": 11131,
"timestamp": "2026-02-08T11:58:15.297007Z"
} | 61de77 | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 148,
"completion_tokens": 759
},
"timestamp": "2026-02-16T03:33:56.093Z",
"answer": 11194
},
{
"id": 11... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
}
... | {
"lo": -6.96,
"mid": -4.56,
"hi": -1.46
} | ||
103e07 | nt_gcd_compute_v1_971394319_880 | Let $m=76852$. Let $N$ be the number of integers $t$ such that $21\le t\le120$ and there exist integers $a$ and $b$ with $1\le a\le4$ and $1\le b\le10$ satisfying
$$t=15a+6b.$$
Let $A=1116128$ and $B=1802976$, and let $G=\gcd(A,B)$. Consider the set of all integers $p$ such that $p>0$ and there exists an integer $q$ wi... | 67,877 | graphs = [
Graph(
let={
"_m": Const(76852),
"_n": CountOverSet(set=SolutionsSet(var=Var("t"), condition=Exists(var=Var(name='a'), condition=Exists(var=Var(name='b'), condition=And(Geq(left=Var(name='a'), right=Const(value=1)), Leq(left=Var(name='a'), right=Const(value=4)), Geq(left=V... | NT | null | COMPUTE | sympy | COPRIME_PAIRS | [
"COPRIME_PAIRS/MAX_PRIME_BELOW",
"LIN_FORM/MAX_PRIME_BELOW"
] | 148047 | nt_gcd_compute_v1 | negation_mod | 6 | 0 | [
"COPRIME_PAIRS",
"LIN_FORM",
"MAX_PRIME_BELOW"
] | 3 | 0.01 | 2026-02-08T13:21:02.936351Z | {
"verified": true,
"answer": 67877,
"timestamp": "2026-02-08T13:21:02.946131Z"
} | eb951c | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 260,
"completion_tokens": 4229
},
"timestamp": "2026-02-15T14:19:19.311Z",
"answer": 67877
},
... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": ... | {
"lo": -5.49,
"mid": 0.22,
"hi": 6.51
} | ||
3e82ce | comb_binomial_compute_v1_1520064083_795 | Let $n = 49$. Define $n_{\text{min}}$ to be the minimum value of $x + y$ over all ordered pairs $(x,y)$ of positive integers such that $x \cdot y = n$. Let $k$ be the number of positive integers $p$ for which there exists a positive integer $q$ such that $p \cdot q = 514500$, $\gcd(p, q) = 1$, and $p < q$. Compute $\bi... | 3,003 | graphs = [
Graph(
let={
"_n": Const(49),
"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 | COPRIME_PAIRS | [
"COPRIME_PAIRS",
"B3"
] | 1999ea | comb_binomial_compute_v1 | null | 6 | 0 | [
"B3",
"COPRIME_PAIRS"
] | 2 | 0.003 | 2026-02-08T03:36:04.109305Z | {
"verified": true,
"answer": 3003,
"timestamp": "2026-02-08T03:36:04.112035Z"
} | 707c02 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 227,
"completion_tokens": 1326
},
"timestamp": "2026-02-10T15:06:27.109Z",
"answer": 3003
},
{
"i... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemm... | {
"lo": -3.46,
"mid": 1.03,
"hi": 5.49
} | ||
ccc017 | sequence_count_fib_divisible_v1_1439011603_1650 | Let $S$ be the set of all ordered pairs $(x, y)$ of positive integers such that $xy = 222784$. Let $m$ be the minimum value of $x + y$ over all pairs $(x, y) \in S$. Let $d = \sum_{k=1}^{2} \phi(k) \left\lfloor \frac{2}{k} \right\rfloor$, where $\phi$ denotes Euler's totient function. Determine the number of positive i... | 45,351 | graphs = [
Graph(
let={
"_n": Const(2),
"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(222784)))), expr=Sum(Var("x"), Var("y"))... | NT | null | COUNT | sympy | B3 | [
"B3",
"K2"
] | f1ea07 | sequence_count_fib_divisible_v1 | null | 6 | 0 | [
"B3",
"K2"
] | 2 | 0.061 | 2026-02-08T16:12:15.805583Z | {
"verified": true,
"answer": 45351,
"timestamp": "2026-02-08T16:12:15.866858Z"
} | 87c4b0 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 202,
"completion_tokens": 2429
},
"timestamp": "2026-02-16T22:56:02.392Z",
"answer": 45351
},
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "K2",
"status": "ok"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "MOD_SU... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
894339 | diophantine_fbi2_min_v1_1874849503_333 | Let $m = \sum_{d \mid 1} \mu(d)$, where $\mu$ denotes the M\"obius function. Define $n = 11^{2m}$ and let $e = \lambda(n)$, where $\lambda$ denotes the Liouville function. Let $a = 6e$ and $k = 64$. Determine the smallest integer $d$ such that $7 \leq d \leq 74$, $d$ divides $k$, and $\frac{k}{d} \geq 5$. | 8 | graphs = [
Graph(
let={
"n1": Const(1),
"m": SumOverDivisors(n=Ref(name='n1'), var='d', expr=MoebiusMu(n=Var(name='d'))),
"p": Const(11),
"n": Pow(Ref("p"), Mul(Const(2), Ref("m"))),
"e": LiouvilleLambda(n=Ref(name='n')),
"k": Const(64)... | NT | null | EXTREMUM | sympy | LIOUVILLE_ONE | [
"LIOUVILLE_ONE",
"MOBIUS_SUM"
] | 6dd3e4 | diophantine_fbi2_min_v1 | null | 4 | 2 | [
"LIOUVILLE_ONE",
"MOBIUS_SUM"
] | 2 | 0.011 | 2026-02-08T12:57:30.599183Z | {
"verified": true,
"answer": 8,
"timestamp": "2026-02-08T12:57:30.609733Z"
} | bf90a4 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 227,
"completion_tokens": 757
},
"timestamp": "2026-02-09T15:52:29.507Z",
"answer": 8
},
{
"id": ... | 2 | [
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "LIOUVILLE_ONE",
"status": "ok"
},
{
"lemma": "MOBIUS_SUM",
"status": "ok"
},
{
"lemma": "MOD_ADD",
"status": "no"... | {
"lo": -10,
"mid": -6.47,
"hi": -2.95
} | ||
c931aa | antilemma_k3_v1_1978505735_8412 | Let $x$ be the sum of $\phi(d)$ over all positive divisors $d$ of $98322$. Compute the remainder when $94013 \cdot x$ is divided by $87257$. | 63,148 | graphs = [
Graph(
let={
"x": SumOverDivisors(n=Const(value=98322), var='d', expr=EulerPhi(n=Var(name='d'))),
"_c": Const(94013),
"Q": Mod(value=Mul(Ref("_c"), Ref("x")), modulus=Const(87257)),
},
goal=Ref("Q"),
)
] | NT | COMB | COMPUTE | sympy | K3 | [
"K3"
] | 54c41e | antilemma_k3_v1 | null | 3 | 0 | [
"K3"
] | 1 | 0.001 | 2026-02-08T20:49:17.320757Z | {
"verified": true,
"answer": 63148,
"timestamp": "2026-02-08T20:49:17.321311Z"
} | 3047c5 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 89,
"completion_tokens": 1690
},
"timestamp": "2026-02-19T01:11:32.306Z",
"answer": 63148
},
{... | 1 | [
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "K3",
"status": "ok"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "V3",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
616798 | comb_sum_binomial_row_v1_153355830_1483 | Let $m = 2$. Let $n_0$ be the smallest integer $d$ such that $d \geq m$ and $d$ divides $5000567$. Let $n$ be the largest prime number such that $2 \leq n \leq n_0$. Compute $2^n$. | 2,048 | graphs = [
Graph(
let={
"_m": Const(2),
"_n": MinOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Ref("_m")), Divides(divisor=Var("d"), dividend=Const(5000567))))),
"n": MaxOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(2)), Leq... | NT | null | SUM | sympy | MIN_PRIME_FACTOR | [
"MIN_PRIME_FACTOR/MAX_PRIME_BELOW"
] | e4e16c | comb_sum_binomial_row_v1 | null | 5 | 0 | [
"MAX_PRIME_BELOW",
"MIN_PRIME_FACTOR"
] | 2 | 0.002 | 2026-02-08T06:26:20.570896Z | {
"verified": true,
"answer": 2048,
"timestamp": "2026-02-08T06:26:20.572421Z"
} | d73b16 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 112,
"completion_tokens": 640
},
"timestamp": "2026-02-13T00:14:04.741Z",
"answer": 2048
},
{
... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok_later"
},
{
"lemma": "MIN_PRIME_FACTOR",
"status": "ok"
},
... | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
2cb334 | algebra_poly_eval_v1_1978505735_7164 | Let $S$ be the set of all positive integers $p$ for which there exists a positive integer $q$ such that $pq = 926100$, $\gcd(p, q) = 1$, and $p < q$. Let $n$ be the number of elements in $S$. Let $\sigma$ be the sum of $\phi(d)$ over all positive divisors $d$ of $n$. Compute the remainder when $44121 \cdot (\sigma \cdo... | 51,975 | graphs = [
Graph(
let={
"_n": Const(2),
"x": Const(21),
"result": Sum(Mul(SumOverDivisors(n=CountOverSet(set=SolutionsSet(var=Var(name='p'), condition=And(IsPositive(arg=Var(name='p')), Exists(var=Var(name='q'), condition=And(Eq(left=Mul(Var(name='p'), Var(name='q')), rig... | NT | null | COMPUTE | sympy | COPRIME_PAIRS | [
"COPRIME_PAIRS/K3"
] | f9481c | algebra_poly_eval_v1 | null | 6 | 0 | [
"COPRIME_PAIRS",
"K3"
] | 2 | 0.003 | 2026-02-08T20:05:40.494322Z | {
"verified": true,
"answer": 51975,
"timestamp": "2026-02-08T20:05:40.497322Z"
} | 4a44d4 | 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": 2672
},
"timestamp": "2026-02-18T23:55:48.321Z",
"answer": 51975
},
... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "K3",
"status": "ok_later"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
},
{
... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
912c5f | algebra_quadratic_discriminant_v1_153355830_238 | Let $p$ and $q$ be positive integers such that $pq = 72$, $\gcd(p, q) = 1$, and $p < q$. Let $n$ be the number of such integers $p$. Define $\text{result} = (-7)^n - 4(-1)(-10)$. Compute the remainder when $72385 \cdot \text{result}$ is divided by $73269$. | 65,313 | graphs = [
Graph(
let={
"_n": Const(73269),
"a": Const(-1),
"b": Const(-7),
"c": Const(-10),
"result": Sub(Pow(Ref("b"), CountOverSet(set=SolutionsSet(var=Var("p"), condition=And(IsPositive(arg=Var(name='p')), Exists(var=Var(name='q'), condition=An... | NT | null | COMPUTE | sympy | COPRIME_PAIRS | [
"COPRIME_PAIRS"
] | 2bb3aa | algebra_quadratic_discriminant_v1 | null | 5 | 0 | [
"COPRIME_PAIRS"
] | 1 | 0.002 | 2026-02-08T02:58:43.349764Z | {
"verified": true,
"answer": 65313,
"timestamp": "2026-02-08T02:58:43.351419Z"
} | c995db | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 202,
"completion_tokens": 2101
},
"timestamp": "2026-02-10T12:25:29.058Z",
"answer": 65313
},
{
"... | 1 | [
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": ... | {
"lo": 1.1,
"mid": 4.17,
"hi": 6.61
} | ||
df9a2d | nt_count_coprime_v1_124444284_6140 | Let $m = 44$. Consider the set of all ordered pairs $(x,y)$ of positive integers such that $x + y = m$. Let $P$ be the set of all products $xy$ for such pairs. Let $n$ be the maximum value in $P$.
Now consider the set of all ordered pairs $(x,y)$ of positive integers such that $xy = n$. Let $S$ be the set of all value... | 5,401 | graphs = [
Graph(
let={
"_m": Const(44),
"_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("_m")))), expr=Mul(Var("x"), Var("y")))),
... | NT | null | COUNT | sympy | B1 | [
"B1/B3"
] | 80b49d | nt_count_coprime_v1 | null | 6 | 0 | [
"B1",
"B3"
] | 2 | 14.242 | 2026-02-08T08:09:02.305686Z | {
"verified": true,
"answer": 5401,
"timestamp": "2026-02-08T08:09:16.547507Z"
} | 08336b | 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": 1248
},
"timestamp": "2026-02-13T15:31:03.394Z",
"answer": 5401
},
{... | 1 | [
{
"lemma": "B1",
"status": "ok"
},
{
"lemma": "B3",
"status": "ok_later"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma"... | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
8f29af | modular_count_residue_v1_2051736721_2826 | Let $ m $ be the number of integers $ n $ with $ 1 \leq n \leq 46 $ such that the sum of the decimal digits of $ n $ is even. Let $ r = 21 $. Determine the value of the number of integers $ n_1 $ with $ 1 \leq n_1 \leq 75625 $ such that $ n_1 \equiv r \pmod{m} $. | 3,288 | graphs = [
Graph(
let={
"_n": Const(2),
"upper": Const(75625),
"m": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Const(46)), Eq(Mod(value=DigitSum(Var("n")), modulus=Ref("_n")), Const(0))))),
"r": Const(21),
... | NT | null | COUNT | sympy | L3B | [
"L3B"
] | cc148f | modular_count_residue_v1 | null | 3 | 0 | [
"L3B"
] | 1 | 2.804 | 2026-02-08T16:55:27.657234Z | {
"verified": true,
"answer": 3288,
"timestamp": "2026-02-08T16:55:30.461365Z"
} | 6a69dc | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 136,
"completion_tokens": 1426
},
"timestamp": "2026-02-17T14:54:54.237Z",
"answer": 3288
},
{... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "L3B",
"status": "ok"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
ea2de7 | alg_poly_preperiod_count_v1_1218484723_5312 | Let $N = a^{2} + a -13 \bmod 31$, let $M = N^{2} + N -13 \bmod 31$, let $R = M^{2} + M -13 \bmod 31$, let $S = R^{2} + R -13 \bmod 31$, let $T = S^{2} + S -13 \bmod 31$, and let $K = T^{2} + T -13 \bmod 31$. Let $Q$ be the number of integers $a$ with $0 \le a \le 36951$ such that $K = M$, $R \ne M$, $S \ne M$, and $T \... | 16,688 | graphs = [
Graph(
let={
"p1": Mod(value=Sum(Pow(Var("a"), Const(2)), Var("a"), Const(-13)), modulus=Const(31)),
"p2": Mod(value=Sum(Pow(Ref("p1"), Const(2)), Ref("p1"), Const(-13)), modulus=Const(31)),
"p3": Mod(value=Sum(Pow(Ref("p2"), Const(2)), Ref("p2"), Const(-13)), ... | ALG | null | COUNT | sympy | POLY_ORBIT_COUNT | [
"POLY_ORBIT_COUNT"
] | 4ad965 | alg_poly_preperiod_count_v1 | null | 7 | null | [
"POLY_ORBIT_COUNT"
] | 1 | 0.04 | 2026-02-25T06:56:15.372657Z | {
"verified": true,
"answer": 16688,
"timestamp": "2026-02-25T06:56:15.412923Z"
} | fbdc62 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 273,
"completion_tokens": 13879
},
"timestamp": "2026-03-29T20:28:39.280Z",
"answer": 16688
},
{
... | 1 | [
{
"lemma": "POLY_ORBIT_COUNT",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
}
] | {
"lo": -3.33,
"mid": 1.03,
"hi": 5.26
} | ||
fd8236 | modular_sum_quadratic_residues_v1_1520064083_8093 | Let $T$ be the set of all integers $t$ such that $24 \leq t \leq 380$ and there exist positive integers $a$ and $b$ with $1 \leq a \leq 19$, $1 \leq b \leq 65$, and $t = 2a + 5b + 17$. Let $p$ be the number of elements in $T$. Compute $\frac{p(p-1)}{4}$. | 31,064 | graphs = [
Graph(
let={
"_n": Const(4),
"p": CountOverSet(set=SolutionsSet(var=Var("t"), condition=Exists(var=Var(name='a'), condition=Exists(var=Var(name='b'), condition=And(Geq(left=Var(name='a'), right=Const(value=1)), Leq(left=Var(name='a'), right=Const(value=19)), Geq(left=Var(n... | NT | null | SUM | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | modular_sum_quadratic_residues_v1 | null | 4 | 0 | [
"LIN_FORM"
] | 1 | 0.002 | 2026-02-08T10:00:52.002991Z | {
"verified": true,
"answer": 31064,
"timestamp": "2026-02-08T10:00:52.005049Z"
} | 97d002 | 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": 2909
},
"timestamp": "2026-02-14T06:04:28.135Z",
"answer": 31064
},
... | 1 | [
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "V8",
"status... | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
b8d558_l | nt_count_divisible_and_v1_1520064083_5278 | Let $N$ be the number of positive integers $n$ such that $1 \leq n \leq 82476$, $n$ is divisible by 12, and $n$ is divisible by 18. Let $S$ be the set of all integers $t$ such that $5 \leq t \leq 17$ and there exist positive integers $a$ and $b$ with $1 \leq a \leq 4$, $1 \leq b \leq 3$, and $t = 2a + 3b$. Compute the ... | 1 | COMB | null | COUNT | sympy | LIN_FORM | [
"LIN_FORM"
] | 1ae498 | nt_count_divisible_and_v1 | bell_mod | 4 | 0 | [
"LIN_FORM"
] | 1 | 2.759 | 2026-02-08T06:42:50.963751Z | {
"verified": false,
"answer": 5,
"timestamp": "2026-02-08T06:42:53.722402Z"
} | 852669 | b8d558 | legacy_text | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 247,
"completion_tokens": 1119
},
"timestamp": "2026-02-24T06:51:50.738Z",
"answer": 5
},
{
"id":... | 1 | [
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "V8",
"status": "no"
},
{
"lemma": "V8_SUM",
"s... | {
"lo": -2.46,
"mid": 0.47,
"hi": 3.59
} | |
c84729 | comb_binomial_compute_v1_1918700295_2774 | Let $n = 14$. Let $k$ be the number of positive integers $p$ for which there exists a positive integer $q$ such that $pq = 36750$, $\gcd(p, q) = 1$, and $p < q$. Compute the remainder when $\binom{n}{k}$ is multiplied by 82351 and then divided by 96835. | 80,298 | graphs = [
Graph(
let={
"n": Const(14),
"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=36750)), Eq(left=GCD(a=Var(name='p'), b=Var(name=... | NT | null | COMPUTE | sympy | COPRIME_PAIRS | [
"COPRIME_PAIRS"
] | 2bb3aa | comb_binomial_compute_v1 | null | 5 | 0 | [
"COPRIME_PAIRS"
] | 1 | 0.001 | 2026-02-08T08:12:06.269543Z | {
"verified": true,
"answer": 80298,
"timestamp": "2026-02-08T08:12:06.270726Z"
} | 2db8d6 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 126,
"completion_tokens": 1760
},
"timestamp": "2026-02-13T15:46:49.871Z",
"answer": 80298
},
... | 1 | [
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
}
] | {
"lo": -3.51,
"mid": 1.33,
"hi": 6.56
} | ||
dcef23 | nt_num_divisors_compute_v1_1918700295_4166 | Let $S$ be the set of all ordered pairs $(x, y)$ of positive integers such that $xy = 110889$. For each such pair, compute $x + y$. Let $n$ be the minimum value of $x + y$ over all such pairs. Find the number of positive divisors of $n$. | 12 | 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(110889)))), expr=Sum(Var("x"), Var("y")))),
"result": NumDiv... | NT | null | COMPUTE | sympy | B3 | [
"B3"
] | 0cd20d | nt_num_divisors_compute_v1 | null | 4 | 0 | [
"B3"
] | 1 | 0.003 | 2026-02-08T09:11:09.023249Z | {
"verified": true,
"answer": 12,
"timestamp": "2026-02-08T09:11:09.025933Z"
} | e82d73 | 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": 1137
},
"timestamp": "2026-02-14T01:46:17.997Z",
"answer": 12
},
{
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
}
] | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
38f711_n | alg_sym_quad_system_v1_1218484723_3793 | A chemist mixes three reagents in positive integer amounts $a$, $b$, and $c$ such that the variances in concentration satisfy $a^2 + b^2 + c^2 = ab + bc + ca$, and the weighted cost $a + 5b + 2c$ totals 2496 units. For each valid combination, the total molecular energy is $a^3 + b^3 + c^3$. Let $N$ be the sum of all su... | 5 | ALG | COMB | COMPUTE | sympy | K3 | [
"STARS_BARS"
] | f6827c | alg_sym_quad_system_v1 | null | 6 | null | [
"K3",
"STARS_BARS"
] | 2 | 0.162 | 2026-02-25T05:26:19.943554Z | null | b5253f | 38f711 | narrative | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 260,
"completion_tokens": 1039
},
"timestamp": "2026-03-30T20:35:44.956Z",
"answer": 5
},
{
"id":... | 1 | [
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "STARS_BARS",
"status": "ok"
}
] | {
"lo": -5.37,
"mid": 0.23,
"hi": 5.22
} | |
a6d493 | antilemma_k2_v1_1520064083_265 | Let $n=2$. Consider the quadratic equation
$$x^2-168x-13969=0.$$
Let $R$ be the set of all integer solutions $x$ of this equation, and let $M$ be the sum of all elements of $R$.
Let $T$ be the integer
$$T=\sum_{k=1}^{M} \varphi(k)\left\lfloor \frac{\displaystyle \sum_{d\mid 168} \varphi(d)}{k} \right\rfloor,$$
where $... | 203 | graphs = [
Graph(
let={
"_n": Const(2),
"x": Summation(var="k", start=Const(1), end=SumOverSet(set=SolutionsSet(var=Var("x"), condition=Eq(Sum(Pow(Var("x"), Ref("_n")), Mul(Const(-168), Var("x")), Const(-13969)), Const(0)))), expr=Mul(EulerPhi(n=Var("k")), Floor(Div(SumOverDivisors(n... | NT | COMB | COMPUTE | sympy | VIETA_SUM | [
"VIETA_SUM/K2",
"K3/K2",
"K2"
] | 4108ea | antilemma_k2_v1 | null | 8 | 0 | [
"K2",
"K3",
"VIETA_SUM"
] | 3 | 0.003 | 2026-02-08T03:09:04.896755Z | {
"verified": true,
"answer": 203,
"timestamp": "2026-02-08T03:09:04.899601Z"
} | 9d166b | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 298,
"completion_tokens": 2162
},
"timestamp": "2026-02-10T13:05:48.130Z",
"answer": 203
},
{
"i... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "K2",
"status": "ok"
},
{
"lemma": "K3",
"status": "ok"
},
{
"lemma": "MOD_SUB",
"... | {
"lo": -1.84,
"mid": 0.79,
"hi": 3.12
} | ||
e7db0a | sequence_count_fib_divisible_v1_2080023795_134 | Let $d$ be a positive integer such that $1 \leq d \leq 452$ and the $d$-th Fibonacci number is divisible by $15$. Find the number of such integers $d$. | 22 | graphs = [
Graph(
let={
"upper": Const(452),
"d": Const(15),
"result": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Ref("upper")), Divides(divisor=Ref("d"), dividend=Fibonacci(arg=Var(name='n')))))),
},
g... | NT | null | COUNT | sympy | C5 | [
"C5"
] | 1d9668 | sequence_count_fib_divisible_v1 | null | 6 | 0 | [
"C5"
] | 1 | 0.126 | 2026-02-08T11:34:15.728963Z | {
"verified": true,
"answer": 22,
"timestamp": "2026-02-08T11:34:15.854510Z"
} | 8140a2 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 160,
"completion_tokens": 2511
},
"timestamp": "2026-02-08T20:45:37.340Z",
"answer": 22
},
{
"id"... | 1 | [
{
"lemma": "C5",
"status": "ok"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
},
{
"lemma": "VAL_SUM_EQ",
"status": "no"
}
] | {
"lo": -2.02,
"mid": 1.77,
"hi": 4.93
} | ||
359818 | antilemma_cartesian_v1_151522320_596 | Compute the remainder when $44121$ times the number of ordered pairs $(i,j)$ with $1 \leq i \leq 30$ and $1 \leq j \leq 32$ is divided by $88217$. | 12,000 | graphs = [
Graph(
let={
"x": CountOverSet(set=CartesianProduct(left=IntegerRange(start=Const(1), end=Const(30)), right=IntegerRange(start=Const(1), end=Const(32)))),
"Q": Mod(value=Mul(Const(44121), Ref("x")), modulus=Const(88217)),
},
goal=Ref("Q"),
)
] | COMB | GEOM | COMPUTE | sympy | COUNT_CARTESIAN | [
"COUNT_CARTESIAN"
] | 409d7d | antilemma_cartesian_v1 | null | 2 | 0 | [
"COUNT_CARTESIAN"
] | 1 | 0.001 | 2026-02-08T03:23:28.308389Z | {
"verified": true,
"answer": 12000,
"timestamp": "2026-02-08T03:23:28.308962Z"
} | 89b8f9 | 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": 845
},
"timestamp": "2026-02-10T14:16:57.327Z",
"answer": 12000
},
{
"i... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "ok"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8_SUM",
"statu... | {
"lo": -3.83,
"mid": -1.68,
"hi": 1.09
} | ||
beb8fb | nt_count_divisible_and_v1_1978505735_5130 | Let $d_1$ be the number of nonnegative integers $j$ such that $0 \le j \le 18433$ and $\binom{18433}{j}$ is odd. Let $d_2 = 12$ and $U = 31392$. Let $\text{result}$ be the number of positive integers $n$ such that $1 \le n \le U$, $n$ is divisible by $d_1$, and $n$ is divisible by $d_2$. Compute the remainder when $441... | 73,267 | graphs = [
Graph(
let={
"_n": Const(18433),
"upper": Const(31392),
"d1": CountOverSet(set=SolutionsSet(var=Var("j"), condition=And(Geq(Var("j"), Const(0)), Leq(Var("j"), Ref("_n")), Eq(Mod(value=Binom(n=Const(18433), k=Var("j")), modulus=Const(2)), Const(1))), domain='non... | ALG | COMB | COUNT | sympy | V8 | [
"V8"
] | 86348e | nt_count_divisible_and_v1 | null | 6 | 0 | [
"V8"
] | 1 | 1.405 | 2026-02-08T18:46:48.157901Z | {
"verified": true,
"answer": 73267,
"timestamp": "2026-02-08T18:46:49.562678Z"
} | 5f7807 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 175,
"completion_tokens": 2744
},
"timestamp": "2026-02-18T19:48:21.880Z",
"answer": 73267
},
... | 1 | [
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "V1",
"status": "no"
},
{
"lemma": "V8",
"status": "ok"
}
] | {
"lo": -3.12,
"mid": 1.47,
"hi": 6.57
} | ||
a7e7c2 | antilemma_k2_v1_1520064083_7530 | Compute the value of $$\sum_{k=1}^{385} \phi(k) \left\lfloor \frac{385}{k} \right\rfloor,$$ where $\phi(k)$ denotes Euler's totient function. | 74,305 | graphs = [
Graph(
let={
"_n": Const(385),
"x": Summation(var="k", start=Const(1), end=Ref("_n"), expr=Mul(EulerPhi(n=Var("k")), Floor(Div(Const(385), Var("k"))))),
},
goal=Ref("x"),
)
] | NT | COMB | COMPUTE | sympy | K2 | [
"K2"
] | 6897ab | antilemma_k2_v1 | null | 7 | 0 | [
"K2"
] | 1 | 0 | 2026-02-08T09:06:05.397801Z | {
"verified": true,
"answer": 74305,
"timestamp": "2026-02-08T09:06:05.398142Z"
} | 9f9520 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 92,
"completion_tokens": 716
},
"timestamp": "2026-02-14T01:02:00.500Z",
"answer": 74305
},
{
... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "K2",
"status": "ok"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
... | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
017548 | sequence_lucas_compute_v1_48377204_2590 | Let $S$ be the set of all positive integers $p$ for which there exists a positive integer $q$ such that $pq = 12$, $\gcd(p, q) = 1$, and $p < q$. Let $m$ be the number of elements in $S$. Let $d$ be the smallest divisor of $10051$ such that $d \geq m$. Define $L$ to be the $d$th Lucas number. Compute the smallest posit... | 2,076 | graphs = [
Graph(
let={
"_n": Const(10051),
"n": 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=... | NT | null | COMPUTE | sympy | COPRIME_PAIRS | [
"COPRIME_PAIRS/MIN_PRIME_FACTOR"
] | 52cee2 | sequence_lucas_compute_v1 | null | 6 | 0 | [
"COPRIME_PAIRS",
"MIN_PRIME_FACTOR"
] | 2 | 0.01 | 2026-02-08T16:49:57.378576Z | {
"verified": true,
"answer": 2076,
"timestamp": "2026-02-08T16:49:57.388544Z"
} | 4893e1 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 178,
"completion_tokens": 3173
},
"timestamp": "2026-02-17T14:29:36.243Z",
"answer": 2076
},
{... | 1 | [
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "MIN_PRIME_FACTOR",
"status": "ok_later"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "MOD_SUB",
"s... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
4f7238 | nt_count_gcd_equals_v1_865884756_3086 | Let $k = 90$ and $d = 15$. Let $N$ be the number of positive integers $n$ such that $1 \leq n \leq 29929$ and $\gcd(n, 90) = 15$. Let $c$ be the minimum value of $x + y$ over all ordered pairs $(x,y)$ of positive integers such that $xy = 5184$. Compute the remainder when $c - N$ is divided by $63952$. | 63,431 | graphs = [
Graph(
let={
"upper": Const(29929),
"k": Const(90),
"d": Const(15),
"result": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Ref("upper")), Eq(GCD(a=Var("n"), b=Ref("k")), Ref("d"))))),
"... | NT | null | COUNT | sympy | B3 | [
"B3"
] | fc629c | nt_count_gcd_equals_v1 | negation_mod | 4 | 0 | [
"B3"
] | 1 | 2.489 | 2026-02-08T17:10:34.255355Z | {
"verified": true,
"answer": 63431,
"timestamp": "2026-02-08T17:10:36.744641Z"
} | ef9807 | 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": 993
},
"timestamp": "2026-02-17T20:53:07.407Z",
"answer": 63431
},
{... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "V8_SUM",
"sta... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
fd580b | sequence_count_fib_divisible_v1_677425708_263 | Let $S$ be the set of all integers $t$ such that $9 \leq t \leq 826$ and there exist positive integers $a$ and $b$ with $1 \leq a \leq 126$, $1 \leq b \leq 49$, and $t = 5a + 4b$. Let $d$ be the minimum value of $x + y$ over all ordered pairs $(x, y)$ of positive integers such that $xy = 81$. Determine the number of po... | 67 | graphs = [
Graph(
let={
"_n": Const(81),
"upper": CountOverSet(set=SolutionsSet(var=Var("t"), condition=Exists(var=Var(name='a'), condition=Exists(var=Var(name='b'), condition=And(Geq(left=Var(name='a'), right=Const(value=1)), Leq(left=Var(name='a'), right=Const(value=126)), Geq(left... | NT | null | COUNT | sympy | LIN_FORM | [
"LIN_FORM",
"B3"
] | 688dbe | sequence_count_fib_divisible_v1 | null | 7 | 0 | [
"B3",
"LIN_FORM"
] | 2 | 0.062 | 2026-02-08T03:10:58.627078Z | {
"verified": true,
"answer": 67,
"timestamp": "2026-02-08T03:10:58.688724Z"
} | becc3a | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 258,
"completion_tokens": 5794
},
"timestamp": "2026-02-23T17:19:00.213Z",
"answer": 67
},
{
"id... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "LTE_SUM",
"status": "... | {
"lo": -3.45,
"mid": 1.18,
"hi": 5.72
} | ||
0f1f14 | sequence_count_fib_divisible_v1_1125832087_1232 | Let $m = 333$. Define $n$ to be the number of positive integers $k$ such that $1 \leq k \leq 2736261$ and $k$ is divisible by $m$. Let $u$ be the number of positive integers $k$ such that $1 \leq k \leq n$ and $k$ is divisible by 9. Let $d = 10$. Define $r$ to be the number of positive integers $n$ such that $1 \leq n ... | 30 | graphs = [
Graph(
let={
"_m": Const(333),
"_n": CountOverSet(set=SolutionsSet(var=Var("k"), condition=And(Geq(Var("k"), Const(1)), Leq(Var("k"), Const(2736261)), Divides(divisor=Ref("_m"), dividend=Var("k"))), domain='positive_integers')),
"upper": CountOverSet(set=Soluti... | NT | null | COUNT | sympy | LIN_FORM | [
"C2/C2"
] | c8a699 | sequence_count_fib_divisible_v1 | null | 5 | 0 | [
"C2",
"LIN_FORM"
] | 2 | 0.161 | 2026-02-08T03:37:40.039527Z | {
"verified": true,
"answer": 30,
"timestamp": "2026-02-08T03:37:40.200737Z"
} | f0bd3b | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 271,
"completion_tokens": 3137
},
"timestamp": "2026-02-10T13:57:58.827Z",
"answer": 30
},
{
"id... | 1 | [
{
"lemma": "C2",
"status": "ok"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
... | {
"lo": -3.42,
"mid": 1.86,
"hi": 7.55
} | ||
2df075_n | alg_poly4_min_v1_1218484723_1618 | An architect designs rectangular foundations with area $342225$ square meters and seeks to minimize the sum of side lengths $x + y$; let $T = x + y$ for this optimal rectangle. Using this $T$, she evaluates the structural cost function $47385b^4 + T a^4 + 31590a^2b^2 - 63180ab^3 - 7020a^3b$ for integer dimensions $a, b... | 9,945 | ALG | null | COMPUTE | sympy | LIN_FORM | [
"B3"
] | 0cd20d | alg_poly4_min_v1 | null | 6 | null | [
"B3",
"LIN_FORM"
] | 2 | 0.91 | 2026-02-25T03:19:18.028164Z | null | 2b1cbe | 2df075 | narrative | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 225,
"completion_tokens": 20413
},
"timestamp": "2026-03-30T17:09:05.727Z",
"answer": 9945
},
{
"... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
}
] | {
"lo": -5.37,
"mid": 0.23,
"hi": 5.22
} | |
dd32e0 | nt_num_divisors_compute_v1_677425708_2883 | Let $d$ be an integer. Define $n$ to be the smallest integer $d \geq 2$ that divides 11025. Compute the number of positive divisors of $n$. | 2 | graphs = [
Graph(
let={
"_n": Const(2),
"n": MinOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Ref("_n")), Divides(divisor=Var("d"), dividend=Const(11025))))),
"result": NumDivisors(n=Ref("n")),
},
goal=Ref("result"),
)
] | NT | null | COMPUTE | sympy | MIN_PRIME_FACTOR | [
"MIN_PRIME_FACTOR"
] | bc3776 | nt_num_divisors_compute_v1 | null | 2 | 0 | [
"MIN_PRIME_FACTOR"
] | 1 | 0.002 | 2026-02-08T05:21:46.838723Z | {
"verified": true,
"answer": 2,
"timestamp": "2026-02-08T05:21:46.840865Z"
} | a6984c | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 1,
"correct": {
"strict": false,
"boxed": false,
"relaxed": true
},
"usage": {
"prompt_tokens": 87,
"completion_tokens": 2601
},
"timestamp": "2026-02-12T07:18:27.462Z",
"answer": 4
},
{
... | 1 | [
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "MIN_PRIME_FACTOR",
"status": "ok"
},
{
"lemma": "V3",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
}
] | {
"lo": -5.55,
"mid": -3.01,
"hi": 0.32
} | ||
78a4a2 | nt_min_phi_inverse_v1_677425708_2690 | Let $S$ be the set of all positive integers $n$ such that $1 \leq n \leq 70$ and $\phi(n) = 20$. Define $m$ to be the smallest element of $S$. Let $t$ be the number of positive integers $n$ such that $1 \leq n \leq 17$ and the sum of the digits of $n$ is even. Compute $m^2 + (1 + 2 + 3) \cdot m + t$. | 783 | graphs = [
Graph(
let={
"upper": Const(70),
"k": Const(20),
"result": MinOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Ref("upper")), Eq(EulerPhi(n=Var("n")), Ref("k"))))),
"Q": Sum(Pow(Ref("result"), Const(2)), Mu... | NT | null | EXTREMUM | sympy | SUM_ARITHMETIC | [
"SUM_ARITHMETIC",
"L3B"
] | ad1d27 | nt_min_phi_inverse_v1 | quadratic_mod | 6 | 0 | [
"L3B",
"SUM_ARITHMETIC"
] | 2 | 0.009 | 2026-02-08T05:12:07.788761Z | {
"verified": true,
"answer": 783,
"timestamp": "2026-02-08T05:12:07.797500Z"
} | 50cd57 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 222,
"completion_tokens": 2946
},
"timestamp": "2026-02-11T23:04:35.633Z",
"answer": 783
},
{
"i... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "L3B",
"status": "ok"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "SUM_ARITHMETIC",
"status": "ok"
},
{
"lemma": "V5",
"status": "no"
},
{
"lemma": "V8_... | {
"lo": -3.42,
"mid": 1.86,
"hi": 7.55
} | ||
aab938 | modular_min_linear_v1_1520064083_7863 | Let $a = 57136$ and $b$ be the largest positive divisor of $351056$ that is at most $592$. Let $m = 89642$. Find the smallest positive integer $x$ such that $1 \leq x \leq m$ and $ax \equiv b \pmod{m}$. | 15,752 | graphs = [
Graph(
let={
"a": Const(57136),
"b": MaxOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Const(1)), Leq(Var("d"), Const(592)), Divides(divisor=Var("d"), dividend=Const(351056))))),
"m": Const(89642),
"result": MinOverSet(set=Soluti... | NT | null | EXTREMUM | sympy | MAX_DIVISOR | [
"MAX_DIVISOR"
] | 51757e | modular_min_linear_v1 | null | 5 | 0 | [
"MAX_DIVISOR"
] | 1 | 3.459 | 2026-02-08T09:20:53.385240Z | {
"verified": true,
"answer": 15752,
"timestamp": "2026-02-08T09:20:56.844660Z"
} | a3a4f6 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 114,
"completion_tokens": 2822
},
"timestamp": "2026-02-14T03:10:00.581Z",
"answer": 15752
},
... | 1 | [
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "MAX_DIVISOR",
"status": "ok"
}
] | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
282b8b | comb_count_partitions_v1_1125832087_1098 | Let $n = 66263$. Define $d_0$ to be the smallest divisor of $86903$ that is at least $2$. Let $P(d_0)$ denote the number of integer partitions of $d_0$. Compute the remainder when $44121 \times P(d_0)$ is divided by $n$. Determine the value of this remainder. | 8,495 | graphs = [
Graph(
let={
"_n": Const(66263),
"n": MinOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Const(2)), Divides(divisor=Var("d"), dividend=Const(86903))))),
"result": Partition(arg=Ref(name='n')),
"Q": Mod(value=Mul(Const(44121), Ref(... | NT | COMB | COUNT | sympy | MIN_PRIME_FACTOR | [
"MIN_PRIME_FACTOR"
] | bc3776 | comb_count_partitions_v1 | null | 6 | 0 | [
"MIN_PRIME_FACTOR"
] | 1 | 0.001 | 2026-02-08T03:31:14.786192Z | {
"verified": true,
"answer": 8495,
"timestamp": "2026-02-08T03:31:14.787298Z"
} | 6c80c3 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 187,
"completion_tokens": 2924
},
"timestamp": "2026-02-10T13:45:53.931Z",
"answer": 30389
},
{
... | 1 | [
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "MIN_PRIME_FACTOR",
"status": "ok"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "V1",
"status": "no"
},
{
"lemma": "V3",
"status": "no"
}
] | {
"lo": 1.94,
"mid": 5.23,
"hi": 8.52
} | ||
1dae22 | alg_sum_ap_v1_1218484723_2639 | Let $m = \min\{x + y \mid x, y > 0,\ xy = 398161\}$. Compute the remainder when $\left(44121 \cdot \left( \sum_{k=0}^{m} (14k + 96) \bmod 7963 \right)\right)$ is divided by $74392$. | 43,766 | graphs = [
Graph(
let={
"_n": Const(14),
"result": Mod(value=Summation(var="k", start=Const(0), end=MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(Mul(Var("x"), Var("y... | ALG | null | COMPUTE | sympy | B3 | [
"B3"
] | 0cd20d | alg_sum_ap_v1 | null | 4 | 0 | [
"B3"
] | 1 | 0.015 | 2026-02-25T04:22:54.023370Z | {
"verified": true,
"answer": 43766,
"timestamp": "2026-02-25T04:22:54.038236Z"
} | 6bba90 | 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": 7813
},
"timestamp": "2026-03-29T05:49:57.247Z",
"answer": 43766
},
{
"... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
}
] | {
"lo": -2.45,
"mid": 1.37,
"hi": 5.29
} | ||
b5b698 | diophantine_fbi2_min_v1_1915831931_661 | Let $x$ be a real number satisfying $x^2 - 130x - 1251 = 0$. Let $u$ be the sum of all such solutions $x$. Let $d$ be a positive integer such that $2 \le d \le u$, $d$ divides $120$, and $\frac{120}{d} \ge \sum_{k=1}^{2} \phi(k) \left\lfloor \frac{2}{k} \right\rfloor$. Determine the minimum possible value of $d$. | 2 | graphs = [
Graph(
let={
"_n": Const(2),
"k": Const(120),
"upper": SumOverSet(set=SolutionsSet(var=Var("x"), condition=Eq(Sum(Pow(Var("x"), Const(2)), Mul(Const(-130), Var("x")), Const(-1251)), Const(0)))),
"result": MinOverSet(set=SolutionsSet(var=Var("d"), co... | NT | null | EXTREMUM | sympy | VIETA_SUM | [
"VIETA_SUM",
"K2"
] | f4a436 | diophantine_fbi2_min_v1 | null | 5 | 0 | [
"K2",
"VIETA_SUM"
] | 2 | 0.015 | 2026-02-08T15:36:28.396727Z | {
"verified": true,
"answer": 2,
"timestamp": "2026-02-08T15:36:28.411859Z"
} | 81b5fa | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 1,
"correct": {
"strict": false,
"boxed": false,
"relaxed": true
},
"usage": {
"prompt_tokens": 180,
"completion_tokens": 940
},
"timestamp": "2026-02-16T06:12:09.998Z",
"answer": 40
},
{
"id": 11,
... | 1 | [
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "K2",
"status": "ok"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "V8",
"status": "no... | {
"lo": -8.26,
"mid": -5.01,
"hi": -1.76
} | ||
11aab8 | nt_count_divisible_and_v1_655260480_780 | Let $d_1$ be the minimum value of $x + y$ over all ordered pairs $(x, y)$ of positive integers such that $x y = 36$. Let $d_2 = 15$ and $\text{upper} = 158820$.
Define $\text{result}$ to be the number of positive integers $n \leq \text{upper}$ such that $n$ is divisible by both $d_1$ and $d_2$.
Let $Q = 38025 - \text... | 35,378 | graphs = [
Graph(
let={
"upper": Const(158820),
"d1": MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(Mul(Var("x"), Var("y")), Const(36)))), expr=Sum(Var("x"), Var("y")... | NT | null | COUNT | sympy | B3 | [
"B3"
] | 0cd20d | nt_count_divisible_and_v1 | null | 4 | 0 | [
"B3"
] | 1 | 6.057 | 2026-02-08T15:36:24.597603Z | {
"verified": true,
"answer": 35378,
"timestamp": "2026-02-08T15:36:30.654375Z"
} | 01037d | 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": 694
},
"timestamp": "2026-02-16T10:25:23.066Z",
"answer": 35378
},
{... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
0370d9 | nt_count_intersection_v1_717093673_2141 | Let $N = 20000$, $a = 11$, and $b = 10$. Define $\text{result}$ to be the number of positive integers $n$ such that $1 \leq n \leq N$, $11$ divides $n$, and $\gcd(n, 10) = 1$. Let $c$ be the largest prime number less than or equal to $7007$. Compute the value of
$$
\left( (\text{result} \bmod 199) + c \cdot (\text{resu... | 72,018 | graphs = [
Graph(
let={
"_n": Const(7007),
"N": Const(20000),
"a": Const(11),
"b": Const(10),
"result": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Ref("N")), Divides(divisor=Ref("a"), dividend=V... | NT | null | COUNT | sympy | MAX_PRIME_BELOW | [
"MAX_PRIME_BELOW"
] | 08a653 | nt_count_intersection_v1 | two_moduli | 5 | 0 | [
"MAX_PRIME_BELOW"
] | 1 | 1.396 | 2026-02-08T16:35:41.449163Z | {
"verified": true,
"answer": 72018,
"timestamp": "2026-02-08T16:35:42.845292Z"
} | b37eb8 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 177,
"completion_tokens": 1949
},
"timestamp": "2026-02-17T08:13:50.342Z",
"answer": 72018
},
... | 1 | [
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok"
},
{
"lemma": "V8",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
75568b | nt_euler_phi_compute_v1_1520064083_3867 | Let $n = 30631$ and $N = 10952$. Compute the remainder when the number of ordered pairs $(x_1, x_2)$ of positive odd integers such that $x_1 + x_2 = N$ minus $\varphi(n)$ is divided by $61792$, where $\varphi$ denotes Euler's totient function. | 36,638 | graphs = [
Graph(
let={
"_n": Const(10952),
"n": Const(30631),
"result": EulerPhi(n=Ref("n")),
"Q": Mod(value=Sub(CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x1"), Var("x2")]), condition=And(IsPositive(arg=Var(name='x1')), IsPositive(arg=Var(name='x... | NT | null | COMPUTE | sympy | COMB1 | [
"COMB1"
] | 9f12f1 | nt_euler_phi_compute_v1 | negation_mod | 5 | 0 | [
"COMB1"
] | 1 | 0.003 | 2026-02-08T05:56:35.699849Z | {
"verified": true,
"answer": 36638,
"timestamp": "2026-02-08T05:56:35.702970Z"
} | 218e1c | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 143,
"completion_tokens": 597
},
"timestamp": "2026-02-17T10:00:54.395Z",
"answer": 36638
},
{
"id": 11,
... | 1 | [
{
"lemma": "COMB1",
"status": "ok"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
}
] | {
"lo": -8.26,
"mid": -5.01,
"hi": -1.76
} | ||
ee6a5a | comb_catalan_compute_v1_784195855_2218 | Let $n = 10$. The $n$th Catalan number is given by
$$
C_n = \frac{1}{n+1} \binom{2n}{n}.
$$
Let $c$ be the number of ordered pairs $(x_1, x_2)$ of positive odd integers such that $x_1 + x_2 = 38$.
Compute the remainder when $c - C_n$ is divided by $56575$. | 39,798 | graphs = [
Graph(
let={
"_n": Const(56575),
"n": Const(10),
"result": Catalan(Ref("n")),
"_c": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x1"), Var("x2")]), condition=And(IsPositive(arg=Var(name='x1')), IsPositive(arg=Var(name='x2')), IsOdd(arg=Var... | COMB | null | COMPUTE | sympy | COMB1 | [
"COMB1"
] | 9f12f1 | comb_catalan_compute_v1 | negation_mod | 4 | 0 | [
"COMB1"
] | 1 | 0.002 | 2026-02-08T05:36:55.578144Z | {
"verified": true,
"answer": 39798,
"timestamp": "2026-02-08T05:36:55.580365Z"
} | 122da9 | 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": 890
},
"timestamp": "2026-02-24T03:57:49.373Z",
"answer": 39798
},
{
"i... | 1 | [
{
"lemma": "COMB1",
"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",
"status":... | {
"lo": -4.93,
"mid": -2.91,
"hi": -0.71
} | ||
0d8fe1 | sequence_count_fib_divisible_v1_677425708_2083 | Let $\phi(n)$ denote Euler's totient function. Let $F_n$ denote the $n$th Fibonacci number, with $F_1 = F_2 = 1$ and $F_{n} = F_{n-1} + F_{n-2}$ for $n \geq 3$. Let $T$ be the set of all integers $n$ such that $\phi(2) \leq n \leq 103$ and $17$ divides $F_n$. Compute the number of elements in $T$, multiply this number ... | 59,876 | graphs = [
Graph(
let={
"upper": Const(103),
"d": Const(17),
"result": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), EulerPhi(n=Const(2))), Leq(Var("n"), Ref("upper")), Divides(divisor=Ref("d"), dividend=Fibonacci(arg=Var(name='n')))))),
... | NT | null | COUNT | sympy | ONE_PHI_2 | [
"ONE_PHI_2"
] | e19278 | sequence_count_fib_divisible_v1 | null | 6 | 0 | [
"ONE_PHI_2"
] | 1 | 0.006 | 2026-02-08T04:45:32.316074Z | {
"verified": true,
"answer": 59876,
"timestamp": "2026-02-08T04:45:32.322519Z"
} | 60d371 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 256,
"completion_tokens": 1393
},
"timestamp": "2026-02-10T05:42:33.970Z",
"answer": 59876
},
{
"... | 1 | [
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "ONE_PHI_2",
"status": "ok"
},
{
"lemma": "V1",
"status": "no"
},
{
"lemma": "V3",
"status": "no"
}
] | {
"lo": -6.5,
"mid": -0.2,
"hi": 6.11
} |
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