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 |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
b3de93 | nt_count_primes_v1_1915831931_2527 | Let $c$ be the number of positive integers $p$ for which there exists a positive integer $q$ such that $pq = 36$, $\gcd(p, q) = 1$, and $p < q$. Let $N$ be the number of prime numbers $n$ such that $c \leq n \leq 78400$. Compute the remainder when $57433 \cdot N$ is divided by $91630$. | 49,642 | graphs = [
Graph(
let={
"upper": Const(78400),
"result": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), CountOverSet(set=SolutionsSet(var=Var("p"), condition=And(IsPositive(arg=Var(name='p')), Exists(var=Var(name='q'), condition=And(Eq(left=Mul(Var(name='p'),... | NT | null | COUNT | sympy | COPRIME_PAIRS | [
"COPRIME_PAIRS"
] | 2bb3aa | nt_count_primes_v1 | null | 4 | 0 | [
"COPRIME_PAIRS"
] | 1 | 1.809 | 2026-02-08T16:55:01.521218Z | {
"verified": true,
"answer": 49642,
"timestamp": "2026-02-08T16:55:03.330116Z"
} | d63436 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 138,
"completion_tokens": 2460
},
"timestamp": "2026-02-17T15:25:06.941Z",
"answer": 49642
},
... | 1 | [
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "VAL_SUM_EQ",
"status":... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
8f1829 | nt_count_divisible_and_v1_2051736721_133 | Let $d_2$ be the minimum value of $x + y$ over all ordered pairs $(x, y)$ of positive integers such that $xy = 36$. Compute the number of positive integers $n$ such that $1 \leq n \leq 232080$, $n$ is divisible by 10, and $n$ is divisible by $d_2$. | 3,868 | graphs = [
Graph(
let={
"upper": Const(232080),
"d1": Const(10),
"d2": MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(Mul(Var("x"), Var("y")), Const(36))))... | NT | null | COUNT | sympy | B3 | [
"B3"
] | 0cd20d | nt_count_divisible_and_v1 | null | 4 | 0 | [
"B3"
] | 1 | 12.614 | 2026-02-08T15:12:26.149834Z | {
"verified": true,
"answer": 3868,
"timestamp": "2026-02-08T15:12:38.763616Z"
} | c4af93 | 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": 585
},
"timestamp": "2026-02-16T02:24:32.172Z",
"answer": 3868
},
{
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
8c1ea1 | geo_count_lattice_triangle_v1_677425708_3048 | Let $m = 100$. Let $P$ be the set of all ordered pairs $(x, y)$ of positive integers such that $x + y = 16$. For each pair $(x, y)$ in $P$, compute $xy$, and let $M$ be the maximum value among these products. Let $c = 2$. Consider a triangle with vertices at $(0,0)$, $(100,0)$, and $(0,100)$. The area of this triangle ... | 15,899 | graphs = [
Graph(
let={
"_c": Const(2),
"_m": Const(100),
"_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(16)))), expr=... | ALG | NT | COUNT | sympy | B1 | [
"B1/C2",
"V8/C2"
] | 67b4bd | geo_count_lattice_triangle_v1 | null | 6 | 0 | [
"B1",
"C2",
"V8"
] | 3 | 0.013 | 2026-02-08T05:27:10.676874Z | {
"verified": true,
"answer": 15899,
"timestamp": "2026-02-08T05:27:10.689487Z"
} | a61f9b | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 220,
"completion_tokens": 2212
},
"timestamp": "2026-02-12T08:54:56.496Z",
"answer": 15899
},
... | 1 | [
{
"lemma": "B1",
"status": "ok"
},
{
"lemma": "C2",
"status": "ok_later"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
... | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
6b0b79 | comb_count_partitions_v1_151522320_2023 | Let $n$ be the number of ordered pairs $(i,j)$ of positive integers such that $i + j = 45$ and $1 \leq i, j \leq 44$. Compute the number of integer partitions of $n$. (An integer partition of a positive integer $m$ is a way of writing $m$ as a sum of positive integers, disregarding order.) | 75,175 | graphs = [
Graph(
let={
"_n": Const(45),
"n": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("i"), Var("j")]), condition=Eq(Sum(Var("i"), Var("j")), Ref("_n")), domain=CartesianProduct(left=IntegerRange(start=Const(1), end=Const(44)), right=IntegerRange(start=Const(1), end=Con... | COMB | null | COUNT | sympy | COUNT_SUM_EQUALS | [
"COUNT_SUM_EQUALS"
] | 75ab0f | comb_count_partitions_v1 | null | 2 | 0 | [
"COUNT_SUM_EQUALS"
] | 1 | 0.009 | 2026-02-08T04:31:54.858811Z | {
"verified": true,
"answer": 75175,
"timestamp": "2026-02-08T04:31:54.868085Z"
} | 38e378 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 192,
"completion_tokens": 2064
},
"timestamp": "2026-02-24T01:05:05.608Z",
"answer": 75175
},
{
"... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "ok"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8",
"status": "no... | {
"lo": -2.46,
"mid": 0.47,
"hi": 3.59
} | ||
aedfda | nt_min_crt_v1_717093673_2605 | Let $m = 3$. Let $k$ be the largest integer such that $3^k \leq 18509$. Let $a = 2$ and $b = 1$. Consider the set of all integers $n$ such that $1 \leq n \leq 24$, $n \equiv a \pmod{m}$, and $n \equiv b \pmod{k}$. Determine the value of the smallest such $n$. | 17 | graphs = [
Graph(
let={
"m": Const(3),
"k": MaxOverSet(set=SolutionsSet(var=Var("k1"), condition=Leq(Pow(Const(3), Var("k1")), Const(18509)))),
"a": Const(2),
"b": Const(1),
"upper": Const(24),
"result": MinOverSet(set=SolutionsSet(var=... | NT | null | EXTREMUM | sympy | L3C | [
"MAX_VAL"
] | 1da621 | nt_min_crt_v1 | null | 5 | 0 | [
"L3C",
"MAX_VAL"
] | 2 | 0.053 | 2026-02-08T17:00:23.333982Z | {
"verified": true,
"answer": 17,
"timestamp": "2026-02-08T17:00:23.387261Z"
} | e3ee09 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 139,
"completion_tokens": 1893
},
"timestamp": "2026-02-17T17:07:39.627Z",
"answer": 17
},
{
... | 1 | [
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K16",
"status": "same_pattern_wrong"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "ok"
},
{
"lemma": "MOD_MUL",
"status": ... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
e23fe5 | sequence_count_fib_divisible_v1_153355830_1019 | Let $ d = 5 $. Determine the number of positive integers $ n $ such that $ 1 \leq n \leq 685 $ and $ d $ divides the $ n $th Fibonacci number $ F_n $. | 137 | graphs = [
Graph(
let={
"upper": Const(685),
"d": Const(5),
"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')))))),
},
go... | NT | null | COUNT | sympy | LIN_FORM | [
"LIN_FORM",
"ONE_PHI_1"
] | e67fb6 | sequence_count_fib_divisible_v1 | null | 4 | 0 | [
"LIN_FORM",
"ONE_PHI_1"
] | 2 | 0.09 | 2026-02-08T04:21:29.815285Z | {
"verified": true,
"answer": 137,
"timestamp": "2026-02-08T04:21:29.904828Z"
} | 749c2d | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 157,
"completion_tokens": 779
},
"timestamp": "2026-02-10T16:12:01.336Z",
"answer": 137
},
{
"id... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "ONE_PHI_1",
"status": "ok"
},
{
"lemma": "V8",
"status": "no"
},
{
"... | {
"lo": -7.01,
"mid": -4.68,
"hi": -2.15
} | ||
95e480 | alg_poly4_min_v1_601307018_6990 | Let $A$ be the number of integers $t$ such that $20 \leq t \leq 1914$ and $t = 6a + 14b$ for some integers $a, b$ with $1 \leq a \leq 109$, $1 \leq b \leq 90$. Let $B$ be the number of integers $t_1$ such that $14 \leq t_1 \leq 7512$ and $t_1 = 6a + 8b$ for some integers $a, b$ with $1 \leq a \leq 124$, $1 \leq b \leq ... | 39,429 | graphs = [
Graph(
let={
"_c": Const(2808),
"_m": Const(285),
"_n": Const(3),
"result": MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("a"), Var("b")]), condition=And(Geq(Var("a"), Const(1)), Leq(Var("a"), CountOverSet(set=SolutionsSet(var=V... | ALG | null | COMPUTE | sympy | QF_PSD_DISTINCT | [
"QF_PSD_DISTINCT",
"LIN_FORM"
] | f4008e | alg_poly4_min_v1 | null | 5 | 0 | [
"LIN_FORM",
"QF_PSD_DISTINCT"
] | 2 | 0.934 | 2026-03-10T07:38:22.328066Z | {
"verified": true,
"answer": 39429,
"timestamp": "2026-03-10T07:38:23.262558Z"
} | 3bbf08 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 418,
"completion_tokens": 5454
},
"timestamp": "2026-04-19T05:45:27.940Z",
"answer": 39429
},
{
... | 1 | [
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "QF_PSD_DISTINCT",
"status": "ok"
}
] | {
"lo": -5.34,
"mid": 1.1,
"hi": 7.53
} | ||
1947a5_n | comb_count_permutations_fixed_v1_601307018_10490 | A theater group has $10$ actors, each assigned a unique costume. For a special performance, $k$ actors will wear their correct costumes (where $k = 2^0 + 2^1 + 2^2$), and the remaining actors must wear costumes such that no one has their own. In how many ways can the costumes be distributed under this rule? | 240 | graphs = [
Graph(
let={
"n": Const(10),
"k": Summation(var="k1", start=Const(0), end=Const(2), expr=Pow(Const(2), Var("k1"))),
"result": Mul(Binom(n=Ref("n"), k=Ref("k")), Subfactorial(arg=Sub(left=Ref(name='n'), right=Ref(name='k')))),
},
goal=Ref("result... | COMB | null | COUNT | sympy | SUM_GEOM | [
"SUM_GEOM"
] | 04214c | comb_count_permutations_fixed_v1 | null | 3 | null | [
"SUM_GEOM"
] | 1 | 0.001 | 2026-03-10T10:57:49.227995Z | null | 179bca | 1947a5 | narrative | CC BY 4.0 | [
{
"id": 36,
"model": "qwen2.5:3b-32k",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 135,
"completion_tokens": 529
},
"timestamp": "2026-04-23T14:37:18.675Z",
"answer": 240
}
] | 2 | [
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "SUM_GEOM",
"status": "ok"
},
{
"lemma": "V8",
"status": "no"
},
{
"lemma": "V8_SUM",
"s... | {
"lo": -10,
"mid": -5.89,
"hi": -1.79
} |
26c5b4 | algebra_quadratic_discriminant_v1_1874849503_1665 | Let $m = 2$. Let $n$ be the maximum value of $xy$ where $x$ and $y$ are positive integers such that $x + y = 6$. Let $a = -1$. Let $b$ be the minimum value of $x + y$ where $x$ and $y$ are positive integers such that $xy = n$. Let $c = 27$. Compute $b^m - (\max(xy) \cdot a \cdot c)$, where the maximum is taken over all... | 144 | graphs = [
Graph(
let={
"_m": Const(2),
"_n": MaxOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(Sum(Var("x"), Var("y")), Const(6)))), expr=Mul(Var("x"), Var("y")))),
... | NT | null | COMPUTE | sympy | B1 | [
"B1/B3"
] | 80b49d | algebra_quadratic_discriminant_v1 | null | 4 | 0 | [
"B1",
"B3"
] | 2 | 0.007 | 2026-02-08T14:01:26.027082Z | {
"verified": true,
"answer": 144,
"timestamp": "2026-02-08T14:01:26.034022Z"
} | 82f582 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 241,
"completion_tokens": 647
},
"timestamp": "2026-02-10T06:14:40.289Z",
"answer": 144
},
{
"id"... | 1 | [
{
"lemma": "B1",
"status": "ok"
},
{
"lemma": "B3",
"status": "ok_later"
},
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"l... | {
"lo": -8.26,
"mid": -5.01,
"hi": -1.76
} | ||
ec6a72 | geo_count_lattice_rect_v1_1978505735_1934 | Let $a = 90$ and $b = 27$. Define $\text{result}$ to be the number of lattice points in the rectangle $[0, a] \times [0, b]$, including the boundary. Let $c = 50176$ and define $Q = c - \text{result}$. Compute $Q$. | 47,628 | graphs = [
Graph(
let={
"a": Const(90),
"b": Const(27),
"result": LatticePointsRect(a=Ref(name='a'), b=Ref(name='b')),
"_c": Const(50176),
"Q": Sub(Ref("_c"), Ref("result")),
},
goal=Ref("Q"),
)
] | GEOM | null | COUNT | sympy | [] | geo_count_lattice_rect_v1 | null | 3 | 0 | null | null | 0.005 | 2026-02-08T16:31:58.661849Z | {
"verified": true,
"answer": 47628,
"timestamp": "2026-02-08T16:31:58.667070Z"
} | 371ef9 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 119,
"completion_tokens": 475
},
"timestamp": "2026-02-24T21:44:14.506Z",
"answer": 47628
},
{... | 2 | [] | {
"lo": -10,
"mid": -7.42,
"hi": -4.85
} | ||||
6d7502 | modular_sum_quadratic_residues_v1_1439011603_1393 | Let $n$ be the number of nonnegative integers $j$ such that $0 \le j \le 528$ and $\binom{528}{j}$ is odd. Let $p$ be the smallest prime divisor of $119103164651$. Compute $\frac{p(p-1)}{n}$. | 83,088 | graphs = [
Graph(
let={
"_m": Const(2),
"_n": CountOverSet(set=SolutionsSet(var=Var("j"), condition=And(Geq(Var("j"), Const(0)), Leq(Var("j"), Const(528)), Eq(Mod(value=Binom(n=Const(528), k=Var("j")), modulus=Ref("_m")), Const(1))), domain='nonnegative_integers')),
"p": ... | NT | null | SUM | sympy | V8 | [
"V8/MIN_PRIME_FACTOR"
] | 7e8253 | modular_sum_quadratic_residues_v1 | null | 6 | 0 | [
"MIN_PRIME_FACTOR",
"V8"
] | 2 | 0.002 | 2026-02-08T16:03:19.113878Z | {
"verified": true,
"answer": 83088,
"timestamp": "2026-02-08T16:03:19.116025Z"
} | dc05fb | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 110,
"completion_tokens": 5640
},
"timestamp": "2026-02-16T19:26:44.073Z",
"answer": 83088
},
... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "MIN_PRIME_FACTOR",
"status": "ok_later"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "V3",
"status"... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
75cc0b | nt_min_coprime_above_v1_153355830_2669 | Let $ a $ be the smallest integer $ n $ such that $ 35344 < n \leq 35362 $ and $ \gcd(n, 8) = 1 $. Let $ S $ be the set of all ordered pairs of positive integers $ (x, y) $ such that $ xy = 484 $. Let $ c $ be the minimum value of $ x + y $ over all pairs $ (x, y) \in S $. Compute the value of $ (c - a) \bmod{55443} $. | 20,142 | graphs = [
Graph(
let={
"start": Const(35344),
"upper": Const(35362),
"modulus": Const(8),
"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 | null | EXTREMUM | sympy | B3 | [
"B3"
] | fc629c | nt_min_coprime_above_v1 | negation_mod | 5 | 0 | [
"B3"
] | 1 | 0.008 | 2026-02-08T07:15:41.501145Z | {
"verified": true,
"answer": 20142,
"timestamp": "2026-02-08T07:15:41.509215Z"
} | 4f6860 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 159,
"completion_tokens": 822
},
"timestamp": "2026-02-13T09:24:36.990Z",
"answer": 20142
},
{... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
}
] | {
"lo": -7.01,
"mid": -4.68,
"hi": -2.15
} | ||
30c5bc | nt_count_divisible_v1_655260480_584 | Let $S$ be the set of all ordered pairs of positive integers $(x, y)$ such that $xy = 225$. Let $m$ be the minimum value of $x + y$ as $(x, y)$ ranges over $S$. Let $p$ be the largest prime number $n$ such that $2 \leq n \leq m$. Compute the number of positive integers $n_1$ with $1 \leq n_1 \leq 46368$ that are divisi... | 40,822 | 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(225)))), expr=Sum(Var("x"), Var("y")))),
"upper": Const(463... | NT | null | COUNT | sympy | B3 | [
"B3/MAX_PRIME_BELOW"
] | f253c0 | nt_count_divisible_v1 | null | 5 | 0 | [
"B3",
"MAX_PRIME_BELOW"
] | 2 | 1.502 | 2026-02-08T15:28:27.350896Z | {
"verified": true,
"answer": 40822,
"timestamp": "2026-02-08T15:28:28.853030Z"
} | 1cf942 | 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": 1343
},
"timestamp": "2026-02-16T07:04:13.816Z",
"answer": 40822
},
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok_later"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
d8424e | comb_count_permutations_fixed_v1_1915831931_3593 | Let $n$ be the smallest divisor of $385$ that is at least $2$. Compute the value of $\binom{n}{0} \cdot !n$, where $!n$ denotes the number of derangements of $n$ elements, and then find the remainder when $61097$ times this value is divided by $54372$. | 24,040 | 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(385))))),
"k": Const(0),
"result": Mul(Binom(n=Ref("n"), k=Ref("k")), Subfactorial(arg=Sub(l... | NT | COMB | COUNT | sympy | MIN_PRIME_FACTOR | [
"MIN_PRIME_FACTOR"
] | bc3776 | comb_count_permutations_fixed_v1 | null | 2 | 0 | [
"MIN_PRIME_FACTOR"
] | 1 | 0.004 | 2026-02-08T17:46:43.752958Z | {
"verified": true,
"answer": 24040,
"timestamp": "2026-02-08T17:46:43.756991Z"
} | 67818c | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 118,
"completion_tokens": 1032
},
"timestamp": "2026-02-18T08:01:14.931Z",
"answer": 24040
},
... | 1 | [
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "MIN_PRIME_FACTOR",
"status": "ok"
},
{
"lemma": "V8",
"statu... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
a8ea22 | modular_count_residue_v1_655260480_2064 | Let $ r $ be the largest prime number less than or equal to 12. Compute the number of positive integers $ n_1 $ less than or equal to 82369 such that $ n_1 \equiv r \pmod{30} $. | 2,746 | graphs = [
Graph(
let={
"_n": Const(12),
"upper": Const(82369),
"m": Const(30),
"r": MaxOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(2)), Leq(Var("n"), Ref("_n")), IsPrime(Var("n"))))),
"result": CountOverSet(set=Solutio... | NT | null | COUNT | sympy | MAX_PRIME_BELOW | [
"MAX_PRIME_BELOW"
] | dc3ad3 | modular_count_residue_v1 | null | 4 | 0 | [
"MAX_PRIME_BELOW"
] | 1 | 3.04 | 2026-02-08T16:32:47.090756Z | {
"verified": true,
"answer": 2746,
"timestamp": "2026-02-08T16:32:50.130971Z"
} | 5d6bc1 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 100,
"completion_tokens": 529
},
"timestamp": "2026-02-17T06:11:07.507Z",
"answer": 2746
},
{
... | 1 | [
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
34de39 | nt_min_phi_inverse_v1_124444284_1875 | Let $k = 16$. Determine the value of the smallest positive integer $n$ such that $1 \leq n \leq 70$ and $\phi(n) = k$, where $\phi(n)$ is the number of positive integers less than or equal to $n$ that are relatively prime to $n$. | 17 | graphs = [
Graph(
let={
"upper": Const(70),
"k": Const(16),
"result": MinOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Ref("upper")), Eq(EulerPhi(n=Var("n")), Ref("k"))))),
},
goal=Ref("result"),
)
] | NT | null | EXTREMUM | sympy | COUNT_PRIMES | [
"LIN_FORM",
"ONE_PHI_1"
] | e67fb6 | nt_min_phi_inverse_v1 | null | 4 | 0 | [
"COUNT_PRIMES",
"LIN_FORM",
"ONE_PHI_1"
] | 3 | 0.084 | 2026-02-08T04:11:48.512331Z | {
"verified": true,
"answer": 17,
"timestamp": "2026-02-08T04:11:48.596216Z"
} | b9044a | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 177,
"completion_tokens": 869
},
"timestamp": "2026-02-10T15:42:20.876Z",
"answer": 17
},
{
"id"... | 1 | [
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "ONE_PHI_1",
"status": "ok"
},
{
"lemma": "V1",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
},
{
"lemma": ... | {
"lo": -3.42,
"mid": 1.86,
"hi": 7.55
} | ||
45d663 | comb_binomial_compute_v1_655260480_2636 | Let $n = 20498$. Define $S$ as the set of all nonnegative integers $j$ with $0 \leq j \leq 20498$ such that $\binom{20498}{j}$ is odd. Let $N$ be the number of elements in $S$. Compute $\binom{N}{8}$. | 12,870 | graphs = [
Graph(
let={
"_n": Const(20498),
"n": CountOverSet(set=SolutionsSet(var=Var("j"), condition=And(Geq(Var("j"), Const(0)), Leq(Var("j"), Const(20498)), Eq(Mod(value=Binom(n=Ref("_n"), k=Var("j")), modulus=Const(2)), Const(1))), domain='nonnegative_integers')),
"k... | ALG | COMB | COMPUTE | sympy | V8 | [
"V8"
] | 86348e | comb_binomial_compute_v1 | null | 6 | 0 | [
"V8"
] | 1 | 0.001 | 2026-02-08T16:52:43.905626Z | {
"verified": true,
"answer": 12870,
"timestamp": "2026-02-08T16:52:43.906661Z"
} | 79ac3a | 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": 3587
},
"timestamp": "2026-02-17T15:08:42.044Z",
"answer": 12870
},
... | 1 | [
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8",
"status": "ok"
}... | {
"lo": -2.38,
"mid": 1.74,
"hi": 6.59
} | ||
7afb1a | modular_sum_quadratic_residues_v1_1440796553_1169 | Let $p = 229$. Define $r = \frac{p(p-1)}{4}$. Let $M$ be the maximum value of $xy$ over all pairs of positive integers $(x, y)$ such that $x + y = 82$. Let $T$ be the set of all positive integers $n$ such that $1 \leq n \leq M$ and the sum of the decimal digits of $n$ leaves a remainder of 1 when divided by 2. Let $c$ ... | 86,458 | graphs = [
Graph(
let={
"_m": Const(4),
"_n": Const(2),
"p": Const(229),
"result": Div(Mul(Ref("p"), Sub(Ref("p"), Const(1))), Ref("_m")),
"_c": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), MaxOve... | NT | null | SUM | sympy | B1 | [
"B1/L3B"
] | d5eba5 | modular_sum_quadratic_residues_v1 | negation_mod | 5 | 0 | [
"B1",
"L3B"
] | 2 | 0.003 | 2026-02-08T12:13:19.518287Z | {
"verified": true,
"answer": 86458,
"timestamp": "2026-02-08T12:13:19.521587Z"
} | 78a4fa | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 181,
"completion_tokens": 2963
},
"timestamp": "2026-02-14T23:05:42.050Z",
"answer": 86458
},
... | 1 | [
{
"lemma": "B1",
"status": "ok"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "L3B",
"status": "ok_later"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "V1",
"status": "no"
},
{
"lemma": "V8",... | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
60c7f7 | nt_count_coprime_v1_1520064083_4636 | Let $k = \sum_{i=1}^{6} \phi(i) \left\lfloor \frac{6}{i} \right\rfloor$, where $\phi(i)$ denotes Euler's totient function. Let $S$ be the set of all integers $n$ such that $1 \leq n \leq 11236$ and $\gcd(n, k) = 1$. Compute the remainder when $93798$ multiplied by the number of elements in $S$ is divided by $91927$. | 63,181 | graphs = [
Graph(
let={
"_n": Const(6),
"upper": Const(11236),
"k": Summation(var="k", start=Const(1), end=Const(6), expr=Mul(EulerPhi(n=Var("k")), Floor(Div(Ref("_n"), Var("k"))))),
"result": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("... | NT | null | COUNT | sympy | K2 | [
"K2"
] | 6897ab | nt_count_coprime_v1 | null | 6 | 0 | [
"K2"
] | 1 | 1.444 | 2026-02-08T06:21:53.334339Z | {
"verified": true,
"answer": 63181,
"timestamp": "2026-02-08T06:21:54.778453Z"
} | c28c01 | 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": 1877
},
"timestamp": "2026-02-12T22:58:57.573Z",
"answer": 63181
},
... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "K2",
"status": "ok"
},
{
"lemma": "L3c",
"status": "no"
}
] | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
6bbee0 | antilemma_cartesian_v1_1978505735_1804 | Let $x$ be the number of ordered pairs $(a, b)$ where $a$ is an integer from 1 to 44 and $b$ is an integer from 1 to 49. Compute the value of
$$
\sum_{i=0}^{\lfloor \log_{10} |x| \rfloor} \left( \text{the } i\text{-th digit of } |x| \right) \cdot (i+1)^2 + 64.
$$ | 131 | graphs = [
Graph(
let={
"x": CountOverSet(set=CartesianProduct(left=IntegerRange(start=Const(1), end=Const(44)), right=IntegerRange(start=Const(1), end=Const(49)))),
"Q": Sum(Summation(var="i", start=Const(0), end=Sub(NumDigits(x=Abs(arg=Ref(name='x')), base=None), Const(1)), expr=Mu... | COMB | GEOM | COMPUTE | sympy | LIN_FORM | [
"COUNT_CARTESIAN"
] | 409d7d | antilemma_cartesian_v1 | null | 3 | 0 | [
"COUNT_CARTESIAN",
"LIN_FORM"
] | 2 | 0.049 | 2026-02-08T16:24:13.140051Z | {
"verified": true,
"answer": 131,
"timestamp": "2026-02-08T16:24:13.189368Z"
} | ebf9f5 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 217,
"completion_tokens": 757
},
"timestamp": "2026-02-24T20:51:40.038Z",
"answer": 131
},
{
"id... | 1 | [
{
"lemma": "COUNT_CARTESIAN",
"status": "ok"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
},
{
"lemma": "V8_SUM",
"status"... | {
"lo": -2.4,
"mid": 1.57,
"hi": 5.75
} | ||
5fccba | geo_visible_lattice_v1_1439011603_1601 | Let $n = 200$. Define $P$ to be the number of ordered pairs $(x, y)$ of integers such that $1 \leq x, y \leq n$ and $\gcd(x, y) = 1$. Compute the remainder when $62369 \cdot P$ is divided by $84360$. | 82,247 | graphs = [
Graph(
let={
"n": Const(200),
"result": VisibleLatticePoints(n=Ref(name='n')),
"Q": Mod(value=Mul(Const(62369), Ref("result")), modulus=Const(84360)),
},
goal=Ref("Q"),
)
] | GEOM | null | COUNT | sympy | [] | geo_visible_lattice_v1 | null | 3 | 0 | null | null | 0.974 | 2026-02-08T16:11:23.557142Z | {
"verified": true,
"answer": 82247,
"timestamp": "2026-02-08T16:11:24.531078Z"
} | 2f3a1f | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 181,
"completion_tokens": 20415
},
"timestamp": "2026-02-24T20:03:19.607Z",
"answer": 82247
},
{
... | 1 | [] | {
"lo": 1.98,
"mid": 5.23,
"hi": 8.52
} | ||||
d624b6 | alg_poly_preperiod_count_v1_601307018_3416 | Define a sequence by $N = a^2 - 8 \bmod 19$, $M = N^2 - 8 \bmod 19$, $R = M^2 - 8 \bmod 19$, $S = R^2 - 8 \bmod 19$, and $T = S^2 - 8 \bmod 19$. Find the number of non-negative integers $a$ with $0 \le a \le 26162$ such that $T = M$, $R \ne M$, and $S \ne M$. | 13,770 | graphs = [
Graph(
let={
"p1": Mod(value=Sum(Pow(Var("a"), Const(2)), Const(-8)), modulus=Const(19)),
"p2": Mod(value=Sum(Pow(Ref("p1"), Const(2)), Const(-8)), modulus=Const(19)),
"p3": Mod(value=Sum(Pow(Ref("p2"), Const(2)), Const(-8)), modulus=Const(19)),
"p4... | ALG | null | COUNT | sympy | POLY_ORBIT_COUNT | [
"POLY_ORBIT_COUNT"
] | 4ad965 | alg_poly_preperiod_count_v1 | null | 7 | null | [
"POLY_ORBIT_COUNT"
] | 1 | 0.036 | 2026-03-10T03:59:59.685390Z | {
"verified": true,
"answer": 13770,
"timestamp": "2026-03-10T03:59:59.721416Z"
} | 1272aa | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 232,
"completion_tokens": 9670
},
"timestamp": "2026-03-29T08:38:51.643Z",
"answer": 13770
},
{
"... | 1 | [
{
"lemma": "POLY_ORBIT_COUNT",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
}
] | {
"lo": 1.23,
"mid": 4.27,
"hi": 6.7
} | ||
8973c5 | diophantine_fbi2_min_v1_458359167_601 | Let $k = 26$. Consider the set of all integers $d$ such that $d \geq 6$, $d \leq 36$, $d$ divides $k$, and $\frac{k}{d} \geq 2$. Determine the minimum value of $d$ in this set. | 13 | graphs = [
Graph(
let={
"k": Const(26),
"a": Const(5),
"b": Const(1),
"upper": Const(36),
"result": MinOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Const(6)), Leq(Var("d"), Ref("upper")), Divides(divisor=Var("d"), dividend=Ref... | NT | null | EXTREMUM | sympy | MAX_DIVISOR | [
"LIN_FORM"
] | 7b2633 | diophantine_fbi2_min_v1 | null | 2 | 0 | [
"LIN_FORM",
"MAX_DIVISOR"
] | 2 | 0.056 | 2026-02-08T03:26:14.510455Z | {
"verified": true,
"answer": 13,
"timestamp": "2026-02-08T03:26:14.566595Z"
} | 1e984b | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 176,
"completion_tokens": 430
},
"timestamp": "2026-02-10T14:22:02.050Z",
"answer": 13
},
{
"id":... | 2 | [
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "MOD_ADD",
"status": ... | {
"lo": -10,
"mid": -7.73,
"hi": -5.46
} | ||
65bc8f | comb_count_partitions_v1_1439011603_1463 | Let $n = 75809$. Let $d$ be the smallest divisor of $n$ such that $d \geq 2$. Compute the number of integer partitions of $d$. | 44,583 | graphs = [
Graph(
let={
"_n": Const(75809),
"n": MinOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Const(2)), Divides(divisor=Var("d"), dividend=Ref("_n"))))),
"result": Partition(arg=Ref(name='n')),
},
goal=Ref("result"),
)
] | NT | COMB | COUNT | sympy | MIN_PRIME_FACTOR | [
"MIN_PRIME_FACTOR"
] | bc3776 | comb_count_partitions_v1 | null | 4 | 0 | [
"MIN_PRIME_FACTOR"
] | 1 | 0.001 | 2026-02-08T16:06:17.002707Z | {
"verified": true,
"answer": 44583,
"timestamp": "2026-02-08T16:06:17.003887Z"
} | 5cf721 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 86,
"completion_tokens": 1161
},
"timestamp": "2026-02-16T21:26:10.405Z",
"answer": 44583
},
{... | 1 | [
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "MIN_PRIME_FACTOR",
"status": "ok"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
82f5f7 | geo_count_lattice_rect_v1_153355830_1648 | Compute the number of lattice points $(x,y)$ such that $0 \leq x \leq 324$ and $0 \leq y \leq 101$. | 33,150 | graphs = [
Graph(
let={
"a": Const(324),
"b": Const(101),
"result": LatticePointsRect(a=Ref(name='a'), b=Ref(name='b')),
},
goal=Ref("result"),
)
] | GEOM | null | COUNT | sympy | [] | geo_count_lattice_rect_v1 | null | 3 | 0 | null | null | 0.001 | 2026-02-08T06:32:33.200160Z | {
"verified": true,
"answer": 33150,
"timestamp": "2026-02-08T06:32:33.200957Z"
} | eaa22c | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 147,
"completion_tokens": 270
},
"timestamp": "2026-02-24T06:28:19.906Z",
"answer": 33150
},
{
"i... | 1 | [] | {
"lo": -9.23,
"mid": -6.18,
"hi": -4.06
} | ||||
7d00db | geo_visible_lattice_v1_601307018_2139 | Find the number of lattice points $(x, y)$ with $1 \le x, y \le 100$ such that $\gcd(x, y) = 1$. Let $N$ be this number. Compute the remainder when $97163N$ is divided by $51912$. | 49,677 | graphs = [
Graph(
let={
"n": Const(100),
"result": VisibleLatticePoints(n=Ref(name='n')),
"Q": Mod(value=Mul(Const(97163), Ref("result")), modulus=Const(51912)),
},
goal=Ref("Q"),
)
] | GEOM | GEOM | COUNT | sympy | [] | geo_visible_lattice_v1 | null | 3 | 0 | null | null | 0.276 | 2026-03-10T02:50:19.613130Z | {
"verified": true,
"answer": 49677,
"timestamp": "2026-03-10T02:50:19.889123Z"
} | f0f496 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 171,
"completion_tokens": 15673
},
"timestamp": "2026-03-29T04:27:29.130Z",
"answer": 49677
},
{
... | 1 | [] | {
"lo": 1.23,
"mid": 4.27,
"hi": 6.7
} | ||||
31aa2d | comb_binomial_compute_v1_601307018_9708 | Let $M$ be the largest positive integer such that $M^2 \leq 15113$ and $M \mid 15113$. Let $k$ be the number of positive integers $n_1$ with $1 \leq n_1 \leq M$ such that $7 \mid n_1$ and $\gcd\left(n_1, \left|\{ n_2 : 1 \leq n_2 \leq 29, \gcd(n_2, 10) = 1 \}\right|\right) = 1$. Compute $\binom{13}{k}$. | 1,716 | graphs = [
Graph(
let={
"_m": Const(29),
"_n": MaxOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Const(1)), Divides(divisor=Var("d"), dividend=Const(15113)), Leq(Mul(Var("d"), Var("d")), Const(15113))))),
"n": Const(13),
"k": CountOverSet(s... | COMB | NT | COMPUTE | sympy | B3_CLOSEST | [
"B3_CLOSEST/C5",
"C4/C5"
] | 393002 | comb_binomial_compute_v1 | null | 5 | 0 | [
"B3_CLOSEST",
"C4",
"C5"
] | 3 | 0.01 | 2026-03-10T10:06:15.527446Z | {
"verified": true,
"answer": 1716,
"timestamp": "2026-03-10T10:06:15.537869Z"
} | dde3ae | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 245,
"completion_tokens": 2397
},
"timestamp": "2026-04-19T11:54:03.555Z",
"answer": 1716
},
{
"... | 1 | [
{
"lemma": "B3_CLOSEST",
"status": "ok"
},
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "C4",
"status": "ok"
},
{
"lemma": "C5",
"status": "ok_later"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "n... | {
"lo": -5.34,
"mid": 1.1,
"hi": 7.53
} | ||
33f904 | diophantine_product_count_v1_1918700295_2104 | Let $S$ be the set of all ordered pairs $(x,y)$ of positive integers such that $xy = 435600$. Let $m$ be the minimum value of $x + y$ over all pairs $(x,y) \in S$. Let $k$ be the number of positive integers $n$ such that $1 \leq n \leq m$ and $n \equiv \left\lfloor \frac{n}{2} \right\rfloor \pmod{11}$. Let $r$ be the n... | 51,322 | graphs = [
Graph(
let={
"k": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("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(Va... | NT | null | COUNT | sympy | B3 | [
"B3/L3C"
] | 345f3b | diophantine_product_count_v1 | null | 7 | 0 | [
"B3",
"L3C"
] | 2 | 0.008 | 2026-02-08T07:41:02.692596Z | {
"verified": true,
"answer": 51322,
"timestamp": "2026-02-08T07:41:02.700260Z"
} | 34753f | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 210,
"completion_tokens": 1931
},
"timestamp": "2026-02-13T11:54:29.666Z",
"answer": 51322
},
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "L3C",
"status": "ok_later"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
... | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
c0b2f1 | comb_count_derangements_v1_601307018_4602 | Let $D_n$ denote the number of derangements of $n$ elements. For an integer $a$ with $0 \le a \le 29790$, define $M = (a^5 + a^4 + a^3 + 3a^2 + 4a) \bmod 29791$ and $R = (M^5 + M^4 + M^3 + 3M^2 + 4M) \bmod 29791$. Let $S$ be the number of such $a$ for which $R = a$ and $M \ne a$. Let $n = \sum_{k=0}^{2} S^k$. Compute $... | 1,854 | graphs = [
Graph(
let={
"_m": Const(5),
"_n": CountOverSet(set=SolutionsSet(var=Var("a"), condition=And(Geq(Var("a"), Const(0)), Leq(Var("a"), Const(29790)), Eq(Ref("_po_p2"), Var("a")), Neq(Ref("_po_p1"), Var("a"))))),
"n": Summation(var="k", start=Const(0), end=Const(2)... | COMB | null | COUNT | sympy | POLY_ORBIT_HENSEL | [
"POLY_ORBIT_HENSEL/SUM_GEOM"
] | 8a1734 | comb_count_derangements_v1 | null | 7 | 0 | [
"POLY_ORBIT_HENSEL",
"SUM_GEOM"
] | 2 | 0.004 | 2026-03-10T05:13:18.726063Z | {
"verified": true,
"answer": 1854,
"timestamp": "2026-03-10T05:13:18.730241Z"
} | f8e8cc | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 261,
"completion_tokens": 32768
},
"timestamp": "2026-03-29T12:51:55.940Z",
"answer": null
},
{
... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "POLY_ORBIT_HENSEL",
"status": "ok"
},
{
"lemma": "SUM_GEOM",
"status": "ok_later"
},
{
"lemma": "V7",
... | {
"lo": 3.34,
"mid": 5.77,
"hi": 8.89
} | ||
fbf212 | comb_sum_binomial_row_v1_1742523217_814 | Let $S$ be the set of all positive integers $p$ for which there exists a positive integer $q$ such that $pq = 54$, $\gcd(p, q) = 1$, and $p < q$. Let $m = |S|$. Compute the remainder when $44121 \times m^{14}$ is divided by $72463$. | 60,039 | graphs = [
Graph(
let={
"n": Const(14),
"result": Pow(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=54)), Eq(left=GCD(a=Var(name='p'), b=Var... | NT | null | SUM | sympy | COPRIME_PAIRS | [
"COPRIME_PAIRS"
] | 2bb3aa | comb_sum_binomial_row_v1 | null | 4 | 0 | [
"COPRIME_PAIRS"
] | 1 | 0.002 | 2026-02-08T03:16:00.898830Z | {
"verified": true,
"answer": 60039,
"timestamp": "2026-02-08T03:16:00.900536Z"
} | 0abb64 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 191,
"completion_tokens": 2460
},
"timestamp": "2026-02-09T07:19:50.346Z",
"answer": 60039
},
{
... | 1 | [
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
},
{
"lemma": "VAL_SUM_EQ",
"status": "no"
}
] | {
"lo": -3.42,
"mid": 1.86,
"hi": 7.55
} | ||
7a07fb | antilemma_cartesian_v1_397696148_212 | Let $x$ be the number of ordered pairs $(a, b)$ such that $1 \leq a \leq 11$ and $1 \leq b \leq 16$. Let $s$ be the number of ordered pairs $(x_1, x_2)$ of positive odd integers such that $x_1 + x_2 = 398$. Let $t$ be the number of positive integers $u$ such that $27 \leq u \leq 15069$ and $u = 15a + 12b$ for some posi... | 26,649 | graphs = [
Graph(
let={
"_n": Const(94895),
"x": CountOverSet(set=CartesianProduct(left=IntegerRange(start=Const(1), end=Const(11)), right=IntegerRange(start=Const(1), end=Const(16)))),
"Q": Mod(value=Sum(Mod(value=Ref("x"), modulus=CountOverSet(set=SolutionsSet(var=Tuple... | COMB | GEOM | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM",
"COMB1",
"COUNT_CARTESIAN"
] | 45c37c | antilemma_cartesian_v1 | two_moduli | 5 | 0 | [
"COMB1",
"COUNT_CARTESIAN",
"LIN_FORM"
] | 3 | 0.005 | 2026-02-08T11:23:08.515721Z | {
"verified": true,
"answer": 26649,
"timestamp": "2026-02-08T11:23:08.521004Z"
} | 3aacee | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 355,
"completion_tokens": 32768
},
"timestamp": "2026-02-24T13:44:45.380Z",
"answer": null
},
{
... | 1 | [
{
"lemma": "COMB1",
"status": "ok"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "ok"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "V7",
"sta... | {
"lo": 3.25,
"mid": 5.68,
"hi": 8.81
} | ||
01d454 | comb_count_surjections_v1_784195855_2147 | Let $T$ be the set of all integers $t$ such that $27 \le t \le 84$ and $t = 6a + 21b$ for some integers $a,b$ with $1 \le a \le 7$ and $1 \le b \le 2$. Let $n$ be the number of ordered pairs $(x_1, x_2)$ of positive odd integers such that $x_1 + x_2 = |T|$. Let $K$ be the set of all integers $t$ such that $5 \le t \le ... | 15,120 | graphs = [
Graph(
let={
"_n": CountOverSet(set=SolutionsSet(var=Var("t"), condition=Exists(var=Var(name='a'), condition=Exists(var=Var(name='b'), condition=And(Geq(left=Var(name='a'), right=Const(value=1)), Leq(left=Var(name='a'), right=Const(value=7)), Geq(left=Var(name='b'), right=Const(value=... | COMB | null | COUNT | sympy | LIN_FORM | [
"LIN_FORM/COMB1"
] | 268a62 | comb_count_surjections_v1 | null | 7 | 0 | [
"COMB1",
"LIN_FORM"
] | 2 | 0.003 | 2026-02-08T05:30:54.007456Z | {
"verified": true,
"answer": 15120,
"timestamp": "2026-02-08T05:30:54.010430Z"
} | 39cd22 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 319,
"completion_tokens": 1770
},
"timestamp": "2026-02-24T03:57:50.723Z",
"answer": 15120
},
{
"... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COMB1",
"status": "ok_later"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "V7",
"status"... | {
"lo": -2.46,
"mid": 0.47,
"hi": 3.59
} | ||
05b04c | nt_num_divisors_compute_v1_2051736721_1637 | Let $S$ be the set of all ordered pairs $(x, y)$ of positive integers such that $x \cdot y = 1936$. Let $s$ be the minimum value of $x + y$ as $(x, y)$ ranges over $S$. Let $n$ be the number of positive integers $n_1$ such that $1 \leq n_1 \leq s$ and $3$ divides the $n_1$-th Fibonacci number. Determine the value of th... | 4 | graphs = [
Graph(
let={
"_m": Const(3),
"_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(1936)))), expr=Sum(Var("x"), Var("y")))),
... | NT | null | COMPUTE | sympy | B3 | [
"B3/COUNT_FIB_DIVISIBLE"
] | 9b7a57 | nt_num_divisors_compute_v1 | null | 5 | 0 | [
"B3",
"COUNT_FIB_DIVISIBLE"
] | 2 | 0.004 | 2026-02-08T16:08:20.064981Z | {
"verified": true,
"answer": 4,
"timestamp": "2026-02-08T16:08:20.069038Z"
} | dabcd6 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 159,
"completion_tokens": 1280
},
"timestamp": "2026-02-16T21:19:11.844Z",
"answer": 4
},
{
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "ok_later"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "MAX_VAL",
"... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
8d5628 | diophantine_sum_product_min_v1_151522320_7 | Let $S = 102$. Let $P$ be the number of positive integers $n$ such that $1 \leq n \leq 2888$ and the sum of the decimal digits of $n$ is odd. Let $x$ be the smallest positive integer such that $1 \leq x \leq 101$ and $x(S - x) = P$. Find the remainder when $37543 \cdot x$ is divided by $62598$. | 12,251 | graphs = [
Graph(
let={
"_n": Const(37543),
"S": Const(102),
"P": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Const(2888)), Eq(Mod(value=DigitSum(Var("n")), modulus=Const(2)), Const(1))))),
"result": MinOver... | NT | null | EXTREMUM | sympy | L3B | [
"L3B"
] | cc148f | diophantine_sum_product_min_v1 | null | 4 | 0 | [
"L3B"
] | 1 | 0.015 | 2026-02-08T02:55:18.468511Z | {
"verified": true,
"answer": 12251,
"timestamp": "2026-02-08T02:55:18.483395Z"
} | e471d8 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 211,
"completion_tokens": 32768
},
"timestamp": "2026-02-23T19:56:36.692Z",
"answer": null
},
{
... | 1 | [
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "L3B",
"status": "ok"
},
{
"lemma": "V1",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
}
] | {
"lo": -0.38,
"mid": 2.56,
"hi": 4.68
} | ||
9745a0 | modular_min_linear_v1_1125832087_1467 | Let $a = 11797$, $b = 32119$, and $m = 84768$. Let $r$ be the smallest positive integer $x$ such that $1 \leq x \leq m$ and $ax \equiv b \pmod{m}$. Let $T$ be the set of all integers $t$ such that $14 \leq t \leq 50$ and there exist integers $a'$, $b'$ with $1 \leq a' \leq 5$, $1 \leq b' \leq 3$, such that $t = 4a' + 1... | 53,819 | graphs = [
Graph(
let={
"a": Const(11797),
"b": Const(32119),
"m": Const(84768),
"result": MinOverSet(set=SolutionsSet(var=Var("x"), condition=And(Geq(Var("x"), Const(1)), Leq(Var("x"), Ref("m")), Eq(Mod(value=Mul(Ref("a"), Var("x")), modulus=Ref("m")), Ref("b... | NT | null | EXTREMUM | sympy | LIN_FORM | [
"LIN_FORM"
] | 812dee | modular_min_linear_v1 | mod_exp | 6 | 0 | [
"LIN_FORM"
] | 1 | 5.418 | 2026-02-08T03:45:05.263193Z | {
"verified": true,
"answer": 53819,
"timestamp": "2026-02-08T03:45:10.681630Z"
} | 4d87df | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 285,
"completion_tokens": 3194
},
"timestamp": "2026-02-10T15:30:11.037Z",
"answer": 53819
},
{
"... | 1 | [
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
}
] | {
"lo": -3.46,
"mid": 1.03,
"hi": 5.49
} | ||
2a6805 | nt_min_coprime_above_v1_397696148_1057 | Let $P$ be the set of all ordered pairs $(x, y)$ of positive integers such that $xy = 262144$. Let $s$ be the minimum value of $x + y$ over all such pairs. Let $n$ be the smallest integer greater than $s$ and at most $1323$ such that $\gcd(n, 289) = 1$. Let $Q = 82751 \cdot n$. Compute the remainder when $Q$ is divided... | 29,929 | graphs = [
Graph(
let={
"start": 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(262144)))), expr=Sum(Var("x"), Var("y")))),
"upper": Con... | NT | null | EXTREMUM | sympy | B3 | [
"B3"
] | 0cd20d | nt_min_coprime_above_v1 | null | 6 | 0 | [
"B3"
] | 1 | 0.028 | 2026-02-08T12:19:47.848284Z | {
"verified": true,
"answer": 29929,
"timestamp": "2026-02-08T12:19:47.875921Z"
} | 633db2 | 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": 1898
},
"timestamp": "2026-02-14T23:51:41.298Z",
"answer": 29929
},
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
}
] | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
36deba | nt_num_divisors_compute_v1_1742523217_949 | Let $m = 18$. Consider the set of all ordered pairs $(x, y)$ of positive integers such that $x + y = m$. For each such pair, compute the product $xy$. Let $n$ be the maximum value of $xy$ over all such pairs. Define $s$ to be the sum of $\phi(d)$ over all positive divisors $d$ of $n$, where $\phi$ is Euler's totient fu... | 5 | graphs = [
Graph(
let={
"_m": Const(18),
"_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 | COMPUTE | sympy | B1 | [
"B1/K3"
] | 759f54 | nt_num_divisors_compute_v1 | null | 5 | 0 | [
"B1",
"K3"
] | 2 | 0.002 | 2026-02-08T03:22:02.888507Z | {
"verified": true,
"answer": 5,
"timestamp": "2026-02-08T03:22:02.890895Z"
} | f3431c | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 216,
"completion_tokens": 699
},
"timestamp": "2026-02-10T01:01:01.200Z",
"answer": 5
},
{
"id": ... | 1 | [
{
"lemma": "B1",
"status": "ok"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "K3",
"status": "ok_later"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{... | {
"lo": -7.01,
"mid": -4.68,
"hi": -2.15
} | ||
d54ad4 | antilemma_k3_v1_1125832087_539 | Let $n = 14802$. Compute the sum of $\phi(d)$ over all positive divisors $d$ of $n$, where $\phi$ denotes Euler's totient function. | 14,802 | graphs = [
Graph(
let={
"_n": Const(14802),
"x": SumOverDivisors(n=Ref(name='_n'), var='d', expr=EulerPhi(n=Var(name='d'))),
},
goal=Ref("x"),
)
] | NT | COMB | COMPUTE | sympy | K3 | [
"K3"
] | 54c41e | antilemma_k3_v1 | null | 3 | 0 | [
"K3"
] | 1 | 0 | 2026-02-08T03:09:01.469077Z | {
"verified": true,
"answer": 14802,
"timestamp": "2026-02-08T03:09:01.469471Z"
} | bfea54 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 149,
"completion_tokens": 386
},
"timestamp": "2026-02-10T13:12:51.640Z",
"answer": 14802
},
{
"i... | 1 | [
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "K3",
"status": "ok"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"statu... | {
"lo": -3.53,
"mid": 1.02,
"hi": 5.49
} | ||
4eaa6a | antilemma_k2_v1_153355830_1499 | Let $ n = 110 $. Define
$$
x = \sum_{k=1}^{n} \phi(k) \left\lfloor \frac{110}{k} \right\rfloor,
$$
where $ \phi(k) $ denotes Euler's totient function. Let $ c = 24631 $. Compute the remainder when $ c \cdot x $ is divided by $ 63595 $. | 33,675 | graphs = [
Graph(
let={
"_n": Const(110),
"x": Summation(var="k", start=Const(1), end=Ref("_n"), expr=Mul(EulerPhi(n=Var("k")), Floor(Div(Const(110), Var("k"))))),
"_c": Const(24631),
"Q": Mod(value=Mul(Ref("_c"), Ref("x")), modulus=Const(63595)),
},
... | NT | COMB | COMPUTE | sympy | IDENTITY_POW_ZERO | [
"IDENTITY_POW_ZERO",
"K2"
] | fce51d | antilemma_k2_v1 | null | 6 | 0 | [
"IDENTITY_POW_ZERO",
"K2"
] | 2 | 0.001 | 2026-02-08T06:27:26.545132Z | {
"verified": true,
"answer": 33675,
"timestamp": "2026-02-08T06:27:26.546128Z"
} | 2c390c | 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": 2113
},
"timestamp": "2026-02-13T00:17:45.916Z",
"answer": 33675
},
... | 1 | [
{
"lemma": "IDENTITY_POW_ZERO",
"status": "ok"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "K2",
"status": "ok"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
... | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
2e2261 | antilemma_k3_v1_1125832087_2346 | Let $n = 85637$. Define $x = \sum_{d \mid n} \phi(d)$, where the sum is taken over all positive divisors $d$ of $n$, and $\phi$ denotes Euler's totient function.
Compute the remainder when $44121 \cdot x$ is divided by $89434$. | 71,879 | graphs = [
Graph(
let={
"_n": Const(85637),
"x": SumOverDivisors(n=Ref(name='_n'), var='d', expr=EulerPhi(n=Var(name='d'))),
"Q": Mod(value=Mul(Const(44121), Ref("x")), modulus=Const(89434)),
},
goal=Ref("Q"),
)
] | NT | COMB | COMPUTE | sympy | K3 | [
"K3"
] | 54c41e | antilemma_k3_v1 | null | 3 | 0 | [
"K3"
] | 1 | 0 | 2026-02-08T04:34:17.709585Z | {
"verified": true,
"answer": 71879,
"timestamp": "2026-02-08T04:34:17.709956Z"
} | 085c1d | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 182,
"completion_tokens": 1687
},
"timestamp": "2026-02-10T17:05:52.432Z",
"answer": 71879
},
{
... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "K3",
"status": "ok"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "V1",
"status": "no"
},
{
"lemma": "V3",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
}
] | {
"lo": -3.42,
"mid": 1.86,
"hi": 7.55
} | ||
487510 | comb_count_surjections_v1_1440796553_879 | Let $k$ be the number of ordered pairs $(i, j)$ with $i, j \in \{1, 2, 3\}$ such that $i + j = 5$. Define $r = k! \cdot S(5, k)$, where $S(n, k)$ denotes the number of ways to partition a set of $n$ elements into $k$ nonempty unlabeled subsets. Compute the value of $$
divisors\left(r + 1\right) + \phi\left(|r| + 1\rig... | 62 | graphs = [
Graph(
let={
"_n": Const(5),
"n": Const(5),
"k": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("i"), Var("j")]), condition=Eq(Sum(Var("i"), Var("j")), Ref("_n")), domain=CartesianProduct(left=IntegerRange(start=Const(1), end=Const(3)), right=IntegerRang... | COMB | NT | COUNT | sympy | COUNT_SUM_EQUALS | [
"COUNT_SUM_EQUALS",
"ONE_BINOM_0"
] | ec98de | comb_count_surjections_v1 | null | 4 | 0 | [
"COUNT_SUM_EQUALS",
"ONE_BINOM_0"
] | 2 | 0.053 | 2026-02-08T12:02:07.918676Z | {
"verified": true,
"answer": 62,
"timestamp": "2026-02-08T12:02:07.971722Z"
} | a2e578 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 285,
"completion_tokens": 745
},
"timestamp": "2026-02-24T15:08:18.239Z",
"answer": 62
},
{
"id":... | 1 | [
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "ok"
},
{
"lemma": "ONE_BINOM_0",
"status": "ok"
},
{
"lemma... | {
"lo": -5.97,
"mid": -3.97,
"hi": -1.93
} | ||
92bd50 | antilemma_sum_equals_v1_655260480_3640 | Let $m = 46$. Define $S$ as the set of all ordered pairs $(i, j)$ of positive integers such that $1 \leq i \leq 46$, $1 \leq j \leq 46$, and $i + j = m$. Let $n$ be the number of elements in $S$.
Define $T$ as the set of all ordered pairs $(i_1, j_1)$ of positive integers such that $1 \leq i_1 \leq 44$, $1 \leq j_1 \l... | 44 | graphs = [
Graph(
let={
"_m": Const(46),
"_n": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("i"), Var("j")]), condition=Eq(Sum(Var("i"), Var("j")), Ref("_m")), domain=CartesianProduct(left=IntegerRange(start=Const(1), end=Const(46)), right=IntegerRange(start=Const(1), end=Co... | COMB | GEOM | COMPUTE | sympy | LIN_FORM | [
"COUNT_SUM_EQUALS/COUNT_SUM_EQUALS",
"COUNT_SUM_EQUALS"
] | ae9919 | antilemma_sum_equals_v1 | null | 3 | 0 | [
"COUNT_SUM_EQUALS",
"LIN_FORM"
] | 2 | 0.065 | 2026-02-08T17:28:47.474997Z | {
"verified": true,
"answer": 44,
"timestamp": "2026-02-08T17:28:47.539527Z"
} | c82227 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 194,
"completion_tokens": 1117
},
"timestamp": "2026-02-18T02:35:59.112Z",
"answer": 44
},
{
... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "ok"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8_SUM",
"status":... | {
"lo": -8,
"mid": -4.75,
"hi": -2.28
} | ||
2bce08 | algebra_quadratic_discriminant_v1_655260480_3431 | Let $a = -2$, $b = 2$, and $c = 0$. 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 pairs in $S$. Compute $|b^2 - a c s_{\text{min}}|$. | 4 | graphs = [
Graph(
let={
"_n": Const(4),
"a": Const(-2),
"b": Const(2),
"c": Const(0),
"result": Sub(Pow(Ref("b"), Const(2)), Mul(MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(n... | NT | null | COMPUTE | sympy | B3 | [
"B3"
] | 0cd20d | algebra_quadratic_discriminant_v1 | null | 3 | 0 | [
"B3"
] | 1 | 0.002 | 2026-02-08T17:22:37.318119Z | {
"verified": true,
"answer": 4,
"timestamp": "2026-02-08T17:22:37.319951Z"
} | 317bdf | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 144,
"completion_tokens": 431
},
"timestamp": "2026-02-16T09:39:40.146Z",
"answer": 4
},
{
"id": 11,
"... | 2 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "V1",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
}
] | {
"lo": -10,
"mid": -7.27,
"hi": -4.54
} | ||
d7f62d | comb_count_partitions_v1_1248542787_958 | Let $m = 1936$. Consider the set of all ordered pairs $(x, y)$ of positive integers such that $xy = m$. Let $n_0$ be the minimum value of $x + y$ over all such pairs.
Now, let $n$ be the number of ordered pairs $(x_1, x_2)$ of positive odd integers such that $x_1 + x_2 = n_0$.
Compute the number of integer partitions... | 75,175 | graphs = [
Graph(
let={
"_m": Const(1936),
"_n": MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(Mul(Var("x"), Var("y")), Ref("_m")))), expr=Sum(Var("x"), Var("y")))),
... | COMB | null | COUNT | sympy | B3 | [
"B3/COMB1"
] | e26f7e | comb_count_partitions_v1 | null | 7 | 0 | [
"B3",
"COMB1"
] | 2 | 0.002 | 2026-02-08T03:30:53.349897Z | {
"verified": true,
"answer": 75175,
"timestamp": "2026-02-08T03:30:53.351722Z"
} | 8e6706 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 216,
"completion_tokens": 1714
},
"timestamp": "2026-02-09T10:31:49.394Z",
"answer": 75175
},
{
"... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COMB1",
"status": "ok_later"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
}... | {
"lo": -0.05,
"mid": 2.89,
"hi": 5.27
} | ||
1cbfcb | nt_sum_gcd_range_mod_v1_1520064083_1675 | Let $N$ be the maximum value of $xy$ over all ordered pairs of positive integers $(x, y)$ such that $x + y = 64$. Let $k = 360$. Compute the sum $\sum_{n=1}^{N} \gcd(n, k)$, and let $M = 11719$. Find the remainder when $44121$ times this sum is divided by $85928$. | 83,560 | graphs = [
Graph(
let={
"_n": Const(64),
"N": MaxOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(Sum(Var("x"), Var("y")), Ref("_n")))), expr=Mul(Var("x"), Var("y")))),
... | NT | null | COMPUTE | sympy | B1 | [
"B1"
] | 5b950e | nt_sum_gcd_range_mod_v1 | null | 5 | 0 | [
"B1"
] | 1 | 0.088 | 2026-02-08T04:12:25.159805Z | {
"verified": true,
"answer": 83560,
"timestamp": "2026-02-08T04:12:25.248268Z"
} | ab7c1d | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 198,
"completion_tokens": 5304
},
"timestamp": "2026-02-10T15:48:50.207Z",
"answer": 83560
},
{
... | 1 | [
{
"lemma": "B1",
"status": "ok"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "V3",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
}
] | {
"lo": -3.42,
"mid": 1.86,
"hi": 7.55
} | ||
79b413 | nt_count_primes_v1_1874849503_1389 | Let $A$ be the number of positive integers $p$ such that there exists a positive integer $q$ with $p < q$, $\gcd(p, q) = 1$, and $pq = 216$. Let $S$ be the set of all prime numbers $n$ such that $A \leq n \leq 24025$. Compute the remainder when $44121 \cdot |S|$ is divided by $53197$. | 6,760 | graphs = [
Graph(
let={
"_n": Const(53197),
"upper": Const(24025),
"result": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), CountOverSet(set=SolutionsSet(var=Var("p"), condition=And(IsPositive(arg=Var(name='p')), Exists(var=Var(name='q'), conditio... | NT | null | COUNT | sympy | COPRIME_PAIRS | [
"COPRIME_PAIRS"
] | 2bb3aa | nt_count_primes_v1 | null | 4 | 0 | [
"COPRIME_PAIRS"
] | 1 | 1.817 | 2026-02-08T13:52:16.560041Z | {
"verified": true,
"answer": 6760,
"timestamp": "2026-02-08T13:52:18.377395Z"
} | 516c05 | 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": 3685
},
"timestamp": "2026-02-15T21:44:57.707Z",
"answer": 6760
},
{... | 1 | [
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
... | {
"lo": -5.49,
"mid": 0.22,
"hi": 6.51
} | ||
6595d8 | sequence_fibonacci_compute_v1_717093673_1909 | Let $n$ be the largest prime number less than or equal to $28$. Find the value of the $n$-th Fibonacci number. | 28,657 | graphs = [
Graph(
let={
"_n": Const(28),
"n": MaxOverSet(set=SolutionsSet(var=Var("n1"), condition=And(Geq(Var("n1"), Const(2)), Leq(Var("n1"), Ref("_n")), IsPrime(Var("n1"))))),
"result": Fibonacci(arg=Ref(name='n')),
},
goal=Ref("result"),
)
] | NT | null | COMPUTE | sympy | MAX_PRIME_BELOW | [
"MAX_PRIME_BELOW"
] | dc3ad3 | sequence_fibonacci_compute_v1 | null | 2 | 0 | [
"MAX_PRIME_BELOW"
] | 1 | 0.002 | 2026-02-08T16:23:24.367655Z | {
"verified": true,
"answer": 28657,
"timestamp": "2026-02-08T16:23:24.369276Z"
} | b247c2 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 76,
"completion_tokens": 604
},
"timestamp": "2026-02-17T02:57:33.147Z",
"answer": 28657
},
{
... | 1 | [
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok"
},
{
"lemma": "VAL_SUM_EQ",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
c6c3d1 | nt_max_prime_below_v1_677425708_3901 | Let $S$ be the set of positive integers $n$ such that $1 \leq n \leq 5$ and $n$ is divisible by $5$. Let $T$ be the set of all positive integers $n$ such that $n$ divides $6^k - 1$, where $k$ is the sum of the elements of $S$. Let $d$ be the largest integer such that $5^d$ divides the product of all elements of $T$. Le... | 12,776 | graphs = [
Graph(
let={
"_m": Const(5),
"_n": Const(5),
"upper": Const(22222),
"result": MaxOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), MaxKDivides(target=Sub(Pow(Const(6), SumOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var(... | NT | null | EXTREMUM | sympy | SUM_DIVISIBLE | [
"SUM_DIVISIBLE/LTE_DIFF"
] | 33bd4a | nt_max_prime_below_v1 | null | 6 | 0 | [
"LTE_DIFF",
"SUM_DIVISIBLE"
] | 2 | 5.194 | 2026-02-08T06:01:34.973765Z | {
"verified": true,
"answer": 12776,
"timestamp": "2026-02-08T06:01:40.168210Z"
} | 0f747e | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 234,
"completion_tokens": 374
},
"timestamp": "2026-02-18T22:15:45.708Z",
"answer": 12776
}
] | 2 | [
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "ok_later"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "SUM_DIVISIBLE",
"status": "ok"
},
{
"lemma": "V8",
"status": ... | {
"lo": -10,
"mid": -6.47,
"hi": -2.95
} | ||
47bf5a | algebra_quadratic_discriminant_v1_865884756_5648 | Let $a = 1$, $b = 3$, $c = 4$, and $n = 2$. Define $d = b^n - 4ac$. Let $c'$ be the number of positive integers $n$ such that $1 \le n \le 15947$ and $\gcd(n, 15) = 1$. Compute the remainder when $c' \cdot d$ is divided by $87113$. | 27,571 | graphs = [
Graph(
let={
"_n": Const(2),
"a": Const(1),
"b": Const(3),
"c": Const(4),
"result": Sub(Pow(Ref("b"), Ref("_n")), Mul(Const(4), Ref("a"), Ref("c"))),
"_c": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"... | NT | null | COMPUTE | sympy | C4 | [
"C4"
] | f51c12 | algebra_quadratic_discriminant_v1 | affine_mod | 3 | 0 | [
"C4"
] | 1 | 0.002 | 2026-02-08T18:44:52.279739Z | {
"verified": true,
"answer": 27571,
"timestamp": "2026-02-08T18:44:52.281312Z"
} | b55e69 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 141,
"completion_tokens": 1008
},
"timestamp": "2026-02-18T18:58:38.765Z",
"answer": 27571
},
... | 1 | [
{
"lemma": "C4",
"status": "ok"
},
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "V1",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
b13733 | geo_count_lattice_triangle_v1_349078426_467 | Let $S$ be the set of all ordered pairs $(x, y)$ of positive integers such that $xy = 2500$. Let $s_{\text{min}}$ be the minimum value of $x + y$ over all pairs $(x, y) \in S$. Define
$$
A = \left| 196 s_{\text{min}} - 264 \right|.
$$
Let $B$ be the sum of the greatest common divisors of the absolute values of the fol... | 9,665 | graphs = [
Graph(
let={
"_m": Const(196),
"_n": Const(196),
"area_2x": Abs(arg=Sum(Mul(MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var(name='x'), Var(name='y')]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(left=Mul(Va... | ALG | NT | COUNT | sympy | B3 | [
"B3",
"B1"
] | 655d51 | geo_count_lattice_triangle_v1 | null | 7 | 0 | [
"B1",
"B3"
] | 2 | 0.01 | 2026-02-08T13:05:40.232811Z | {
"verified": true,
"answer": 9665,
"timestamp": "2026-02-08T13:05:40.242657Z"
} | 72b8dc | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 186,
"completion_tokens": 610
},
"timestamp": "2026-02-15T09:25:16.637Z",
"answer": 9665
},
{
... | 1 | [
{
"lemma": "B1",
"status": "ok"
},
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
}
] | {
"lo": -6.96,
"mid": -4.56,
"hi": -1.46
} | ||
d70f84 | comb_sum_binomial_mod_v1_1520064083_657 | Let $m = 3$. Let $d$ be a positive divisor of 181882 that is at most 422. Define $n$ to be the largest such divisor. For integers $k$ from 17 to 402 inclusive and integers $j$ from 1 to 5 inclusive, consider the binomial coefficients $\binom{n}{k}$. Let $S$ be the sum of all such binomial coefficients over these values... | 836 | graphs = [
Graph(
let={
"_m": Const(3),
"_n": MaxOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Const(1)), Leq(Var("d"), Const(422)), Divides(divisor=Var("d"), dividend=Const(181882))))),
"sum": Div(Mul(Ref("_m"), SumOverSet(set=MapOverSet(set=Solution... | NT | null | COMPUTE | sympy | MAX_DIVISOR | [
"MAX_DIVISOR/SUM_INDEPENDENT"
] | af3b48 | comb_sum_binomial_mod_v1 | null | 4 | 0 | [
"MAX_DIVISOR",
"SUM_INDEPENDENT"
] | 2 | 0.059 | 2026-02-08T03:31:31.112297Z | {
"verified": true,
"answer": 836,
"timestamp": "2026-02-08T03:31:31.171269Z"
} | 63be24 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 249,
"completion_tokens": 17012
},
"timestamp": "2026-02-23T20:34:27.487Z",
"answer": 836
},
{
"... | 1 | [
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "MAX_DIVISOR",
"status": "ok"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{... | {
"lo": 4.28,
"mid": 7.01,
"hi": 10
} | ||
3c4c30 | alg_telescope_v1_1218484723_940 | Let
$$T = \sum_{k=0}^{931} \left|\left\{ a : 0 \le a \le 72,\ 3\bigl(3(3a^{3} + a - 3 \bmod 73)^{3} + (3a^{3} + a - 3 \bmod M) - 3 \bmod 73\bigr)^{3} + \bigl(3(3a^{3} + a - 3 \bmod 73)^{3} + (3a^{3} + a - 3 \bmod 73) - 3 \bmod 73\bigr) - 3 \bmod 73 = a,\\ 3a^{3} + a - 3 \bmod 73 \ne a,\\ 3(3a^{3} + a - 3 \bmod 73)^{3} ... | 34,670 | graphs = [
Graph(
let={
"_d": Const(3),
"_m": Const(51493),
"_n": Const(3),
"result": Mod(value=Summation(var="k", start=Const(0), end=Const(931), expr=Sum(Mul(CountOverSet(set=SolutionsSet(var=Var("a"), condition=And(Geq(Var("a"), Const(0)), Leq(Var("a"), Con... | ALG | null | COMPUTE | sympy | QF_PSD_DISTINCT | [
"QF_PSD_DISTINCT/POLY_ORBIT_COUNT",
"POLY3_MIN"
] | e681dd | alg_telescope_v1 | null | 8 | 0 | [
"POLY3_MIN",
"POLY_ORBIT_COUNT",
"QF_PSD_DISTINCT"
] | 3 | 0.596 | 2026-02-25T02:38:02.435600Z | {
"verified": true,
"answer": 34670,
"timestamp": "2026-02-25T02:38:03.031508Z"
} | 4c6654 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 540,
"completion_tokens": 32768
},
"timestamp": "2026-03-10T03:09:39.422Z",
"answer": null
},
{
... | 0 | [
{
"lemma": "POLY3_MIN",
"status": "ok"
},
{
"lemma": "POLY_ORBIT_COUNT",
"status": "ok_later"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "QF_PSD_DISTINCT",
"status": "ok"
}
] | {
"lo": 5.81,
"mid": 8.21,
"hi": 10
} | ||
8e6867 | comb_count_partitions_v1_1526740231_372 | Let $T$ be the set of all integers $t$ such that $18 \le t \le 122$ and $t = 10a + 8b$ for some integers $a, b$ with $1 \le a \le 5$ and $1 \le b \le 9$. Let $n$ be the number of elements in $T$. Compute the number of integer partitions of $n$, denoted $p(n)$. Find the remainder when $79308 \cdot p(n)$ is divided by $6... | 42,179 | graphs = [
Graph(
let={
"_n": Const(60895),
"n": CountOverSet(set=SolutionsSet(var=Var("t"), condition=Exists(var=Var(name='a'), condition=Exists(var=Var(name='b'), condition=And(Geq(left=Var(name='a'), right=Const(value=1)), Leq(left=Var(name='a'), right=Const(value=5)), Geq(left=Va... | COMB | null | COUNT | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | comb_count_partitions_v1 | null | 6 | 0 | [
"LIN_FORM"
] | 1 | 0.019 | 2026-02-08T11:29:38.965996Z | {
"verified": true,
"answer": 42179,
"timestamp": "2026-02-08T11:29:38.984821Z"
} | f4bd4c | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 1,
"correct": {
"strict": false,
"boxed": false,
"relaxed": true
},
"usage": {
"prompt_tokens": 227,
"completion_tokens": 32768
},
"timestamp": "2026-02-24T14:05:38.411Z",
"answer": null
},
{
... | 1 | [
{
"lemma": "C2",
"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",
"status": "no... | {
"lo": 3.25,
"mid": 5.68,
"hi": 8.81
} | ||
ca5254 | sequence_fibonacci_compute_v1_151522320_2327 | Let $n$ be the number of ordered pairs $(x_1, x_2)$ of positive odd integers such that $x_1 + x_2 = 40$. Let $F_n$ denote the $n$th Fibonacci number, where $F_1 = F_2 = 1$ and $F_k = F_{k-1} + F_{k-2}$ for $k \geq 3$. Compute the remainder when $44121 \cdot F_n$ is divided by 51874. Determine the value of this remainde... | 47,443 | graphs = [
Graph(
let={
"_n": Const(51874),
"n": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x1"), Var("x2")]), condition=And(IsPositive(arg=Var(name='x1')), IsPositive(arg=Var(name='x2')), IsOdd(arg=Var(name='x1')), IsOdd(arg=Var(name='x2')), Eq(Sum(Var("x1"), Var("x2")),... | NT | null | COMPUTE | sympy | LIN_FORM | [
"COMB1"
] | 567f58 | sequence_fibonacci_compute_v1 | null | 4 | 0 | [
"COMB1",
"LIN_FORM"
] | 2 | 0.12 | 2026-02-08T04:44:36.089242Z | {
"verified": true,
"answer": 47443,
"timestamp": "2026-02-08T04:44:36.209207Z"
} | 975ed6 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 228,
"completion_tokens": 1590
},
"timestamp": "2026-02-11T21:55:28.730Z",
"answer": 47443
},
{
... | 1 | [
{
"lemma": "COMB1",
"status": "ok"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
}
] | {
"lo": -3.42,
"mid": 1.86,
"hi": 7.55
} | ||
fe93bd | alg_poly_orbit_count_v1_1218484723_1901 | Define the sequence $N, M, R, S, T, K$ recursively for a non-negative integer $a$ by:
\begin{align*}
N &= (2a^3) \bmod 71,\\
M &= (2N^3) \bmod 71,\\
R &= (2M^3) \bmod 71,\\
S &= (2R^3) \bmod 71,\\
T &= (2S^3) \bmod 71,\\
K &= (2T^3) \bmod 71.
\end{align*}
Find the number of non-negative integers $a$ with $0 \le a \le 1... | 17,328 | graphs = [
Graph(
let={
"p1": Mod(value=Mul(Const(2), Pow(Var("a"), Const(3))), modulus=Const(71)),
"p2": Mod(value=Mul(Const(2), Pow(Ref("p1"), Const(3))), modulus=Const(71)),
"p3": Mod(value=Mul(Const(2), Pow(Ref("p2"), Const(3))), modulus=Const(71)),
"p4": ... | ALG | null | COUNT | sympy | POLY_ORBIT_COUNT | [
"POLY_ORBIT_COUNT"
] | 4ad965 | alg_poly_orbit_count_v1 | null | 6 | null | [
"POLY_ORBIT_COUNT"
] | 1 | 0.022 | 2026-02-25T03:38:16.715299Z | {
"verified": true,
"answer": 17328,
"timestamp": "2026-02-25T03:38:16.736921Z"
} | e193b9 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 293,
"completion_tokens": 5623
},
"timestamp": "2026-03-29T01:57:38.177Z",
"answer": 17328
},
{
"... | 1 | [
{
"lemma": "POLY_ORBIT_COUNT",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
}
] | {
"lo": 3.14,
"mid": 5.37,
"hi": 7.61
} | ||
6680fd | nt_min_coprime_above_v1_48377204_20 | Let $m$ be the largest prime number $n$ such that $2 \leq n \leq 156$. Let $r$ be the smallest integer $n_1$ such that $26244 < n_1 \leq 26405$ and $\gcd(n_1, m) = 1$. Compute the smallest positive integer $k$ such that the $k$-th Fibonacci number is divisible by $|r| + 2$. | 9,436 | graphs = [
Graph(
let={
"start": Const(26244),
"upper": Const(26405),
"modulus": MaxOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(2)), Leq(Var("n"), Const(156)), IsPrime(Var("n"))))),
"result": MinOverSet(set=SolutionsSet(var=Var("n1... | NT | null | EXTREMUM | sympy | MAX_PRIME_BELOW | [
"MAX_PRIME_BELOW"
] | dc3ad3 | nt_min_coprime_above_v1 | null | 5 | 0 | [
"MAX_PRIME_BELOW"
] | 1 | 0.182 | 2026-02-08T15:08:51.648206Z | {
"verified": true,
"answer": 9436,
"timestamp": "2026-02-08T15:08:51.829893Z"
} | 27db2f | 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": 2516
},
"timestamp": "2026-02-16T01:39:41.561Z",
"answer": 9436
},
{... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "V... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
f3daf6 | geo_visible_lattice_v1_717093673_3300 | Let $n = 99$. Define $L$ to be the number of ordered pairs $(x, y)$ of positive integers such that $1 \le x, y \le n$ and $\gcd(x, y) = 1$. Let $c = 81046$. Compute the remainder when $c \cdot L$ is divided by $91107$. | 58,621 | graphs = [
Graph(
let={
"n": Const(99),
"result": VisibleLatticePoints(n=Ref(name='n')),
"_c": Const(81046),
"Q": Mod(value=Mul(Ref("_c"), Ref("result")), modulus=Const(91107)),
},
goal=Ref("Q"),
)
] | GEOM | null | COUNT | sympy | [] | geo_visible_lattice_v1 | null | 3 | 0 | null | null | 0.808 | 2026-02-08T17:29:30.871004Z | {
"verified": true,
"answer": 58621,
"timestamp": "2026-02-08T17:29:31.678929Z"
} | a7482c | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 122,
"completion_tokens": 3826
},
"timestamp": "2026-02-18T03:50:33.601Z",
"answer": 58621
},
... | 1 | [] | {
"lo": -2.38,
"mid": 1.74,
"hi": 6.59
} | ||||
57149a | comb_catalan_compute_v1_784195855_3226 | Let $n$ be the number of integers $t$ such that $15 \leq t \leq 48$ and there exist integers $a$ and $b$ with $1 \leq a \leq 5$, $1 \leq b \leq 2$, and $t = 6a + 9b$.
Define $\_n = 44121$ and let $C_n$ denote the $n$-th Catalan number. Compute the remainder when $\_n \cdot C_n$ is divided by $82564$. | 44,416 | graphs = [
Graph(
let={
"_n": Const(44121),
"n": CountOverSet(set=SolutionsSet(var=Var("t"), condition=Exists(var=Var(name='a'), condition=Exists(var=Var(name='b'), condition=And(Geq(left=Var(name='a'), right=Const(value=1)), Leq(left=Var(name='a'), right=Const(value=5)), Geq(left=Va... | COMB | null | COMPUTE | sympy | COMB1 | [
"LIN_FORM"
] | 7b2633 | comb_catalan_compute_v1 | null | 5 | 0 | [
"COMB1",
"LIN_FORM"
] | 2 | 0.023 | 2026-02-08T06:18:12.475620Z | {
"verified": true,
"answer": 44416,
"timestamp": "2026-02-08T06:18:12.498797Z"
} | 680b31 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 231,
"completion_tokens": 32768
},
"timestamp": "2026-02-24T05:54:28.228Z",
"answer": null
},
{
... | 1 | [
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "V8",
"status": "no"
},
{
"lemma": "V8_SUM",
"st... | {
"lo": -0.06,
"mid": 2.89,
"hi": 5.27
} | ||
47369c | algebra_vieta_sum_v1_124444284_1614 | Let $c = 90016$. Define $r$ to be the sum of all real numbers $x$ such that $$2x^4 + 22x^3 + \left(\sum_{x} (x^2 - 80x + 1591 = 0)\right) x^2 + 96x = 0,$$ where the inner sum is taken over all real solutions $x$ to the equation $x^2 - 80x + 1591 = 0$. Compute the remainder when $c \cdot r$ is divided by $94229$. | 46,343 | graphs = [
Graph(
let={
"_n": Const(2),
"result": SumOverSet(set=SolutionsSet(var=Var("x"), condition=Eq(Sum(Mul(Const(2), Pow(Var("x"), Const(4))), Mul(Const(22), Pow(Var("x"), Const(3))), Mul(SumOverSet(set=SolutionsSet(var=Var("x"), condition=Eq(Sum(Pow(Var("x"), Const(2)), Mul(Co... | NT | null | COMPUTE | sympy | VIETA_SUM | [
"VIETA_SUM"
] | b33a7a | algebra_vieta_sum_v1 | null | 6 | 0 | [
"VIETA_SUM"
] | 1 | 0.157 | 2026-02-08T04:02:35.612581Z | {
"verified": true,
"answer": 46343,
"timestamp": "2026-02-08T04:02:35.769478Z"
} | 7ae159 | 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": 1946
},
"timestamp": "2026-02-11T08:12:38.890Z",
"answer": 46343
},
{
"... | 1 | [
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "V3",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
},
{
"lemma": "VIETA_SUM",
"status": "ok"
}
] | {
"lo": 1.71,
"mid": 5.04,
"hi": 8.38
} | ||
289b39 | comb_count_permutations_fixed_v1_898971024_1416 | Let $S$ be the set of all ordered pairs $(x,y)$ of positive integers such that $xy = 9$. Let $n$ be the minimum value of $x + y$ over all such pairs. Compute $\binom{n}{4} \cdot !(n-4)$, where $!k$ denotes the number of derangements of $k$ elements. Multiply this result by 57157 and find the remainder when the product ... | 10,395 | 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(9)))), expr=Sum(Var("x"), Var("y")))),
"k": Const(4),
... | COMB | null | COUNT | sympy | B3 | [
"B3"
] | 0cd20d | comb_count_permutations_fixed_v1 | null | 4 | 0 | [
"B3"
] | 1 | 0.003 | 2026-02-08T16:06:29.125498Z | {
"verified": true,
"answer": 10395,
"timestamp": "2026-02-08T16:06:29.128431Z"
} | ee3158 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 211,
"completion_tokens": 665
},
"timestamp": "2026-02-24T19:57:55.594Z",
"answer": 10395
},
{
"... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "V8_SUM",
"stat... | {
"lo": -5.65,
"mid": -3.17,
"hi": -0.81
} | ||
8cc9ef | geo_count_lattice_rect_v1_784195855_6959 | Compute the number of lattice points $(x, y)$ such that $0 \leq x \leq 66$ and $0 \leq y \leq 30$. | 2,077 | graphs = [
Graph(
let={
"a": Const(66),
"b": Const(30),
"result": LatticePointsRect(a=Ref(name='a'), b=Ref(name='b')),
},
goal=Ref("result"),
)
] | GEOM | null | COUNT | sympy | [] | geo_count_lattice_rect_v1 | null | 3 | 0 | null | null | 0.001 | 2026-02-08T09:01:46.558349Z | {
"verified": true,
"answer": 2077,
"timestamp": "2026-02-08T09:01:46.558927Z"
} | 3a5ded | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 148,
"completion_tokens": 265
},
"timestamp": "2026-02-24T10:23:52.945Z",
"answer": 2077
},
{
"id... | 2 | [] | {
"lo": -10,
"mid": -7.79,
"hi": -5.57
} | ||||
b33ae6 | sequence_count_fib_divisible_v1_349078426_1196 | Let $d_{\text{max}}$ be the largest positive divisor of $357603$ that does not exceed $597$. Let $r$ be the number of positive integers $n$ such that $1 \leq n \leq d_{\text{max}}$ and $20$ divides the $n$-th Fibonacci number. Compute the smallest positive integer $k$ such that the $k$-th Fibonacci number is divisible ... | 8 | graphs = [
Graph(
let={
"_n": Const(597),
"upper": MaxOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Const(1)), Leq(Var("d"), Ref("_n")), Divides(divisor=Var("d"), dividend=Const(357603))))),
"d": Const(20),
"result": CountOverSet(set=Solut... | NT | null | COUNT | sympy | V5 | [
"MAX_DIVISOR"
] | 51757e | sequence_count_fib_divisible_v1 | null | 5 | 0 | [
"MAX_DIVISOR",
"V5"
] | 2 | 0.111 | 2026-02-08T13:30:35.351377Z | {
"verified": true,
"answer": 8,
"timestamp": "2026-02-08T13:30:35.462769Z"
} | 31d077 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 141,
"completion_tokens": 5749
},
"timestamp": "2026-02-15T16:51:25.957Z",
"answer": 8
},
{
... | 1 | [
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "MAX_DIVISOR",
"status": "ok"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "V1",
"status": "no"
}
] | {
"lo": -5.49,
"mid": 0.22,
"hi": 6.51
} | ||
cb5de7 | algebra_quadratic_discriminant_v1_1520064083_7258 | Let $a = 9$, $b = -10$, and $n = 2$. Let $S$ be the set of all ordered pairs $(x, y)$ of positive integers such that $xy = 25$. Define $c$ to be the minimum value of $x + y$ over all such pairs. Compute $\text{result} = b^n - 4ac$, and let $Q = |\text{result}|$. Find the value of $Q$. | 260 | graphs = [
Graph(
let={
"_n": Const(2),
"a": Const(9),
"b": Const(-10),
"c": MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(Mul(Var("x"), Var("... | NT | null | COMPUTE | sympy | B3 | [
"B3"
] | 0cd20d | algebra_quadratic_discriminant_v1 | null | 3 | 0 | [
"B3"
] | 1 | 0.001 | 2026-02-08T08:51:48.061169Z | {
"verified": true,
"answer": 260,
"timestamp": "2026-02-08T08:51:48.062524Z"
} | 965c8d | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 147,
"completion_tokens": 440
},
"timestamp": "2026-02-13T22:04:24.445Z",
"answer": 260
},
{
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
}
] | {
"lo": -7.01,
"mid": -4.68,
"hi": -2.15
} | ||
8d3631 | algebra_poly_eval_v1_1978505735_8263 | Let $k = 16$. Define $c$ to be the number of positive integers $p$ for which there exists a positive integer $q$ such that $p \cdot q = 41160$, $\gcd(p, q) = 1$, and $p < q$. Compute the value of
$$
c \cdot k^3 - 6k^2 + 5k + 3.$$ | 31,315 | graphs = [
Graph(
let={
"_n": Const(2),
"k": Const(16),
"result": Sum(Mul(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=41160)),... | NT | null | COMPUTE | sympy | COPRIME_PAIRS | [
"COPRIME_PAIRS"
] | 2bb3aa | algebra_poly_eval_v1 | null | 4 | 0 | [
"COPRIME_PAIRS"
] | 1 | 0.004 | 2026-02-08T20:45:14.276168Z | {
"verified": true,
"answer": 31315,
"timestamp": "2026-02-08T20:45:14.279687Z"
} | 569f27 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 133,
"completion_tokens": 3636
},
"timestamp": "2026-02-19T01:02:45.554Z",
"answer": 31315
},
... | 1 | [
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "V8_SUM",
... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
14e951 | nt_count_coprime_v1_168721529_496 | Let $k = 13$. Compute the number of positive integers $n$ such that $1 \leq n \leq 89401$ and $\gcd(n, 13) = 1$. Denote this number by $c$. Let $p_0$ be the number of ordered pairs $(p, q)$ of positive integers such that $p < q$, $pq = 24$, and $\gcd(p, q) = 1$. Compute the value of $c + \left(p_0\right)^{c \bmod{14}} ... | 82,780 | graphs = [
Graph(
let={
"_n": Const(14),
"upper": Const(89401),
"k": Const(13),
"result": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Ref("upper")), Eq(GCD(a=Var("n"), b=Ref("k")), Const(1))))),
... | NT | null | COUNT | sympy | COPRIME_PAIRS | [
"COPRIME_PAIRS"
] | 64a51e | nt_count_coprime_v1 | mod_exp | 5 | 0 | [
"COPRIME_PAIRS"
] | 1 | 8.474 | 2026-02-08T13:04:20.478711Z | {
"verified": true,
"answer": 82780,
"timestamp": "2026-02-08T13:04:28.952748Z"
} | e7eae8 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 242,
"completion_tokens": 1385
},
"timestamp": "2026-02-09T05:35:53.547Z",
"answer": 82780
},
{
"... | 1 | [
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "V3",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
},
{
"lemma": "VAL_SUM_EQ",
"status": "no"
}... | {
"lo": -2,
"mid": 1.85,
"hi": 5.2
} | ||
a9b532 | modular_modexp_compute_v1_677425708_2675 | Let $a = 43$, $n = 111$, and $m = 20160$. Let $e$ be the largest positive divisor of $78083732$ that is at most $8836$. Define $r = a^e \mod m$. Compute the remainder when $n - r$ is divided by $84694$. | 73,044 | graphs = [
Graph(
let={
"_n": Const(111),
"a": Const(43),
"e": MaxOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Const(1)), Leq(Var("d"), Const(8836)), Divides(divisor=Var("d"), dividend=Const(78083732))))),
"m": Const(20160),
"... | NT | null | COMPUTE | sympy | MAX_DIVISOR | [
"MAX_DIVISOR"
] | 51757e | modular_modexp_compute_v1 | null | 5 | 0 | [
"MAX_DIVISOR"
] | 1 | 0.002 | 2026-02-08T05:11:13.751919Z | {
"verified": true,
"answer": 73044,
"timestamp": "2026-02-08T05:11:13.753834Z"
} | 0e6222 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 181,
"completion_tokens": 6997
},
"timestamp": "2026-02-11T23:04:23.146Z",
"answer": 73044
},
{
... | 1 | [
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "MAX_DIVISOR",
"status": "ok"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
}
] | {
"lo": -3.42,
"mid": 1.86,
"hi": 7.55
} | ||
51a48e | antilemma_k3_v1_1520064083_6482 | Let $x$ be the sum of $\phi(d)$ over all positive divisors $d$ of $1521$, where $\phi$ denotes Euler's totient function. Find the remainder when $11 - x$ is divided by $51431$. Compute this value. | 49,921 | graphs = [
Graph(
let={
"x": SumOverDivisors(n=Const(value=1521), var='d', expr=EulerPhi(n=Var(name='d'))),
"Q": Mod(value=Sub(Const(11), Ref("x")), modulus=Const(51431)),
},
goal=Ref("Q"),
)
] | NT | COMB | COMPUTE | sympy | K3 | [
"K3"
] | 54c41e | antilemma_k3_v1 | null | 3 | 0 | [
"K3"
] | 1 | 0 | 2026-02-08T08:06:59.366191Z | {
"verified": true,
"answer": 49921,
"timestamp": "2026-02-08T08:06:59.366579Z"
} | cdf232 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 101,
"completion_tokens": 489
},
"timestamp": "2026-02-13T15:07:41.265Z",
"answer": 49921
},
{... | 1 | [
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "K3",
"status": "ok"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
}
] | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
5e585e | sequence_count_fib_divisible_v1_1520064083_4746 | Let $n = 40804$. Consider the set of all ordered pairs $(x, y)$ of positive integers such that $xy = n$. For each such pair, compute $x + y$, and let $S$ be the set of all such sums. Let $m$ be the minimum value in $S$. Determine the number of positive integers $k$ such that $1 \leq k \leq m$ and $3$ divides the $k$-th... | 101 | graphs = [
Graph(
let={
"_n": Const(40804),
"upper": MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(Mul(Var("x"), Var("y")), Ref("_n")))), expr=Sum(Var("x"), Var("y"))... | NT | null | COUNT | sympy | B3 | [
"B3"
] | 0cd20d | sequence_count_fib_divisible_v1 | null | 6 | 0 | [
"B3"
] | 1 | 0.047 | 2026-02-08T06:25:13.259783Z | {
"verified": true,
"answer": 101,
"timestamp": "2026-02-08T06:25:13.307042Z"
} | 61d130 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 150,
"completion_tokens": 1862
},
"timestamp": "2026-02-12T23:34:29.335Z",
"answer": 101
},
{
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
}
] | {
"lo": -5.92,
"mid": -3.14,
"hi": 0.26
} | ||
1249c2 | comb_binomial_compute_v1_153355830_429 | Consider all ordered pairs $(x,y)$ of positive integers such that
\[xy=K,\]
where $K$ is the number of positive integers $p$ for which there exists a positive integer $q$ satisfying
\[pq=150089940,\quad \gcd(p,q)=1,\quad p<q.
\]
For each such pair $(x,y)$, consider the sum $x+y$. Let $n$ be the smallest possible value ... | 11,440 | 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")), CountOverSet(set=SolutionsSet(var=Var("p"), condition=And(IsPositive(arg=Var(n... | NT | null | COMPUTE | sympy | COPRIME_PAIRS | [
"COPRIME_PAIRS/B3"
] | 3f0fb0 | comb_binomial_compute_v1 | null | 8 | 0 | [
"B3",
"COPRIME_PAIRS"
] | 2 | 0.003 | 2026-02-08T03:06:02.361678Z | {
"verified": true,
"answer": 11440,
"timestamp": "2026-02-08T03:06:02.364663Z"
} | e2f61c | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 245,
"completion_tokens": 6329
},
"timestamp": "2026-02-10T12:52:42.857Z",
"answer": 11440
},
{
"... | 1 | [
{
"lemma": "B3",
"status": "ok_later"
},
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "V3",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
},
{
"lemma"... | {
"lo": -0.14,
"mid": 2.22,
"hi": 4.26
} | ||
9059dc | nt_min_coprime_above_v1_1742523217_4645 | Let $A$ be the set of integers $n$ such that $71824 < n \leq 71951$ and $\gcd(n, 117) = 1$. Define $\text{result}$ to be the minimum element of $A$. Let $B$ be the set of all ordered pairs $(x,y)$ of positive integers such that $x \cdot y = 396900$. Define $s$ to be the minimum value of $x + y$ over all such pairs in $... | 65,699 | graphs = [
Graph(
let={
"start": Const(71824),
"upper": Const(71951),
"modulus": Const(117),
"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(... | NT | null | EXTREMUM | sympy | B3 | [
"B3"
] | fc629c | nt_min_coprime_above_v1 | negation_mod | 5 | 0 | [
"B3"
] | 1 | 0.013 | 2026-02-08T09:01:19.688313Z | {
"verified": true,
"answer": 65699,
"timestamp": "2026-02-08T09:01:19.701337Z"
} | c44593 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 179,
"completion_tokens": 1185
},
"timestamp": "2026-02-13T23:12:43.775Z",
"answer": 65699
},
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
}
] | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
02fa53 | antilemma_cartesian_v1_865884756_2979 | Let $x$ be the number of ordered pairs $(i, j)$ such that $1 \leq i \leq 43$ and $1 \leq j \leq 45$. Let $m = |x| + 2$. The Fibonacci entry point modulo $m$ is the smallest positive integer $k$ for which the $k$-th Fibonacci number is divisible by $m$. Compute this Fibonacci entry point. | 259 | graphs = [
Graph(
let={
"x": CountOverSet(set=CartesianProduct(left=IntegerRange(start=Const(1), end=Const(43)), right=IntegerRange(start=Const(1), end=Const(45)))),
"Q": FibonacciEntryPoint(modulus=Sum(Abs(arg=Ref(name='x')), Const(value=2))),
},
goal=Ref("Q"),
)... | COMB | GEOM | COMPUTE | sympy | COUNT_CARTESIAN | [
"COUNT_CARTESIAN"
] | 409d7d | antilemma_cartesian_v1 | null | 3 | 0 | [
"COUNT_CARTESIAN"
] | 1 | 0.009 | 2026-02-08T17:04:42.809796Z | {
"verified": true,
"answer": 259,
"timestamp": "2026-02-08T17:04:42.818897Z"
} | 315a2e | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 133,
"completion_tokens": 1746
},
"timestamp": "2026-02-17T19:49:09.499Z",
"answer": 259
},
{
... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "ok"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
}
] | {
"lo": -2.38,
"mid": 1.74,
"hi": 6.59
} | ||
ebe0dd_n | alg_sum_ap_v1_1218484723_6591 | A solar panel array generates power levels modeled by the quadratic $2x^2 - 64650x + 521073352$, where $x$ is the hour of operation. The system is considered efficient during hours $x$ (with $1 \le x \le 17088$) when power consumption is non-positive. Let $n$ be the number of efficient hours. The total diagnostic score... | 3,695 | ALG | null | COMPUTE | sympy | QUADRATIC_INEQ | [
"QUADRATIC_INEQ"
] | 241de8 | alg_sum_ap_v1 | null | 3 | null | [
"QUADRATIC_INEQ"
] | 1 | 0.019 | 2026-02-25T08:08:23.986088Z | null | 995b04 | ebe0dd | narrative | 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": 2184
},
"timestamp": "2026-03-31T01:36:32.705Z",
"answer": 3695
},
{
"i... | 1 | [
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "QUADRATIC_INEQ",
"status": "ok"
}
] | {
"lo": -5.37,
"mid": 0.23,
"hi": 5.22
} | |
93a070 | nt_count_divisors_in_range_v1_1978505735_3092 | Let $n = 5040$, $a = 17$, and $b = 2521$. Define $r$ to be the number of positive divisors $d$ of $n$ such that $a \leq d \leq b$. Let $s$ be the minimum value of $x + y$ over all ordered pairs $(x, y)$ of positive integers such that $xy = 1024$. Compute $s - r$. | 19 | graphs = [
Graph(
let={
"n": Const(5040),
"a": Const(17),
"b": Const(2521),
"result": CountOverSet(set=SolutionsSet(var=Var("d"), condition=And(Divides(divisor=Var("d"), dividend=Ref("n")), Geq(Var("d"), Ref("a")), Leq(Var("d"), Ref("b"))))),
"Q": ... | NT | null | COUNT | sympy | B3 | [
"B3"
] | fc629c | nt_count_divisors_in_range_v1 | negation_mod | 4 | 0 | [
"B3"
] | 1 | 0.183 | 2026-02-08T17:20:43.819999Z | {
"verified": true,
"answer": 19,
"timestamp": "2026-02-08T17:20:44.002713Z"
} | ddb441 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 139,
"completion_tokens": 1813
},
"timestamp": "2026-02-18T00:38:49.873Z",
"answer": 19
},
{
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "V1",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
12b0ac | modular_min_linear_v1_124444284_2313 | Let $a = 6348$ and $b = 4950$. Let $m$ be the number of positive integers $k$ such that $1 \leq k \leq 2945399$ and $361$ divides $k$. Determine the value of $x$, where $x$ is the smallest positive integer such that $1 \leq x \leq m$ and
$$
6348x \equiv 4950 \pmod{m}.
$$ | 3,633 | graphs = [
Graph(
let={
"a": Const(6348),
"b": Const(4950),
"m": CountOverSet(set=SolutionsSet(var=Var("k"), condition=And(Geq(Var("k"), Const(1)), Leq(Var("k"), Const(2945399)), Divides(divisor=Const(361), dividend=Var("k"))), domain='positive_integers')),
"r... | ALG | NT | EXTREMUM | sympy | C2 | [
"C2"
] | 9685eb | modular_min_linear_v1 | null | 6 | 0 | [
"C2"
] | 1 | 0.328 | 2026-02-08T04:35:39.209460Z | {
"verified": true,
"answer": 3633,
"timestamp": "2026-02-08T04:35:39.537026Z"
} | 15e524 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 212,
"completion_tokens": 1805
},
"timestamp": "2026-02-10T17:15:33.693Z",
"answer": 3633
},
{
"... | 1 | [
{
"lemma": "C2",
"status": "ok"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
}
] | {
"lo": -3.42,
"mid": 1.86,
"hi": 7.55
} | ||
e3e5e4 | comb_bell_compute_v1_458359167_904 | Let $n$ be the number of positive integers $k$ such that $1 \leq k \leq 324$ and $k$ divides $36$. Compute the Bell number $B_n$, which counts the number of partitions of a set of $n$ elements. | 21,147 | graphs = [
Graph(
let={
"_n": Const(36),
"n": CountOverSet(set=SolutionsSet(var=Var("k"), condition=And(Geq(Var("k"), Const(1)), Leq(Var("k"), Const(324)), Divides(divisor=Ref("_n"), dividend=Var("k"))), domain='positive_integers')),
"result": Bell(Ref("n")),
},
... | NT | COMB | COMPUTE | sympy | C2 | [
"C2"
] | 9685eb | comb_bell_compute_v1 | null | 5 | 0 | [
"C2"
] | 1 | 0.001 | 2026-02-08T04:10:15.137489Z | {
"verified": true,
"answer": 21147,
"timestamp": "2026-02-08T04:10:15.138577Z"
} | c11975 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 168,
"completion_tokens": 446
},
"timestamp": "2026-02-10T15:35:24.975Z",
"answer": 21147
},
{
"... | 1 | [
{
"lemma": "C2",
"status": "ok"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"... | {
"lo": -5.55,
"mid": -3.01,
"hi": 0.33
} | ||
37a6f5 | comb_binomial_compute_v1_1918700295_345 | Let $A$ be the set of all positive integers $p$ for which there exists a positive integer $q$ such that $pq = 54$, $\gcd(p, q) = 1$, and $p < q$. Let $c$ be the number of elements in $A$. Let $k$ be the largest prime number that is at least $c$ and at most 6. Let $\binom{12}{k}$ denote the binomial coefficient. Compute... | 792 | graphs = [
Graph(
let={
"_n": Const(6),
"n": Const(12),
"k": MaxOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), CountOverSet(set=SolutionsSet(var=Var("p"), condition=And(IsPositive(arg=Var(name='p')), Exists(var=Var(name='q'), condition=And(Eq(left=Mul(... | NT | null | COMPUTE | sympy | COPRIME_PAIRS | [
"COPRIME_PAIRS/MAX_PRIME_BELOW"
] | 2248fc | comb_binomial_compute_v1 | null | 5 | 0 | [
"COPRIME_PAIRS",
"MAX_PRIME_BELOW"
] | 2 | 0.002 | 2026-02-08T03:10:10.227181Z | {
"verified": true,
"answer": 792,
"timestamp": "2026-02-08T03:10:10.229383Z"
} | b67457 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 222,
"completion_tokens": 1339
},
"timestamp": "2026-02-10T13:23:01.459Z",
"answer": 792
},
{
"id... | 2 | [
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
... | {
"lo": -10,
"mid": -7.73,
"hi": -5.46
} | ||
e12c60 | nt_min_with_divisor_count_v1_655260480_442 | Let $D$ be the number of ordered pairs $(i, j)$ with $1 \le i \le 2$, $1 \le j \le 8$, and $\gcd(i, j) = 1$.
Find the smallest positive integer $n$ such that $1 \le n \le 60025$ and the number of positive divisors of $n$ is equal to $D$.
Compute the smallest positive integer $k$ such that the $k$-th Fibonacci number ... | 30 | graphs = [
Graph(
let={
"upper": Const(60025),
"div_count": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("i"), Var("j")]), condition=Eq(GCD(a=Var("i"), b=Var("j")), Const(1)), domain=CartesianProduct(left=IntegerRange(start=Const(1), end=Const(2)), right=IntegerRange(start=C... | NT | null | EXTREMUM | sympy | COUNT_COPRIME_GRID | [
"COUNT_COPRIME_GRID"
] | 20ec03 | nt_min_with_divisor_count_v1 | null | 5 | 0 | [
"COUNT_COPRIME_GRID"
] | 1 | 5.314 | 2026-02-08T15:23:31.141669Z | {
"verified": true,
"answer": 30,
"timestamp": "2026-02-08T15:23:36.455293Z"
} | 5ed6d4 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 159,
"completion_tokens": 2329
},
"timestamp": "2026-02-16T05:24:17.806Z",
"answer": 30
},
{
... | 1 | [
{
"lemma": "COUNT_COPRIME_GRID",
"status": "ok"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "V7",
"sta... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
f804e3 | geo_count_lattice_rect_v1_1918700295_3290 | Compute the number of lattice points in the rectangle $[0, 47] \times [0, 34]$, including the boundary. | 1,680 | graphs = [
Graph(
let={
"a": Const(47),
"b": Const(34),
"result": LatticePointsRect(a=Ref(name='a'), b=Ref(name='b')),
},
goal=Ref("result"),
)
] | GEOM | null | COUNT | sympy | [] | geo_count_lattice_rect_v1 | null | 2 | 0 | null | null | 0 | 2026-02-08T08:30:25.042518Z | {
"verified": true,
"answer": 1680,
"timestamp": "2026-02-08T08:30:25.043017Z"
} | 897827 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 139,
"completion_tokens": 173
},
"timestamp": "2026-02-24T09:37:18.962Z",
"answer": 1680
},
{
"id... | 1 | [] | {
"lo": -9.23,
"mid": -6.18,
"hi": -4.06
} | ||||
56289b | modular_count_residue_v1_677425708_2255 | Let $m = 18$ and $r = \sum_{k=1}^{4} k = 10$. Let $A$ be the set of all positive integers $n \leq 65536$ such that $n \equiv r \pmod{m}$. Let $c$ be the number of elements in $A$. Let $B$ be the set of all real solutions $x$ to the equation $x^2 - 333x - 34528 = 0$. Let $s$ be the sum of all elements in $B$. Compute th... | 79,126 | graphs = [
Graph(
let={
"upper": Const(65536),
"m": Const(18),
"r": Summation(var="k", start=Const(1), end=Const(4), expr=Var("k")),
"result": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Ref("upper")), Eq(Mo... | NT | null | COUNT | sympy | VIETA_SUM | [
"VIETA_SUM",
"SUM_ARITHMETIC"
] | de6db6 | modular_count_residue_v1 | negation_mod | 5 | 0 | [
"SUM_ARITHMETIC",
"VIETA_SUM"
] | 2 | 2.16 | 2026-02-08T04:52:28.376931Z | {
"verified": true,
"answer": 79126,
"timestamp": "2026-02-08T04:52:30.536973Z"
} | 3e4617 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 246,
"completion_tokens": 1199
},
"timestamp": "2026-02-11T22:35:26.220Z",
"answer": 79126
},
{
... | 1 | [
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "SUM_ARITHMETIC... | {
"lo": -8.32,
"mid": -5.11,
"hi": -2.37
} | ||
34f683 | antilemma_k2_v1_124444284_909 | Let $x = \sum_{k=1}^{431} \phi(k) \left\lfloor \frac{431}{k} \right\rfloor$, where $\phi$ denotes Euler's totient function. Let $s = \sum_{d \mid 499} \phi(d)$. Compute the remainder when $\left( x \bmod 199 \right) + 5003 \cdot \left( x \bmod s \right)$ is divided by 98057. | 38,211 | graphs = [
Graph(
let={
"_n": Const(431),
"x": Summation(var="k", start=Const(1), end=Const(431), expr=Mul(EulerPhi(n=Var("k")), Floor(Div(Ref("_n"), Var("k"))))),
"_c": Const(5003),
"Q": Mod(value=Sum(Mod(value=Ref("x"), modulus=Const(199)), Mul(Ref("_c"), Mo... | NT | COMB | COMPUTE | sympy | K13 | [
"K3",
"K2"
] | da970e | antilemma_k2_v1 | two_moduli | 6 | 0 | [
"K13",
"K2",
"K3"
] | 3 | 0.003 | 2026-02-08T03:35:50.180843Z | {
"verified": true,
"answer": 38211,
"timestamp": "2026-02-08T03:35:50.183670Z"
} | ebeddf | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 215,
"completion_tokens": 1525
},
"timestamp": "2026-02-09T23:48:56.463Z",
"answer": 38211
},
{
"... | 1 | [
{
"lemma": "K2",
"status": "ok"
},
{
"lemma": "K3",
"status": "ok"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "V3",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
},
{
"lemma": "VAL_SUM_EQ",... | {
"lo": -3.53,
"mid": 1.02,
"hi": 5.49
} | ||
004c89 | nt_count_coprime_and_v1_1439011603_1824 | Let $k_1$ be the number of positive integers $j$ such that $1 \leq j \leq 5$ and $j^5 \leq 3125$. Let $k_2 = 9$. Determine the number of positive integers $n$ such that $1 \leq n \leq 15939$, $\gcd(n, k_1) = 1$, and $\gcd(n, k_2) = 1$. | 8,501 | graphs = [
Graph(
let={
"upper": Const(15939),
"k1": CountOverSet(set=SolutionsSet(var=Var("j"), condition=And(Geq(Var("j"), Const(1)), Leq(Var("j"), Const(5)), Leq(Pow(Var("j"), Const(5)), Const(3125))), domain='positive_integers')),
"k2": Const(9),
"result":... | NT | null | COUNT | sympy | C3 | [
"C3"
] | 8a214c | nt_count_coprime_and_v1 | null | 4 | 0 | [
"C3"
] | 1 | 6.869 | 2026-02-08T16:18:11.879927Z | {
"verified": true,
"answer": 8501,
"timestamp": "2026-02-08T16:18:18.748698Z"
} | 8185a3 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 141,
"completion_tokens": 1026
},
"timestamp": "2026-02-17T00:41:37.386Z",
"answer": 8501
},
{... | 1 | [
{
"lemma": "C3",
"status": "ok"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
6d7d60 | comb_count_surjections_v1_1353956133_451 | Let $n$ be the number of ordered pairs $(a, b)$ such that $a \in \{1, 2\}$ and $b \in \{1, 2, 3, 4\}$. Let $k$ be the number of ordered pairs $(x_1, x_2)$ of positive odd integers such that $x_1 + x_2 = 8$. Compute $k! \cdot S(n, k)$, where $S(n, k)$ denotes the Stirling number of the second kind. | 40,824 | graphs = [
Graph(
let={
"_n": Const(8),
"n": CountOverSet(set=CartesianProduct(left=IntegerRange(start=Const(1), end=Const(2)), right=IntegerRange(start=Const(1), end=Const(4)))),
"k": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x1"), Var("x2")]), condition=And... | COMB | null | COUNT | sympy | COUNT_CARTESIAN | [
"COUNT_CARTESIAN",
"COMB1"
] | e44290 | comb_count_surjections_v1 | null | 4 | 0 | [
"COMB1",
"COUNT_CARTESIAN"
] | 2 | 0.002 | 2026-02-08T11:27:20.546451Z | {
"verified": true,
"answer": 40824,
"timestamp": "2026-02-08T11:27:20.548218Z"
} | aa9e00 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 226,
"completion_tokens": 1993
},
"timestamp": "2026-02-24T13:58:31.024Z",
"answer": 40824
},
{
"... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COMB1",
"status": "ok"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "ok"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
},
{
... | {
"lo": -3.84,
"mid": -1.67,
"hi": 1.32
} | ||
661c9e | nt_count_divisible_and_v1_784195855_10346 | Let $d_1 = 10$ and $d_2 = \sum_{k=1}^{5} k$. Determine the number of positive integers $n \leq 112830$ that are divisible by both $d_1$ and $d_2$. Compute this number. | 3,761 | graphs = [
Graph(
let={
"upper": Const(112830),
"d1": Const(10),
"d2": Summation(var="k", start=Const(1), end=Const(5), expr=Var("k")),
"result": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Ref("upper")), Eq... | NT | null | COUNT | sympy | SUM_ARITHMETIC | [
"SUM_ARITHMETIC"
] | eb34f0 | nt_count_divisible_and_v1 | null | 3 | 0 | [
"SUM_ARITHMETIC"
] | 1 | 4.044 | 2026-02-08T17:34:49.823340Z | {
"verified": true,
"answer": 3761,
"timestamp": "2026-02-08T17:34:53.867217Z"
} | 76787e | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 107,
"completion_tokens": 376
},
"timestamp": "2026-02-18T07:40:32.833Z",
"answer": 3761
},
{
... | 1 | [
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "SUM_ARITHMETIC",
"status": "ok"
},
{
"lemma": "V3",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
4c0e3a | antilemma_k3_v1_1918700295_1978 | Let $x$ be the sum of $\phi(d)$ over all positive divisors $d$ of $97838$. Find the remainder when $62001 - x$ is divided by $95171$. | 59,334 | graphs = [
Graph(
let={
"x": SumOverDivisors(n=Const(value=97838), var='d', expr=EulerPhi(n=Var(name='d'))),
"Q": Mod(value=Sub(Const(62001), Ref("x")), modulus=Const(95171)),
},
goal=Ref("Q"),
)
] | NT | COMB | COMPUTE | sympy | K3 | [
"K3"
] | 54c41e | antilemma_k3_v1 | null | 3 | 0 | [
"K3"
] | 1 | 0.001 | 2026-02-08T07:36:05.251011Z | {
"verified": true,
"answer": 59334,
"timestamp": "2026-02-08T07:36:05.251636Z"
} | c6a2f4 | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 106,
"completion_tokens": 442
},
"timestamp": "2026-02-15T19:01:54.455Z",
"answer": 13082
},
{
"id": 11... | 1 | [
{
"lemma": "K3",
"status": "ok"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
}
] | {
"lo": -5.55,
"mid": -3.01,
"hi": 0.34
} | ||
53f2a8 | antilemma_k2_v1_1080341949_217 | Let $x$ be the value of
$$x = \sum_{k=1}^{46} \varphi(k)\left\lfloor \frac{46}{k} \right\rfloor,$$
where $\varphi$ is Euler's totient function.
Let $S$ be the set of all integers $t$ such that
$$t^2 - 2022t - 142120 = 0.$$
Let $N$ be the sum of all elements of $S$.
Let
$$Q = \sum_{d \mid N} \varphi(d) - x.$$
Compute... | 941 | graphs = [
Graph(
let={
"_m": Const(46),
"_n": Const(46),
"x": Summation(var="k", start=Const(1), end=Ref("_m"), expr=Mul(EulerPhi(n=Var("k")), Floor(Div(Ref("_n"), Var("k"))))),
"Q": Sub(SumOverDivisors(n=SumOverSet(set=SolutionsSet(var=Var(name='x'), conditi... | NT | COMB | COMPUTE | sympy | K13 | [
"VIETA_SUM/K3",
"IDENTITY_MUL_ZERO",
"K2"
] | 27bffd | antilemma_k2_v1 | negation_mod | 6 | 0 | [
"IDENTITY_MUL_ZERO",
"K13",
"K2",
"K3",
"VIETA_SUM"
] | 5 | 0.008 | 2026-02-08T13:18:13.504837Z | {
"verified": true,
"answer": 941,
"timestamp": "2026-02-08T13:18:13.512427Z"
} | 7ed2a4 | 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": 999
},
"timestamp": "2026-02-15T14:42:50.422Z",
"answer": 941
},
{
... | 1 | [
{
"lemma": "IDENTITY_MUL_ZERO",
"status": "ok"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "K2",
"status": "ok"
},
{
"lemma": "K3",
"status": "ok_later"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
... | {
"lo": -5.49,
"mid": 0.22,
"hi": 6.51
} | ||
fd93b0 | modular_inverse_v1_1820931509_759 | Let $a = 581$ and $m = 1151$. Let $P$ be the set of all ordered pairs $(x, y)$ of positive integers such that $xy = 330625$. Let $s$ be the minimum value of $x + y$ over all such pairs. Let $T$ be the set of all integers $x$ such that $1 \leq x \leq s$ and $ax \equiv 1 \pmod{m}$. Compute the smallest element of $T$. | 628 | graphs = [
Graph(
let={
"a": Const(581),
"m": Const(1151),
"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(330625)))... | NT | null | EXTREMUM | sympy | B3 | [
"B3"
] | 0cd20d | modular_inverse_v1 | null | 5 | 0 | [
"B3"
] | 1 | 0.128 | 2026-02-08T11:51:41.562574Z | {
"verified": true,
"answer": 628,
"timestamp": "2026-02-08T11:51:41.691066Z"
} | 6ff7d0 | 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": 1780
},
"timestamp": "2026-02-14T19:38:15.940Z",
"answer": 628
},
{
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "V1",
"status": "no"
},
{
"lemma": "V3",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
}
] | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
8da97a | geo_visible_lattice_v1_48377204_2166 | Let $n = 64$. Define $r$ to be the number of ordered pairs $(x, y)$ such that $1 \leq x \leq 64$, $1 \leq y \leq 64$, and $\gcd(x, y) = 1$.
Compute the remainder when $4 - r$ is divided by $88978$. | 86,463 | graphs = [
Graph(
let={
"n": Const(64),
"result": VisibleLatticePoints(n=Ref(name='n')),
"Q": Mod(value=Sub(Const(4), Ref("result")), modulus=Const(88978)),
},
goal=Ref("Q"),
)
] | GEOM | null | COUNT | sympy | [] | geo_visible_lattice_v1 | null | 3 | 0 | null | null | 0.093 | 2026-02-08T16:37:38.525981Z | {
"verified": true,
"answer": 86463,
"timestamp": "2026-02-08T16:37:38.619356Z"
} | 99a705 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 119,
"completion_tokens": 4397
},
"timestamp": "2026-02-17T09:11:20.944Z",
"answer": 86463
},
... | 1 | [] | {
"lo": -2.38,
"mid": 1.74,
"hi": 6.59
} | ||||
9bc5b5 | nt_sum_gcd_range_mod_v1_168721529_395 | Let $N = \sum_{k=1}^{140} \varphi(k) \left\lfloor \frac{140}{k} \right\rfloor$. Let $k$ be the minimum value of $x + y$ over all pairs of positive integers $(x, y)$ such that $x \cdot y = 57600$. Define $\text{sum} = \sum_{n=1}^{N} \gcd(n, k)$. Find the remainder when $\text{sum}$ is divided by $10651$. | 7,550 | graphs = [
Graph(
let={
"_n": Const(57600),
"N": Summation(var="k", start=Const(1), end=Const(140), expr=Mul(EulerPhi(n=Var("k")), Floor(Div(Const(140), Var("k"))))),
"k": MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(I... | NT | null | COMPUTE | sympy | K2 | [
"K2",
"B3"
] | f1ea07 | nt_sum_gcd_range_mod_v1 | null | 7 | 0 | [
"B3",
"K2"
] | 2 | 0.55 | 2026-02-08T13:02:02.675416Z | {
"verified": true,
"answer": 7550,
"timestamp": "2026-02-08T13:02:03.225388Z"
} | 448c68 | CC BY 4.0 | [
{
"id": 4,
"model": "NousResearch/Hermes-4-405B",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 171,
"completion_tokens": 384
},
"timestamp": "2026-02-09T16:15:10.766Z",
"answer": 8447
},
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "K2",
"status": "ok"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
},
{
"lemma": "VAL_SUM_EQ",... | {
"lo": -1.9,
"mid": 2.34,
"hi": 6.68
} | ||
048726 | diophantine_fbi2_count_v1_1520064083_418 | Let $k$ be the sum of all real solutions $x$ to the equation $x^2 - 840x - 43561 = 0$. Determine the number of positive integers $d$ such that $3 \leq d \leq 83$, $d$ divides $k$, and $3 \leq \frac{k}{d} \leq 83$. Let $Q$ be the remainder when $89764$ times this number is divided by $80259$. Find the value of $Q$. | 52,811 | graphs = [
Graph(
let={
"k": SumOverSet(set=SolutionsSet(var=Var("x"), condition=Eq(Sum(Pow(Var("x"), Const(2)), Mul(Const(-840), Var("x")), Const(-43561)), Const(0)))),
"result": CountOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Const(3)), Leq(Var("d"), Const(8... | NT | null | COUNT | sympy | VIETA_SUM | [
"VIETA_SUM"
] | b33a7a | diophantine_fbi2_count_v1 | null | 4 | 0 | [
"VIETA_SUM"
] | 1 | 0.008 | 2026-02-08T03:21:11.528905Z | {
"verified": true,
"answer": 52811,
"timestamp": "2026-02-08T03:21:11.536409Z"
} | c7cad6 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 220,
"completion_tokens": 2430
},
"timestamp": "2026-02-10T13:15:17.801Z",
"answer": 52811
},
{
... | 1 | [
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "VIETA_SUM",
"status": "ok"
}
] | {
"lo": -3.42,
"mid": 1.86,
"hi": 7.55
} | ||
74e927 | nt_max_prime_below_v1_397696148_2497 | Let $S$ be the set of all positive integers $p$ for which there exists a positive integer $q$ such that $pq = 18$, $\gcd(p, q) = 1$, and $p < q$. Let $m$ be the number of elements in $S$. Determine the largest prime number $n$ such that $m \leq n \leq 27889$. | 27,883 | graphs = [
Graph(
let={
"upper": Const(27889),
"result": MaxOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), CountOverSet(set=SolutionsSet(var=Var("p"), condition=And(IsPositive(arg=Var(name='p')), Exists(var=Var(name='q'), condition=And(Eq(left=Mul(Var(name='p'), V... | NT | null | EXTREMUM | sympy | COPRIME_PAIRS | [
"COPRIME_PAIRS"
] | 2bb3aa | nt_max_prime_below_v1 | null | 4 | 0 | [
"COPRIME_PAIRS"
] | 1 | 4.745 | 2026-02-08T13:21:05.716570Z | {
"verified": true,
"answer": 27883,
"timestamp": "2026-02-08T13:21:10.461639Z"
} | c21b42 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 129,
"completion_tokens": 2816
},
"timestamp": "2026-02-15T14:42:40.067Z",
"answer": 27883
},
... | 1 | [
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "V8_SUM",
"status":... | {
"lo": -5.49,
"mid": 0.22,
"hi": 6.51
} | ||
74d4c1 | antilemma_k3_v1_1125832087_1147 | Let $x = \sum_{d \mid 53295} \phi(d)$, where $\phi$ denotes Euler's totient function. Let $Q = \left( (x \bmod 251) + 7001 \cdot (x \bmod 397) \right) \bmod 56294$. Find the value of $Q$. | 3,652 | graphs = [
Graph(
let={
"x": SumOverDivisors(n=Const(value=53295), var='d', expr=EulerPhi(n=Var(name='d'))),
"_c": Const(7001),
"Q": Mod(value=Sum(Mod(value=Ref("x"), modulus=Const(251)), Mul(Ref("_c"), Mod(value=Ref("x"), modulus=Const(397)))), modulus=Const(56294)),
... | NT | COMB | COMPUTE | sympy | K3 | [
"K3"
] | 54c41e | antilemma_k3_v1 | null | 5 | 0 | [
"K3"
] | 1 | 0 | 2026-02-08T03:33:49.162636Z | {
"verified": true,
"answer": 3652,
"timestamp": "2026-02-08T03:33:49.163112Z"
} | 5e2a0f | 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": 458
},
"timestamp": "2026-02-10T14:54:37.584Z",
"answer": 3652
},
{
"id... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "K3",
"status": "ok"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
}
] | {
"lo": -3.46,
"mid": 1.03,
"hi": 5.49
} | ||
3b3671 | nt_lcm_compute_v1_458359167_1898 | Let $a = 2528$ and $b = 760$. Let $L = \mathrm{lcm}(a, b)$. Let $d_{\text{min}}$ be the smallest integer $d \geq 2$ that divides $47027$. Compute the remainder when
$$
L^2 + d_{\text{min}} \cdot L + 8
$$
is divided by $67836$. | 63,640 | graphs = [
Graph(
let={
"_n": Const(2),
"a": Const(2528),
"b": Const(760),
"result": LCM(a=Ref("a"), b=Ref("b")),
"Q": Mod(value=Sum(Pow(Ref("result"), Ref("_n")), Mul(MinOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Const(2)),... | NT | null | COMPUTE | sympy | MIN_PRIME_FACTOR | [
"MIN_PRIME_FACTOR"
] | 76121b | nt_lcm_compute_v1 | quadratic_mod | 4 | 0 | [
"MIN_PRIME_FACTOR"
] | 1 | 0.002 | 2026-02-08T04:55:38.840252Z | {
"verified": true,
"answer": 63640,
"timestamp": "2026-02-08T04:55:38.841945Z"
} | 5985b3 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 201,
"completion_tokens": 2505
},
"timestamp": "2026-02-11T22:27:18.049Z",
"answer": 63640
},
{
... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MIN_PRIME_FACTOR",
"status": "ok"
},
{
"lemma": "V3",
"status": "no"
}
... | {
"lo": -3.42,
"mid": 1.86,
"hi": 7.55
} | ||
5ccbc9 | comb_bell_compute_v1_124444284_4765 | Let $n$ be the number of positive integers $p$ for which there exists a positive integer $q$ such that $pq = 37800$, $\gcd(p, q) = 1$, and $p < q$. Compute the Bell number of $n$. | 4,140 | graphs = [
Graph(
let={
"n": CountOverSet(set=SolutionsSet(var=Var("p"), condition=And(IsPositive(arg=Var(name='p')), Exists(var=Var(name='q'), condition=And(Eq(left=Mul(Var(name='p'), Var(name='q')), right=Const(value=37800)), Eq(left=GCD(a=Var(name='p'), b=Var(name='q')), right=Const(value=1))... | NT | COMB | COMPUTE | sympy | COPRIME_PAIRS | [
"COPRIME_PAIRS"
] | 2bb3aa | comb_bell_compute_v1 | null | 6 | 0 | [
"COPRIME_PAIRS"
] | 1 | 0.002 | 2026-02-08T06:13:06.271411Z | {
"verified": true,
"answer": 4140,
"timestamp": "2026-02-08T06:13:06.273714Z"
} | c51fbf | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 103,
"completion_tokens": 1094
},
"timestamp": "2026-02-12T21:14:58.217Z",
"answer": 4140
},
{... | 1 | [
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "V1",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
}
] | {
"lo": -3.51,
"mid": 1.33,
"hi": 6.56
} | ||
5db2ef | alg_linear_system_2x2_v1_1419126231_284 | Let $N$ be the number of positive integers $x$ with $1 \le x \le 19149$ such that $x^2 - 37825x + 357680676 \le 0$. Let $\det = -2 \cdot (-6) - 4 \cdot (-9)$, $S = -102047 \cdot (-6) - 200614 \cdot (-9)$, and $T = -2 \cdot 200614 - \left|\{ (a, b) : 1 \le a \le b \le 25,\ 2b^2 + 2a^2 - 4ab = 882 \}\right| \cdot (-10204... | 34,233 | graphs = [
Graph(
let={
"_m": Const(4),
"_n": Const(2),
"num_x": Sub(Mul(Const(-102047), Const(-6)), Mul(Const(200614), Const(-9))),
"num_y": Sub(Mul(Const(-2), Const(200614)), Mul(CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("a"), Var("b")]), conditi... | ALG | null | COMPUTE | sympy | QUADRATIC_INEQ | [
"QUADRATIC_INEQ",
"QF_PSD_ORBIT"
] | 2d7544 | alg_linear_system_2x2_v1 | negation_mod | 5 | 0 | [
"QF_PSD_ORBIT",
"QUADRATIC_INEQ"
] | 2 | 0.008 | 2026-02-25T09:49:11.069972Z | {
"verified": true,
"answer": 34233,
"timestamp": "2026-02-25T09:49:11.078255Z"
} | 1ec23c | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 305,
"completion_tokens": 2241
},
"timestamp": "2026-03-30T07:53:12.160Z",
"answer": 34233
},
{
"... | 1 | [
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "QF_PSD_ORBIT",
"status": "ok"
},
{
"lemma": "QUADRATIC_INEQ",
"status": "ok"
}
] | {
"lo": -5.37,
"mid": 0.23,
"hi": 5.22
} | ||
600842 | geo_count_lattice_rect_v1_1918700295_4167 | Compute the number of lattice points $(x, y)$ such that $0 \leq x \leq 120$ and $0 \leq y \leq 46$. | 5,687 | graphs = [
Graph(
let={
"a": Const(120),
"b": Const(46),
"result": LatticePointsRect(a=Ref(name='a'), b=Ref(name='b')),
},
goal=Ref("result"),
)
] | GEOM | null | COUNT | sympy | [] | geo_count_lattice_rect_v1 | null | 2 | 0 | null | null | 0.002 | 2026-02-08T09:11:09.029525Z | {
"verified": true,
"answer": 5687,
"timestamp": "2026-02-08T09:11:09.031256Z"
} | 18f3a8 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 148,
"completion_tokens": 158
},
"timestamp": "2026-02-24T10:46:26.889Z",
"answer": 5687
},
{
"id... | 1 | [] | {
"lo": -5.97,
"mid": -3.97,
"hi": -1.93
} | ||||
c4afa0 | sequence_fibonacci_compute_v1_601307018_1934 | Let $F_n$ denote the $n$-th Fibonacci number. Find the number $n$ of ordered pairs $(a, b)$ of positive integers with $1 \le a, b \le 35$ satisfying
\[
128a^3 + 384a^2b + 384ab^2 + 128b^3 = 1557376.
\]
Compute $F_n$. | 17,711 | graphs = [
Graph(
let={
"_n": Const(35),
"n": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("a"), Var("b")]), condition=And(Geq(Var("a"), Const(1)), Leq(Var("a"), Const(35)), Geq(Var("b"), Const(1)), Leq(Var("b"), Ref("_n")), Eq(Sum(Mul(Const(128), Pow(Var("a"), Const(3))), M... | ALG | null | COMPUTE | sympy | POLY3_COUNT | [
"POLY3_COUNT"
] | 355dbe | sequence_fibonacci_compute_v1 | null | 5 | 0 | [
"POLY3_COUNT"
] | 1 | 0.003 | 2026-03-10T02:42:13.592869Z | {
"verified": true,
"answer": 17711,
"timestamp": "2026-03-10T02:42:13.595519Z"
} | 59b98b | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 195,
"completion_tokens": 750
},
"timestamp": "2026-03-29T03:52:32.230Z",
"answer": 17711
},
{
"i... | 1 | [
{
"lemma": "POLY3_COUNT",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
}
] | {
"lo": -6.5,
"mid": -3.34,
"hi": -0.89
} | ||
6f6b6e | modular_inverse_v1_655260480_6150 | Let $a = 639$ and $m = 1097$. Consider the set of all ordered pairs $(x, y)$ of positive integers such that $x \cdot y = 300304$. Let $S$ be the set of all values $x + y$ for such pairs. Define $u$ to be the minimum element of $S$. Find the smallest positive integer $x_1$ such that $1 \leq x_1 \leq u$ and $a \cdot x_1 ... | 4,061 | graphs = [
Graph(
let={
"a": Const(639),
"m": Const(1097),
"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(300304)))... | NT | null | EXTREMUM | sympy | B3 | [
"B3"
] | 0cd20d | modular_inverse_v1 | null | 6 | 0 | [
"B3"
] | 1 | 0.047 | 2026-02-08T18:52:28.010509Z | {
"verified": true,
"answer": 4061,
"timestamp": "2026-02-08T18:52:28.057559Z"
} | d18a01 | 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": 2683
},
"timestamp": "2026-02-18T20:04:46.688Z",
"answer": 4061
},
{... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
ccaaea | antilemma_sum_equals_v1_1978505735_4430 | Let $S$ be the set of all ordered pairs $(i, j)$ where $i$ is an integer from 1 to 88 and $j$ is an integer from 1 to 89. Compute the number of pairs $(i, j) \in S$ such that $i + j = 90$. | 88 | graphs = [
Graph(
let={
"_n": CountOverSet(set=CartesianProduct(left=IntegerRange(start=Const(1), end=Const(9)), right=IntegerRange(start=Const(1), end=Const(10)))),
"x": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("i"), Var("j")]), condition=Eq(Sum(Var("i"), Var("j")), Ref... | COMB | GEOM | COMPUTE | sympy | LIN_FORM | [
"COUNT_CARTESIAN/COUNT_SUM_EQUALS",
"COUNT_SUM_EQUALS"
] | 8bee9e | antilemma_sum_equals_v1 | null | 3 | 0 | [
"COUNT_CARTESIAN",
"COUNT_SUM_EQUALS",
"LIN_FORM"
] | 3 | 0.02 | 2026-02-08T18:14:41.708175Z | {
"verified": true,
"answer": 88,
"timestamp": "2026-02-08T18:14:41.728510Z"
} | 55199f | 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": 869
},
"timestamp": "2026-02-24T23:46:40.416Z",
"answer": 88
},
{
... | 2 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "ok"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "ok"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8",
"status": "no... | {
"lo": -10,
"mid": -7.4,
"hi": -4.8
} | ||
9d41e8 | nt_count_intersection_v1_2051736721_2604 | Let $N$ be the minimum value of $x + y$ over all ordered pairs $(x, y)$ of positive integers such that $xy = 25000000$. Let $a = 9$ and $b = 22$. Define $r$ to be the number of positive integers $n$ such that $1 \leq n \leq N$, $a$ divides $n$, and $\gcd(n, b) = 1$. Compute $r + 2^r \bmod 56162$, where the exponent is ... | 507 | graphs = [
Graph(
let={
"_n": Const(14),
"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(25000000)))), expr=Sum(Var("x"), Var("y")))... | NT | null | COUNT | sympy | B3 | [
"B3"
] | 0cd20d | nt_count_intersection_v1 | null | 5 | 0 | [
"B3"
] | 1 | 0.338 | 2026-02-08T16:48:48.900253Z | {
"verified": true,
"answer": 507,
"timestamp": "2026-02-08T16:48:49.238015Z"
} | bd7833 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 189,
"completion_tokens": 1744
},
"timestamp": "2026-02-17T12:02:56.657Z",
"answer": 507
},
{
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": ... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
45f683 | modular_count_residue_v1_124444284_7588 | Let $r = \sum_{k=1}^{6} k$. Determine the number of positive integers $n$ such that $1 \leq n \leq 60516$ and $n \equiv r \pmod{30}$. | 2,017 | graphs = [
Graph(
let={
"_n": Const(6),
"upper": Const(60516),
"m": Const(30),
"r": Summation(var="k", start=Const(1), end=Ref("_n"), expr=Var("k")),
"result": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(V... | NT | null | COUNT | sympy | SUM_ARITHMETIC | [
"SUM_ARITHMETIC"
] | eb34f0 | modular_count_residue_v1 | null | 3 | 0 | [
"SUM_ARITHMETIC"
] | 1 | 2.017 | 2026-02-08T09:11:48.161293Z | {
"verified": true,
"answer": 2017,
"timestamp": "2026-02-08T09:11:50.178284Z"
} | 37f409 | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 109,
"completion_tokens": 327
},
"timestamp": "2026-02-15T20:36:15.600Z",
"answer": 2017
},
{
"id": 11,
... | 2 | [
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "SUM_ARITHMETIC",
"status": "ok"
},
{
"lemma": "V8_SUM",
"status": "no"
}
] | {
"lo": -10,
"mid": -7.27,
"hi": -4.54
} |
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