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 |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
77d1b3 | diophantine_fbi2_count_v1_124444284_10368 | Let $ k = 120 $ and $ \ell = 5 $. Consider the set of all positive integers $ d $ satisfying the following conditions:
- $ d $ divides 130940501,
- $ d \geq 2 $,
- and let $ m $ be the smallest such $ d $ that satisfies these two conditions.
Now consider the set of all positive integers $ d $ such that:
- $ d $ divi... | 8 | graphs = [
Graph(
let={
"_n": Const(5),
"k": Const(120),
"result": CountOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Const(5)), Leq(Var("d"), MinOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Const(2)), Divides(divisor=Var("d"), d... | NT | null | COUNT | sympy | MIN_PRIME_FACTOR | [
"MIN_PRIME_FACTOR"
] | bc3776 | diophantine_fbi2_count_v1 | null | 4 | 0 | [
"MIN_PRIME_FACTOR"
] | 1 | 0.008 | 2026-02-08T13:01:46.826388Z | {
"verified": true,
"answer": 8,
"timestamp": "2026-02-08T13:01:46.834131Z"
} | 43a770 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 198,
"completion_tokens": 1857
},
"timestamp": "2026-02-15T09:03:07.847Z",
"answer": 8
},
{
... | 1 | [
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "MIN_PRIME_FACTOR",
"status": "ok"
},
{
"lemma": "V1",
"status": "no"
},
{
"lemma": "V5",
"sta... | {
"lo": -6.96,
"mid": -4.56,
"hi": -1.46
} | ||
7ac90b | modular_inverse_v1_1125832087_1316 | Let $N$ be the number of positive integers $k$ such that $1 \leq k \leq 30540$ and $30$ divides $k$. Find the smallest positive integer $x$ such that $1 \leq x \leq N$ and $$
407x \equiv 1 \pmod{1019}.
$$ | 338 | graphs = [
Graph(
let={
"_n": Const(30540),
"a": Const(407),
"m": Const(1019),
"upper": CountOverSet(set=SolutionsSet(var=Var("k"), condition=And(Geq(Var("k"), Const(1)), Leq(Var("k"), Ref("_n")), Divides(divisor=Const(30), dividend=Var("k"))), domain='positiv... | ALG | NT | EXTREMUM | sympy | C2 | [
"C2"
] | 9685eb | modular_inverse_v1 | null | 6 | 0 | [
"C2"
] | 1 | 0.043 | 2026-02-08T03:41:03.656260Z | {
"verified": true,
"answer": 338,
"timestamp": "2026-02-08T03:41:03.699011Z"
} | 9f46ad | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 185,
"completion_tokens": 1562
},
"timestamp": "2026-02-10T15:23:55.673Z",
"answer": 338
},
{
"id... | 1 | [
{
"lemma": "C2",
"status": "ok"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
}... | {
"lo": -7.01,
"mid": -4.68,
"hi": -2.15
} | ||
b6fd7a | nt_sum_totient_over_divisors_v1_153355830_84 | Let $n_2 = 28561$. Define $s$ to be the sum of $\phi(d)$ over all positive divisors $d$ of $n_2$, minus $n_2$ itself. Let $n_1$ be the number of positive integers $n$ with $1 \le n \le 21$ such that the sum of the decimal digits of $n$ is odd, plus $s$. Let $m = \mu(n_1)^2$, where $\mu$ denotes the Möbius function. Let... | 55,500 | graphs = [
Graph(
let={
"_n": Const(2),
"n2": Const(28561),
"s": Sub(SumOverDivisors(n=Ref(name='n2'), var='d', expr=EulerPhi(n=Var(name='d'))), Ref("n2")),
"n1": Sum(CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n... | NT | null | COMPUTE | sympy | L3B | [
"L3B/EULER_TOTIENT_SUM/MOBIUS_SQUAREFREE"
] | 5d0c8a | nt_sum_totient_over_divisors_v1 | null | 6 | 2 | [
"EULER_TOTIENT_SUM",
"L3B",
"MOBIUS_SQUAREFREE"
] | 3 | 0.004 | 2026-02-08T02:53:00.815238Z | {
"verified": true,
"answer": 55500,
"timestamp": "2026-02-08T02:53:00.819659Z"
} | f76a0a | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 297,
"completion_tokens": 1239
},
"timestamp": "2026-02-08T22:45:43.288Z",
"answer": 55500
},
{
... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "EULER_TOTIENT_SUM",
"status": "ok_later"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "L3B",
"status": "ok"
},
{
"le... | {
"lo": -6.49,
"mid": 0.51,
"hi": 7.52
} | ||
bbfc2b | nt_count_coprime_and_v1_168721529_823 | Let $n = 2$ and let the upper bound be $44229$. Define $k_1 = 3$. Let $k_2$ be the smallest integer $d \ge 2$ that divides $1001$. Compute the number of positive integers $n$ such that $1 \le n \le 44229$, $\gcd(n, 3) = 1$, and $\gcd(n, k_2) = 1$. | 25,274 | graphs = [
Graph(
let={
"_n": Const(2),
"upper": Const(44229),
"k1": Const(3),
"k2": MinOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Ref("_n")), Divides(divisor=Var("d"), dividend=Const(1001))))),
"result": CountOverSet(set=So... | NT | null | COUNT | sympy | MIN_PRIME_FACTOR | [
"MIN_PRIME_FACTOR"
] | bc3776 | nt_count_coprime_and_v1 | null | 4 | 0 | [
"MIN_PRIME_FACTOR"
] | 1 | 5.011 | 2026-02-08T13:18:55.970271Z | {
"verified": true,
"answer": 25274,
"timestamp": "2026-02-08T13:19:00.981488Z"
} | 698769 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 211,
"completion_tokens": 1892
},
"timestamp": "2026-02-09T09:38:30.947Z",
"answer": 25274
},
{
"... | 1 | [
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "MIN_PRIME_FACTOR",
"status": "ok"
},
{
"lemma": "V5",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
}
] | {
"lo": -5.3,
"mid": -2.04,
"hi": 1.9
} | ||
ca1e8a | comb_sum_binomial_row_v1_1978505735_1778 | Let $n = 1 + 2 + 3 + 4 + 5$. Compute the remainder when $96253 \cdot 2^n$ is divided by $87869$. | 48,418 | graphs = [
Graph(
let={
"_n": Const(5),
"n": Summation(var="k", start=Const(1), end=Ref("_n"), expr=Var("k")),
"result": Pow(Const(2), Ref("n")),
"_c": Const(96253),
"Q": Mod(value=Mul(Ref("_c"), Ref("result")), modulus=Const(87869)),
},
... | NT | null | SUM | sympy | SUM_ARITHMETIC | [
"SUM_ARITHMETIC"
] | eb34f0 | comb_sum_binomial_row_v1 | null | 2 | 0 | [
"SUM_ARITHMETIC"
] | 1 | 0.002 | 2026-02-08T16:23:56.908517Z | {
"verified": true,
"answer": 48418,
"timestamp": "2026-02-08T16:23:56.910065Z"
} | 882690 | 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": 1024
},
"timestamp": "2026-02-17T02:30:12.129Z",
"answer": 48418
},
{... | 1 | [
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "SUM_ARITHMETIC",
"status": "ok"
},
{
"lemma": "V8",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
4a0a38 | comb_count_permutations_fixed_v1_601307018_4372 | Let $D_n$ denote the number of derangements of $n$ elements. Let $k = \sum_{k_1=0}^{1} (-1)^{k_1} \binom{1}{k_1}$, and let $n = 7$. Define $M = \binom{n}{k} \cdot D_{n - k}$. Compute $27720 - M$. | 25,866 | graphs = [
Graph(
let={
"n": Const(7),
"k": Summation(var="k1", start=Const(0), end=Const(1), expr=Mul(Pow(Const(-1), Var("k1")), Binom(n=Const(1), k=Var("k1")))),
"result": Mul(Binom(n=Ref("n"), k=Ref("k")), Subfactorial(arg=Sub(left=Ref(name='n'), right=Ref(name='k'))))... | COMB | null | COUNT | sympy | POLY_ORBIT_LEGENDRE | [
"BINOMIAL_ALTERNATING"
] | c21569 | comb_count_permutations_fixed_v1 | null | 2 | 0 | [
"BINOMIAL_ALTERNATING",
"POLY_ORBIT_LEGENDRE"
] | 2 | 0.199 | 2026-03-10T04:55:44.141401Z | {
"verified": true,
"answer": 25866,
"timestamp": "2026-03-10T04:55:44.340771Z"
} | a9fd6b | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 198,
"completion_tokens": 1320
},
"timestamp": "2026-03-29T12:03:23.899Z",
"answer": 25866
},
{
"... | 1 | [
{
"lemma": "BINOMIAL_ALTERNATING",
"status": "ok"
},
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "V8_S... | {
"lo": -6.2,
"mid": -2.87,
"hi": 0.44
} | ||
80b277 | comb_count_derangements_v1_784195855_9274 | Let $S$ be the set of all positive integers $p$ for which there exists a positive integer $q$ such that $p \cdot q = 4200$, $\gcd(p, q) = 1$, and $p < q$. Let $n$ be the number of elements in $S$.
Define $d_n$ as the number of derangements of $n$ elements, also known as the subfactorial of $n$.
Let $m = |d_n| + 2$. F... | 1,320 | graphs = [
Graph(
let={
"n": CountOverSet(set=SolutionsSet(var=Var("p"), condition=And(IsPositive(arg=Var(name='p')), Exists(var=Var(name='q'), condition=And(Eq(left=Mul(Var(name='p'), Var(name='q')), right=Const(value=4200)), Eq(left=GCD(a=Var(name='p'), b=Var(name='q')), right=Const(value=1)),... | NT | COMB | COUNT | sympy | COPRIME_PAIRS | [
"COPRIME_PAIRS"
] | 2bb3aa | comb_count_derangements_v1 | null | 6 | 0 | [
"COPRIME_PAIRS"
] | 1 | 0.002 | 2026-02-08T16:40:35.702821Z | {
"verified": true,
"answer": 1320,
"timestamp": "2026-02-08T16:40:35.704360Z"
} | c4f89e | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 175,
"completion_tokens": 2007
},
"timestamp": "2026-02-17T09:27:42.972Z",
"answer": 1320
},
{... | 1 | [
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "VAL_SUM_EQ",
"status": "no"
}... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
162aa7 | modular_count_residue_v1_898971024_1743 | Let $m$ be the largest prime number less than or equal to 13. Compute the number of positive integers $n_1$ such that $1 \leq n_1 \leq 70756$ and $n_1 \equiv 10 \pmod{m}$. | 5,443 | graphs = [
Graph(
let={
"upper": Const(70756),
"m": MaxOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(2)), Leq(Var("n"), Const(13)), IsPrime(Var("n"))))),
"r": Const(10),
"result": CountOverSet(set=SolutionsSet(var=Var("n1"), conditio... | NT | null | COUNT | sympy | MAX_PRIME_BELOW | [
"MAX_PRIME_BELOW"
] | dc3ad3 | modular_count_residue_v1 | null | 3 | 0 | [
"MAX_PRIME_BELOW"
] | 1 | 2.443 | 2026-02-08T16:17:09.314921Z | {
"verified": true,
"answer": 5443,
"timestamp": "2026-02-08T16:17:11.758114Z"
} | fe9403 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 104,
"completion_tokens": 658
},
"timestamp": "2026-02-17T01:20:32.680Z",
"answer": 5443
},
{
... | 1 | [
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "V1",
"status": "no"
},
{
"lemma": "V8",
"status": "n... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
51222e | algebra_poly_eval_v1_1978505735_2165 | Let $p$ and $q$ be positive integers such that $pq = 1350$, $\gcd(p, q) = 1$, and $p < q$. Let $N$ be the number of such ordered pairs $(p, q)$. For each pair of positive integers $(x_1, y)$ such that $x_1 + y = N$, compute the product $x_1 y$. Let $M$ be the maximum value of $x_1 y$ over all such pairs. Define
$$
\tex... | 2,120 | graphs = [
Graph(
let={
"_m": Const(5),
"_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=1350)), Eq(left=GCD(a=Var(name='p'), b=Var(name=... | NT | null | COMPUTE | sympy | COPRIME_PAIRS | [
"COPRIME_PAIRS/B1"
] | 75b1e0 | algebra_poly_eval_v1 | null | 7 | 0 | [
"B1",
"COPRIME_PAIRS"
] | 2 | 0.008 | 2026-02-08T16:42:16.277687Z | {
"verified": true,
"answer": 2120,
"timestamp": "2026-02-08T16:42:16.285663Z"
} | cceab6 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 235,
"completion_tokens": 3424
},
"timestamp": "2026-02-17T11:15:34.739Z",
"answer": 2120
},
{... | 1 | [
{
"lemma": "B1",
"status": "ok_later"
},
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "V1",
"status": "no"
},
{
"lem... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
88f14d | sequence_count_fib_divisible_v1_1978505735_1606 | Let $d = 17$. Determine the number of positive integers $n$ such that $1 \leq n \leq 521$ and $d$ divides the $n$-th Fibonacci number. | 57 | graphs = [
Graph(
let={
"upper": Const(521),
"d": Const(17),
"result": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Ref("upper")), Divides(divisor=Ref("d"), dividend=Fibonacci(arg=Var(name='n')))))),
},
g... | NT | null | COUNT | sympy | COMB1 | [
"COMB1"
] | 567f58 | sequence_count_fib_divisible_v1 | null | 5 | 0 | [
"COMB1"
] | 1 | 0.07 | 2026-02-08T16:16:57.994932Z | {
"verified": true,
"answer": 57,
"timestamp": "2026-02-08T16:16:58.064979Z"
} | 143a76 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 88,
"completion_tokens": 3307
},
"timestamp": "2026-02-16T23:52:22.349Z",
"answer": 57
},
{
... | 1 | [
{
"lemma": "COMB1",
"status": "ok"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
1deab8 | v7_endings_v1_124444284_698 | Compute the sum $$\sum_{k=0}^{2714} e_k,$$ where $e_k$ is the largest integer $e$ such that $2^e$ divides $\binom{2714}{k}$. | 13,560 | graphs = [
Graph(
let={
"total": Summation(var="k", start=Const(0), end=Const(2714), expr=MaxKDivides(target=Binom(n=Const(2714), k=Var("k")), base=Const(2))),
},
goal=Ref("total"),
)
] | NT | null | COMPUTE | sympy | V7 | [
"V7"
] | 0672d4 | v7_endings_v1 | null | 7 | null | [
"V7"
] | 1 | 0.003 | 2026-02-08T03:27:35.461884Z | {
"verified": true,
"answer": 13560,
"timestamp": "2026-02-08T03:27:35.464962Z"
} | b83462 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 158,
"completion_tokens": 4868
},
"timestamp": "2026-02-09T20:47:32.572Z",
"answer": 13560
},
{
"... | 1 | [
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "V7",
"status": "ok"
}
] | {
"lo": -6.51,
"mid": -0.31,
"hi": 5.43
} | ||
878f0d_n | comb_catalan_compute_v1_601307018_4616 | A game board has tokens that can move in steps of size $3a + 2b$, where $a$ is a roll from a 3-sided die and $b$ is a roll from a 4-sided die (both at least 1). A move is valid if its total length $t$ is between 5 and 17 inclusive. Let $n$ be the number of distinct valid move lengths. The number of winning sequences fo... | 22,182 | COMB | null | COMPUTE | sympy | POLY_ORBIT_LEGENDRE | [
"LIN_FORM"
] | 7b2633 | comb_catalan_compute_v1 | null | 4 | null | [
"LIN_FORM",
"POLY_ORBIT_LEGENDRE"
] | 2 | 0.233 | 2026-03-10T05:15:26.805376Z | null | 1c5fa0 | 878f0d | narrative | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 243,
"completion_tokens": 8168
},
"timestamp": "2026-03-29T19:01:31.174Z",
"answer": 22182
},
{
"... | 1 | [
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8_SUM",
"st... | {
"lo": -5.36,
"mid": 0.27,
"hi": 5.45
} | |
2ea11a | antilemma_k2_v1_1520064083_7586 | Let $n = 233$. Compute the value of $$\sum_{k=1}^{233} \phi(k) \left\lfloor \frac{1}{k} \sum_{d \mid 233} \phi(d) \right\rfloor,$$ where $\phi$ denotes Euler's totient function. | 27,261 | graphs = [
Graph(
let={
"_n": Const(233),
"x": Summation(var="k", start=Const(1), end=Const(233), expr=Mul(EulerPhi(n=Var("k")), Floor(Div(SumOverDivisors(n=Ref(name='_n'), var='d', expr=EulerPhi(n=Var(name='d'))), Var("k"))))),
},
goal=Ref("x"),
)
] | NT | COMB | COMPUTE | sympy | K3 | [
"K3/K2",
"K2"
] | c7f244 | antilemma_k2_v1 | null | 6 | 0 | [
"K2",
"K3"
] | 2 | 0.001 | 2026-02-08T09:10:23.675545Z | {
"verified": true,
"answer": 27261,
"timestamp": "2026-02-08T09:10:23.676681Z"
} | 99ba78 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 111,
"completion_tokens": 2421
},
"timestamp": "2026-02-14T01:31:01.611Z",
"answer": 27261
},
... | 1 | [
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K2",
"status": "ok"
},
{
"lemma": "K3",
"status": "ok"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
},
{
"lemma": "V8",
"s... | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
8ea26a | modular_modexp_compute_v1_124444284_3907 | Let $a = 11$ and $m = 33124$. Define $e$ to be the minimum value of $x + y$ over all ordered pairs $(x, y)$ of positive integers such that $xy = 20250000$. Let
\[
Q = a^e \bmod m + \left(2^{(a^e \bmod m) \bmod 15}\right) \bmod 52639.
\]
Find the value of $Q$. | 3,209 | graphs = [
Graph(
let={
"_n": Const(2),
"a": Const(11),
"e": 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(20250000)))), ex... | NT | null | COMPUTE | sympy | B3 | [
"B3"
] | 0cd20d | modular_modexp_compute_v1 | null | 6 | 0 | [
"B3"
] | 1 | 0.001 | 2026-02-08T05:39:51.114592Z | {
"verified": true,
"answer": 3209,
"timestamp": "2026-02-08T05:39:51.115915Z"
} | e67249 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 149,
"completion_tokens": 3023
},
"timestamp": "2026-02-12T11:59:21.337Z",
"answer": 3209
},
{... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
... | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
da1220 | diophantine_fbi2_min_v1_898971024_2844 | Let $m=337$, $n=7$, $k=81$, and $u=91$. Let $D$ be the set of all integers $d$ such that
\[
n\le d\le u,\quad d\text{ divides }k,\quad \frac{k}{d}\ge 4.
\]
Assume $D$ is nonempty, and let $r$ be the smallest element of $D$.
Let $E$ be the set of all ordered pairs $(x_1,y_1)$ of positive integers such that
\[
x_1y_1=22... | 2,016 | graphs = [
Graph(
let={
"_m": Const(337),
"_n": Const(7),
"k": Const(81),
"upper": Const(91),
"result": MinOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Ref("_n")), Leq(Var("d"), Ref("upper")), Divides(divisor=Var("d"), dividen... | NT | null | EXTREMUM | sympy | B3 | [
"B3/C4/B1"
] | c9d6ee | diophantine_fbi2_min_v1 | negation_mod | 7 | 0 | [
"B1",
"B3",
"C4"
] | 3 | 0.019 | 2026-02-08T17:01:33.568534Z | {
"verified": true,
"answer": 2016,
"timestamp": "2026-02-08T17:01:33.587105Z"
} | 10a504 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 350,
"completion_tokens": 1353
},
"timestamp": "2026-02-17T17:32:33.765Z",
"answer": 2016
},
{... | 1 | [
{
"lemma": "B1",
"status": "ok_later"
},
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "C4",
"status": "ok_later"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemm... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
d8000f | sequence_fibonacci_compute_v1_153355830_2788 | Let $n$ be the number of integers $t$ such that $11 \leq t \leq 40$ and there exist positive integers $a$ and $b$ with $1 \leq a \leq 12$, $1 \leq b \leq 2$, and $t = 2a + 7b + 2$. Compute the $n$th Fibonacci number. | 46,368 | 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=12)), Geq(left=Var(name='b'), right=Const(value=... | NT | null | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | sequence_fibonacci_compute_v1 | null | 4 | 0 | [
"LIN_FORM"
] | 1 | 0.182 | 2026-02-08T07:21:42.212502Z | {
"verified": true,
"answer": 46368,
"timestamp": "2026-02-08T07:21:42.394500Z"
} | fbae72 | 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": 1231
},
"timestamp": "2026-02-13T10:06:10.915Z",
"answer": 46368
},
... | 1 | [
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "V1",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
}
] | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
c1a499 | lin_form_endings_v1_809748730_1451 | Let $a = 56$, $b = 32$, and $k = 284$. Let $d = \gcd(a, b)$ and let $g = \gcd(k, d)$. Define $r = \left\lfloor \frac{k}{g} \right\rfloor$. Let $s = 17818 \cdot r$ and let $M = 81475$. Compute the remainder when $s$ is divided by $M$. | 42,953 | graphs = [
Graph(
let={
"a_coeff": Const(56),
"b_coeff": Const(32),
"k_val": Const(284),
"step": GCD(a=Ref("a_coeff"), b=Ref("b_coeff")),
"_inner_result": Floor(Div(Ref("k_val"), GCD(a=Ref("k_val"), b=Ref("step")))),
"_scale_k": Const(1... | COMB | NT | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | lin_form_endings_v1 | null | 4 | null | [
"LIN_FORM"
] | 1 | 0 | 2026-02-08T12:25:58.104789Z | {
"verified": true,
"answer": 42953,
"timestamp": "2026-02-08T12:25:58.105190Z"
} | 06333d | 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": 619
},
"timestamp": "2026-02-15T01:18:58.158Z",
"answer": 42953
},
{... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "V8",
"statu... | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
4c71e2 | modular_min_linear_v1_1248542787_922 | Let $p$ and $q$ be positive integers such that $pq = 12$, $\gcd(p, q) = 1$, and $p < q$. Define $c$ to be the number of such integers $p$. Let $\phi$ denote Euler's totient function, and define $s = \phi(\phi(c))$. Let $x$ be an integer satisfying $x \geq s$, $x \leq 63315$, and
$$
47032x \equiv 22345 \pmod{63315}.
$$
... | 15,497 | graphs = [
Graph(
let={
"a": Const(47032),
"b": Const(22345),
"m": Const(63315),
"result": MinOverSet(set=SolutionsSet(var=Var("x"), condition=And(Geq(Var("x"), EulerPhi(n=EulerPhi(n=CountOverSet(set=SolutionsSet(var=Var("p"), condition=And(IsPositive(arg=Var(... | NT | null | EXTREMUM | sympy | COPRIME_PAIRS | [
"COPRIME_PAIRS/ONE_PHI_2/ONE_PHI_1"
] | 90c501 | modular_min_linear_v1 | null | 7 | 0 | [
"COPRIME_PAIRS",
"ONE_PHI_1",
"ONE_PHI_2"
] | 3 | 2.497 | 2026-02-08T03:29:06.137244Z | {
"verified": true,
"answer": 15497,
"timestamp": "2026-02-08T03:29:08.634299Z"
} | 222e2f | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 260,
"completion_tokens": 4636
},
"timestamp": "2026-02-09T10:05:52.845Z",
"answer": 15497
},
{
"... | 1 | [
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
... | {
"lo": -6.51,
"mid": -0.31,
"hi": 5.43
} | ||
3f09f0 | comb_count_permutations_fixed_v1_2080023795_200 | Let $n = 7$ and $k = 3$. Define
$$
r = \binom{7}{3} \cdot !4,
$$
where $!4$ denotes the number of derangements of 4 elements. Let $m = |r| + 2$. Find the smallest positive integer $e$ such that the $e$-th Fibonacci number is divisible by $m$. Compute $e$. | 159 | graphs = [
Graph(
let={
"n": Const(7),
"k": Const(3),
"result": Mul(Binom(n=Ref("n"), k=Ref("k")), Subfactorial(arg=Sub(left=Ref(name='n'), right=Ref(name='k')))),
"Q": FibonacciEntryPoint(modulus=Sum(Abs(arg=Ref(name='result')), Const(value=2))),
},
... | NT | COMB | COUNT | sympy | MAX_PRIME_BELOW | [
"MAX_PRIME_BELOW"
] | dc3ad3 | comb_count_permutations_fixed_v1 | null | 5 | 0 | [
"MAX_PRIME_BELOW"
] | 1 | 0.016 | 2026-02-08T11:35:40.589889Z | {
"verified": true,
"answer": 159,
"timestamp": "2026-02-08T11:35:40.605686Z"
} | 593a48 | 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": 4801
},
"timestamp": "2026-02-11T07:26:45.326Z",
"answer": 159
},
{
"i... | 1 | [
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok"
}... | {
"lo": -1.84,
"mid": 2.85,
"hi": 7.63
} | ||
ed6f66 | comb_catalan_compute_v1_865884756_3418 | Let $n$ be the number of integers $t$ with $16 \leq t \leq 27$ for which there exist positive integers $a$ and $b$ such that $1 \leq a \leq 5$, $1 \leq b \leq 2$, and $t = 2a + 3b + 11$. Compute the $n$-th Catalan number. | 16,796 | graphs = [
Graph(
let={
"n": CountOverSet(set=SolutionsSet(var=Var("t"), condition=Exists(var=Var(name='a'), condition=Exists(var=Var(name='b'), condition=And(Geq(left=Var(name='a'), right=Const(value=1)), Leq(left=Var(name='a'), right=Const(value=5)), Geq(left=Var(name='b'), right=Const(value=1... | COMB | null | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | comb_catalan_compute_v1 | null | 4 | 0 | [
"LIN_FORM"
] | 1 | 0.022 | 2026-02-08T17:22:28.571470Z | {
"verified": true,
"answer": 16796,
"timestamp": "2026-02-08T17:22:28.593359Z"
} | 0e361d | 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": 1143
},
"timestamp": "2026-02-18T02:18:29.807Z",
"answer": 16796
},
... | 1 | [
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8",
"st... | {
"lo": -4.1,
"mid": -1.76,
"hi": 1.32
} | ||
987601 | sequence_count_fib_divisible_v1_48377204_2029 | Let $N = 50625$. Define $\text{upper}$ to be the minimum value of $x + y$ over all ordered pairs $(x, y)$ of positive integers such that $xy = N$. Let
$$
d = \sum_{k=1}^{5} \phi(k) \left\lfloor \frac{5}{k} \right\rfloor,
$$
where $\phi$ denotes Euler's totient function. Let $\text{result}$ be the number of positive int... | 35,466 | graphs = [
Graph(
let={
"_n": Const(50625),
"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",
"K2"
] | f1ea07 | sequence_count_fib_divisible_v1 | null | 7 | 0 | [
"B3",
"K2"
] | 2 | 0.083 | 2026-02-08T16:33:41.686012Z | {
"verified": true,
"answer": 35466,
"timestamp": "2026-02-08T16:33:41.769068Z"
} | 88dee4 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 203,
"completion_tokens": 1923
},
"timestamp": "2026-02-17T06:25:52.208Z",
"answer": 35466
},
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "K2",
"status": "ok"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
49d561 | comb_sum_binomial_row_v1_601307018_6822 | Let $n$ be the number of ordered pairs $(a, b)$ of positive integers with $1 \le a, b \le 15$ such that $-189a^3 = -96768$. Let $M = 2^n$. Find the remainder when $44121M$ is divided by $94412$. | 25,972 | graphs = [
Graph(
let={
"_n": Const(94412),
"n": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("a"), Var("b")]), condition=And(Geq(Var("a"), Const(1)), Leq(Var("a"), Const(15)), Geq(Var("b"), Const(1)), Leq(Var("b"), Const(15)), Eq(Mul(Const(-189), Pow(Var("a"), Const(3))), C... | COMB | null | SUM | sympy | POLY3_COUNT | [
"POLY3_COUNT"
] | 355dbe | comb_sum_binomial_row_v1 | null | 4 | 0 | [
"POLY3_COUNT"
] | 1 | 0.004 | 2026-03-10T07:27:55.335701Z | {
"verified": true,
"answer": 25972,
"timestamp": "2026-03-10T07:27:55.339383Z"
} | a254f2 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 179,
"completion_tokens": 3117
},
"timestamp": "2026-04-19T05:22:49.352Z",
"answer": 25972
},
{
... | 1 | [
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "POLY3_COUNT",
"status": "ok"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8",
"sta... | {
"lo": -5.34,
"mid": 1.1,
"hi": 7.53
} | ||
6b1804 | modular_inverse_v1_2051736721_2340 | Let $a = 645$ and $m = 733$. Let $U$ be the set of all positive integers $t$ such that $10 \le t \le 1476$ and there exist positive integers $a'$ and $b'$ with $1 \le a' \le 282$, $1 \le b' \le 58$, and $t = 4a' + 6b'$. Let $\text{upper}$ be the number of elements in $U$. Let $R$ be the smallest positive integer $x$ su... | 198 | graphs = [
Graph(
let={
"_n": Const(82057),
"a": Const(645),
"m": Const(733),
"upper": CountOverSet(set=SolutionsSet(var=Var("t"), condition=Exists(var=Var(name='a'), condition=Exists(var=Var(name='b'), condition=And(Geq(left=Var(name='a'), right=Const(value=1... | NT | null | EXTREMUM | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | modular_inverse_v1 | null | 6 | 0 | [
"LIN_FORM"
] | 1 | 0.061 | 2026-02-08T16:35:42.851364Z | {
"verified": true,
"answer": 198,
"timestamp": "2026-02-08T16:35:42.911953Z"
} | 626135 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 221,
"completion_tokens": 5979
},
"timestamp": "2026-02-17T08:42:28.620Z",
"answer": 198
},
{
... | 1 | [
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "V1",
"status": "no"... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
387be7 | nt_count_gcd_equals_v1_784195855_5336 | Let $k = \sum_{d \mid 272} \phi(d)$, where $\phi$ denotes Euler's totient function. Let $s$ be the minimum value of $x + y$ over all pairs of positive integers $(x, y)$ such that $xy = 25000000$. Determine the number of positive integers $n$ with $1 \leq n \leq s$ such that $\gcd(n, k) = 136$. Multiply this count by 33... | 12,469 | graphs = [
Graph(
let={
"_n": Const(337),
"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(25000000)))), expr=Sum(Var("x"), Var("... | NT | null | COUNT | sympy | K3 | [
"K3",
"B3"
] | b88822 | nt_count_gcd_equals_v1 | null | 7 | 0 | [
"B3",
"K3"
] | 2 | 3.457 | 2026-02-08T07:49:43.796969Z | {
"verified": true,
"answer": 12469,
"timestamp": "2026-02-08T07:49:47.253897Z"
} | 39cc7a | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 151,
"completion_tokens": 1493
},
"timestamp": "2026-02-13T12:33:21.313Z",
"answer": 12469
},
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K3",
"status": "ok"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "V7",
"s... | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
5019c5 | modular_sum_quadratic_residues_v1_1978505735_5069 | Let $p = 617$. Define $r = \frac{p(p-1)}{4}$. Let $A$ be the set of prime numbers $n$ such that $2 \leq n \leq 3$. Let $k = |A|$. Compute the value of $$ r + \left( k^{r \bmod 14} \bmod 86447 \right). $$ | 95,019 | graphs = [
Graph(
let={
"_n": Const(4),
"p": Const(617),
"result": Div(Mul(Ref("p"), Sub(Ref("p"), Const(1))), Ref("_n")),
"Q": Sum(Ref("result"), Mod(value=Pow(CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(2)), Leq(Var("n"), Co... | NT | null | SUM | sympy | COUNT_PRIMES | [
"COUNT_PRIMES"
] | 6ccaed | modular_sum_quadratic_residues_v1 | mod_exp | 4 | 0 | [
"COUNT_PRIMES"
] | 1 | 0.003 | 2026-02-08T18:45:23.639236Z | {
"verified": true,
"answer": 95019,
"timestamp": "2026-02-08T18:45:23.641935Z"
} | 1069c0 | 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": 705
},
"timestamp": "2026-02-18T19:11:30.036Z",
"answer": 95019
},
{... | 1 | [
{
"lemma": "COUNT_PRIMES",
"status": "ok"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
},
{
"lemma": "VAL_SUM_EQ",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
a0114a | nt_gcd_compute_v1_971394319_1625 | Let $a$ be the minimum value of $x + y$ where $x$ and $y$ are positive integers such that $xy = 14976900$. Let $b = 17415$. Compute $\gcd(a, b)$. | 1,935 | graphs = [
Graph(
let={
"a": MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(Mul(Var("x"), Var("y")), Const(14976900)))), expr=Sum(Var("x"), Var("y")))),
"b": Const(174... | NT | null | COMPUTE | sympy | B3 | [
"B3"
] | 0cd20d | nt_gcd_compute_v1 | null | 5 | 0 | [
"B3"
] | 1 | 0.006 | 2026-02-08T13:47:21.358403Z | {
"verified": true,
"answer": 1935,
"timestamp": "2026-02-08T13:47:21.364722Z"
} | 7d90e5 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 97,
"completion_tokens": 1638
},
"timestamp": "2026-02-15T21:04:30.103Z",
"answer": 1935
},
{
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
}
] | {
"lo": -5.49,
"mid": 0.22,
"hi": 6.51
} | ||
ad5da1 | sequence_count_fib_divisible_v1_677425708_1265 | Compute the number of positive integers $n \leq 868$ such that the $n$th Fibonacci number is even. | 289 | graphs = [
Graph(
let={
"upper": Const(868),
"d": Const(2),
"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 | V1 | [
"MIN_PRIME_FACTOR",
"LIN_FORM"
] | 41af5a | sequence_count_fib_divisible_v1 | null | 4 | 0 | [
"LIN_FORM",
"MIN_PRIME_FACTOR",
"V1"
] | 3 | 0.132 | 2026-02-08T04:03:10.574819Z | {
"verified": true,
"answer": 289,
"timestamp": "2026-02-08T04:03:10.707282Z"
} | 22ebfb | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 136,
"completion_tokens": 216
},
"timestamp": "2026-02-09T17:42:02.899Z",
"answer": 289
},
{
"id"... | 1 | [
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "MIN_PRIME_FACTOR",
"status": "ok... | {
"lo": -7.01,
"mid": -4.68,
"hi": -2.15
} | ||
476e97 | geo_count_lattice_triangle_v1_168721529_1173 | Let $A$ be the set of all ordered pairs $(x, y)$ of positive integers such that $x \cdot y = 8100$. Define $P$ to be the sum of $x + y$ over all such pairs. Let $T$ be twice the area of the triangle with vertices at $(0,0)$, $(180,24)$, and $(80,121)$, computed as $|180 \cdot 121 - 80 \cdot 24|$. Define the boundary te... | 16,654 | graphs = [
Graph(
let={
"_n": Const(121),
"area_2x": Abs(arg=Sum(Mul(Const(value=180), Const(value=121)), Mul(Const(value=80), Sub(left=Const(value=0), right=Const(value=24))))),
"boundary": Sum(GCD(a=Abs(arg=MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[... | NT | null | COUNT | sympy | B3 | [
"B3"
] | 0cd20d | geo_count_lattice_triangle_v1 | null | 6 | 0 | [
"B3"
] | 1 | 0.011 | 2026-02-08T13:31:00.451149Z | {
"verified": true,
"answer": 16654,
"timestamp": "2026-02-08T13:31:00.462375Z"
} | d70624 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 1,
"correct": {
"strict": false,
"boxed": false,
"relaxed": true
},
"usage": {
"prompt_tokens": 338,
"completion_tokens": 3713
},
"timestamp": "2026-02-09T14:23:30.126Z",
"answer": 24784
},
{
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "VAL_SUM_EQ",
"status"... | {
"lo": 1.84,
"mid": 5.05,
"hi": 8.38
} | ||
d2d5b2 | nt_num_divisors_compute_v1_809748730_165 | Let $m = 11$. Let $p$ be the largest prime number such that $2 \leq p \leq 11$. Define
$$
n = \sum_{k=1}^{m} \phi(k) \left\lfloor \frac{p}{k} \right\rfloor,
$$
where $\phi(k)$ denotes Euler's totient function. Compute the number of positive divisors of $n$. | 8 | graphs = [
Graph(
let={
"_m": Const(11),
"_n": MaxOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(2)), Leq(Var("n"), Const(11)), IsPrime(Var("n"))))),
"n": Summation(var="k", start=Const(1), end=Ref("_m"), expr=Mul(EulerPhi(n=Var("k")), Floor(Div(... | NT | null | COMPUTE | sympy | MAX_PRIME_BELOW | [
"MAX_PRIME_BELOW/K2"
] | 7eb1ee | nt_num_divisors_compute_v1 | null | 5 | 0 | [
"K2",
"MAX_PRIME_BELOW"
] | 2 | 0.004 | 2026-02-08T11:21:22.598706Z | {
"verified": true,
"answer": 8,
"timestamp": "2026-02-08T11:21:22.602744Z"
} | 705827 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 130,
"completion_tokens": 1280
},
"timestamp": "2026-02-14T12:30:27.283Z",
"answer": 8
},
{
... | 1 | [
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K2",
"status": "ok_later"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "n... | {
"lo": -9.12,
"mid": -6.02,
"hi": -3.62
} | ||
051689 | modular_count_residue_v1_1918700295_1969 | Let $r$ be the number of nonnegative integers $j$ such that $0 \leq j \leq 2144$ and $\binom{2144}{j}$ is odd. Determine the number of positive integers $n$ such that $1 \leq n \leq 86436$ and $n \equiv r \pmod{13}$. Multiply this count by $79463$, and find the remainder when the product is divided by $55248$. | 12,863 | graphs = [
Graph(
let={
"upper": Const(86436),
"m": Const(13),
"r": CountOverSet(set=SolutionsSet(var=Var("j"), condition=And(Geq(Var("j"), Const(0)), Leq(Var("j"), Const(2144)), Eq(Mod(value=Binom(n=Const(2144), k=Var("j")), modulus=Const(2)), Const(1))), domain='nonnega... | ALG | COMB | COUNT | sympy | V8 | [
"V8"
] | 86348e | modular_count_residue_v1 | null | 7 | 0 | [
"V8"
] | 1 | 2.835 | 2026-02-08T06:12:05.987417Z | {
"verified": true,
"answer": 12863,
"timestamp": "2026-02-08T06:12:08.822265Z"
} | e629f9 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 212,
"completion_tokens": 2178
},
"timestamp": "2026-02-24T08:16:25.794Z",
"answer": 12863
},
{
"... | 1 | [
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "V8",
"status": "ok"
}
] | {
"lo": 1.15,
"mid": 4.18,
"hi": 6.61
} | ||
8d5936 | nt_count_divisible_v1_2051736721_6063 | Let $n$ be a positive integer such that $1 \leq n \leq 74529$ and $n$ is divisible by $29$. Let $r$ be the number of such integers $n$. Let $d$ be the smallest divisor of $1573$ that is at least $2$. Compute the Bell number $B_{r \bmod d}$. | 203 | graphs = [
Graph(
let={
"upper": Const(74529),
"divisor": Const(29),
"result": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Ref("upper")), Eq(Mod(value=Var("n"), modulus=Ref("divisor")), Const(0))))),
"Q": Be... | NT | COMB | COUNT | sympy | MOBIUS_COPRIME | [
"MIN_PRIME_FACTOR"
] | 58d7e9 | nt_count_divisible_v1 | bell_mod | 5 | 0 | [
"MIN_PRIME_FACTOR",
"MOBIUS_COPRIME"
] | 2 | 10.636 | 2026-02-08T18:55:11.421593Z | {
"verified": true,
"answer": 203,
"timestamp": "2026-02-08T18:55:22.057809Z"
} | 146d28 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 124,
"completion_tokens": 1002
},
"timestamp": "2026-02-18T20:41:31.691Z",
"answer": 203
},
{
... | 1 | [
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "MIN_PRIME_FACTOR",
"status": "ok... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
3930b7 | nt_num_divisors_compute_v1_677425708_2478 | Let $n$ be the number of ordered pairs of positive odd integers $(x_1, x_2)$ such that $x_1 + x_2 = 720$. Let $d(n)$ denote the number of positive divisors of $n$. Compute the remainder when $48625 \cdot d(n)$ is divided by $97251$. | 97,239 | graphs = [
Graph(
let={
"_n": Const(720),
"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")), R... | NT | null | COMPUTE | sympy | COMB1 | [
"COMB1"
] | 567f58 | nt_num_divisors_compute_v1 | null | 4 | 0 | [
"COMB1"
] | 1 | 0.002 | 2026-02-08T05:04:25.147604Z | {
"verified": true,
"answer": 97239,
"timestamp": "2026-02-08T05:04:25.149527Z"
} | d9cb19 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 183,
"completion_tokens": 1072
},
"timestamp": "2026-02-11T22:49:53.779Z",
"answer": 97239
},
{
... | 1 | [
{
"lemma": "COMB1",
"status": "ok"
},
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "... | {
"lo": -3.42,
"mid": 1.86,
"hi": 7.55
} | ||
dc798a | alg_poly3_sum_v1_1218484723_5349 | Let $C = \left|\{ (a_2, b_2) : 1 \le a_2, b_2 \le 40,\ 54a_2b_2 + 26a_2^2 + 29b_2^2 \le 102241 \}\right|$. Let $B = \left|\{ (a_1, b_1) : 1 \le a_1, b_1 \le 15,\ 10a_1^2 - 18a_1b_1 + 25b_1^2 \le C \}\right|$. Find the remainder when \[\sum_{a=1}^{47} \sum_{b=1}^{47} \sum_{c=1}^{47} \left( 3a^3 - 181c^3 + 102a^2b - 444a... | 25,758 | graphs = [
Graph(
let={
"_c": Const(102),
"_m": Const(47),
"_n": Const(47),
"result": Mod(value=SumOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("a"), Var("b"), Var("c")]), condition=And(Geq(Var("a"), Const(1)), Leq(Var("a"), Const(47)), Geq(... | NT | null | COMPUTE | sympy | QF_PSD_COUNT_LEQ | [
"QF_PSD_COUNT_LEQ/QF_PSD_COUNT_LEQ",
"MAX_PRIME_BELOW"
] | 76adf7 | alg_poly3_sum_v1 | null | 6 | 0 | [
"MAX_PRIME_BELOW",
"QF_PSD_COUNT_LEQ"
] | 2 | 0.756 | 2026-02-25T06:57:06.994581Z | {
"verified": true,
"answer": 25758,
"timestamp": "2026-02-25T06:57:07.750544Z"
} | ff30ce | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 373,
"completion_tokens": 15787
},
"timestamp": "2026-03-29T20:41:48.577Z",
"answer": 1114
},
{
... | 1 | [
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "QF_PSD_COUNT_LEQ",
"status": "... | {
"lo": 3.81,
"mid": 6.33,
"hi": 9.49
} | ||
94d295 | comb_sum_binomial_row_v1_48377204_1489 | Let $m$ be the number of positive integers $p$ for which there exists a positive integer $q$ such that $pq = 216$, $\gcd(p,q) = 1$, and $p < q$. Let $n$ be the number of positive integers $p_1$ for which there exists a positive integer $q$ such that $p_1 q = 2263800$, $\gcd(p_1, q) = 1$, and $p_1 < q$. Compute $m^n$. | 65,536 | 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=216)), Eq(left=GCD(a=Var(name='p'), b=Var(name='q')), right=Const(value=1)),... | NT | null | SUM | sympy | K2 | [
"COPRIME_PAIRS/COPRIME_PAIRS"
] | 3bbd71 | comb_sum_binomial_row_v1 | null | 5 | 0 | [
"COPRIME_PAIRS",
"K2"
] | 2 | 0.016 | 2026-02-08T16:08:01.554682Z | {
"verified": true,
"answer": 65536,
"timestamp": "2026-02-08T16:08:01.570686Z"
} | c53d9f | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 156,
"completion_tokens": 2602
},
"timestamp": "2026-02-16T21:12:29.624Z",
"answer": 65536
},
... | 1 | [
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
},
{
"lemma": "VAL_SUM_EQ",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
673e81 | algebra_poly_eval_v1_48377204_1147 | Let $a = 7$. Let $T$ be the set of integers $t$ with $9 \leq t \leq 68$ for which there exist positive integers $a'$ and $b$ such that $1 \leq a' \leq 4$, $1 \leq b \leq 12$, and $t = 5a' + 4b$. Let $N$ be the number of elements in the Cartesian product of the sets $\{1, 2, \dots, 10\}$ and $\{1, 2, \dots, 16\}$. Defin... | 3,632 | graphs = [
Graph(
let={
"_c": Const(70382),
"_m": Const(4),
"_n": Const(83091),
"a": Const(7),
"result": Div(Sum(Mul(CountOverSet(set=SolutionsSet(var=Var("t"), condition=Exists(var=Var(name='a'), condition=Exists(var=Var(name='b'), condition=And(G... | NT | null | COMPUTE | sympy | COUNT_CARTESIAN | [
"COUNT_CARTESIAN",
"LIN_FORM",
"K2"
] | f15da0 | algebra_poly_eval_v1 | null | 6 | 0 | [
"COUNT_CARTESIAN",
"K2",
"LIN_FORM"
] | 3 | 0.021 | 2026-02-08T15:54:56.474725Z | {
"verified": true,
"answer": 3632,
"timestamp": "2026-02-08T15:54:56.496171Z"
} | 0f9338 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 267,
"completion_tokens": 2488
},
"timestamp": "2026-02-16T16:21:10.553Z",
"answer": 3632
},
{... | 1 | [
{
"lemma": "COUNT_CARTESIAN",
"status": "ok"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K2",
"status": ... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
37bcc5 | comb_count_surjections_v1_2080023795_207 | Let $n_1 = 0$ and $n_2 = 0$. Define
$$
c = \sum_{k=0}^{n_2} (-1)^k \binom{n_2}{k}
\quad\text{and}\quad
f = \sum_{k=0}^{n_1} (-1)^k \binom{n_1}{k}.
$$
Let $n = 6c$ and $k = 4f$. Compute $k! \cdot S(n, k)$, where $S(n, k)$ denotes the Stirling number of the second kind, the number of ways to partition a set of $n$ elemen... | 1,560 | graphs = [
Graph(
let={
"n2": Const(0),
"c": Summation(var="k", start=Const(0), end=Ref("n2"), expr=Mul(Pow(Const(-1), Var("k")), Binom(n=Ref("n2"), k=Var("k")))),
"n1": Const(0),
"f": Summation(var="k", start=Const(0), end=Ref("n1"), expr=Mul(Pow(Const(-1), V... | COMB | null | COUNT | sympy | BINOMIAL_ALTERNATING | [
"BINOMIAL_ALTERNATING"
] | c21569 | comb_count_surjections_v1 | null | 3 | 2 | [
"BINOMIAL_ALTERNATING"
] | 1 | 0.001 | 2026-02-08T11:35:58.319731Z | {
"verified": true,
"answer": 1560,
"timestamp": "2026-02-08T11:35:58.321193Z"
} | f9bad6 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 268,
"completion_tokens": 861
},
"timestamp": "2026-02-08T20:51:58.523Z",
"answer": 1560
},
{
"id... | 1 | [
{
"lemma": "BINOMIAL_ALTERNATING",
"status": "ok"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8"... | {
"lo": -3.91,
"mid": -1.87,
"hi": 0.46
} | ||
e82231 | nt_max_prime_below_v1_168721529_2085 | Let $T$ be the set of all positive integers $p$ for which there exists a positive integer $q$ such that $p < q$, $\gcd(p, q) = 1$, and $pq = 36$. Let $m$ be the number of elements in $T$. Let $S$ be the set of all prime numbers $n$ such that $m \leq n \leq 24336$. Determine the largest element of $S$. | 24,329 | graphs = [
Graph(
let={
"upper": Const(24336),
"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 | 0.905 | 2026-02-08T14:06:59.668441Z | {
"verified": true,
"answer": 24329,
"timestamp": "2026-02-08T14:07:00.573064Z"
} | b9f53e | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 209,
"completion_tokens": 3029
},
"timestamp": "2026-02-11T11:02:18.381Z",
"answer": 24329
},
{
... | 1 | [
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "V1",
"status": "no"
}
] | {
"lo": -7.08,
"mid": 0.22,
"hi": 7.52
} | ||
6e280e | modular_min_linear_v1_1874849503_284 | Let $a = 45469$, $b = 47243$, and $m = 80397$. Determine the smallest positive integer $x$ such that $x \geq \phi(2)$, $x \leq m$, and $a \cdot x \equiv b \pmod{m}$. Let $c = 14236$. Compute the remainder when $c$ multiplied by this smallest $x$ is divided by $64809$. | 7,385 | graphs = [
Graph(
let={
"a": Const(45469),
"b": Const(47243),
"m": Const(80397),
"result": MinOverSet(set=SolutionsSet(var=Var("x"), condition=And(Geq(Var("x"), EulerPhi(n=Const(2))), Leq(Var("x"), Ref("m")), Eq(Mod(value=Mul(Ref("a"), Var("x")), modulus=Ref("... | NT | null | EXTREMUM | sympy | ONE_PHI_2 | [
"ONE_PHI_2"
] | e19278 | modular_min_linear_v1 | null | 5 | 0 | [
"ONE_PHI_2"
] | 1 | 3.122 | 2026-02-08T12:55:35.240655Z | {
"verified": true,
"answer": 7385,
"timestamp": "2026-02-08T12:55:38.362699Z"
} | 684c47 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 212,
"completion_tokens": 3370
},
"timestamp": "2026-02-09T15:22:24.302Z",
"answer": 7385
},
{
"i... | 1 | [
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "ONE_PHI_2",
"status": "ok"
},
{
"lemma": "V1",
"status": "no"
}
] | {
"lo": -6.51,
"mid": -0.31,
"hi": 5.43
} | ||
c04f53_l | antilemma_sum_equals_v1_124444284_1569 | Let $x$ be the number of ordered pairs $(i, j)$ of integers with $1 \leq i \leq 33$ and $1 \leq j \leq 33$ such that $i + j = 33$. Compute the Bell number of $|x| \mod 11$, and then find the remainder when this Bell number is divided by $85450$. | 1 | COMB | GEOM | COMPUTE | sympy | COMB1 | [
"COUNT_SUM_EQUALS"
] | 75ab0f | antilemma_sum_equals_v1 | null | 4 | 0 | [
"COMB1",
"COUNT_SUM_EQUALS"
] | 2 | 0.082 | 2026-02-08T04:00:40.519317Z | {
"verified": false,
"answer": 30525,
"timestamp": "2026-02-08T04:00:40.600973Z"
} | 42b60a | c04f53 | legacy_text | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 193,
"completion_tokens": 1546
},
"timestamp": "2026-02-11T15:47:32.390Z",
"answer": 30525
},
{
"... | 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": -2.46,
"mid": 0.47,
"hi": 3.59
} | |
ebc94c | alg_poly3_sum_v1_601307018_1478 | Let $S$ be the set of integers $t$ such that $t = 7a + 5b$ for some integers $a, b$ with $1 \leq a \leq 29$, $1 \leq b \leq 25$, and $12 \leq t \leq 328$. Let $L = |S|$. Compute the remainder when $$\sum_{\substack{a \geq 1,\, a \leq L \\ b \geq 1,\, b \leq 293}} \left(177a^2b + 26b^3 - 189a^3 - 147ab^2\right)$$ is div... | 24,259 | graphs = [
Graph(
let={
"_n": Const(3),
"result": Mod(value=SumOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("a"), Var("b")]), condition=And(Geq(Var("a"), Const(1)), Leq(Var("a"), CountOverSet(set=SolutionsSet(var=Var("t"), condition=Exists(var=Var(name='a'), condit... | ALG | null | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | alg_poly3_sum_v1 | null | 6 | 0 | [
"LIN_FORM"
] | 1 | 0.203 | 2026-03-10T02:12:53.084312Z | {
"verified": true,
"answer": 24259,
"timestamp": "2026-03-10T02:12:53.287656Z"
} | dd3a18 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 266,
"completion_tokens": 6638
},
"timestamp": "2026-03-29T02:18:19.626Z",
"answer": 58838
},
{
... | 1 | [
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
}
] | {
"lo": 4.01,
"mid": 6.11,
"hi": 9.15
} | ||
0eb574 | nt_min_crt_v1_124444284_4633 | Let $u$ and $v$ be positive integers such that $uv = 400$. Define $s = u + v$. Let $S$ be the set of all such values of $s$. Let $m$ be the smallest element of $S$. Find the smallest positive integer $n$ such that $n \le m$, $n \equiv 0 \pmod{5}$, and $n \equiv 6 \pmod{8}$. | 30 | graphs = [
Graph(
let={
"m": Const(5),
"k": Const(8),
"a": Const(0),
"b": Const(6),
"upper": MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='... | NT | null | EXTREMUM | sympy | ONE_PHI_2 | [
"B3"
] | 0cd20d | nt_min_crt_v1 | null | 4 | 0 | [
"B3",
"ONE_PHI_2"
] | 2 | 0.051 | 2026-02-08T06:07:52.511242Z | {
"verified": true,
"answer": 30,
"timestamp": "2026-02-08T06:07:52.562509Z"
} | 439981 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 142,
"completion_tokens": 758
},
"timestamp": "2026-02-12T20:35:56.755Z",
"answer": 30
},
{
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "VAL_SUM_EQ",
"status": "no"
}
] | {
"lo": -5.55,
"mid": -3.01,
"hi": 0.32
} | ||
f67281 | comb_binomial_compute_v1_1419126231_519 | Let $n$ be the number of ordered pairs $(a, b)$ of positive integers with $1 \le a, b \le 20$ such that $128a^3 + 384a^2b + 384ab^2 + 128b^3 = 2519424$. Compute $\binom{n}{7}$. | 3,432 | graphs = [
Graph(
let={
"_n": Const(2),
"n": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("a"), Var("b")]), condition=And(Geq(Var("a"), Const(1)), Leq(Var("a"), Const(20)), Geq(Var("b"), Const(1)), Leq(Var("b"), Const(20)), Eq(Sum(Mul(Const(128), Pow(Var("b"), Const(3))), Mu... | COMB | null | COMPUTE | sympy | POLY3_COUNT | [
"POLY3_COUNT"
] | 355dbe | comb_binomial_compute_v1 | null | 4 | 0 | [
"POLY3_COUNT"
] | 1 | 0.002 | 2026-02-25T10:03:02.350917Z | {
"verified": true,
"answer": 3432,
"timestamp": "2026-02-25T10:03:02.352579Z"
} | 60a24e | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 183,
"completion_tokens": 1230
},
"timestamp": "2026-03-30T08:48:27.952Z",
"answer": 3432
},
{
"i... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "POLY3_COUNT",
"status": "ok"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
}... | {
"lo": -5.37,
"mid": 0.23,
"hi": 5.22
} | ||
18a8fc | antilemma_k3_v1_1526740231_439 | Let $n = 74516$. Compute $$\sum_{d \mid n} \phi(d),$$ where $\phi$ denotes Euler's totient function. Then determine the smallest positive integer $k$ such that the $k$-th Fibonacci number is divisible by the sum of this total and $2$. | 1,026 | graphs = [
Graph(
let={
"_n": Const(74516),
"x": SumOverDivisors(n=Ref(name='_n'), var='d', expr=EulerPhi(n=Var(name='d'))),
"Q": FibonacciEntryPoint(modulus=Sum(Abs(arg=Ref(name='x')), Const(value=2))),
},
goal=Ref("Q"),
)
] | NT | COMB | COMPUTE | sympy | K3 | [
"K3"
] | 54c41e | antilemma_k3_v1 | null | 3 | 0 | [
"K3"
] | 1 | 0.002 | 2026-02-08T11:31:25.861235Z | {
"verified": true,
"answer": 1026,
"timestamp": "2026-02-08T11:31:25.863515Z"
} | 1520e9 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 109,
"completion_tokens": 3789
},
"timestamp": "2026-02-14T16:11:41.742Z",
"answer": 1026
},
{... | 1 | [
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "K3",
"status": "ok"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "V3",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
}
] | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
eea883 | nt_count_divisible_v1_717093673_624 | Let $n = 6$. Define $d$ to be the sum
$$
\sum_{k=1}^{6} \phi(k) \left\lfloor \frac{6}{k} \right\rfloor,
$$
where $\phi(k)$ denotes Euler's totient function. Let $S$ be the set of all positive integers $n$ such that $1 \leq n \leq 32768$ and $n$ is divisible by $d$. Compute the number of elements in $S$. | 1,560 | graphs = [
Graph(
let={
"_n": Const(6),
"upper": Const(32768),
"divisor": 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... | NT | null | COUNT | sympy | K2 | [
"K2"
] | 6897ab | nt_count_divisible_v1 | null | 4 | 0 | [
"K2"
] | 1 | 1.21 | 2026-02-08T15:34:25.845489Z | {
"verified": true,
"answer": 1560,
"timestamp": "2026-02-08T15:34:27.055022Z"
} | c684fe | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 174,
"completion_tokens": 612
},
"timestamp": "2026-02-16T06:08:03.114Z",
"answer": 1560
},
{
"id": 11,
... | 2 | [
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "K2",
"status": "ok"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
}
] | {
"lo": -10,
"mid": -7.27,
"hi": -4.54
} | ||
d72b41 | comb_bell_compute_v1_1520064083_8919 | Let $S$ be the set of all integers $t$ such that $10 \leq t \leq 30$ and there exist positive integers $a$ and $b$, each at most 3, satisfying $t = 4a + 6b$. Let $n$ be the number of elements in $S$. Compute $37636 - B_n$, where $B_n$ denotes the $n$-th Bell number. | 16,489 | graphs = [
Graph(
let={
"_n": Const(37636),
"n": CountOverSet(set=SolutionsSet(var=Var("t"), condition=Exists(var=Var(name='a'), condition=Exists(var=Var(name='b'), condition=And(Geq(left=Var(name='a'), right=Const(value=1)), Leq(left=Var(name='a'), right=Const(value=3)), Geq(left=Va... | COMB | null | COMPUTE | sympy | SUM_ARITHMETIC | [
"LIN_FORM"
] | 7b2633 | comb_bell_compute_v1 | null | 5 | 0 | [
"LIN_FORM",
"SUM_ARITHMETIC"
] | 2 | 0.008 | 2026-02-08T10:26:38.495411Z | {
"verified": true,
"answer": 16489,
"timestamp": "2026-02-08T10:26:38.502992Z"
} | 75d73b | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 203,
"completion_tokens": 598
},
"timestamp": "2026-02-24T12:02:47.082Z",
"answer": 16489
},
{
"i... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "V8",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no... | {
"lo": -3.84,
"mid": -1.67,
"hi": 1.32
} | ||
f40863 | nt_sum_divisors_mod_v1_1125832087_129 | Let $n$ be the number of positive integers $m$ such that $1 \leq m \leq 35273$, $7$ divides $m$, and $\gcd(m, 12) = 1$. Let $\sigma(n)$ denote the sum of all positive divisors of $n$. Compute the remainder when $41 - (\sigma(n) \bmod 10771)$ is divided by $61014$. | 55,103 | graphs = [
Graph(
let={
"_n": Const(41),
"n": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Const(35273)), Divides(divisor=Const(7), dividend=Var("n")), Eq(GCD(a=Var("n"), b=Const(12)), Const(1))))),
"M": Const(10771),
... | NT | null | COMPUTE | sympy | C5 | [
"C5"
] | 1d9668 | nt_sum_divisors_mod_v1 | null | 5 | 0 | [
"C5"
] | 1 | 0.002 | 2026-02-08T02:52:42.121808Z | {
"verified": true,
"answer": 55103,
"timestamp": "2026-02-08T02:52:42.123362Z"
} | f3c8f7 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 200,
"completion_tokens": 2508
},
"timestamp": "2026-02-10T11:46:59.969Z",
"answer": 55103
},
{
"... | 1 | [
{
"lemma": "C5",
"status": "ok"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
}
] | {
"lo": 0.72,
"mid": 2.32,
"hi": 3.82
} | ||
0a453c | comb_count_permutations_fixed_v1_1520064083_866 | Let $ k = \sum_{i=1}^{2} i $. Compute the value of
$$
\binom{9}{k} \cdot !(9 - k),
$$
where $ !m $ denotes the number of derangements of $ m $ elements. | 22,260 | graphs = [
Graph(
let={
"_n": Const(2),
"n": Const(9),
"k": Summation(var="k", start=Const(1), end=Ref("_n"), expr=Var("k")),
"result": Mul(Binom(n=Ref("n"), k=Ref("k")), Subfactorial(arg=Sub(left=Ref(name='n'), right=Ref(name='k')))),
},
goal=... | COMB | null | COUNT | sympy | C5 | [
"SUM_ARITHMETIC"
] | eb34f0 | comb_count_permutations_fixed_v1 | null | 4 | 0 | [
"C5",
"SUM_ARITHMETIC"
] | 2 | 0.035 | 2026-02-08T03:38:19.878117Z | {
"verified": true,
"answer": 22260,
"timestamp": "2026-02-08T03:38:19.912745Z"
} | 94ef63 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 167,
"completion_tokens": 666
},
"timestamp": "2026-02-10T15:15:36.700Z",
"answer": 22260
},
{
"i... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "SUM_ARITHMETIC",
"status": "ok"
},
{
"lemma": "V8",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no... | {
"lo": -7.18,
"mid": -4.99,
"hi": -3
} | ||
87ec4c | modular_count_residue_v1_1874849503_1241 | Let $n_0 = 2$ and $U = 56644$.
First, let $A$ be the number of integers $j$ with $0 \le j \le 5840$ such that
$$\binom{5840}{j} \equiv 1 \pmod{2}.$$
Next, consider all ordered pairs $(x,y)$ of positive integers such that
$$xy = A.$$
For each such pair, form the sum $x + y$. Let $M$ be the minimum of all these sums.
... | 7,080 | graphs = [
Graph(
let={
"_n": Const(2),
"upper": Const(56644),
"m": MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(Mul(Var("x"), Var("y")), MinOverSet(set=... | ALG | COMB | COUNT | sympy | B3 | [
"B3/B3",
"V8/B3"
] | afea9a | modular_count_residue_v1 | null | 8 | 0 | [
"B3",
"V8"
] | 2 | 2.057 | 2026-02-08T13:43:28.648796Z | {
"verified": true,
"answer": 7080,
"timestamp": "2026-02-08T13:43:30.705848Z"
} | 7f06cb | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 324,
"completion_tokens": 1097
},
"timestamp": "2026-02-10T02:39:12.632Z",
"answer": 7080
},
{
"i... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "V8",
"status": "ok"
... | {
"lo": -2.78,
"mid": -0.68,
"hi": 1.45
} | ||
d4acdc | nt_count_divisors_in_range_v1_153355830_2125 | Let $n = 840$. Compute the number of positive divisors $d$ of $n$ such that $2 \leq d \leq 177$. Let $r$ be this number. Let $c$ be the number of positive integers $j \leq 555$ such that $j^3 \leq 170953875$. Compute $r^2 + 36r + c$. | 2,256 | graphs = [
Graph(
let={
"n": Const(840),
"a": Const(2),
"b": Const(177),
"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"))))),
"_c": Co... | NT | null | COUNT | sympy | C3 | [
"C3"
] | db1a9e | nt_count_divisors_in_range_v1 | quadratic_mod | 4 | 0 | [
"C3"
] | 1 | 0.015 | 2026-02-08T06:55:47.159082Z | {
"verified": true,
"answer": 2256,
"timestamp": "2026-02-08T06:55:47.174099Z"
} | 708da8 | 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": 1156
},
"timestamp": "2026-02-13T05:38:59.325Z",
"answer": 2256
},
{... | 1 | [
{
"lemma": "C3",
"status": "ok"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "V3",
"status": "no"
}
] | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
2cd418 | modular_mod_compute_v1_798873815_429 | Let $m$ be the sum of all real solutions $x$ to the equation $x^2 - 2304x + 125888 = 0$. Find the remainder when $-60025$ is divided by $m$. | 2,183 | graphs = [
Graph(
let={
"_n": Const(2),
"a": Const(-60025),
"m": SumOverSet(set=SolutionsSet(var=Var("x"), condition=Eq(Sum(Pow(Var("x"), Ref("_n")), Mul(Const(-2304), Var("x")), Const(125888)), Const(0)))),
"result": Mod(value=Ref("a"), modulus=Ref("m")),
... | NT | null | COMPUTE | sympy | VIETA_SUM | [
"VIETA_SUM"
] | b33a7a | modular_mod_compute_v1 | null | 3 | 0 | [
"VIETA_SUM"
] | 1 | 0.001 | 2026-02-08T02:38:32.145510Z | {
"verified": true,
"answer": 2183,
"timestamp": "2026-02-08T02:38:32.146628Z"
} | e2b9bb | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 163,
"completion_tokens": 919
},
"timestamp": "2026-02-08T19:31:12.714Z",
"answer": 2183
},
{
"id... | 1 | [
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "V1",
"status": "no"
},
{
"lemma": "V3",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
},
{
"lemma": "VIETA_SUM",
"status": "ok"
}
] | {
"lo": -3.9,
"mid": -1.9,
"hi": 0.1
} | ||
5035c6 | comb_sum_binomial_row_v1_677425708_662 | Let $n$ be the minimum value of $x + y$ over all pairs of positive integers $(x, y)$ such that $xy = 25$. Compute $2^n$. Let $d$ be the smallest integer $\geq 2$ that divides 6137. Find the remainder when $d - 2^n$ is divided by 93755. | 92,748 | graphs = [
Graph(
let={
"_m": Const(2),
"_n": Const(25),
"n": MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(Mul(Var("x"), Var("y")), Ref("_n")))), expr=Su... | NT | null | SUM | sympy | MIN_PRIME_FACTOR | [
"MIN_PRIME_FACTOR",
"B3"
] | c17f06 | comb_sum_binomial_row_v1 | negation_mod | 4 | 0 | [
"B3",
"MIN_PRIME_FACTOR"
] | 2 | 0.003 | 2026-02-08T03:39:56.066402Z | {
"verified": true,
"answer": 92748,
"timestamp": "2026-02-08T03:39:56.068965Z"
} | 600b69 | 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": 814
},
"timestamp": "2026-02-08T20:53:09.865Z",
"answer": 92748
},
{
"i... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "MIN_PRIME_FACTOR",
"status": "ok"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
... | {
"lo": -5.55,
"mid": -3.02,
"hi": 0.31
} | ||
502703 | comb_sum_binomial_row_v1_349078426_700 | Let $S$ be the set of all ordered pairs $(k, j)$ of positive integers such that $1 \le k \le 4$ and $1 \le j \le 6$. Define $t$ to be the sum of $k$ over all pairs $(k, j)$ in $S$. Let $n = \frac{6 \cdot t}{36}$. Compute $2^n$. | 1,024 | graphs = [
Graph(
let={
"_m": Const(6),
"_n": Const(2),
"n": Div(Mul(Ref("_m"), SumOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("k"), Var("_j")]), condition=Const(1), domain=CartesianProduct(left=IntegerRange(start=Const(1), end=Const(4)), right=Integer... | NT | null | SUM | sympy | SUM_INDEPENDENT | [
"SUM_INDEPENDENT/SUM_ARITHMETIC"
] | 87e6cf | comb_sum_binomial_row_v1 | null | 2 | 0 | [
"SUM_ARITHMETIC",
"SUM_INDEPENDENT"
] | 2 | 0.001 | 2026-02-08T13:13:26.777349Z | {
"verified": true,
"answer": 1024,
"timestamp": "2026-02-08T13:13:26.778684Z"
} | b21c24 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 132,
"completion_tokens": 390
},
"timestamp": "2026-02-15T11:29:01.695Z",
"answer": 1024
},
{
... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "SUM_ARITHMETIC",
"status": "ok_later"
},
... | {
"lo": -6.96,
"mid": -4.56,
"hi": -1.46
} | ||
12bb04 | nt_count_divisible_v1_1918700295_2389 | Let $u = 33489$ and let $r$ be the number of positive integers $n \leq u$ that are divisible by $29$. Let $s$ be the minimum value of $x + y$ over all ordered pairs of positive integers $(x, y)$ such that $xy = 521284$. Compute $s - r$. | 290 | graphs = [
Graph(
let={
"upper": Const(33489),
"divisor": Const(29),
"result": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Ref("upper")), Eq(Mod(value=Var("n"), modulus=Ref("divisor")), Const(0))))),
"_c": M... | NT | null | COUNT | sympy | B3 | [
"B3"
] | fc629c | nt_count_divisible_v1 | negation_mod | 4 | 0 | [
"B3"
] | 1 | 1.414 | 2026-02-08T07:51:37.164741Z | {
"verified": true,
"answer": 290,
"timestamp": "2026-02-08T07:51:38.579034Z"
} | 31f337 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 120,
"completion_tokens": 1012
},
"timestamp": "2026-02-13T13:04:51.470Z",
"answer": 290
},
{
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
}
] | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
9a399a | sequence_fibonacci_compute_v1_2051736721_5110 | Let $n$ be the number of prime numbers $p$ such that $2 \leq p \leq 89$. Compute the $n$th Fibonacci number. | 46,368 | graphs = [
Graph(
let={
"_n": Const(2),
"n": CountOverSet(set=SolutionsSet(var=Var("n1"), condition=And(Geq(Var("n1"), Ref("_n")), Leq(Var("n1"), Const(89)), IsPrime(Var("n1"))))),
"result": Fibonacci(arg=Ref(name='n')),
},
goal=Ref("result"),
)
] | NT | null | COMPUTE | sympy | COUNT_PRIMES | [
"COUNT_PRIMES"
] | 07c874 | sequence_fibonacci_compute_v1 | null | 3 | 0 | [
"COUNT_PRIMES"
] | 1 | 0.001 | 2026-02-08T18:22:30.438064Z | {
"verified": true,
"answer": 46368,
"timestamp": "2026-02-08T18:22:30.439391Z"
} | 446dc3 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 81,
"completion_tokens": 712
},
"timestamp": "2026-02-18T16:26:37.508Z",
"answer": 46368
},
{
... | 1 | [
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "COUNT_PRIMES",
"status": "ok"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
92217f | modular_sum_quadratic_residues_v1_865884756_1225 | Let $p$ be the largest prime number less than or equal to 459. Compute $\frac{p(p-1)}{4}$. | 52,098 | graphs = [
Graph(
let={
"_n": Const(4),
"p": MaxOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(2)), Leq(Var("n"), Const(459)), IsPrime(Var("n"))))),
"result": Div(Mul(Ref("p"), Sub(Ref("p"), Const(1))), Ref("_n")),
},
goal=Ref("re... | NT | null | SUM | sympy | MAX_PRIME_BELOW | [
"MAX_PRIME_BELOW"
] | dc3ad3 | modular_sum_quadratic_residues_v1 | null | 3 | 0 | [
"MAX_PRIME_BELOW"
] | 1 | 0.003 | 2026-02-08T15:50:49.251856Z | {
"verified": true,
"answer": 52098,
"timestamp": "2026-02-08T15:50:49.255223Z"
} | 5e6a1f | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 74,
"completion_tokens": 822
},
"timestamp": "2026-02-16T14:17:09.364Z",
"answer": 52098
},
{
... | 1 | [
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok"
},
{
"lemma": "V8_SUM",
"st... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
59be4f | comb_factorial_compute_v1_1218484723_3424 | Let $n$ be the number of ordered pairs $(a, b)$ of positive integers with $1 \le a, b \le 25$ such that $64a^3 + 108ab^2 + 144a^2b + 27b^3 = 857375$. Compute $n!$. | 5,040 | graphs = [
Graph(
let={
"_n": Const(2),
"n": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("a"), Var("b")]), condition=And(Geq(Var("a"), Const(1)), Leq(Var("a"), Const(25)), Geq(Var("b"), Const(1)), Leq(Var("b"), Const(25)), Eq(Sum(Mul(Const(108), Var("a"), Pow(Var("b"), Ref(... | COMB | null | COMPUTE | sympy | POLY3_COUNT | [
"POLY3_COUNT"
] | 355dbe | comb_factorial_compute_v1 | null | 4 | 0 | [
"POLY3_COUNT"
] | 1 | 0.002 | 2026-02-25T05:07:55.116829Z | {
"verified": true,
"answer": 5040,
"timestamp": "2026-02-25T05:07:55.118513Z"
} | b77b98 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 177,
"completion_tokens": 1194
},
"timestamp": "2026-03-29T10:09:40.881Z",
"answer": 5040
},
{
"i... | 1 | [
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "POLY3_COUNT",
"status": "ok"
},
{
"lemma": "V8",
"status": "no"
},
{
"lemma": "V8_SUM",
... | {
"lo": -2.45,
"mid": 1.37,
"hi": 5.29
} | ||
fb1947 | nt_count_digit_sum_v1_151522320_1385 | Let $S$ be the set of integers $t$ such that $9 \leq t \leq 41$ and there exist positive integers $a$ and $b$ with $1 \leq a \leq 3$, $1 \leq b \leq 10$, and $t = 7a + 2b$. Let $\sigma = \sum_{d \mid |S|} \phi(d)$. Find the number of positive integers $n \leq 48841$ such that the sum of the digits of $n$ is equal to $\... | 1,659 | graphs = [
Graph(
let={
"upper": Const(48841),
"target_sum": SumOverDivisors(n=CountOverSet(set=SolutionsSet(var=Var(name='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'),... | NT | null | COUNT | sympy | LIN_FORM | [
"LIN_FORM/K3"
] | c7df50 | nt_count_digit_sum_v1 | null | 6 | 0 | [
"K3",
"LIN_FORM"
] | 2 | 1.769 | 2026-02-08T03:58:18.321400Z | {
"verified": true,
"answer": 1659,
"timestamp": "2026-02-08T03:58:20.090253Z"
} | 10dcc2 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 236,
"completion_tokens": 7472
},
"timestamp": "2026-02-10T14:51:35.671Z",
"answer": 1659
},
{
"... | 1 | [
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "K3",
"status": "ok_later"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
... | {
"lo": -3.42,
"mid": 1.86,
"hi": 7.55
} | ||
f49759 | geo_count_lattice_triangle_v1_124444284_1356 | Let $A$ be twice the area of the triangle with vertices at $(0,0)$, $(128,3)$, and $(60,121)$. Let $B$ be the number of lattice points on the boundary of this triangle, computed using the formula $B = \gcd(128,3) + \gcd(60-128,121-3) + \gcd(0-60,0-121)$. The number of interior lattice points is given by $I = \frac{A - ... | 1,458 | graphs = [
Graph(
let={
"area_2x": Abs(arg=Sum(Mul(Const(value=128), Const(value=121)), Mul(Const(value=60), Sub(left=Const(value=0), right=Const(value=3))))),
"boundary": Sum(GCD(a=Abs(arg=Const(value=128)), b=Abs(arg=Const(value=3))), GCD(a=Abs(arg=Sub(left=Const(value=60), right=C... | NT | null | COUNT | sympy | [] | geo_count_lattice_triangle_v1 | null | 6 | 0 | null | null | 0.004 | 2026-02-08T03:50:44.589239Z | {
"verified": true,
"answer": 1458,
"timestamp": "2026-02-08T03:50:44.593009Z"
} | c635d9 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 253,
"completion_tokens": 2298
},
"timestamp": "2026-02-10T06:39:38.475Z",
"answer": 1458
},
{
"i... | 1 | [] | {
"lo": -6.5,
"mid": -0.2,
"hi": 6.11
} | ||||
8a1ad0 | nt_count_squarefree_v1_1742523217_97 | Let $\phi(n)$ denote Euler's totient function and $\mu(n)$ denote the M\"obius function. Let $S$ be the set of all integers $n$ such that $1 \leq n \leq 59536$ and $\mu(n)^2 = 1$. Compute the number of elements in $S$. | 36,192 | graphs = [
Graph(
let={
"upper": Const(59536),
"result": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), EulerPhi(n=Const(1))), Leq(Var("n"), Ref("upper")), Eq(Mul(MoebiusMu(n=Var(name='n')), MoebiusMu(n=Var(name='n'))), Const(1))))),
},
goal=R... | NT | null | COUNT | sympy | ONE_PHI_1 | [
"ONE_PHI_1"
] | f6b5a5 | nt_count_squarefree_v1 | null | 4 | 0 | [
"ONE_PHI_1"
] | 1 | 7.689 | 2026-02-08T02:52:46.967397Z | {
"verified": true,
"answer": 36192,
"timestamp": "2026-02-08T02:52:54.656570Z"
} | db3506 | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 170,
"completion_tokens": 636
},
"timestamp": "2026-02-17T15:07:10.189Z",
"answer": 14280
}
] | 0 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "ONE_PHI_1",
"status"... | {
"lo": -6.48,
"mid": 1.54,
"hi": 9.56
} | ||
8a51e8 | comb_sum_binomial_row_v1_1742523217_1038 | Define $n_1 = 0$ and $n_2 = 0$. Let
$$
s = \sum_{k=0}^{n_1} (-1)^k \binom{n_1}{k}
\quad\text{and}\quad
t = \sum_{k=0}^{n_2} (-1)^k \binom{n_2}{k}.
$$
Let $n = 11 \cdot t \cdot s$, and let $\text{result} = 2^n$. Let $S$ be the set of all ordered pairs $(x_1, x_2)$ of positive odd integers such that $x_1 + x_2 = 12346$. ... | 8,984 | graphs = [
Graph(
let={
"_n": Const(11),
"n2": Const(0),
"t": Summation(var="k", start=Const(0), end=Ref("n2"), expr=Mul(Pow(Const(-1), Var("k")), Binom(n=Ref("n2"), k=Var("k")))),
"n1": Const(0),
"s": Summation(var="k", start=Const(0), end=Ref("n1... | COMB | null | SUM | sympy | COMB1 | [
"COMB1",
"BINOMIAL_ALTERNATING"
] | 15edbc | comb_sum_binomial_row_v1 | affine_mod | 3 | 2 | [
"BINOMIAL_ALTERNATING",
"COMB1"
] | 2 | 0.002 | 2026-02-08T03:23:49.182157Z | {
"verified": true,
"answer": 8984,
"timestamp": "2026-02-08T03:23:49.183846Z"
} | 09fcd7 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 287,
"completion_tokens": 733
},
"timestamp": "2026-02-10T02:21:17.648Z",
"answer": 8984
},
{
"id... | 1 | [
{
"lemma": "BINOMIAL_ALTERNATING",
"status": "ok"
},
{
"lemma": "COMB1",
"status": "ok"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8",
"stat... | {
"lo": -2.46,
"mid": 0.47,
"hi": 3.59
} | ||
2d51f3 | comb_sum_binomial_mod_v1_601307018_8709 | Let $S = \min\{ 45a \cdot b^2 + 135a^2 \cdot b + 35b^3 : a, b \in \mathbb{Z}^+,\, 1 \leq a \leq 23,\, 1 \leq b \leq 23 \}$. Compute $\sum_{k=0}^{208} \binom{S}{k}$, let $M$ be this sum modulo $10631$, and find the remainder when $44121M$ is divided by $61942$. | 43,950 | graphs = [
Graph(
let={
"_n": Const(35),
"sum": Summation(var="k", start=Const(0), end=Const(208), expr=Binom(n=MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("a"), Var("b")]), condition=And(Geq(Var("a"), Const(1)), Leq(Var("a"), Const(23)), Geq(Var("b"), Const(1)... | COMB | null | COMPUTE | sympy | POLY3_MIN | [
"POLY3_MIN"
] | e2e279 | comb_sum_binomial_mod_v1 | null | 5 | 0 | [
"POLY3_MIN"
] | 1 | 0.021 | 2026-03-10T09:10:36.085237Z | {
"verified": true,
"answer": 43950,
"timestamp": "2026-03-10T09:10:36.106421Z"
} | df0e7e | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 233,
"completion_tokens": 5115
},
"timestamp": "2026-04-19T09:36:58.063Z",
"answer": 43950
},
{
... | 1 | [
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "POLY3_MIN",
"status": "ok"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8",
"s... | {
"lo": -5.34,
"mid": 1.1,
"hi": 7.53
} | ||
6b3815 | antilemma_sum_factor_cartesian_v1_798873815_293 | Let $x$ be the sum of $i \cdot j$ over all ordered pairs $(i, j)$ where $1 \leq i \leq 10$ and $1 \leq j \leq 5$. Compute the multiplicative order of $2$ modulo $2|x| + 3$. | 252 | graphs = [
Graph(
let={
"x": SumOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("i"), Var("j")]), condition=Const(1), domain=CartesianProduct(left=IntegerRange(start=Const(1), end=Const(10)), right=IntegerRange(start=Const(1), end=Const(5)))), expr=Mul(Var("i"), Var("j")))),
... | NT | null | COMPUTE | sympy | SUM_FACTOR_CARTESIAN | [
"SUM_FACTOR_CARTESIAN"
] | d9e436 | antilemma_sum_factor_cartesian_v1 | null | 4 | 0 | [
"SUM_FACTOR_CARTESIAN"
] | 1 | 0.001 | 2026-02-08T02:32:35.870446Z | {
"verified": true,
"answer": 252,
"timestamp": "2026-02-08T02:32:35.871898Z"
} | 570bee | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 183,
"completion_tokens": 1671
},
"timestamp": "2026-02-08T19:19:54.001Z",
"answer": 252
},
{
"id... | 1 | [
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "SUM_FACTOR_CARTESIAN",
"status": "ok"
},
{
"lemma": "V8_SUM",
... | {
"lo": -4.84,
"mid": -1.65,
"hi": 1.89
} | ||
5fc4a8 | algebra_poly_eval_v1_1520064083_8265 | Let $m = 2$ and $n = 3$. Let $d_{\min}$ be the smallest integer $d \geq 2$ that divides $525$. Define
$$
n = \sum_{k=1}^{3} \phi(k) \left\lfloor \frac{d_{\min}}{k} \right\rfloor,
$$
where $\phi$ denotes Euler's totient function. Compute the value of
$$
n^4 - 2n^3 - 2n^2 - 8n - 10.
$$ | 734 | graphs = [
Graph(
let={
"_m": Const(2),
"_n": Const(3),
"n": Summation(var="k", start=Const(1), end=Const(3), expr=Mul(EulerPhi(n=Var("k")), Floor(Div(MinOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Const(2)), Divides(divisor=Var("d"), dividend=Const... | NT | null | COMPUTE | sympy | MIN_PRIME_FACTOR | [
"MIN_PRIME_FACTOR/K2"
] | 352a97 | algebra_poly_eval_v1 | null | 5 | 0 | [
"K2",
"MIN_PRIME_FACTOR"
] | 2 | 0.003 | 2026-02-08T10:06:38.410443Z | {
"verified": true,
"answer": 734,
"timestamp": "2026-02-08T10:06:38.413345Z"
} | 1dedea | 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": 805
},
"timestamp": "2026-02-14T06:26:42.955Z",
"answer": 734
},
{
... | 1 | [
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K2",
"status": "ok_later"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MIN_PRIME_FACTOR",
"status": "ok"
},
{... | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
02377e | sequence_fibonacci_compute_v1_124444284_7614 | Let $n$ be the number of integers $t$ with $10 \leq t \leq 36$ such that there exist positive integers $a$ and $b$ with $1 \leq a \leq 9$, $1 \leq b \leq 3$, and $t = 2a + 5b + 3$. Compute the remainder when $44121$ times the $n$-th Fibonacci number is divided by $52273$. | 48,446 | graphs = [
Graph(
let={
"_n": Const(52273),
"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=9)), Geq(left=Va... | NT | null | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | sequence_fibonacci_compute_v1 | null | 3 | 0 | [
"LIN_FORM"
] | 1 | 0.001 | 2026-02-08T09:13:35.635548Z | {
"verified": true,
"answer": 48446,
"timestamp": "2026-02-08T09:13:35.636551Z"
} | 4b4ceb | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 142,
"completion_tokens": 2579
},
"timestamp": "2026-02-14T01:58:27.506Z",
"answer": 48446
},
... | 1 | [
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
}
] | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
d5ba34 | algebra_poly_eval_v1_798873815_461 | Let $y = 7$. Let $P$ be the set of all ordered pairs of positive integers $(x, y)$ such that $x + y = 6$. Let $M$ be the maximum value of $xy$ as $(x, y)$ ranges over $P$. Compute the value of $3y^4 + 7y^3 + M y^2 + 8y + 7$, and then compute the remainder when $44121$ times this value is divided by $65603$. | 5,874 | graphs = [
Graph(
let={
"_n": Const(2),
"y": Const(7),
"result": Sum(Mul(Const(3), Pow(Ref("y"), Const(4))), Mul(Const(7), Pow(Ref("y"), Const(3))), Mul(MaxOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(n... | NT | null | COMPUTE | sympy | B1 | [
"B1"
] | 5b950e | algebra_poly_eval_v1 | null | 3 | 0 | [
"B1"
] | 1 | 0.003 | 2026-02-08T02:39:10.822211Z | {
"verified": true,
"answer": 5874,
"timestamp": "2026-02-08T02:39:10.824820Z"
} | 554412 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 221,
"completion_tokens": 1640
},
"timestamp": "2026-02-08T19:34:53.459Z",
"answer": 5874
},
{
"i... | 1 | [
{
"lemma": "B1",
"status": "ok"
},
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
}
] | {
"lo": -0.24,
"mid": 1.63,
"hi": 3.25
} | ||
f4fbb8 | algebra_quadratic_discriminant_v1_2051736721_5758 | Let $a = -2$, $b = -16$, $c = -30$, and $n = 4$. Let $E$ be the set of all positive integers $n'$ such that $1 \leq n' \leq 2$ and $n'$ is even. Let $s = \sum_{n' \in E} n'$. Compute the value of $b^s - n \cdot a \cdot c$. | 16 | graphs = [
Graph(
let={
"_n": Const(4),
"a": Const(-2),
"b": Const(-16),
"c": Const(-30),
"result": Sub(Pow(Ref("b"), SumOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Const(2)), Eq(Mod(value=Var("n"), m... | NT | null | COMPUTE | sympy | MIN_PRIME_FACTOR | [
"SUM_DIVISIBLE"
] | 02dbe3 | algebra_quadratic_discriminant_v1 | null | 2 | 0 | [
"MIN_PRIME_FACTOR",
"SUM_DIVISIBLE"
] | 2 | 0.023 | 2026-02-08T18:47:26.752778Z | {
"verified": true,
"answer": 16,
"timestamp": "2026-02-08T18:47:26.776043Z"
} | 418c77 | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 151,
"completion_tokens": 200
},
"timestamp": "2026-02-16T16:06:54.666Z",
"answer": 16
},
{
"id": 11,
... | 2 | [
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "SUM_DIVISIBLE",
"status": "ok"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
}
] | {
"lo": -10,
"mid": -7.27,
"hi": -4.54
} | ||
227523 | comb_count_surjections_v1_1439011603_321 | Let $n = 5$ and $k = 3$. Define $r = k! \cdot S(n, k)$, where $S(n, k)$ denotes the Stirling number of the second kind. Let $A$ be the set of all ordered pairs $(x_1, x_2)$ of positive odd integers such that $x_1 + x_2 = 24$. Let $s = |A|$. Compute
$$
\sum_{m=0}^{|r|} \tau(m),
$$
where $\tau(m)$ denotes the number of p... | 780 | graphs = [
Graph(
let={
"n": Const(5),
"k": Const(3),
"result": Mul(Factorial(Ref("k")), Stirling2(n=Ref(name='n'), k=Ref(name='k'))),
"Q": Summation(var="n1", start=Binom(n=CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x1"), Var("x2")]), condition=An... | COMB | NT | COUNT | sympy | COMB1 | [
"COMB1/ONE_BINOM_0"
] | efbf9f | comb_count_surjections_v1 | sum_divisor_count | 6 | 0 | [
"COMB1",
"ONE_BINOM_0"
] | 2 | 0.005 | 2026-02-08T15:25:01.132243Z | {
"verified": true,
"answer": 780,
"timestamp": "2026-02-08T15:25:01.137645Z"
} | bd7060 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 246,
"completion_tokens": 6082
},
"timestamp": "2026-02-24T20:46:33.704Z",
"answer": 780
},
{
"id... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COMB1",
"status": "ok"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "ONE_BINOM_0",
"status": "ok_later"
},
{
"lemma": "V8",
"status"... | {
"lo": -2.43,
"mid": 1.2,
"hi": 4.84
} | ||
d1230b | diophantine_product_count_v1_1918700295_1563 | Let $S$ be the set of all ordered pairs $(i, j)$ of positive integers such that $1 \leq i \leq 119$, $1 \leq j \leq 127$, and $\gcd(i, j) = 1$. Let $n$ be the number of elements in $S$. Let $d_{\text{max}}$ be the largest positive divisor $d$ of $n$ such that $1 \leq d \leq 92$. Let $T$ be the set of all positive integ... | 16 | graphs = [
Graph(
let={
"_m": Const(92),
"_n": 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(119)), right=IntegerRange(start=Const(1), en... | NT | null | COUNT | sympy | VIETA_SUM | [
"COUNT_COPRIME_GRID/MAX_DIVISOR"
] | 1b194f | diophantine_product_count_v1 | null | 7 | 0 | [
"COUNT_COPRIME_GRID",
"MAX_DIVISOR",
"VIETA_SUM"
] | 3 | 0.104 | 2026-02-08T05:53:14.108973Z | {
"verified": true,
"answer": 16,
"timestamp": "2026-02-08T05:53:14.212670Z"
} | 04f651 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 207,
"completion_tokens": 6172
},
"timestamp": "2026-02-12T15:51:54.729Z",
"answer": 16
},
{
... | 1 | [
{
"lemma": "COUNT_COPRIME_GRID",
"status": "ok"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "MAX_DIVISOR",
"status": "ok_later"
},
{
"lemma": "MOD_FACTORIAL",... | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
9599fa | geo_count_lattice_triangle_v1_1918700295_1065 | Let $A$ be the area of the triangle with vertices at $(105, 144)$, $(225, 289)$, and $(0, 0)$, multiplied by $2$. Let $b$ be the number of lattice points on the boundary of this triangle, computed as the sum of the greatest common divisors of the absolute differences in coordinates along each edge. Let $I$ be the numbe... | 28,217 | graphs = [
Graph(
let={
"area_2x": Abs(arg=Sum(Mul(Const(value=105), Const(value=289)), Mul(Const(value=225), Sub(left=Const(value=0), right=Const(value=144))))),
"boundary": Sum(GCD(a=Abs(arg=Const(value=105)), b=Abs(arg=Const(value=144))), GCD(a=Abs(arg=Sub(left=Const(value=225), r... | ALG | NT | COUNT | sympy | [] | geo_count_lattice_triangle_v1 | null | 6 | 0 | null | null | 0.002 | 2026-02-08T05:32:31.481701Z | {
"verified": true,
"answer": 28217,
"timestamp": "2026-02-08T05:32:31.483844Z"
} | 4bf408 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 160,
"completion_tokens": 1684
},
"timestamp": "2026-02-12T10:12:28.149Z",
"answer": 28217
},
... | 1 | [] | {
"lo": -5.55,
"mid": -3.01,
"hi": 0.32
} | ||||
1a7a1c | algebra_poly_eval_v1_784195855_9481 | Let $x = 9$. Compute
$$
8 \cdot x^{\#\{p\, \mid\, p \text{ is a positive integer},\ \exists q : pq = 216,\ \gcd(p,q) = 1,\ p < q\}} + 8x + 2.
$$ | 722 | graphs = [
Graph(
let={
"x": Const(9),
"result": Sum(Mul(Const(8), Pow(Ref("x"), 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=216)), Eq(lef... | NT | null | COMPUTE | sympy | COPRIME_PAIRS | [
"COPRIME_PAIRS"
] | 2bb3aa | algebra_poly_eval_v1 | null | 4 | 0 | [
"COPRIME_PAIRS"
] | 1 | 0.001 | 2026-02-08T16:50:55.071284Z | {
"verified": true,
"answer": 722,
"timestamp": "2026-02-08T16:50:55.072702Z"
} | bcaf6c | 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": 979
},
"timestamp": "2026-02-17T13:44:55.000Z",
"answer": 722
},
{
... | 1 | [
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "V3",
"status": "no"
... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
2b579b | antilemma_sum_equals_v1_655260480_5570 | Let $m = 128$. Let $n$ be the number of ordered pairs $(x_1, x_2)$ of positive odd integers such that $x_1 + x_2 = m$. Compute the number of ordered pairs $(i, j)$ with $1 \leq i \leq 62$ and $1 \leq j \leq 63$ such that $i + j = n$. | 62 | graphs = [
Graph(
let={
"_m": Const(128),
"_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")), ... | COMB | GEOM | COMPUTE | sympy | COMB1 | [
"COMB1/COUNT_SUM_EQUALS",
"COUNT_SUM_EQUALS"
] | 3e1adf | antilemma_sum_equals_v1 | null | 4 | 0 | [
"COMB1",
"COUNT_SUM_EQUALS"
] | 2 | 0.019 | 2026-02-08T18:33:56.569866Z | {
"verified": true,
"answer": 62,
"timestamp": "2026-02-08T18:33:56.588875Z"
} | d7e926 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 132,
"completion_tokens": 1609
},
"timestamp": "2026-02-18T17:52:34.772Z",
"answer": 62
},
{
... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COMB1",
"status": "ok"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "ok"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
},
{... | {
"lo": -5.39,
"mid": -2.64,
"hi": 0.63
} | ||
3904b1 | sequence_lucas_compute_v1_784195855_1582 | Let $n = \sum_{k=1}^{6} k$. Define $L_n$ to be the $n$-th Lucas number, where $L_1 = 1$, $L_2 = 3$, and $L_k = L_{k-1} + L_{k-2}$ for $k \geq 3$. Compute the remainder when $20927 \cdot L_n$ is divided by $57780$. | 47,332 | graphs = [
Graph(
let={
"_n": Const(57780),
"n": Summation(var="k", start=Const(1), end=Const(6), expr=Var("k")),
"result": Lucas(arg=Ref(name='n')),
"Q": Mod(value=Mul(Const(20927), Ref("result")), modulus=Ref("_n")),
},
goal=Ref("Q"),
)
] | NT | null | COMPUTE | sympy | SUM_ARITHMETIC | [
"SUM_ARITHMETIC"
] | eb34f0 | sequence_lucas_compute_v1 | null | 3 | 0 | [
"SUM_ARITHMETIC"
] | 1 | 0.001 | 2026-02-08T05:09:04.517669Z | {
"verified": true,
"answer": 47332,
"timestamp": "2026-02-08T05:09:04.518432Z"
} | 579cdb | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 205,
"completion_tokens": 1790
},
"timestamp": "2026-02-11T22:57:30.079Z",
"answer": 47332
},
{
... | 1 | [
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "SUM_ARITHMETIC",
"status": "ok"
},
{
"lemma": "V8",
"status": "no"
},
{
"lemma": "VAL_SUM_EQ",
"status": "no"
}
] | {
"lo": -3.42,
"mid": 1.86,
"hi": 7.55
} | ||
76229d | diophantine_product_count_v1_677425708_788 | Let $m = 15$ and $c = 4$. Define $n$ to be the minimum value of $x + y$ over all ordered pairs $(x, y)$ of positive integers such that $xy = 139129$. Let $k$ be the number of positive integers $n \leq 7560$ such that $c$ divides the $n$th Fibonacci number. Define $\text{upper}$ to be the number of positive integers $n ... | 30 | graphs = [
Graph(
let={
"_c": Const(4),
"_m": Const(15),
"_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(139129)))), ex... | NT | null | COUNT | sympy | SUM_DIVISIBLE | [
"COUNT_FIB_DIVISIBLE",
"B3/C4"
] | 24faa0 | diophantine_product_count_v1 | null | 7 | 0 | [
"B3",
"C4",
"COUNT_FIB_DIVISIBLE",
"SUM_DIVISIBLE"
] | 4 | 5.89 | 2026-02-08T03:43:53.567573Z | {
"verified": true,
"answer": 30,
"timestamp": "2026-02-08T03:43:59.457828Z"
} | cd9aa8 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 275,
"completion_tokens": 2386
},
"timestamp": "2026-02-10T14:25:45.888Z",
"answer": 30
},
{
"id... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "C4",
"status": "ok_later"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "ok"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
... | {
"lo": -3.42,
"mid": 1.86,
"hi": 7.55
} | ||
faf049 | nt_count_coprime_v1_971394319_459 | Let $k$ be the largest positive integer such that $3^k \leq 10454485$. Determine the number of positive integers $n$ with $1 \leq n \leq 76636$ such that $\gcd(n, k) = 1$. | 32,844 | graphs = [
Graph(
let={
"_n": Const(3),
"upper": Const(76636),
"k": MaxOverSet(set=SolutionsSet(var=Var("k"), condition=Leq(Pow(Ref("_n"), Var("k")), Const(10454485)))),
"result": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)... | NT | null | COUNT | sympy | MAX_VAL | [
"MAX_VAL"
] | 1da621 | nt_count_coprime_v1 | null | 4 | 0 | [
"MAX_VAL"
] | 1 | 6.847 | 2026-02-08T13:06:35.366569Z | {
"verified": true,
"answer": 32844,
"timestamp": "2026-02-08T13:06:42.213958Z"
} | 500e89 | 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": 2402
},
"timestamp": "2026-02-15T09:44:09.168Z",
"answer": 32844
},
... | 1 | [
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "K16",
"status": "same_pattern_wrong"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": ... | {
"lo": -5.49,
"mid": 0.22,
"hi": 6.51
} | ||
e3ed40 | modular_min_linear_v1_1978505735_4859 | Let $a$ be the number of integers $t$ with $9 \leq t \leq 172$ for which there exist positive integers $a'$ and $b'$ such that $1 \leq a' \leq 51$, $1 \leq b' \leq 10$, and $t = 2a' + 7b'$.
Let $m = 58311$ and $b = 39780$. Determine the value of $x$, where $x$ is the smallest positive integer satisfying $1 \leq x \leq... | 1,728 | graphs = [
Graph(
let={
"a": CountOverSet(set=SolutionsSet(var=Var("t"), condition=Exists(var=Var(name='a'), condition=Exists(var=Var(name='b'), condition=And(Geq(left=Var(name='a'), right=Const(value=1)), Leq(left=Var(name='a'), right=Const(value=51)), Geq(left=Var(name='b'), right=Const(value=... | NT | null | EXTREMUM | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | modular_min_linear_v1 | null | 6 | 0 | [
"LIN_FORM"
] | 1 | 5.5 | 2026-02-08T18:36:09.167011Z | {
"verified": true,
"answer": 1728,
"timestamp": "2026-02-08T18:36:14.667489Z"
} | 0f9a50 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 178,
"completion_tokens": 6313
},
"timestamp": "2026-02-18T18:02:38.981Z",
"answer": 1728
},
{... | 1 | [
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
7f12b2 | comb_count_surjections_v1_48377204_1847 | Let $n$ be the number of ordered pairs $(x_1, x_2)$ of positive odd integers such that $x_1 + x_2 = 16$. Let $k$ be the number of ordered pairs $(i, j)$ of integers with $1 \le i \le 5$ and $1 \le j \le 5$ such that $i + j = 5$. Define $s = k! \cdot S(n, k)$, where $S(n, k)$ denotes the number of ways to partition a se... | 56,850 | graphs = [
Graph(
let={
"_m": Const(71879),
"_n": Const(5),
"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')), E... | COMB | null | COUNT | sympy | COUNT_SUM_EQUALS | [
"COUNT_SUM_EQUALS",
"COMB1"
] | 938829 | comb_count_surjections_v1 | null | 6 | 0 | [
"COMB1",
"COUNT_SUM_EQUALS"
] | 2 | 0.023 | 2026-02-08T16:27:12.997188Z | {
"verified": true,
"answer": 56850,
"timestamp": "2026-02-08T16:27:13.020153Z"
} | aaad6c | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 261,
"completion_tokens": 1516
},
"timestamp": "2026-02-24T21:10:48.380Z",
"answer": 56850
},
{
... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COMB1",
"status": "ok"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "ok"
},
{
"lemma": "V7",
"status":... | {
"lo": -2.4,
"mid": 1.57,
"hi": 5.75
} | ||
7b1a32 | comb_count_permutations_fixed_v1_2051736721_752 | Let $n$ be the largest prime number less than or equal to $10$. Compute the value of $\binom{n}{3} \cdot !(n-3)$, where $!k$ denotes the number of derangements of $k$ elements. | 315 | graphs = [
Graph(
let={
"_n": Const(10),
"n": MaxOverSet(set=SolutionsSet(var=Var("n1"), condition=And(Geq(Var("n1"), Const(2)), Leq(Var("n1"), Ref("_n")), IsPrime(Var("n1"))))),
"k": Const(3),
"result": Mul(Binom(n=Ref("n"), k=Ref("k")), Subfactorial(arg=Sub(... | NT | COMB | COUNT | sympy | MAX_PRIME_BELOW | [
"MAX_PRIME_BELOW"
] | dc3ad3 | comb_count_permutations_fixed_v1 | null | 4 | 0 | [
"MAX_PRIME_BELOW"
] | 1 | 0.003 | 2026-02-08T15:39:15.428480Z | {
"verified": true,
"answer": 315,
"timestamp": "2026-02-08T15:39:15.431597Z"
} | cfb5a2 | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 110,
"completion_tokens": 466
},
"timestamp": "2026-02-16T06:14:35.890Z",
"answer": 315
},
{
"id": 11,
... | 2 | [
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok"
},
{
"lemma": "V1",
"status": "no"
}
] | {
"lo": -10,
"mid": -7.27,
"hi": -4.54
} | ||
2a7521 | diophantine_fbi2_count_v1_1520064083_3609 | Let $k$ be the sum of all real solutions to the equation $x^2 - 1260x + 69716 = 0$. Let $\text{result}$ be the number of integers $d$ with $3 \leq d \leq 91$ such that $d$ divides $k$, and $\frac{k}{d}$ is an integer satisfying $5 \leq \frac{k}{d} \leq 93$. Let $Q$ be the remainder when $74853 \cdot \text{result}$ is d... | 42,186 | graphs = [
Graph(
let={
"_n": Const(55022),
"k": SumOverSet(set=SolutionsSet(var=Var("x"), condition=Eq(Sum(Pow(Var("x"), Const(2)), Mul(Const(-1260), Var("x")), Const(69716)), Const(0)))),
"result": CountOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), ... | NT | null | COUNT | sympy | VIETA_SUM | [
"VIETA_SUM",
"C4"
] | de2b6f | diophantine_fbi2_count_v1 | null | 6 | 0 | [
"C4",
"VIETA_SUM"
] | 2 | 0.009 | 2026-02-08T05:46:49.605118Z | {
"verified": true,
"answer": 42186,
"timestamp": "2026-02-08T05:46:49.614133Z"
} | 48f2b8 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 170,
"completion_tokens": 1321
},
"timestamp": "2026-02-12T13:50:51.680Z",
"answer": 42186
},
... | 1 | [
{
"lemma": "C4",
"status": "ok"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "VAL_SUM_EQ",
"status": "no"... | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
6e3bab | antilemma_k2_v1_1978505735_1948 | Let $m = 75855$ and $n = 236$. Define $$ x = \sum_{k=1}^{236} \phi(k) \left\lfloor \frac{1}{k} \sum_{d \mid 236} \phi(d) \right\rfloor. $$ Compute $m - x$. | 47,889 | graphs = [
Graph(
let={
"_m": Const(75855),
"_n": Const(236),
"x": Summation(var="k", start=Const(1), end=Ref("_n"), expr=Mul(EulerPhi(n=Var("k")), Floor(Div(SumOverDivisors(n=Const(value=236), var='d', expr=EulerPhi(n=Var(name='d'))), Var("k"))))),
"Q": Sub(R... | NT | COMB | COMPUTE | sympy | K3 | [
"K3/K2",
"K2"
] | c7f244 | antilemma_k2_v1 | null | 5 | 0 | [
"K2",
"K3"
] | 2 | 0.002 | 2026-02-08T16:34:26.337076Z | {
"verified": true,
"answer": 47889,
"timestamp": "2026-02-08T16:34:26.339226Z"
} | 8011a1 | 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": 1026
},
"timestamp": "2026-02-17T07:11:52.481Z",
"answer": 47889
},
... | 1 | [
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "K2",
"status": "ok"
},
{
"lemma": "K3",
"status": "ok"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "V8_SUM",
... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
59c146 | diophantine_fbi2_min_v1_1520064083_9774 | Let $k = 21$. Let $u$ be the largest prime number $n$ such that $2 \le n \le 31$. Find the smallest integer $d \ge 2$ such that $d$ divides $k$ and $\frac{k}{d} \ge 3$. Compute the value of this integer $d$. | 3 | graphs = [
Graph(
let={
"_n": Const(2),
"k": Const(21),
"upper": MaxOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Ref("_n")), Leq(Var("n"), Const(31)), IsPrime(Var("n"))))),
"result": MinOverSet(set=SolutionsSet(var=Var("d"), condition=And... | NT | null | EXTREMUM | sympy | LIN_FORM | [
"MAX_PRIME_BELOW"
] | dc3ad3 | diophantine_fbi2_min_v1 | null | 3 | 0 | [
"LIN_FORM",
"MAX_PRIME_BELOW"
] | 2 | 0.031 | 2026-02-08T11:00:16.871491Z | {
"verified": true,
"answer": 3,
"timestamp": "2026-02-08T11:00:16.902655Z"
} | 0884e4 | 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": 579
},
"timestamp": "2026-02-14T09:52:50.477Z",
"answer": 3
},
{
... | 1 | [
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "V1",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
},
{
"lemma": "VAL_SUM_EQ",
"status": "no"
}
] | {
"lo": -9.12,
"mid": -6.02,
"hi": -3.62
} | ||
5e5d3f | lin_form_endings_v1_1978505735_5105 | Let $a = 35$ and $b = 14$. Define $k = 6717$ and let $M = 92291$. Compute the remainder when $k \cdot \left\lfloor \frac{a}{\gcd(a, b)} \right\rfloor$ is divided by $M$. | 33,585 | graphs = [
Graph(
let={
"a_coeff": Const(35),
"b_coeff": Const(14),
"_inner_result": Floor(Div(Const(35), GCD(a=Ref("a_coeff"), b=Ref("b_coeff")))),
"_scale_k": Const(6717),
"_scaled": Mul(Ref("_scale_k"), Ref("_inner_result")),
"_mod_M... | COMB | NT | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | lin_form_endings_v1 | null | 2 | null | [
"LIN_FORM"
] | 1 | 0.001 | 2026-02-08T18:46:18.091971Z | {
"verified": true,
"answer": 33585,
"timestamp": "2026-02-08T18:46:18.092519Z"
} | 244fed | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 130,
"completion_tokens": 216
},
"timestamp": "2026-02-16T15:35:00.609Z",
"answer": 33585
},
{
"id": 11,
... | 2 | [
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
... | {
"lo": -10,
"mid": -7.27,
"hi": -4.54
} | ||
cbefac | antilemma_sum_equals_v1_124444284_8347 | Let $m = 76138$. Let $n$ be the number of integers $t$ such that $18 \leq t \leq 31$ and there exist integers $a$ and $b$ satisfying $1 \leq a \leq 2$, $1 \leq b \leq 5$, and $t = 5a + 2b + 11$. Let $x$ be the number of ordered pairs $(i, j)$ of positive integers such that $1 \leq i \leq 9$, $1 \leq j \leq 10$, and $i ... | 16,399 | graphs = [
Graph(
let={
"_m": Const(76138),
"_n": CountOverSet(set=SolutionsSet(var=Var("t"), condition=Exists(var=Var(name='a'), condition=Exists(var=Var(name='b'), condition=And(Geq(left=Var(name='a'), right=Const(value=1)), Leq(left=Var(name='a'), right=Const(value=2)), Geq(left=V... | COMB | GEOM | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM/COUNT_SUM_EQUALS",
"COUNT_SUM_EQUALS"
] | ada383 | antilemma_sum_equals_v1 | null | 5 | 0 | [
"COUNT_SUM_EQUALS",
"LIN_FORM"
] | 2 | 0.011 | 2026-02-08T09:39:07.808740Z | {
"verified": true,
"answer": 16399,
"timestamp": "2026-02-08T09:39:07.819896Z"
} | 014d7d | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 262,
"completion_tokens": 894
},
"timestamp": "2026-02-24T11:39:03.819Z",
"answer": 16499
},
{
... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "ok"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "V7",
"st... | {
"lo": 1.15,
"mid": 4.18,
"hi": 6.61
} | ||
cb8a0e | sequence_count_fib_divisible_v1_1742523217_2906 | Let $a$ be the number of positive integers $n \le 21816$ such that $14$ divides the $n$-th Fibonacci number. Let $b$ be the number of positive integers $n \le a$ such that $15$ divides the $n$-th Fibonacci number. Compute the remainder when $1 - b$ is divided by $89509$. | 89,465 | graphs = [
Graph(
let={
"_n": Const(14),
"upper": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Const(21816)), Divides(divisor=Ref("_n"), dividend=Fibonacci(arg=Var(name='n')))))),
"d": Const(15),
"result": Co... | NT | null | COUNT | sympy | COUNT_FIB_DIVISIBLE | [
"COUNT_FIB_DIVISIBLE"
] | 66de3c | sequence_count_fib_divisible_v1 | null | 6 | 0 | [
"COUNT_FIB_DIVISIBLE"
] | 1 | 0.067 | 2026-02-08T05:27:28.532900Z | {
"verified": true,
"answer": 89465,
"timestamp": "2026-02-08T05:27:28.600096Z"
} | 6837a1 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 125,
"completion_tokens": 1534
},
"timestamp": "2026-02-12T09:02:32.423Z",
"answer": 89465
},
... | 1 | [
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "ok"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "V8",
... | {
"lo": -3.51,
"mid": 1.33,
"hi": 6.56
} | ||
a069fd | nt_min_with_divisor_count_v1_809748730_1815 | Let $S$ be the set of all ordered pairs $(x,y)$ of positive integers such that $xy = 16370116$. Let $T$ be the set of all values $x + y$ where $(x,y) \in S$. Let $M$ be the minimum value in $T$.
Let $A$ be the set of all positive integers $n$ such that $1 \leq n \leq M$ and $n \equiv \left\lfloor \frac{n}{2} \right\rf... | 48 | graphs = [
Graph(
let={
"upper": 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(Mu... | NT | null | EXTREMUM | sympy | ONE_PHI_1 | [
"B3/L3C"
] | 345f3b | nt_min_with_divisor_count_v1 | null | 6 | 0 | [
"B3",
"L3C",
"ONE_PHI_1"
] | 3 | 2.202 | 2026-02-08T12:42:13.954407Z | {
"verified": true,
"answer": 48,
"timestamp": "2026-02-08T12:42:16.156230Z"
} | 89cda0 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 227,
"completion_tokens": 2639
},
"timestamp": "2026-02-15T04:21:40.328Z",
"answer": 48
},
{
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "L3C",
"status": "ok_later"
},
{
"lemma": "V3",
"status": "no"
},
{
"le... | {
"lo": -6.96,
"mid": -4.56,
"hi": -1.46
} | ||
c4330e | antilemma_count_primes_v1_798873815_103 | Compute the number of prime numbers $n$ such that $2 \leq n \leq 1877$. | 288 | graphs = [
Graph(
let={
"x": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(2)), Leq(Var("n"), Const(1877)), IsPrime(Var("n"))))),
},
goal=Ref("x"),
)
] | NT | null | COMPUTE | sympy | COUNT_PRIMES | [
"COUNT_PRIMES"
] | 07c874 | antilemma_count_primes_v1 | null | 3 | 0 | [
"COUNT_PRIMES"
] | 1 | 0 | 2026-02-08T02:26:11.364273Z | {
"verified": true,
"answer": 288,
"timestamp": "2026-02-08T02:26:11.364618Z"
} | fdedce | CC BY 4.0 | [
{
"id": 4,
"model": "NousResearch/Hermes-4-405B",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 81,
"completion_tokens": 336
},
"timestamp": "2026-02-08T20:29:12.467Z",
"answer": 284
},
... | 0 | [
{
"lemma": "COUNT_PRIMES",
"status": "ok"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
}
] | {
"lo": 2.6,
"mid": 6.26,
"hi": 10
} | ||
b6048d | nt_count_gcd_equals_v1_1874849503_1602 | Let $U$ be the number of integers $t$ with $9 \leq t \leq 7589$ for which there exist positive integers $a \leq 686$ and $b \leq 969$ such that $t = 4a + 5b$. Let $d = 364$. Determine the value of $k$ such that $1 \leq k \leq U$ and $\gcd(k, 364) = 364$, and let $C$ be the number of such $k$. Compute the remainder when... | 78,236 | graphs = [
Graph(
let={
"upper": CountOverSet(set=SolutionsSet(var=Var("t"), condition=Exists(var=Var(name='a'), condition=Exists(var=Var(name='b'), condition=And(Geq(left=Var(name='a'), right=Const(value=1)), Leq(left=Var(name='a'), right=Const(value=686)), Geq(left=Var(name='b'), right=Const(v... | NT | null | COUNT | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | nt_count_gcd_equals_v1 | null | 4 | 0 | [
"LIN_FORM"
] | 1 | 0.816 | 2026-02-08T13:59:57.998734Z | {
"verified": true,
"answer": 78236,
"timestamp": "2026-02-08T13:59:58.814772Z"
} | f5934f | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 244,
"completion_tokens": 2003
},
"timestamp": "2026-02-10T05:42:35.438Z",
"answer": 78136
},
{
... | 1 | [
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
}
] | {
"lo": 1.69,
"mid": 5.03,
"hi": 8.38
} | ||
534a9a | algebra_poly_eval_v1_809748730_307 | Let $A$ be the set of all integers $n$ such that $1 \leq n \leq 2067$ and $n \equiv \left\lfloor \frac{n}{2} \right\rfloor \pmod{11}$. Let $m$ be the largest prime number satisfying $2 \leq m \leq 29$. Compute the value of $$\frac{35m^3 - 45m^2 - 73m - 16}{|A|}.$$. | 4,351 | graphs = [
Graph(
let={
"_m": Const(3),
"_n": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Const(2067)), Congruent(a=Var(name='n'), b=Floor(arg=Div(left=Var(name='n'), right=Const(value=2))), modulus=Const(value=11))))),
... | NT | null | COMPUTE | sympy | L3C | [
"L3C/MAX_PRIME_BELOW"
] | 8ff24e | algebra_poly_eval_v1 | null | 6 | 0 | [
"L3C",
"MAX_PRIME_BELOW"
] | 2 | 0.006 | 2026-02-08T11:26:52.333173Z | {
"verified": true,
"answer": 4351,
"timestamp": "2026-02-08T11:26:52.338725Z"
} | bc625a | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 149,
"completion_tokens": 1354
},
"timestamp": "2026-02-14T14:04:30.402Z",
"answer": 4351
},
{... | 1 | [
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "L3C",
"status": "ok"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok_later"
},
{
"lemma": "V3",
"status": "no"
},
{
"... | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
d2b736 | comb_sum_binomial_row_v1_1915831931_1138 | Let $P$ be the set of all positive integers $p$ such that there exists a positive integer $q$ with $pq = 216$, $\gcd(p, q) = 1$, and $p < q$. Let $L$ be the number of elements in $P$. Let $Q$ be the set of all prime numbers $n_1$ such that $L \leq n_1 \leq 6$. Let $M$ be the largest element of $Q$. Compute
\[
\sum_{k=1... | 32,768 | graphs = [
Graph(
let={
"_m": Const(5),
"_n": Const(2),
"n": Summation(var="k", start=Const(1), end=MaxOverSet(set=SolutionsSet(var=Var("n1"), condition=And(Geq(Var("n1"), CountOverSet(set=SolutionsSet(var=Var("p"), condition=And(IsPositive(arg=Var(name='p')), Exists(var=... | NT | null | SUM | sympy | COPRIME_PAIRS | [
"COPRIME_PAIRS/MAX_PRIME_BELOW/K2"
] | 02ea01 | comb_sum_binomial_row_v1 | null | 7 | 0 | [
"COPRIME_PAIRS",
"K2",
"MAX_PRIME_BELOW"
] | 3 | 0.003 | 2026-02-08T15:54:40.418174Z | {
"verified": true,
"answer": 32768,
"timestamp": "2026-02-08T15:54:40.421028Z"
} | e940f1 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 195,
"completion_tokens": 1180
},
"timestamp": "2026-02-16T16:34:23.172Z",
"answer": 32768
},
... | 1 | [
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "K2",
"status": "ok_later"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok_later"
},
{
"lemma... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
e521f2 | comb_count_surjections_v1_1439011603_2095 | Let $n$ be the number of ordered pairs $(x_1,x_2)$ of positive odd integers such that
$$x_1 + x_2 = 14.$$
Let $k = 4$, and define
$$R = k! \cdot S(n,k),$$
where $S(n,k)$ is the number of ways to partition an $n$-element set into $k$ nonempty unlabeled subsets.
Let $T$ be the number of integers $t$ such that $21 \le t ... | 877 | graphs = [
Graph(
let={
"n": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x1"), Var("x2")]), condition=And(IsPositive(arg=Var(name='x1')), IsPositive(arg=Var(name='x2')), IsOdd(arg=Var(name='x1')), IsOdd(arg=Var(name='x2')), Eq(Sum(Var("x1"), Var("x2")), Const(14))))),
"k":... | COMB | null | COUNT | sympy | LIN_FORM | [
"LIN_FORM/COUNT_SUM_EQUALS",
"COMB1"
] | 28ed6d | comb_count_surjections_v1 | bell_mod | 6 | 0 | [
"COMB1",
"COUNT_SUM_EQUALS",
"LIN_FORM"
] | 3 | 0.017 | 2026-02-08T16:30:18.832998Z | {
"verified": true,
"answer": 877,
"timestamp": "2026-02-08T16:30:18.850423Z"
} | 202dbc | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 312,
"completion_tokens": 1234
},
"timestamp": "2026-02-17T05:59:34.100Z",
"answer": 877
},
{
... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COMB1",
"status": "ok"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "ok_later"
},
{
"lemma": "LIN_FORM",
... | {
"lo": -2.38,
"mid": 1.74,
"hi": 6.59
} | ||
c6d799 | comb_count_partitions_v1_151522320_1602 | Let $n$ be the minimum value of $x + y$ over all ordered pairs $(x, y)$ of positive integers such that $xy = 484$. Let $p(n)$ denote the number of integer partitions of $n$. Compute the value of $$\sum_{i=0}^{d-1} d_i (i+1)^2 + 21904,$$ where $d$ is the number of decimal digits of $p(n)$ and $d_i$ is the $i$-th digit o... | 22,201 | graphs = [
Graph(
let={
"_n": Const(2),
"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(484)))), expr=Sum(Var("x"), Var("y")))),
... | COMB | null | COUNT | sympy | B3 | [
"B3"
] | 0cd20d | comb_count_partitions_v1 | null | 6 | 0 | [
"B3"
] | 1 | 0.002 | 2026-02-08T04:08:06.566868Z | {
"verified": true,
"answer": 22201,
"timestamp": "2026-02-08T04:08:06.569193Z"
} | 35d837 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 235,
"completion_tokens": 2326
},
"timestamp": "2026-02-23T23:38:20.845Z",
"answer": 22201
},
{
"... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
}
] | {
"lo": -2.46,
"mid": 0.47,
"hi": 3.59
} | ||
ee94ea | comb_count_permutations_fixed_v1_784195855_4448 | Let $m = 36928$. Define $s$ to be the number of positive integers $p$ for which there exists a positive integer $q$ such that $pq = 12$, $\gcd(p, q) = 1$, and $p < q$. Let $n$ be the number of nonnegative integers $j$ such that $0 \le j \le m$ and
$$
\binom{m}{j} \equiv 1 \pmod{s}.
$$
Compute the value of
$$
\binom{n}{... | 630 | graphs = [
Graph(
let={
"_m": Const(36928),
"_n": CountOverSet(set=SolutionsSet(var=Var("p"), condition=And(IsPositive(arg=Var(name='p')), Exists(var=Var(name='q'), condition=And(Eq(left=Mul(Var(name='p'), Var(name='q')), right=Const(value=12)), Eq(left=GCD(a=Var(name='p'), b=Var(nam... | NT | COMB | COUNT | sympy | COPRIME_PAIRS | [
"COPRIME_PAIRS/V8"
] | 93b9b8 | comb_count_permutations_fixed_v1 | null | 6 | 0 | [
"COPRIME_PAIRS",
"V8"
] | 2 | 0.004 | 2026-02-08T07:06:54.788874Z | {
"verified": true,
"answer": 630,
"timestamp": "2026-02-08T07:06:54.792585Z"
} | 37b1cd | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 186,
"completion_tokens": 2536
},
"timestamp": "2026-02-13T08:08:34.344Z",
"answer": 630
},
{
... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemm... | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
6723f4 | antilemma_k2_v1_1125832087_1130 | Let $m = 189$ and $n = 189$. Define
$$
x = \sum_{k=1}^{\sum_{d \mid m} \phi(d)} \phi(k) \left\lfloor \frac{n}{k} \right\rfloor.
$$
Let $c$ be the sum of all real solutions $x$ to the equation $x^2 - 800x - 23184 = 0$. Compute the remainder when $c - x$ is divided by $82884$. | 65,729 | graphs = [
Graph(
let={
"_m": Const(189),
"_n": Const(189),
"x": Summation(var="k", start=Const(1), end=SumOverDivisors(n=Ref(name='_m'), var='d', expr=EulerPhi(n=Var(name='d'))), expr=Mul(EulerPhi(n=Var("k")), Floor(Div(Ref("_n"), Var("k"))))),
"_c": SumOverS... | NT | COMB | COMPUTE | sympy | K13 | [
"VIETA_SUM",
"K3/K2",
"K2"
] | 9cedc8 | antilemma_k2_v1 | negation_mod | 5 | 0 | [
"K13",
"K2",
"K3",
"VIETA_SUM"
] | 4 | 0.004 | 2026-02-08T03:33:05.215639Z | {
"verified": true,
"answer": 65729,
"timestamp": "2026-02-08T03:33:05.219200Z"
} | 7b7fb3 | 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": 7619
},
"timestamp": "2026-02-10T14:54:03.405Z",
"answer": 65729
},
{
"... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "K2",
"status": "ok"
},
{
"lemma": "K3",
"status": "ok"
},
{
"lemma": "K5",
... | {
"lo": 1.71,
"mid": 5.04,
"hi": 8.38
} | ||
61ec45 | diophantine_fbi2_min_v1_784195855_9406 | Let $d$ be an integer satisfying $3 \leq d \leq 31$ such that $d$ divides $21$ and $\frac{21}{d} \geq 5$. Determine the value of the smallest such $d$. Let $Q$ be the remainder when $70502$ multiplied by this value is divided by $96301$. Compute $Q$. | 18,904 | graphs = [
Graph(
let={
"_n": Const(3),
"k": Const(21),
"upper": Const(31),
"result": MinOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Ref("_n")), Leq(Var("d"), Ref("upper")), Divides(divisor=Var("d"), dividend=Ref("k")), Geq(Div(Ref("k"),... | NT | null | EXTREMUM | sympy | COPRIME_PAIRS | [
"COPRIME_PAIRS"
] | 2bb3aa | diophantine_fbi2_min_v1 | null | 3 | 0 | [
"COPRIME_PAIRS"
] | 1 | 0.005 | 2026-02-08T16:47:30.870857Z | {
"verified": true,
"answer": 18904,
"timestamp": "2026-02-08T16:47:30.875705Z"
} | d1d800 | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 144,
"completion_tokens": 452
},
"timestamp": "2026-02-16T07:50:54.979Z",
"answer": 18994
},
{
"id": 11... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"... | {
"lo": -8.26,
"mid": -5.01,
"hi": -1.76
} | ||
3ef7fb | antilemma_k2_v1_2051736721_2485 | Let $c = 173$. Let $m = \sum_{d \mid c} \varphi(d)$, where $\varphi$ denotes Euler's totient function. Let $n = \sum_{d_1 \mid m} \varphi(d_1)$. Compute $\sum_{k=1}^{c} \varphi(k) \left\lfloor \frac{n}{k} \right\rfloor$. | 15,051 | graphs = [
Graph(
let={
"_c": Const(173),
"_m": SumOverDivisors(n=Const(value=173), var='d', expr=EulerPhi(n=Var(name='d'))),
"_n": SumOverDivisors(n=Ref(name='_m'), var='d1', expr=EulerPhi(n=Var(name='d1'))),
"x": Summation(var="k", start=Const(1), end=Ref("_... | NT | COMB | COMPUTE | sympy | K3 | [
"K3/K3/K2",
"K2"
] | d92398 | antilemma_k2_v1 | null | 5 | 0 | [
"K2",
"K3"
] | 2 | 0.001 | 2026-02-08T16:43:03.896196Z | {
"verified": true,
"answer": 15051,
"timestamp": "2026-02-08T16:43:03.897457Z"
} | 1cf12c | 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": 908
},
"timestamp": "2026-02-17T10:33:06.473Z",
"answer": 15051
},
{... | 1 | [
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "K2",
"status": "ok"
},
{
"lemma": "K3",
"status": "ok"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
edee8d | diophantine_sum_product_min_v1_809748730_1163 | Let $S = 30$ and $P = 225$. Let $x$ be the smallest positive integer such that $1 \leq x \leq 29$ and $x(S - x) = P$. Let $c$ be the number of integers $t$ in the range $18 \leq t \leq 160$ for which there exist positive integers $a$ and $b$ with $1 \leq a \leq 15$, $1 \leq b \leq 4$, and $t = 8a + 10b$. Compute $x^2 +... | 525 | graphs = [
Graph(
let={
"_n": Const(2),
"S": Const(30),
"P": Const(225),
"result": MinOverSet(set=SolutionsSet(var=Var("x"), condition=And(Geq(Var("x"), Const(1)), Leq(Var("x"), Const(29)), Eq(Mul(Var("x"), Sub(Ref("S"), Var("x"))), Ref("P"))))),
"... | NT | null | EXTREMUM | sympy | LIN_FORM | [
"LIN_FORM"
] | 2ba0ea | diophantine_sum_product_min_v1 | quadratic_mod | 4 | 0 | [
"LIN_FORM"
] | 1 | 0.009 | 2026-02-08T12:13:02.352909Z | {
"verified": true,
"answer": 525,
"timestamp": "2026-02-08T12:13:02.361924Z"
} | 7b39af | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 182,
"completion_tokens": 1282
},
"timestamp": "2026-02-14T22:50:17.517Z",
"answer": 525
},
{
... | 1 | [
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
... | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
b7cb05 | nt_count_coprime_and_v1_677425708_1842 | Let $k_1$ be the largest integer $k$ such that $2^k \leq 500$, and let $k_2$ be the largest integer $k$ such that $2^k \leq 62672$. Let $N$ be the number of positive integers $n$ such that $1 \leq n \leq 25391$, $\gcd(n, k_1) = 1$, and $\gcd(n, k_2) = 1$. Multiply $N$ by $35464$, and compute the remainder when the resu... | 25,457 | graphs = [
Graph(
let={
"_n": Const(2),
"upper": Const(25391),
"k1": MaxOverSet(set=SolutionsSet(var=Var("k"), condition=Leq(Pow(Const(2), Var("k")), Const(500)))),
"k2": MaxOverSet(set=SolutionsSet(var=Var("k"), condition=Leq(Pow(Ref("_n"), Var("k")), Const(6... | NT | null | COUNT | sympy | MAX_VAL | [
"MAX_VAL"
] | 1da621 | nt_count_coprime_and_v1 | null | 5 | 0 | [
"MAX_VAL"
] | 1 | 2.382 | 2026-02-08T04:29:23.935816Z | {
"verified": true,
"answer": 25457,
"timestamp": "2026-02-08T04:29:26.317670Z"
} | adcdf7 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 240,
"completion_tokens": 2063
},
"timestamp": "2026-02-10T01:48:58.650Z",
"answer": 25457
},
{
"... | 1 | [
{
"lemma": "K16",
"status": "same_pattern_wrong"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "ok"
},
{
"lemma": "V1",
"status": "no"... | {
"lo": -3.46,
"mid": 1.03,
"hi": 5.49
} | ||
6985e4 | sequence_fibonacci_compute_v1_397696148_1066 | Let $ n $ be the number of elements in the Cartesian product of the sets $ \{1, 2, 3, 4\} $ and $ \{1, 2, 3, 4, 5\} $. Let $ F_n $ denote the $ n $-th Fibonacci number, where $ F_1 = 1 $, $ F_2 = 1 $, and $ F_k = F_{k-1} + F_{k-2} $ for $ k \geq 3 $. Compute the remainder when $ 18225 \cdot F_n $ is divided by 84437. | 14,105 | graphs = [
Graph(
let={
"_n": Const(84437),
"n": CountOverSet(set=CartesianProduct(left=IntegerRange(start=Const(1), end=Const(4)), right=IntegerRange(start=Const(1), end=Const(5)))),
"result": Fibonacci(arg=Ref(name='n')),
"_c": Const(18225),
"Q":... | NT | null | COMPUTE | sympy | COUNT_CARTESIAN | [
"COUNT_CARTESIAN"
] | 409d7d | sequence_fibonacci_compute_v1 | null | 2 | 0 | [
"COUNT_CARTESIAN"
] | 1 | 0.001 | 2026-02-08T12:20:04.972710Z | {
"verified": true,
"answer": 14105,
"timestamp": "2026-02-08T12:20:04.973976Z"
} | 3fb2cd | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 175,
"completion_tokens": 1126
},
"timestamp": "2026-02-15T00:22:28.395Z",
"answer": 14105
},
... | 1 | [
{
"lemma": "COUNT_CARTESIAN",
"status": "ok"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
}
] | {
"lo": -5.49,
"mid": 0.22,
"hi": 6.51
} | ||
034bd5 | sequence_lucas_compute_v1_655260480_4672 | Let $n$ be the number of integers $t$ for which there exist integers $u$ and $v$ satisfying $1\le u\le 3$, $1\le v\le 7$, $7\le t\le 33$, and
$$t=4u+3v.$$
Let $L$ be the $n$th Lucas number. Let $m=2$ and let $p$ be the largest prime integer $r$ such that $2\le r\le 35$.
Let $D$ be the number of prime integers $s$ wit... | 1 | graphs = [
Graph(
let={
"_m": Const(2),
"_n": Const(35),
"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=Con... | NT | COMB | COMPUTE | sympy | MAX_PRIME_BELOW | [
"MAX_PRIME_BELOW/COUNT_PRIMES",
"LIN_FORM"
] | f664bc | sequence_lucas_compute_v1 | bell_mod | 4 | 0 | [
"COUNT_PRIMES",
"LIN_FORM",
"MAX_PRIME_BELOW"
] | 3 | 0.003 | 2026-02-08T18:03:03.264484Z | {
"verified": true,
"answer": 1,
"timestamp": "2026-02-08T18:03:03.267919Z"
} | dab7ad | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 235,
"completion_tokens": 1829
},
"timestamp": "2026-02-18T12:46:27.370Z",
"answer": 1
},
{
... | 1 | [
{
"lemma": "COUNT_PRIMES",
"status": "ok_later"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": ... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
93770e | lin_form_endings_v1_1742523217_2875 | Let $a = 24$ and $b = 40$. Let $\ell$ be the least common multiple of $a$ and $b$. Multiply $\ell$ by $11451$, and let $s$ be the result. Compute the remainder when $s$ is divided by $93965$. | 58,610 | graphs = [
Graph(
let={
"a_coeff": Const(24),
"b_coeff": Const(40),
"_inner_result": LCM(a=Ref("a_coeff"), b=Ref("b_coeff")),
"_scale_k": Const(11451),
"_scaled": Mul(Ref("_scale_k"), Ref("_inner_result")),
"_mod_M": Const(93965),
... | COMB | NT | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | lin_form_endings_v1 | null | 2 | null | [
"LIN_FORM"
] | 1 | 0 | 2026-02-08T05:25:27.971434Z | {
"verified": true,
"answer": 58610,
"timestamp": "2026-02-08T05:25:27.971753Z"
} | 13c4a9 | 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": 696
},
"timestamp": "2026-02-12T08:27:02.829Z",
"answer": 58610
},
{... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
}
] | {
"lo": -3.51,
"mid": 1.33,
"hi": 6.56
} | ||
e4ad8f | comb_count_surjections_v1_1116507919_328 | Let $n = 7$ and let $\_n = 12$. Define $k$ to be the number of ordered pairs $(x_1, x_2)$ of positive odd integers such that $x_1 + x_2 = \_n$. Let $\text{result} = k! \cdot S(n, k)$, where $S(n, k)$ denotes the Stirling number of the second kind. Compute the remainder when $44121 \cdot \text{result}$ is divided by $81... | 57,264 | graphs = [
Graph(
let={
"_n": Const(12),
"n": Const(7),
"k": 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(Su... | COMB | null | COUNT | sympy | COMB1 | [
"COMB1"
] | 567f58 | comb_count_surjections_v1 | null | 5 | 0 | [
"COMB1"
] | 1 | 0.002 | 2026-02-08T02:31:38.152401Z | {
"verified": true,
"answer": 57264,
"timestamp": "2026-02-08T02:31:38.154008Z"
} | 620a53 | 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": 697
},
"timestamp": "2026-02-08T19:23:03.093Z",
"answer": 57264
},
{
"i... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COMB1",
"status": "ok"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
}
] | {
"lo": 1.37,
"mid": 2.65,
"hi": 3.89
} |
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