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 |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
95e963 | antilemma_k3_v1_798873815_505 | Let $ x = \sum_{d \mid 50903} \varphi(d) $, where $ \varphi $ is Euler's totient function. Let $ m = 11 $ and compute $ s = \sum_{d \mid m} \varphi(d) $. Let $ r = |x| \bmod s $. Compute the Bell number $ B_r $, which counts the number of partitions of a set of $ r $ elements. | 203 | graphs = [
Graph(
let={
"_m": Const(11),
"_n": Const(50903),
"x": SumOverDivisors(n=Ref(name='_n'), var='d', expr=EulerPhi(n=Var(name='d'))),
"Q": Bell(Mod(value=Abs(arg=Ref(name='x')), modulus=SumOverDivisors(n=Ref(name='_m'), var='d', expr=EulerPhi(n=Var(nam... | NT | COMB | COMPUTE | sympy | K13 | [
"K3",
"K3"
] | 1dcb5e | antilemma_k3_v1 | bell_mod | 5 | 0 | [
"K13",
"K3"
] | 2 | 0.001 | 2026-02-08T02:40:22.570355Z | {
"verified": true,
"answer": 203,
"timestamp": "2026-02-08T02:40:22.571488Z"
} | c3d8b7 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 208,
"completion_tokens": 1275
},
"timestamp": "2026-02-08T19:37:45.059Z",
"answer": 203
},
{
"id... | 1 | [
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K3",
"status": "ok"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
},
{
"lemma": "VAL_SUM_EQ",
"status": "no"
}
] | {
"lo": -1.74,
"mid": 0.29,
"hi": 2.16
} | ||
b3d44e | comb_count_derangements_v1_784195855_4252 | Let $m$ be the number of positive integers $p$ for which there exists a positive integer $q > p$ such that $pq = 18$ and $\gcd(p, q) = 1$. Let $n$ be the number of positive integers $p$ for which there exists a positive integer $q > p$ such that $pq = 14700$ and $\gcd(p, q) = 1$. Let $r$ be the largest prime number bet... | 1,854 | graphs = [
Graph(
let={
"_m": CountOverSet(set=SolutionsSet(var=Var("p"), condition=And(IsPositive(arg=Var(name='p')), Exists(var=Var(name='q'), condition=And(Eq(left=Mul(Var(name='p'), Var(name='q')), right=Const(value=18)), Eq(left=GCD(a=Var(name='p'), b=Var(name='q')), right=Const(value=1)), ... | NT | COMB | COUNT | sympy | COPRIME_PAIRS | [
"COPRIME_PAIRS/COPRIME_PAIRS/MAX_PRIME_BELOW"
] | 6694fa | comb_count_derangements_v1 | null | 6 | 0 | [
"COPRIME_PAIRS",
"MAX_PRIME_BELOW"
] | 2 | 0.002 | 2026-02-08T06:56:34.272285Z | {
"verified": true,
"answer": 1854,
"timestamp": "2026-02-08T06:56:34.274587Z"
} | f7a6e1 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 171,
"completion_tokens": 2425
},
"timestamp": "2026-02-13T07:11:56.372Z",
"answer": 1854
},
{... | 1 | [
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "o... | {
"lo": -3.51,
"mid": 1.33,
"hi": 6.56
} | ||
e2f162_n | algebra_poly_eval_v1_601307018_1245 | A video game assigns experience points (XP) through two types of quests: minor quests give $4$ XP and major quests give $7$ XP. A player completes between $1$ and $693$ minor quests and $1$ to $113$ major quests. Let $T$ be the number of distinct total XP values between $11$ and $3563$ achievable this way. Define $R$ a... | 28,405 | ALG | null | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM"
] | 3d6396 | algebra_poly_eval_v1 | affine_mod | 5 | null | [
"LIN_FORM"
] | 1 | 0.007 | 2026-03-10T01:55:52.336297Z | null | 48fb49 | e2f162 | narrative | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 276,
"completion_tokens": 31556
},
"timestamp": "2026-03-29T15:00:42.543Z",
"answer": 28405
},
{
... | 1 | [
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
}
] | {
"lo": 1.7,
"mid": 5.03,
"hi": 8.38
} | |
b11a2d | modular_modexp_compute_v1_1978505735_3845 | Let $a = 41$ and $n = 2$. Let $e$ be the smallest divisor of $680621$ that is at least $n$. Compute the remainder when $41^e$ is divided by $14161$. | 5,214 | graphs = [
Graph(
let={
"_n": Const(2),
"a": Const(41),
"e": MinOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Ref("_n")), Divides(divisor=Var("d"), dividend=Const(680621))))),
"m": Const(14161),
"result": ModExp(base=Ref("a"), ... | NT | null | COMPUTE | sympy | MIN_PRIME_FACTOR | [
"MIN_PRIME_FACTOR"
] | bc3776 | modular_modexp_compute_v1 | null | 4 | 0 | [
"MIN_PRIME_FACTOR"
] | 1 | 0.001 | 2026-02-08T17:53:57.304343Z | {
"verified": true,
"answer": 5214,
"timestamp": "2026-02-08T17:53:57.305409Z"
} | 852ef1 | 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": 4856
},
"timestamp": "2026-02-18T09:22:26.297Z",
"answer": 5214
},
{
... | 1 | [
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "MIN_PRIME_FACTOR",
"status": "ok"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "V1",
"status": "no"
},
{
"lemma": "V3",
"status"... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
9db80b | comb_count_partitions_v1_1431428450_1218 | Let $a = 4$ and $b = 2$. Define $n_2 = a + b$. Let
$$
f = \sum_{k=0}^{n_2} (-1)^k \binom{n_2}{k}.
$$
Let $n_1 = 0$ and define
$$
w = \sum_{k=0}^{n_1} (-1)^k \binom{n_1}{k}.
$$
Let $n = 40 + f$, and let $p(n)$ denote the number of integer partitions of $n$. Define
$$
Q = \sum_{i=0}^{\mathrm{NumDigits}(p(n)) - 1} \left( ... | 33,567 | graphs = [
Graph(
let={
"a": Const(4),
"b": Const(2),
"n2": Sum(Ref("a"), Ref("b")),
"f": 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),
"w": Summat... | COMB | null | COUNT | sympy | BINOMIAL_ALTERNATING | [
"BINOMIAL_ALTERNATING"
] | c21569 | comb_count_partitions_v1 | null | 5 | 2 | [
"BINOMIAL_ALTERNATING"
] | 1 | 0.002 | 2026-02-08T13:58:15.610493Z | {
"verified": true,
"answer": 33567,
"timestamp": "2026-02-08T13:58:15.612617Z"
} | ffb72c | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 353,
"completion_tokens": 1033
},
"timestamp": "2026-02-24T19:25:28.120Z",
"answer": 33567
},
{
"... | 1 | [
{
"lemma": "BINOMIAL_ALTERNATING",
"status": "ok"
},
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
},
{
"lemma": "V8_SUM",
"st... | {
"lo": -2.37,
"mid": 1.22,
"hi": 4.84
} | ||
4f87b7 | alg_poly3_sum_v1_1218484723_219 | Find the remainder when $\sum_{a=1}^{57} \sum_{b=1}^{57} \sum_{c=1}^{57} \left(-93a^2b + 219ab^2 + 162b^2c + 108bc^2 + 27c^3 + D \cdot a^3 + 306abc + 108ac^2 + 88b^3 - 72a^2c\right)$ is divided by $80616$, where $D = \left|\left\{(a_1, b_1) : 1 \le a_1, b_1 \le 35,\ 17b_1^2 + 34a_1b_1 + 17a_1^2 = 14297\right\}\right|$ | 74,457 | graphs = [
Graph(
let={
"_n": Const(2),
"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(57)), Geq(Var("b"), Const(1)), Leq(Var("b"), Const(57)), Geq(Var("c"),... | ALG | null | COMPUTE | sympy | QF_PSD_COUNT | [
"QF_PSD_COUNT"
] | 09ce67 | alg_poly3_sum_v1 | null | 5 | 0 | [
"QF_PSD_COUNT"
] | 1 | 0.91 | 2026-02-25T01:54:11.645388Z | {
"verified": true,
"answer": 74457,
"timestamp": "2026-02-25T01:54:12.555243Z"
} | 5502b6 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 286,
"completion_tokens": 7125
},
"timestamp": "2026-03-10T08:53:47.684Z",
"answer": 19461
},
{
... | 1 | [
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "QF_PSD_COUNT",
"status": "ok"
}
] | {
"lo": 3.81,
"mid": 5.7,
"hi": 7.82
} | ||
0e8754 | comb_count_permutations_fixed_v1_1978505735_7060 | Let $n$ be the smallest divisor of $2431$ that is at least $2$, and let $k = 9$. Compute $\binom{n}{k} \cdot !(n - k)$, where $!m$ denotes the number of derangements of $m$ elements. | 55 | graphs = [
Graph(
let={
"_n": Const(2),
"n": MinOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Ref("_n")), Divides(divisor=Var("d"), dividend=Const(2431))))),
"k": Const(9),
"result": Mul(Binom(n=Ref("n"), k=Ref("k")), Subfactorial(arg=Sub(... | NT | COMB | COUNT | sympy | MIN_PRIME_FACTOR | [
"MIN_PRIME_FACTOR"
] | bc3776 | comb_count_permutations_fixed_v1 | null | 3 | 0 | [
"MIN_PRIME_FACTOR"
] | 1 | 0.002 | 2026-02-08T20:02:07.414811Z | {
"verified": true,
"answer": 55,
"timestamp": "2026-02-08T20:02:07.416439Z"
} | bbab63 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 107,
"completion_tokens": 697
},
"timestamp": "2026-02-18T23:50:28.753Z",
"answer": 55
},
{
... | 1 | [
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "MIN_PRIME_FACTOR",
"status": "ok"
},
{
"lemma": "V3",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
ec5442 | diophantine_fbi2_min_v1_655260480_2164 | Let $k = 22$ and let $u$ be the number of positive integers $p$ for which there exists a positive integer $q$ such that $p \cdot q = 688647960$, $\gcd(p, q) = 1$, and $p < q$. Let $d_{\text{min}}$ be the smallest integer $d$ such that $2 \le d \le u$, $d$ divides $k$, and $\frac{k}{d} \ge 4$. Compute $48681$ times $d_{... | 97,362 | graphs = [
Graph(
let={
"_n": Const(4),
"k": Const(22),
"upper": 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=688647960)), Eq(l... | NT | null | EXTREMUM | sympy | COPRIME_PAIRS | [
"COPRIME_PAIRS"
] | 2bb3aa | diophantine_fbi2_min_v1 | null | 4 | 0 | [
"COPRIME_PAIRS"
] | 1 | 0.008 | 2026-02-08T16:35:58.708919Z | {
"verified": true,
"answer": 97362,
"timestamp": "2026-02-08T16:35:58.717126Z"
} | 58457d | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 188,
"completion_tokens": 407
},
"timestamp": "2026-02-16T07:30:59.258Z",
"answer": 535491
},
{
"id": 1... | 1 | [
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "V3",
"status": "n... | {
"lo": -8.26,
"mid": -5.01,
"hi": -1.76
} | ||
d70e6d | diophantine_sum_product_min_v1_1918700295_2086 | Let $S = 50$. Let $P$ be the number of positive integers $k$ such that $1 \leq k \leq 108864$ and $324$ divides $k$. Determine the smallest positive integer $x$ such that $1 \leq x \leq 49$ and $$ x(S - x) = P. $$ Compute the value of $x$. | 8 | graphs = [
Graph(
let={
"S": Const(50),
"P": CountOverSet(set=SolutionsSet(var=Var("k"), condition=And(Geq(Var("k"), Const(1)), Leq(Var("k"), Const(108864)), Divides(divisor=Const(324), dividend=Var("k"))), domain='positive_integers')),
"result": MinOverSet(set=SolutionsS... | ALG | NT | EXTREMUM | sympy | C2 | [
"C2"
] | 9685eb | diophantine_sum_product_min_v1 | null | 6 | 0 | [
"C2"
] | 1 | 0.007 | 2026-02-08T07:40:54.081433Z | {
"verified": true,
"answer": 8,
"timestamp": "2026-02-08T07:40:54.088640Z"
} | 304b6f | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 126,
"completion_tokens": 627
},
"timestamp": "2026-02-13T11:50:44.654Z",
"answer": 8
},
{
... | 1 | [
{
"lemma": "C2",
"status": "ok"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "V3",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
}
] | {
"lo": -8.32,
"mid": -5.11,
"hi": -2.37
} | ||
7f66fb | nt_count_divisible_v1_1248542787_946 | Let $g = \gcd(64, 48)$. Compute $\sum_{d \mid g} \mu(d)$, where $\mu$ is the M\"obius function. Let $c$ be this sum. Determine the number of positive integers $n$ such that $1 \le n \le 60025$ and $n \equiv c \pmod{21}$. Let $k$ be this count. Compute the remainder when $12635 \cdot k$ is divided by $92262$. | 36,388 | graphs = [
Graph(
let={
"upper": Const(60025),
"divisor": Const(21),
"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")), SumOverDivisors(n=GCD(a=Const(val... | NT | null | COUNT | sympy | MOBIUS_COPRIME | [
"MOBIUS_COPRIME"
] | ac54ac | nt_count_divisible_v1 | null | 4 | 0 | [
"MOBIUS_COPRIME"
] | 1 | 3.938 | 2026-02-08T03:30:03.479417Z | {
"verified": true,
"answer": 36388,
"timestamp": "2026-02-08T03:30:07.417344Z"
} | 043bc6 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 225,
"completion_tokens": 2502
},
"timestamp": "2026-02-09T10:21:00.822Z",
"answer": 36388
},
{
"... | 1 | [
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "MOBIUS_COPRIME",
"status": "ok"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "V1",
"status": "no"
}
] | {
"lo": -6.51,
"mid": -0.31,
"hi": 5.43
} | ||
df8669_n | comb_binomial_compute_v1_601307018_4423 | A digital lock has a sensor that counts how many integers from $1$ to $16$ have squares no greater than $256$. This count is $n$. The system then computes $M = \binom{n}{9}$ and displays the result of $53361 - M$. What number appears on the display? | 41,921 | COMB | null | COMPUTE | sympy | C3 | [
"C3"
] | 8a214c | comb_binomial_compute_v1 | null | 3 | null | [
"C3"
] | 1 | 0.003 | 2026-03-10T04:58:47.068972Z | null | 15e8ee | df8669 | narrative | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 176,
"completion_tokens": 664
},
"timestamp": "2026-03-29T18:40:41.925Z",
"answer": 41921
},
{
"i... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "C3",
"status": "ok"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
}
] | {
"lo": -5.36,
"mid": 0.27,
"hi": 5.45
} | |
169f32 | comb_count_surjections_v1_971394319_1288 | Let $S$ be the set of all ordered triples $(x_1, x_2, x_3)$ of positive odd integers such that $x_1 + x_2 + x_3 = 9$. Let $m$ be the number of elements in $S$. Now, let $T$ be the set of all ordered pairs $(x_1, x_2)$ of positive odd integers such that $x_1 + x_2 = m$. Let $n$ be the number of elements in $T$. Define $... | 25,471 | graphs = [
Graph(
let={
"_n": Const(64991),
"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 | null | COUNT | sympy | COMB1 | [
"COMB1/COMB1"
] | b2c526 | comb_count_surjections_v1 | null | 5 | 0 | [
"COMB1"
] | 1 | 0.004 | 2026-02-08T13:35:27.416228Z | {
"verified": true,
"answer": 25471,
"timestamp": "2026-02-08T13:35:27.419761Z"
} | 8c3479 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 283,
"completion_tokens": 1836
},
"timestamp": "2026-02-24T18:47:47.571Z",
"answer": 25471
},
{
"... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COMB1",
"status": "ok"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
}
... | {
"lo": -2.35,
"mid": 1.22,
"hi": 4.84
} | ||
ffbacc | nt_count_with_divisor_count_v1_151522320_1571 | Let $d$ be the sum $\sum_{k=1}^{5} k$. Determine the value of the number of positive integers $n$ such that $1 \le n \le 60025$ and the number of positive divisors of $n$ is exactly $d$. | 33 | graphs = [
Graph(
let={
"_n": Const(5),
"upper": Const(60025),
"div_count": Summation(var="k", start=Const(1), end=Ref("_n"), expr=Var("k")),
"result": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Ref("upper"... | NT | null | COUNT | sympy | SUM_ARITHMETIC | [
"SUM_ARITHMETIC"
] | eb34f0 | nt_count_with_divisor_count_v1 | null | 5 | 0 | [
"SUM_ARITHMETIC"
] | 1 | 2.502 | 2026-02-08T04:06:10.777812Z | {
"verified": true,
"answer": 33,
"timestamp": "2026-02-08T04:06:13.279461Z"
} | d5654b | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 2,
"correct": {
"strict": false,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 169,
"completion_tokens": 3137
},
"timestamp": "2026-02-10T15:20:25.506Z",
"answer": null
},
{
... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "SUM_ARITHMETIC",
"status": "ok"
},
{
"lemma": "V8",
"status": "no"
}
] | {
"lo": 1.96,
"mid": 5.23,
"hi": 8.52
} | ||
27ce52 | diophantine_fbi2_min_v1_458359167_2796 | Let $k = 64$ and let $\text{upper}$ be the minimum value of $x + y$ over all ordered pairs $(x, y)$ of positive integers such that $xy = 1369$. Compute the smallest integer $d \geq 2$ such that $d \leq \text{upper}$, $d$ divides $k$, and $\frac{k}{d} \geq 3$. | 2 | graphs = [
Graph(
let={
"k": Const(64),
"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(1369)))), expr=Sum(Var("x"), Var("y"))))... | NT | null | EXTREMUM | sympy | LIN_FORM | [
"B3"
] | 0cd20d | diophantine_fbi2_min_v1 | null | 4 | 0 | [
"B3",
"LIN_FORM"
] | 2 | 0.028 | 2026-02-08T06:46:25.184643Z | {
"verified": true,
"answer": 2,
"timestamp": "2026-02-08T06:46:25.213122Z"
} | e84632 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 133,
"completion_tokens": 819
},
"timestamp": "2026-02-13T04:44:47.252Z",
"answer": 2
},
{
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "n... | {
"lo": -5.55,
"mid": -3.01,
"hi": 0.32
} | ||
029dc7 | antilemma_k3_v1_784195855_10255 | Let $x = \sum_{d \mid 10092} \phi(d)$, where $\phi$ denotes Euler's totient function.
Compute the remainder when $15837 \cdot x$ is divided by $89944$.
| 86,460 | graphs = [
Graph(
let={
"x": SumOverDivisors(n=Const(value=10092), var='d', expr=EulerPhi(n=Var(name='d'))),
"Q": Mod(value=Mul(Const(15837), Ref("x")), modulus=Const(89944)),
},
goal=Ref("Q"),
)
] | NT | COMB | COMPUTE | sympy | K3 | [
"K3"
] | 54c41e | antilemma_k3_v1 | null | 3 | 0 | [
"K3"
] | 1 | 0.001 | 2026-02-08T17:32:32.129301Z | {
"verified": true,
"answer": 86460,
"timestamp": "2026-02-08T17:32:32.129915Z"
} | b6a40e | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 93,
"completion_tokens": 7089
},
"timestamp": "2026-02-18T03:25:33.668Z",
"answer": 86460
},
{... | 1 | [
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K3",
"status": "ok"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "V1",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
3a492b | comb_sum_binomial_row_v1_865884756_6400 | Let $n$ be the number of nonnegative integers $j$ such that $0 \le j \le 11280$ and $\binom{11280}{j}$ is odd. Compute $2^n$. | 65,536 | graphs = [
Graph(
let={
"_n": Const(11280),
"n": CountOverSet(set=SolutionsSet(var=Var("j"), condition=And(Geq(Var("j"), Const(0)), Leq(Var("j"), Ref("_n")), Eq(Mod(value=Binom(n=Const(11280), k=Var("j")), modulus=Const(2)), Const(1))), domain='nonnegative_integers')),
"r... | ALG | COMB | SUM | sympy | V8 | [
"V8"
] | 86348e | comb_sum_binomial_row_v1 | null | 5 | 0 | [
"V8"
] | 1 | 0.002 | 2026-02-08T19:10:26.197330Z | {
"verified": true,
"answer": 65536,
"timestamp": "2026-02-08T19:10:26.199743Z"
} | 14ad39 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 91,
"completion_tokens": 1863
},
"timestamp": "2026-02-18T21:30:52.610Z",
"answer": 65536
},
{... | 1 | [
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "V1",
"status": "no"
},
{
"lemma": "V8",
"status": "ok"
}
] | {
"lo": -3.12,
"mid": 1.47,
"hi": 6.57
} | ||
ea1c73 | sequence_lucas_compute_v1_865884756_3953 | Let $n$ be the smallest divisor of $14742701$ that is at least $2$. Compute the $n$-th Lucas number $L_n$. | 64,079 | graphs = [
Graph(
let={
"_n": Const(2),
"n": MinOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Ref("_n")), Divides(divisor=Var("d"), dividend=Const(14742701))))),
"result": Lucas(arg=Ref(name='n')),
},
goal=Ref("result"),
)
] | NT | null | COMPUTE | sympy | MIN_PRIME_FACTOR | [
"MIN_PRIME_FACTOR"
] | bc3776 | sequence_lucas_compute_v1 | null | 3 | 0 | [
"MIN_PRIME_FACTOR"
] | 1 | 0.002 | 2026-02-08T17:40:46.521708Z | {
"verified": true,
"answer": 64079,
"timestamp": "2026-02-08T17:40:46.523652Z"
} | 1babf4 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 80,
"completion_tokens": 1279
},
"timestamp": "2026-02-18T06:33:20.885Z",
"answer": 64079
},
{... | 1 | [
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MIN_PRIME_FACTOR",
"status": "ok"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "VAL_SUM_EQ",
"status": "no... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
63d7bd | modular_sum_quadratic_residues_v1_677425708_3506 | Let $m = 4112$. Define $n$ to be the number of integers $j$ with $0 \leq j \leq 4112$ such that $\binom{m}{j}$ is odd. Let $p = 233$. Consider the set of all ordered pairs $(x, y)$ of positive integers such that $xy = n$. Compute the value of $\frac{p(p-1)}{\min(x+y)}$ over all such pairs. | 13,514 | graphs = [
Graph(
let={
"_m": Const(4112),
"_n": CountOverSet(set=SolutionsSet(var=Var("j"), condition=And(Geq(Var("j"), Const(0)), Leq(Var("j"), Const(4112)), Eq(Mod(value=Binom(n=Ref("_m"), k=Var("j")), modulus=Const(2)), Const(1))), domain='nonnegative_integers')),
"p"... | ALG | COMB | SUM | sympy | V8 | [
"V8/B3"
] | b4fc86 | modular_sum_quadratic_residues_v1 | null | 7 | 0 | [
"B3",
"V8"
] | 2 | 0.006 | 2026-02-08T05:47:12.722851Z | {
"verified": true,
"answer": 13514,
"timestamp": "2026-02-08T05:47:12.729065Z"
} | 535327 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 210,
"completion_tokens": 1629
},
"timestamp": "2026-02-24T04:37:52.648Z",
"answer": 13514
},
{
"... | 1 | [
{
"lemma": "B3",
"status": "ok_later"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8",
"status": "ok"
},
... | {
"lo": -2.46,
"mid": 0.47,
"hi": 3.59
} | ||
d81a78 | nt_count_divisible_and_v1_1742523217_5439 | Let $n = 8592$. Define $u$ to be the number of ordered pairs $(x_1, x_2)$ of positive odd integers such that $x_1 + x_2 = n$. Let $d_1 = 6$ and $d_2 = 8$. Compute the number of positive integers $k$ such that $1 \leq k \leq u$, $k$ is divisible by $6$, and $k$ is divisible by $8$. | 179 | graphs = [
Graph(
let={
"_n": Const(8592),
"upper": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x1"), Var("x2")]), condition=And(IsPositive(arg=Var(name='x1')), IsPositive(arg=Var(name='x2')), IsOdd(arg=Var(name='x1')), IsOdd(arg=Var(name='x2')), Eq(Sum(Var("x1"), Var("x2"... | NT | null | COUNT | sympy | COMB1 | [
"COMB1"
] | 567f58 | nt_count_divisible_and_v1 | null | 4 | 0 | [
"COMB1"
] | 1 | 0.149 | 2026-02-08T10:59:23.144022Z | {
"verified": true,
"answer": 179,
"timestamp": "2026-02-08T10:59:23.293161Z"
} | 5a97f5 | 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": 766
},
"timestamp": "2026-02-14T10:10:53.148Z",
"answer": 179
},
{
... | 1 | [
{
"lemma": "COMB1",
"status": "ok"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
}
] | {
"lo": -9.12,
"mid": -6.02,
"hi": -3.62
} | ||
057bfd | nt_max_prime_below_v1_168721529_533 | Let $S$ be the set of all ordered pairs of positive integers $(p, q)$ such that $p \cdot q = 72$, $\gcd(p, q) = 1$, and $p < q$. Let $k$ be the number of elements in $S$. Let $n$ be a prime number satisfying $k \leq n \leq 11881$. Determine the value of the largest such prime $n$. | 11,867 | graphs = [
Graph(
let={
"upper": Const(11881),
"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 | 0.667 | 2026-02-08T13:05:55.585413Z | {
"verified": true,
"answer": 11867,
"timestamp": "2026-02-08T13:05:56.252171Z"
} | 06b7a4 | CC BY 4.0 | [
{
"id": 4,
"model": "NousResearch/Hermes-4-405B",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 149,
"completion_tokens": 7992
},
"timestamp": "2026-02-09T18:25:29.061Z",
"answer": 11867
},
... | 1 | [
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
}
] | {
"lo": -5.3,
"mid": -2.04,
"hi": 1.93
} | ||
da2b84 | antilemma_k2_v1_898971024_67 | Let $S$ be the set of all positive integers $x_1$ such that $x_1^2 - 176x_1 - 25017 = 0$. Let $N$ be the sum of all elements in $S$. Compute $$\sum_{k=1}^{N} \phi(k) \left\lfloor \frac{176}{k} \right\rfloor,$$ where $\phi(k)$ denotes Euler's totient function. | 15,576 | graphs = [
Graph(
let={
"_n": Const(2),
"x": Summation(var="k", start=Const(1), end=SumOverSet(set=SolutionsSet(var=Var("x1"), condition=Eq(Sum(Pow(Var("x1"), Ref("_n")), Mul(Const(-176), Var("x1")), Const(-25017)), Const(0)))), expr=Mul(EulerPhi(n=Var("k")), Floor(Div(Const(176), Va... | NT | COMB | COMPUTE | sympy | VIETA_SUM | [
"VIETA_SUM/K2",
"K2"
] | 6be084 | antilemma_k2_v1 | null | 5 | 0 | [
"K2",
"VIETA_SUM"
] | 2 | 0.001 | 2026-02-08T15:10:45.758743Z | {
"verified": true,
"answer": 15576,
"timestamp": "2026-02-08T15:10:45.760142Z"
} | 95fb08 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 141,
"completion_tokens": 1323
},
"timestamp": "2026-02-16T01:01:29.243Z",
"answer": 15576
},
... | 1 | [
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K2",
"status": "ok"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
},
{
"lem... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
aaf56e | diophantine_fbi2_min_v1_124444284_4823 | Let $n = 5$. Define $k$ to be the number of positive integers $p$ for which there exists a positive integer $q$ such that $p \cdot q = 27427200801000$, $\gcd(p, q) = 1$, and $p < q$. Let $d$ be an integer satisfying $d \ge n$, $d \le 74$, $d$ divides $k$, and $\frac{k}{d} \ge 2$. Determine the value of the smallest suc... | 78,306 | graphs = [
Graph(
let={
"_n": Const(5),
"k": CountOverSet(set=SolutionsSet(var=Var("p"), condition=And(IsPositive(arg=Var(name='p')), Exists(var=Var(name='q'), condition=And(Eq(left=Mul(Var(name='p'), Var(name='q')), right=Const(value=27427200801000)), Eq(left=GCD(a=Var(name='p'), b=... | NT | null | EXTREMUM | sympy | COPRIME_PAIRS | [
"COPRIME_PAIRS"
] | 2bb3aa | diophantine_fbi2_min_v1 | null | 6 | 0 | [
"COPRIME_PAIRS"
] | 1 | 0.013 | 2026-02-08T06:14:40.579832Z | {
"verified": true,
"answer": 78306,
"timestamp": "2026-02-08T06:14:40.592422Z"
} | 3dbc91 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 251,
"completion_tokens": 5065
},
"timestamp": "2026-02-12T21:37:54.660Z",
"answer": 78306
},
... | 1 | [
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
}
] | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
009e46 | modular_count_residue_v1_655260480_654 | Let $m = \sum_{k=1}^{3} k$. Determine the number of positive integers $n$ such that $1 \le n \le 85849$ and $n \equiv 1 \pmod{m}$. | 14,309 | graphs = [
Graph(
let={
"upper": Const(85849),
"m": Summation(var="k", start=Const(1), end=Const(3), expr=Var("k")),
"r": Const(1),
"result": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Ref("upper")), Eq(Mod... | NT | null | COUNT | sympy | SUM_ARITHMETIC | [
"SUM_ARITHMETIC"
] | eb34f0 | modular_count_residue_v1 | null | 2 | 0 | [
"SUM_ARITHMETIC"
] | 1 | 3.356 | 2026-02-08T15:30:26.182938Z | {
"verified": true,
"answer": 14309,
"timestamp": "2026-02-08T15:30:29.538726Z"
} | ab42f1 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 96,
"completion_tokens": 425
},
"timestamp": "2026-02-16T08:30:22.152Z",
"answer": 14309
},
{
... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "SUM_ARITHMETIC",
"status": "ok"
},
{
"lemma": "V7",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
99cb1d | comb_count_derangements_v1_865884756_3261 | Let $T$ be the set of all nonnegative integers $j \leq 74304$ such that $\binom{74304}{j}$ is odd. Let $n$ be the minimum value of $x + y$ over all pairs of positive integers $(x, y)$ such that $xy = |T|$. Compute the number of derangements of $n$ elements. | 14,833 | graphs = [
Graph(
let={
"_m": Const(2),
"_n": CountOverSet(set=SolutionsSet(var=Var("j"), condition=And(Geq(Var("j"), Const(0)), Leq(Var("j"), Const(74304)), Eq(Mod(value=Binom(n=Const(74304), k=Var("j")), modulus=Ref("_m")), Const(1))), domain='nonnegative_integers')),
"... | COMB | null | COUNT | sympy | V8 | [
"V8/B3"
] | b4fc86 | comb_count_derangements_v1 | null | 7 | 0 | [
"B3",
"V8"
] | 2 | 0.003 | 2026-02-08T17:14:57.684223Z | {
"verified": true,
"answer": 14833,
"timestamp": "2026-02-08T17:14:57.687107Z"
} | 5065ec | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 126,
"completion_tokens": 1829
},
"timestamp": "2026-02-17T22:17:18.928Z",
"answer": 14833
},
... | 1 | [
{
"lemma": "B3",
"status": "ok_later"
},
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "MOD_SUB",
"stat... | {
"lo": -2.38,
"mid": 1.74,
"hi": 6.59
} | ||
11eded | algebra_poly_eval_v1_784195855_8277 | Compute the value of $$
5^4 \cdot |\{n \in \mathbb{Z}^+ : 1 \leq n \leq 32,\ 2 \mid n,\ \gcd(n, 21) = 1\}| - 10 \cdot 5^3 - 9 \cdot 5^2 - 3 \cdot 5 + 9.
$$Then, find the remainder when $18859$ times this value is divided by $77199$. | 26,308 | graphs = [
Graph(
let={
"_n": Const(2),
"k": Const(5),
"result": Sum(Mul(CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Const(32)), Divides(divisor=Const(2), dividend=Var("n")), Eq(GCD(a=Var("n"), b=Const(21)), Const(1))))... | NT | null | COMPUTE | sympy | C5 | [
"C5"
] | 1d9668 | algebra_poly_eval_v1 | null | 4 | 0 | [
"C5"
] | 1 | 0.004 | 2026-02-08T15:59:10.863715Z | {
"verified": true,
"answer": 26308,
"timestamp": "2026-02-08T15:59:10.867509Z"
} | 0b7e76 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 146,
"completion_tokens": 2327
},
"timestamp": "2026-02-16T17:48:47.548Z",
"answer": 26308
},
... | 1 | [
{
"lemma": "C5",
"status": "ok"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "V1",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
807cef | comb_sum_binomial_row_v1_784195855_8838 | Let $m = 10249$. Let $T$ be the set of all positive integers $p$ for which there exists a positive integer $q$ such that $p \cdot q = 108$, $\gcd(p, q) = 1$, and $p < q$. Let $n$ be the number of nonnegative integers $j$ such that $0 \leq j \leq m$ and
$$
\binom{10249}{j} \equiv 1 \pmod{|T|}.
$$
Compute $2^n$. | 65,536 | graphs = [
Graph(
let={
"_m": Const(10249),
"_n": Const(2),
"n": CountOverSet(set=SolutionsSet(var=Var("j"), condition=And(Geq(Var("j"), Const(0)), Leq(Var("j"), Ref("_m")), Eq(Mod(value=Binom(n=Const(10249), k=Var("j")), modulus=CountOverSet(set=SolutionsSet(var=Var("p")... | NT | null | SUM | sympy | COPRIME_PAIRS | [
"COPRIME_PAIRS/V8"
] | 93b9b8 | comb_sum_binomial_row_v1 | null | 7 | 0 | [
"COPRIME_PAIRS",
"V8"
] | 2 | 0.002 | 2026-02-08T16:22:35.560103Z | {
"verified": true,
"answer": 65536,
"timestamp": "2026-02-08T16:22:35.562484Z"
} | f25d8b | 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": 1762
},
"timestamp": "2026-02-17T02:13:46.170Z",
"answer": 65536
},
... | 1 | [
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "V5",
"status": "no... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
1ee39a | nt_count_divisible_v1_1470522791_1419 | Let $d = \sum_{k=1}^{7} \phi(k) \cdot \left\lfloor \frac{7}{k} \right\rfloor$, where $\phi$ denotes Euler's totient function. Determine the number of positive integers $n$ such that $1 \leq n \leq 32768$ and $n \equiv 0 \pmod{d}$. Multiply this count by $70405$, and compute the remainder when the result is divided by $... | 637 | graphs = [
Graph(
let={
"upper": Const(32768),
"divisor": Summation(var="k", start=Const(1), end=Const(7), expr=Mul(EulerPhi(n=Var("k")), Floor(Div(Const(7), Var("k"))))),
"result": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var... | NT | null | COUNT | sympy | K2 | [
"K2"
] | 6897ab | nt_count_divisible_v1 | null | 5 | 0 | [
"K2"
] | 1 | 1.067 | 2026-02-08T13:37:55.594828Z | {
"verified": true,
"answer": 637,
"timestamp": "2026-02-08T13:37:56.662301Z"
} | d55a93 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 148,
"completion_tokens": 1108
},
"timestamp": "2026-02-15T19:16:58.417Z",
"answer": 637
},
{
... | 1 | [
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "K2",
"status": "ok"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "V1",
"status": "no"
}
] | {
"lo": -5.49,
"mid": 0.22,
"hi": 6.51
} | ||
9317e6 | nt_lcm_compute_v1_1116507919_432 | Let $a$ be the largest integer such that $3^a$ divides $9^{274}$, and let $b = 624$. Compute the least common multiple of $a$ and $b$. | 85,488 | graphs = [
Graph(
let={
"_n": Const(9),
"a": MaxKDivides(target=Pow(Ref("_n"), Const(274)), base=Const(3)),
"b": Const(624),
"result": LCM(a=Ref("a"), b=Ref("b")),
},
goal=Ref("result"),
)
] | NT | null | COMPUTE | sympy | K14 | [
"K14"
] | a49bcb | nt_lcm_compute_v1 | null | 3 | 0 | [
"K14"
] | 1 | 0.001 | 2026-02-08T02:34:11.482141Z | {
"verified": true,
"answer": 85488,
"timestamp": "2026-02-08T02:34:11.482823Z"
} | ee0309 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 157,
"completion_tokens": 732
},
"timestamp": "2026-02-08T19:32:42.033Z",
"answer": 85488
},
{
"i... | 1 | [
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "K14",
"status": "ok"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "MOD_ADD",
"stat... | {
"lo": -7.44,
"mid": -4.14,
"hi": -0.84
} | ||
e27d11 | algebra_poly_eval_v1_1742523217_1823 | Let $y$ be the smallest prime divisor of 847. Compute $8y^3 - 7y^2 - 4y - 7$. | 2,366 | graphs = [
Graph(
let={
"_n": Const(8),
"y": MinOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Const(2)), Divides(divisor=Var("d"), dividend=Const(847))))),
"result": Sum(Mul(Ref("_n"), Pow(Ref("y"), Const(3))), Mul(Const(-7), Pow(Ref("y"), Const(2))),... | NT | null | COMPUTE | sympy | MIN_PRIME_FACTOR | [
"MIN_PRIME_FACTOR"
] | bc3776 | algebra_poly_eval_v1 | null | 2 | 0 | [
"MIN_PRIME_FACTOR"
] | 1 | 0.002 | 2026-02-08T04:16:34.328739Z | {
"verified": true,
"answer": 2366,
"timestamp": "2026-02-08T04:16:34.330245Z"
} | f2a403 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 143,
"completion_tokens": 524
},
"timestamp": "2026-02-10T16:09:10.079Z",
"answer": 2366
},
{
"i... | 2 | [
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "MIN_PRIME_FACTOR",
"status": "ok"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
}
] | {
"lo": -10,
"mid": -7.73,
"hi": -5.46
} | ||
36da6a | nt_count_with_divisor_count_v1_151522320_2141 | Let $u = 24649$ and $d = 14$. Compute the number of positive integers $n$ such that $1 \leq n \leq u$ and $n$ has exactly $d$ positive divisors. Let $r$ denote this count. Let $p$ be the largest prime number less than or equal to $11$. Find the value of the Bell number $B_{r \bmod p}$. | 21,147 | graphs = [
Graph(
let={
"upper": Const(24649),
"div_count": Const(14),
"result": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Ref("upper")), Eq(NumDivisors(n=Var("n")), Ref("div_count"))))),
"Q": Bell(Mod(val... | NT | COMB | COUNT | sympy | MAX_PRIME_BELOW | [
"MAX_PRIME_BELOW"
] | 88ea9c | nt_count_with_divisor_count_v1 | bell_mod | 6 | 0 | [
"MAX_PRIME_BELOW"
] | 1 | 1.006 | 2026-02-08T04:38:50.996046Z | {
"verified": true,
"answer": 21147,
"timestamp": "2026-02-08T04:38:52.001630Z"
} | 856e79 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 202,
"completion_tokens": 2479
},
"timestamp": "2026-02-11T21:38:53.129Z",
"answer": 21147
},
{
... | 1 | [
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"statu... | {
"lo": -3.42,
"mid": 1.86,
"hi": 7.55
} | ||
2a785d | geo_count_lattice_triangle_v1_1218484723_5350 | Let $M$ be the largest prime number $n$ with $2 \le n \le 191$. Let $R = |111M + 200(0 - 111)|$. Let $S = \gcd(111, 111) + \gcd\left(\left|\max\{ d : d \mid 45400,\ 1 \le d \le 200\} - 111\right|, |191 - 111|\right) + \gcd(|0 - 200|, |0 - 191|)$. Compute $\frac{R + 2 - S}{2}$. | 444 | graphs = [
Graph(
let={
"_m": Const(111),
"_n": MaxOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(2)), Leq(Var("n"), Const(191)), IsPrime(Var("n"))))),
"area_2x": Abs(arg=Sum(Mul(Const(value=111), Ref(name='_n')), Mul(Const(value=200), Sub(left=C... | GEOM | NT | COUNT | sympy | MAX_PRIME_BELOW | [
"MAX_PRIME_BELOW/MAX_DIVISOR"
] | c8e97a | geo_count_lattice_triangle_v1 | null | 6 | 0 | [
"MAX_DIVISOR",
"MAX_PRIME_BELOW"
] | 2 | 0.009 | 2026-02-25T06:57:07.891439Z | {
"verified": true,
"answer": 444,
"timestamp": "2026-02-25T06:57:07.900684Z"
} | 2cd19e | 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": 1552
},
"timestamp": "2026-03-29T20:40:50.043Z",
"answer": 444
},
{
"id... | 1 | [
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "MAX_DIVISOR",
"status": "ok_later... | {
"lo": -3.33,
"mid": 1.03,
"hi": 5.26
} | ||
bde1a3 | comb_count_permutations_fixed_v1_784195855_10186 | Let $n = 5$ and $k = 2$. Compute $\binom{n}{k} \cdot !(n - k)$, where $!m$ denotes the number of derangements of $m$ elements. Let $Q = 38416$ minus this value. Find the value of $Q$. | 38,396 | graphs = [
Graph(
let={
"n": Const(5),
"k": Const(2),
"result": Mul(Binom(n=Ref("n"), k=Ref("k")), Subfactorial(arg=Sub(left=Ref(name='n'), right=Ref(name='k')))),
"_c": Const(38416),
"Q": Sub(Ref("_c"), Ref("result")),
},
goal=Ref(... | COMB | null | COUNT | sympy | SUM_ARITHMETIC | [
"SUM_ARITHMETIC/B1"
] | 844731 | comb_count_permutations_fixed_v1 | null | 3 | 0 | [
"B1",
"SUM_ARITHMETIC"
] | 2 | 0.014 | 2026-02-08T17:29:13.711359Z | {
"verified": true,
"answer": 38396,
"timestamp": "2026-02-08T17:29:13.724971Z"
} | ce4e56 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 112,
"completion_tokens": 520
},
"timestamp": "2026-02-18T03:18:10.396Z",
"answer": 38396
},
{... | 1 | [
{
"lemma": "B1",
"status": "ok_later"
},
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "SUM_ARITHMETIC",
"status": "ok"
},
{
"lemma": "V7",
"status"... | {
"lo": -8,
"mid": -4.75,
"hi": -2.28
} | ||
3d30eb | antilemma_k3_v1_1918700295_1052 | Let $x$ be the sum of $\phi(d)$ over all positive divisors $d$ of $75398$. Let $a = |x| + 1$ and $b = |x| + 1$. Let $c = \tau(b)$, where $\tau(n)$ denotes the number of positive divisors of $n$. Define $s = x + \phi(a) + c$. Compute the remainder when $s$ is divided by $67848$. | 56,518 | graphs = [
Graph(
let={
"x": SumOverDivisors(n=Const(value=75398), var='d', expr=EulerPhi(n=Var(name='d'))),
"Q": Mod(value=Sum(Ref("x"), EulerPhi(n=Sum(Abs(arg=Ref(name='x')), Const(1))), NumDivisors(n=Sum(Abs(arg=Ref(name='x')), Div(Const(80), Const(80))))), modulus=Const(67848)),
... | NT | COMB | COMPUTE | sympy | IDENTITY_DIV_SELF | [
"IDENTITY_DIV_SELF",
"K3"
] | 7b3820 | antilemma_k3_v1 | null | 4 | 0 | [
"IDENTITY_DIV_SELF",
"K3"
] | 2 | 0.001 | 2026-02-08T05:32:27.183344Z | {
"verified": true,
"answer": 56518,
"timestamp": "2026-02-08T05:32:27.184599Z"
} | e1c0e6 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 143,
"completion_tokens": 6565
},
"timestamp": "2026-02-12T10:11:31.427Z",
"answer": 56518
},
... | 1 | [
{
"lemma": "IDENTITY_DIV_SELF",
"status": "ok"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "K3",
"status": "ok"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
... | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
715e0d | comb_count_permutations_fixed_v1_1218484723_5148 | Let $k = \sum_{d=1}^{2} \varphi(d) \cdot \left\lfloor \frac{2}{d} \right\rfloor$, $n = 5$, and $M = \binom{5}{k} \cdot D_{5-k}$, where $D_m$ is the number of derangements of $m$ elements. Let $d_i(M)$ denote the $i$-th digit of $M$ in base 10 (starting from $i=0$ for the units place). Compute $\sum_{i=0}^{d(M)-1} d_i(M... | 65,540 | graphs = [
Graph(
let={
"n": Const(5),
"k": Summation(var="k1", start=Const(1), end=Const(2), expr=Mul(EulerPhi(n=Var("k1")), Floor(Div(Const(2), Var("k1"))))),
"result": Mul(Binom(n=Ref("n"), k=Ref("k")), Subfactorial(arg=Sub(left=Ref(name='n'), right=Ref(name='k')))),
... | COMB | NT | COUNT | sympy | K2 | [
"K2"
] | 6897ab | comb_count_permutations_fixed_v1 | null | 5 | 0 | [
"K2"
] | 1 | 0.002 | 2026-02-25T06:46:49.349554Z | {
"verified": true,
"answer": 65540,
"timestamp": "2026-02-25T06:46:49.351933Z"
} | 79b98e | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 273,
"completion_tokens": 607
},
"timestamp": "2026-03-29T19:38:13.254Z",
"answer": 65540
},
{
"i... | 2 | [
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "K2",
"status": "ok"
},
{
"lemma": "V7",
... | {
"lo": -10,
"mid": -6.24,
"hi": -2.48
} | ||
1a76a9 | modular_modexp_compute_v1_1874849503_493 | Let $e$ be the number of prime numbers less than or equal to 40231. Compute the remainder when $37^e$ is divided by 50625. | 30,682 | graphs = [
Graph(
let={
"_n": Const(40231),
"a": Const(37),
"e": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(2)), Leq(Var("n"), Ref("_n")), IsPrime(Var("n"))))),
"m": Const(50625),
"result": ModExp(base=Ref("a"), e... | NT | null | COMPUTE | sympy | COUNT_PRIMES | [
"COUNT_PRIMES"
] | 07c874 | modular_modexp_compute_v1 | null | 5 | 0 | [
"COUNT_PRIMES"
] | 1 | 0.007 | 2026-02-08T13:07:41.431034Z | {
"verified": true,
"answer": 30682,
"timestamp": "2026-02-08T13:07:41.437910Z"
} | b67eaa | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 82,
"completion_tokens": 4524
},
"timestamp": "2026-02-15T09:38:42.202Z",
"answer": 30682
},
{... | 1 | [
{
"lemma": "COUNT_PRIMES",
"status": "ok"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "V3",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
}
] | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
5d4d6a_n | comb_count_partitions_v1_601307018_2256 | Two players take turns collecting gold coins, and together they collect exactly 86 coins. Each player must collect an odd number of coins. How many different ways can the coins be distributed between them? Let $n$ be that number. A wizard then computes $p(n)$, the number of ways to write $n$ as a sum of positive intege... | 63,261 | COMB | null | COUNT | sympy | COMB1 | [
"COMB1"
] | 567f58 | comb_count_partitions_v1 | null | 3 | null | [
"COMB1"
] | 1 | 0.006 | 2026-03-10T02:55:30.076207Z | null | b97c5b | 5d4d6a | narrative | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 191,
"completion_tokens": 2411
},
"timestamp": "2026-03-29T16:00:07.390Z",
"answer": 63061
},
{
... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COMB1",
"status": "ok"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
}
] | {
"lo": 1.7,
"mid": 5.03,
"hi": 8.38
} | |
5e5043 | nt_sum_divisors_compute_v1_1742523217_883 | Let $t$ be the minimum value of $x + y$ over all ordered pairs $(x,y)$ of positive integers such that $xy = 900$. Let $n_2 = t^2$. Define $u$ to be the remainder when the number of positive divisors of $n_2$ is divided by $2$. Let $v = \Omega(1)$, the number of prime factors of $1$ counted with multiplicity. Let $n = 2... | 585 | graphs = [
Graph(
let={
"_n": Const(55172),
"t": MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(Mul(Var("x"), Var("y")), Const(900)))), expr=Sum(Var("x"), Var("y")))),... | NT | null | COMPUTE | sympy | B3 | [
"B3/DIVISOR_PARITY",
"BIG_OMEGA_ZERO"
] | 15e254 | nt_sum_divisors_compute_v1 | null | 5 | 2 | [
"B3",
"BIG_OMEGA_ZERO",
"DIVISOR_PARITY"
] | 3 | 0.003 | 2026-02-08T03:19:22.870614Z | {
"verified": true,
"answer": 585,
"timestamp": "2026-02-08T03:19:22.874015Z"
} | e7b955 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 257,
"completion_tokens": 2462
},
"timestamp": "2026-02-10T00:00:07.760Z",
"answer": 585
},
{
"id... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "BIG_OMEGA_ZERO",
"status": "ok"
},
{
"lemma": "DIVISOR_PARITY",
"status": "ok_later"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{... | {
"lo": -6.51,
"mid": -0.31,
"hi": 5.43
} | ||
543453 | nt_gcd_compute_v1_2051736721_4815 | Let $a = 348222$ and $b = 646698$. Let $d = \gcd(a, b)$. Let $c$ be the number of positive integers $j$ such that $1 \leq j \leq 5165$ and $j^4 \leq 711674333700625$. Compute the remainder when $c \cdot d$ is divided by $80927$. | 75,792 | graphs = [
Graph(
let={
"_n": Const(5165),
"a": Const(348222),
"b": Const(646698),
"result": GCD(a=Ref("a"), b=Ref("b")),
"_c": CountOverSet(set=SolutionsSet(var=Var("j"), condition=And(Geq(Var("j"), Const(1)), Leq(Var("j"), Ref("_n")), Leq(Pow(Var... | NT | null | COMPUTE | sympy | C3 | [
"C3"
] | 887000 | nt_gcd_compute_v1 | affine_mod | 3 | 0 | [
"C3"
] | 1 | 0.002 | 2026-02-08T18:10:33.938333Z | {
"verified": true,
"answer": 75792,
"timestamp": "2026-02-08T18:10:33.940233Z"
} | 5783fe | 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": 3677
},
"timestamp": "2026-02-18T15:13:36.635Z",
"answer": 75792
},
... | 1 | [
{
"lemma": "C3",
"status": "ok"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "V3",
"status": "no"
},
{
"lemma": "VAL_SUM_EQ",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
58fde0 | sequence_lucas_compute_v1_1520064083_6770 | Let $n$ be the number of positive integers $k$ such that $1 \leq k \leq 198$ and $k \equiv \left\lfloor \frac{k}{2} \right\rfloor \pmod{11}$. Compute $n$. Let $L_n$ denote the $n$-th Lucas number, defined by $L_1 = 1$, $L_2 = 3$, and $L_k = L_{k-1} + L_{k-2}$ for $k \geq 3$. Find the remainder when $67153 \times L_n$ i... | 13,542 | graphs = [
Graph(
let={
"_n": Const(67153),
"n": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Const(198)), 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"
] | 73f8b0 | sequence_lucas_compute_v1 | null | 6 | 0 | [
"L3C"
] | 1 | 0.001 | 2026-02-08T08:19:54.436141Z | {
"verified": true,
"answer": 13542,
"timestamp": "2026-02-08T08:19:54.437022Z"
} | 82c356 | 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": 1807
},
"timestamp": "2026-02-13T17:24:11.406Z",
"answer": 13542
},
... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "L3C",
"status": "ok"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
}
] | {
"lo": -3.51,
"mid": 1.33,
"hi": 6.56
} | ||
1471d0 | antilemma_k3_v1_784195855_6401 | Let $n = 65538$, and let $x = \sum_{d \mid n} \phi(d)$, where $\phi$ denotes Euler's totient function. Let $c = 32041$. Compute $$
\sum_{i=0}^{d-1} \left( \text{the } i\text{-th digit of } |x| \right) \cdot (i+1)^2 + c,
$$ where $d$ is the number of decimal digits of $|x|$. | 32,336 | graphs = [
Graph(
let={
"_n": Const(65538),
"x": SumOverDivisors(n=Ref(name='_n'), var='d', expr=EulerPhi(n=Var(name='d'))),
"_c": Const(32041),
"Q": Sum(Summation(var="i", start=Mod(value=Const(75), modulus=Const(75)), end=Sub(NumDigits(x=Abs(arg=Ref(name='x'... | NT | COMB | COMPUTE | sympy | IDENTITY_MOD_SELF | [
"IDENTITY_MOD_SELF",
"K3"
] | 0006fa | antilemma_k3_v1 | null | 5 | 0 | [
"IDENTITY_MOD_SELF",
"K3"
] | 2 | 0.003 | 2026-02-08T08:39:02.095110Z | {
"verified": true,
"answer": 32336,
"timestamp": "2026-02-08T08:39:02.098150Z"
} | 8d4965 | 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": 913
},
"timestamp": "2026-02-13T20:04:00.427Z",
"answer": 32336
},
{... | 1 | [
{
"lemma": "IDENTITY_MOD_SELF",
"status": "ok"
},
{
"lemma": "K3",
"status": "ok"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "V3",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
},
{
... | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
96ea81 | nt_count_divisors_in_range_v1_124444284_5938 | Let $n = 221760$ and let $a$ be the sum of all positive integers at most $117$ that are divisible by $117$. Let $b$ be the number of integers $t$ such that $22 \leq t \leq 7452$ and there exist positive integers $a$ and $b$ with $1 \leq a \leq 536$, $1 \leq b \leq 226$, and $t = 8a + 14b$. Compute the number of positiv... | 86 | graphs = [
Graph(
let={
"_n": Const(117),
"n": Const(221760),
"a": SumOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Const(117)), Eq(Mod(value=Var("n"), modulus=Ref("_n")), Const(0))))),
"b": CountOverSet(set=Soluti... | NT | null | COUNT | sympy | K13 | [
"SUM_DIVISIBLE",
"LIN_FORM"
] | 56af5e | nt_count_divisors_in_range_v1 | null | 4 | 0 | [
"K13",
"LIN_FORM",
"SUM_DIVISIBLE"
] | 3 | 0.086 | 2026-02-08T06:57:20.794358Z | {
"verified": true,
"answer": 86,
"timestamp": "2026-02-08T06:57:20.880468Z"
} | e9acce | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 173,
"completion_tokens": 4762
},
"timestamp": "2026-02-13T06:19:04.178Z",
"answer": 86
},
{
... | 1 | [
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "SUM_DIVISIBLE",
"status": "ok"
},
{
"lemma": "V8",
"status": "no"
},
{
"lem... | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
21f535 | geo_count_lattice_triangle_v1_1742523217_2537 | Let $A$ be the area of a triangle with vertices at $(128, 111)$, $(128, 231)$, and $(0, 0)$, multiplied by $2$. Let $B$ be the number of lattice points on the boundary of this triangle. Compute the value of $\frac{A + 2 - B}{2}$. | 7,620 | graphs = [
Graph(
let={
"_m": Const(231),
"_n": Const(2),
"area_2x": Abs(arg=Sum(Mul(Const(value=128), Const(value=111)), Mul(Const(value=128), Sub(left=Const(value=0), right=Const(value=231))))),
"boundary": Sum(GCD(a=Abs(arg=Const(value=128)), b=Abs(arg=Cons... | ALG | NT | COUNT | sympy | MAX_PRIME_BELOW | [
"MAX_PRIME_BELOW/K14"
] | 0ea9d7 | geo_count_lattice_triangle_v1 | null | 6 | 0 | [
"K14",
"MAX_PRIME_BELOW"
] | 2 | 0.007 | 2026-02-08T04:50:06.677561Z | {
"verified": true,
"answer": 7620,
"timestamp": "2026-02-08T04:50:06.684262Z"
} | 23891f | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 184,
"completion_tokens": 1959
},
"timestamp": "2026-02-11T22:06:10.420Z",
"answer": 7620
},
{
"... | 1 | [
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K14",
"status": "ok_later"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "V3",
"status": "no"
},
... | {
"lo": -3.42,
"mid": 1.86,
"hi": 7.55
} | ||
5f1ea0 | comb_count_partitions_v1_1520064083_2404 | Let $ n = 45 $. Let $ p $ be the number of integer partitions of $ n $. Let $ q = p \bmod 11 $. Compute the Bell number $ B_q $. | 1 | graphs = [
Graph(
let={
"n": Const(45),
"result": Partition(arg=Ref(name='n')),
"Q": Bell(Mod(value=Abs(arg=Ref(name='result')), modulus=Const(11))),
},
goal=Ref("Q"),
)
] | COMB | null | COUNT | sympy | COMB1 | [
"COMB1"
] | d93ba8 | comb_count_partitions_v1 | bell_mod | 6 | 0 | [
"COMB1"
] | 1 | 0.007 | 2026-02-08T04:42:12.777359Z | {
"verified": true,
"answer": 1,
"timestamp": "2026-02-08T04:42:12.784316Z"
} | 0cf2ef | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 150,
"completion_tokens": 1188
},
"timestamp": "2026-02-11T21:50:02.852Z",
"answer": 1
},
{
"id":... | 1 | [
{
"lemma": "COMB1",
"status": "ok"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8",
"statu... | {
"lo": -3.83,
"mid": -1.68,
"hi": 1.09
} | ||
4e9094 | antilemma_k2_v1_458359167_1189 | Compute
$$
\sum_{k=1}^{157} \varphi(k) \left\lfloor \frac{157}{k} \right\rfloor,
$$
where $\varphi$ denotes Euler's totient function. Multiply this sum by $37625$, and compute the remainder when the result is divided by $79133$. | 15,574 | graphs = [
Graph(
let={
"_n": Const(157),
"x": Summation(var="k", start=Const(1), end=Const(157), expr=Mul(EulerPhi(n=Var("k")), Floor(Div(Ref("_n"), Var("k"))))),
"_c": Const(37625),
"Q": Mod(value=Mul(Ref("_c"), Ref("x")), modulus=Const(79133)),
},
... | NT | COMB | COMPUTE | sympy | K13 | [
"K2"
] | 6897ab | antilemma_k2_v1 | null | 4 | 0 | [
"K13",
"K2"
] | 2 | 0.001 | 2026-02-08T04:29:09.660368Z | {
"verified": true,
"answer": 15574,
"timestamp": "2026-02-08T04:29:09.661527Z"
} | 93946c | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 182,
"completion_tokens": 2000
},
"timestamp": "2026-02-10T16:53:19.515Z",
"answer": 15574
},
{
... | 1 | [
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K2",
"status": "ok"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "V1",
"status": "no"
}
] | {
"lo": -3.49,
"mid": 1.84,
"hi": 7.55
} | ||
2ff80e | comb_factorial_compute_v1_238844314_542 | Let $ n $ be the number of integers $ t $ with $ 5 \leq t \leq 14 $ such that there exist integers $ a $ and $ b $ satisfying $ 1 \leq a \leq 2 $, $ 1 \leq b \leq 4 $, and $ t = 3a + 2b $. Compute the value of $ n! $. | 40,320 | 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=2)), Geq(left=Var(name='b'), right=Const(value=1... | ALG | COMB | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | comb_factorial_compute_v1 | null | 2 | 0 | [
"LIN_FORM"
] | 1 | 0.001 | 2026-02-08T13:23:38.435945Z | {
"verified": true,
"answer": 40320,
"timestamp": "2026-02-08T13:23:38.437117Z"
} | a57396 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 195,
"completion_tokens": 496
},
"timestamp": "2026-02-24T18:11:05.015Z",
"answer": 40320
},
{
"i... | 1 | [
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
}
] | {
"lo": -7.18,
"mid": -5,
"hi": -3.01
} | ||
ba9b4c | nt_count_intersection_v1_1978505735_5815 | Let $N$ be the number of positive integers $n$ such that $1 \leq n \leq 87490$, $10$ divides $n$, and $\gcd(n, 21) = 1$. Define $a = 5$ and $b = 6$. Let $result$ be the number of positive integers $n_1$ such that $1 \leq n_1 \leq N$, $5$ divides $n_1$, and $\gcd(n_1, 6) = 1$. Compute $result$. | 333 | graphs = [
Graph(
let={
"_n": Const(10),
"N": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Const(87490)), Divides(divisor=Ref("_n"), dividend=Var("n")), Eq(GCD(a=Var("n"), b=Const(21)), Const(1))))),
"a": Const(5),
... | NT | null | COUNT | sympy | C5 | [
"C5"
] | 1d9668 | nt_count_intersection_v1 | null | 5 | 0 | [
"C5"
] | 1 | 0.544 | 2026-02-08T19:14:46.167935Z | {
"verified": true,
"answer": 333,
"timestamp": "2026-02-08T19:14:46.712115Z"
} | f2d471 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 161,
"completion_tokens": 1512
},
"timestamp": "2026-02-18T21:43:47.206Z",
"answer": 333
},
{
... | 1 | [
{
"lemma": "C5",
"status": "ok"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
},
{
"lemma": "VAL_SUM_EQ",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
3ffc67 | nt_min_with_divisor_count_v1_677425708_2203 | Let $N = 16$. Consider the set of all ordered pairs $(x, y)$ of positive integers such that $xy = 16$. Let $s$ be the minimum value of $x + y$ over all such pairs. Let $U = 30976$. Find the smallest positive integer $n$ such that $1 \leq n \leq U$ and the number of positive divisors of $n$ is equal to $s$. | 24 | graphs = [
Graph(
let={
"_n": Const(16),
"upper": Const(30976),
"div_count": 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("_... | NT | null | EXTREMUM | sympy | SUM_ARITHMETIC | [
"B3"
] | 0cd20d | nt_min_with_divisor_count_v1 | null | 6 | 0 | [
"B3",
"SUM_ARITHMETIC"
] | 2 | 1.456 | 2026-02-08T04:51:01.450740Z | {
"verified": true,
"answer": 24,
"timestamp": "2026-02-08T04:51:02.906601Z"
} | f4cc12 | 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": 1124
},
"timestamp": "2026-02-11T22:09:25.313Z",
"answer": 24
},
{
"id... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "V1",
"status": "no"
},
{
"lemma": "V3",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
}
] | {
"lo": -8.32,
"mid": -5.11,
"hi": -2.37
} | ||
9b2e94 | sequence_count_fib_divisible_v1_458359167_1004 | Let $d$ be the number of positive integers $p$ for which there exists a positive integer $q$ such that $pq = 36$, $\gcd(p, q) = 1$, and $p < q$.
Let $n$ be an integer such that $1 \le n \le 470$ and $d$ divides the $n$-th Fibonacci number.
Compute the number of such integers $n$. | 156 | graphs = [
Graph(
let={
"upper": Const(470),
"d": CountOverSet(set=SolutionsSet(var=Var("p"), condition=And(IsPositive(arg=Var(name='p')), Exists(var=Var(name='q'), condition=And(Eq(left=Mul(Var(name='p'), Var(name='q')), right=Const(value=36)), Eq(left=GCD(a=Var(name='p'), b=Var(nam... | NT | null | COUNT | sympy | MIN_PRIME_FACTOR | [
"COPRIME_PAIRS"
] | 2bb3aa | sequence_count_fib_divisible_v1 | null | 6 | 0 | [
"COPRIME_PAIRS",
"MIN_PRIME_FACTOR"
] | 2 | 1.902 | 2026-02-08T04:13:18.814872Z | {
"verified": true,
"answer": 156,
"timestamp": "2026-02-08T04:13:20.716713Z"
} | e1e096 | 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": 1144
},
"timestamp": "2026-02-10T15:52:57.386Z",
"answer": 156
},
{
"i... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "n... | {
"lo": -3.42,
"mid": 1.86,
"hi": 7.55
} | ||
2164fb | comb_count_partitions_v1_458359167_1522 | Let $n$ be the number of positive integers $k$ such that $1 \leq k \leq 516$ and $12$ divides the $k$-th Fibonacci number. Compute the number of integer partitions of $n$. | 63,261 | graphs = [
Graph(
let={
"_n": Const(12),
"n": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Const(516)), Divides(divisor=Ref("_n"), dividend=Fibonacci(arg=Var(name='n')))))),
"result": Partition(arg=Ref(name='n')),
... | NT | COMB | COUNT | sympy | COUNT_FIB_DIVISIBLE | [
"COUNT_FIB_DIVISIBLE"
] | 66de3c | comb_count_partitions_v1 | null | 7 | 0 | [
"COUNT_FIB_DIVISIBLE"
] | 1 | 0.001 | 2026-02-08T04:41:45.808704Z | {
"verified": true,
"answer": 63261,
"timestamp": "2026-02-08T04:41:45.810141Z"
} | 8f7299 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 161,
"completion_tokens": 3750
},
"timestamp": "2026-02-11T21:51:38.958Z",
"answer": 63261
},
{
... | 1 | [
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "ok"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
}
] | {
"lo": -3.42,
"mid": 1.86,
"hi": 7.55
} | ||
72d36e | antilemma_k3_v1_677425708_2039 | Let $n = 68516$. Define $x = \sum_{d \mid n} \phi(d)$, where the sum is over all positive divisors $d$ of $n$ and $\phi$ is Euler's totient function. Compute the remainder when $16651x$ is divided by $93860$. | 85,476 | graphs = [
Graph(
let={
"_n": Const(68516),
"x": SumOverDivisors(n=Ref(name='_n'), var='d', expr=EulerPhi(n=Var(name='d'))),
"Q": Mod(value=Mul(Const(16651), Ref("x")), modulus=Const(93860)),
},
goal=Ref("Q"),
)
] | NT | COMB | COMPUTE | sympy | K3 | [
"K3"
] | 54c41e | antilemma_k3_v1 | null | 4 | 0 | [
"K3"
] | 1 | 0.001 | 2026-02-08T04:43:19.377383Z | {
"verified": true,
"answer": 85476,
"timestamp": "2026-02-08T04:43:19.377896Z"
} | 3e1593 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 178,
"completion_tokens": 1902
},
"timestamp": "2026-02-10T04:58:26.761Z",
"answer": 85476
},
{
"... | 1 | [
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K3",
"status": "ok"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "V3",
"status": "no"
}
] | {
"lo": -3.45,
"mid": 1.15,
"hi": 6.18
} | ||
c25b99 | nt_min_with_divisor_count_v1_1918700295_3948 | Define $U$ to be the number of integers $t$ such that $7 \leq t \leq 1610$ and there exist positive integers $a$ and $b$ with $1 \leq a \leq 298$, $1 \leq b \leq 60$, and $t = 5a + 2b$. Let $d = 8$. Define $n_{\min}$ to be the smallest positive integer $n$ such that $1 \leq n \leq U$ and $n$ has exactly $d$ positive di... | 61,491 | 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=298)), Geq(left=Var(name='b'), right=Const(v... | NT | null | EXTREMUM | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | nt_min_with_divisor_count_v1 | null | 5 | 0 | [
"LIN_FORM"
] | 1 | 0.066 | 2026-02-08T09:03:38.643284Z | {
"verified": true,
"answer": 61491,
"timestamp": "2026-02-08T09:03:38.709400Z"
} | 263859 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 185,
"completion_tokens": 5401
},
"timestamp": "2026-02-14T00:02:44.200Z",
"answer": 61491
},
... | 1 | [
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"... | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
9732c1 | nt_count_divisors_in_range_v1_1978505735_5589 | Let $n$ be the number of positive integers at most $11759$ that are relatively prime to $14$. Determine the number of positive divisors $d$ of $n$ such that $1 \leq d \leq 219$. | 43 | graphs = [
Graph(
let={
"n": CountOverSet(set=SolutionsSet(var=Var("n1"), condition=And(Geq(Var("n1"), Const(1)), Leq(Var("n1"), Const(11759)), Eq(GCD(a=Var("n1"), b=Const(14)), Const(1))))),
"a": Const(1),
"b": Const(219),
"result": CountOverSet(set=Solutions... | NT | null | COUNT | sympy | COMB1 | [
"C4"
] | 08d162 | nt_count_divisors_in_range_v1 | null | 4 | 0 | [
"C4",
"COMB1"
] | 2 | 0.165 | 2026-02-08T19:05:50.832651Z | {
"verified": true,
"answer": 43,
"timestamp": "2026-02-08T19:05:50.997195Z"
} | 293eab | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 96,
"completion_tokens": 3486
},
"timestamp": "2026-02-18T21:21:26.085Z",
"answer": 43
},
{
... | 1 | [
{
"lemma": "C4",
"status": "ok"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "V3",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
7125df | nt_count_gcd_equals_v1_1918700295_1168 | Let $T$ be the set of all positive integers $t$ such that $9 \leq t \leq 7589$ and there exist positive integers $a \leq 836$ and $b \leq 849$ satisfying $t = 4a + 5b$. Let $\text{upper}$ be the number of elements in $T$. Compute the number of positive integers $n$ such that $1 \leq n \leq \text{upper}$ and $\gcd(n, 12... | 118 | 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=836)), Geq(left=Var(name='b'), right=Const(v... | NT | null | COUNT | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | nt_count_gcd_equals_v1 | null | 5 | 0 | [
"LIN_FORM"
] | 1 | 0.64 | 2026-02-08T05:36:38.522816Z | {
"verified": true,
"answer": 118,
"timestamp": "2026-02-08T05:36:39.162951Z"
} | 74f114 | 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": 4866
},
"timestamp": "2026-02-12T11:06:01.106Z",
"answer": 118
},
{
... | 1 | [
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
}
] | {
"lo": -5.55,
"mid": -3.01,
"hi": 0.32
} | ||
607766 | comb_factorial_compute_v1_2051736721_4798 | Let $P$ be the set of all positive integers $p$ for which there exists a positive integer $q$ such that $pq = 5880$, $\gcd(p, q) = 1$, and $p < q$. Let $n$ be the number of elements in $P$. Compute $n!$. Let $c = 65331$ and $N = 62792$. Find the remainder when $c \cdot n!$ is divided by $N$. | 21,520 | graphs = [
Graph(
let={
"_n": Const(62792),
"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=5880)), Eq(left=GCD(a=Var(name='p'), b=Var(na... | NT | null | COMPUTE | sympy | COPRIME_PAIRS | [
"COPRIME_PAIRS"
] | 2bb3aa | comb_factorial_compute_v1 | null | 4 | 0 | [
"COPRIME_PAIRS"
] | 1 | 0.002 | 2026-02-08T18:09:48.671865Z | {
"verified": true,
"answer": 21520,
"timestamp": "2026-02-08T18:09:48.674202Z"
} | 1abc72 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 147,
"completion_tokens": 3149
},
"timestamp": "2026-02-18T14:28:24.159Z",
"answer": 21520
},
... | 1 | [
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "V7",
"status": "no... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
fa4f64 | nt_count_digit_sum_v1_397696148_1818 | Let $s$ be the number of integers $t$ with $20 \leq t \leq 96$ such that there exist integers $a$ and $b$ satisfying $1 \leq a \leq 3$, $1 \leq b \leq 9$, and $t = 14a + 6b$. Let $N$ be the number of positive integers $n$ with $1 \leq n \leq 83521$ such that the sum of the decimal digits of $n$ is equal to $s$. Compute... | 32,726 | graphs = [
Graph(
let={
"_n": Const(83723),
"upper": Const(83521),
"target_sum": CountOverSet(set=SolutionsSet(var=Var("t"), condition=Exists(var=Var(name='a'), condition=Exists(var=Var(name='b'), condition=And(Geq(left=Var(name='a'), right=Const(value=1)), Leq(left=Var(n... | NT | null | COUNT | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | nt_count_digit_sum_v1 | null | 5 | 0 | [
"LIN_FORM"
] | 1 | 6.369 | 2026-02-08T12:47:06.487488Z | {
"verified": true,
"answer": 32726,
"timestamp": "2026-02-08T12:47:12.856666Z"
} | 5df586 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 176,
"completion_tokens": 4554
},
"timestamp": "2026-02-15T05:47:15.861Z",
"answer": 32726
},
... | 1 | [
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "V3",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
},
{
"lemma": "VAL_SUM_EQ",
"status": "no"
}
] | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
09812d | comb_count_derangements_v1_677425708_3510 | Let $n$ be the number of positive integers $p$ for which there exists a positive integer $q$ such that $p \cdot q = 13230$, $\gcd(p, q) = 1$, and $p < q$. Let $!n$ denote the number of derangements of $n$ elements. Find the remainder when $61678 \cdot !n$ is divided by 82623. | 67,918 | graphs = [
Graph(
let={
"_n": Const(82623),
"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=13230)), Eq(left=GCD(a=Var(name='p'), b=Var(n... | NT | COMB | COUNT | sympy | COPRIME_PAIRS | [
"COPRIME_PAIRS"
] | 2bb3aa | comb_count_derangements_v1 | null | 5 | 0 | [
"COPRIME_PAIRS"
] | 1 | 0.001 | 2026-02-08T05:47:12.841643Z | {
"verified": true,
"answer": 67918,
"timestamp": "2026-02-08T05:47:12.842618Z"
} | 1ac5e0 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 134,
"completion_tokens": 1952
},
"timestamp": "2026-02-12T15:02:24.634Z",
"answer": 67918
},
... | 1 | [
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "MOD_MUL",
... | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
64790a | comb_count_surjections_v1_809748730_754 | Let $n$ be the number of ordered pairs $(i, j)$ of positive integers such that $i \leq 6$, $j \leq 7$, and $i + j = 8$. Compute the remainder when $77429 \cdot (5! \cdot S(n, 5))$ is divided by $91313$, where $S(n, 5)$ denotes the Stirling number of the second kind. | 28,562 | graphs = [
Graph(
let={
"_n": Const(8),
"n": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("i"), Var("j")]), condition=Eq(Sum(Var("i"), Var("j")), Ref("_n")), domain=CartesianProduct(left=IntegerRange(start=Const(1), end=Const(6)), right=IntegerRange(start=Const(1), end=Const... | COMB | null | COUNT | sympy | COUNT_SUM_EQUALS | [
"COUNT_SUM_EQUALS"
] | 75ab0f | comb_count_surjections_v1 | null | 3 | 0 | [
"COUNT_SUM_EQUALS"
] | 1 | 0.013 | 2026-02-08T11:43:35.041966Z | {
"verified": true,
"answer": 28562,
"timestamp": "2026-02-08T11:43:35.055273Z"
} | 0160a2 | 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": 1628
},
"timestamp": "2026-02-24T14:38:47.500Z",
"answer": 28562
},
{
"... | 1 | [
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "ok"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8",
... | {
"lo": -2.35,
"mid": 1.22,
"hi": 4.84
} | ||
2e8ad4 | comb_binomial_compute_v1_397696148_180 | Let $n = \sum_{k=1}^{5} k$. Define $\text{result} = \binom{n}{8}$. Compute the remainder when the product of $80453$ and $\text{result}$ is divided by $91002$. | 4,677 | graphs = [
Graph(
let={
"_n": Const(80453),
"n": Summation(var="k", start=Const(1), end=Const(5), expr=Var("k")),
"k": Const(8),
"result": Binom(n=Ref("n"), k=Ref("k")),
"Q": Mod(value=Mul(Ref("_n"), Ref("result")), modulus=Const(91002)),
}... | ALG | COMB | COMPUTE | sympy | SUM_ARITHMETIC | [
"SUM_ARITHMETIC"
] | eb34f0 | comb_binomial_compute_v1 | null | 2 | 0 | [
"SUM_ARITHMETIC"
] | 1 | 0.001 | 2026-02-08T11:21:01.173654Z | {
"verified": true,
"answer": 4677,
"timestamp": "2026-02-08T11:21:01.174808Z"
} | 22c443 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 165,
"completion_tokens": 1207
},
"timestamp": "2026-02-24T13:30:50.620Z",
"answer": 4677
},
{
"i... | 1 | [
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "SUM_ARITHMETIC",
"status": "ok"
}
] | {
"lo": -2.35,
"mid": 1.22,
"hi": 4.84
} | ||
0d009d | diophantine_sum_product_min_v1_260342960_45 | Let $ S = 73 $, $ P = 1332 $, and $ n = 72 $. Let $ x $ be the smallest integer such that $ 1 \leq x \leq n $ and $ x(S - x) = P $. Define
$$
Q = x^2 + 8x + \sum_{k=1}^{m} k,
$$
where
$$
m = \sum_{k=1}^{8} \phi(k) \left\lfloor \frac{8}{k} \right\rfloor.
$$
Compute the value of $ Q $. | 2,250 | graphs = [
Graph(
let={
"_n": Const(72),
"S": Const(73),
"P": Const(1332),
"result": MinOverSet(set=SolutionsSet(var=Var("x"), condition=And(Geq(Var("x"), Const(1)), Leq(Var("x"), Ref("_n")), Eq(Mul(Var("x"), Sub(Ref("S"), Var("x"))), Ref("P"))))),
... | NT | null | EXTREMUM | sympy | K2 | [
"K2/SUM_ARITHMETIC"
] | eeca34 | diophantine_sum_product_min_v1 | quadratic_mod | 5 | 0 | [
"K2",
"SUM_ARITHMETIC"
] | 2 | 0.018 | 2026-02-08T11:12:00.700193Z | {
"verified": true,
"answer": 2250,
"timestamp": "2026-02-08T11:12:00.718317Z"
} | c5100e | 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": 841
},
"timestamp": "2026-02-08T20:28:02.074Z",
"answer": 2250
},
{
"id... | 1 | [
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K2",
"status": "ok"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
... | {
"lo": -5.54,
"mid": -3.03,
"hi": -0.32
} | ||
6fea29 | algebra_poly_eval_v1_458359167_5239 | Let $n$ be the number of integers $t$ with $9 \le t \le 34$ for which there exist positive integers $a$ and $b$ such that $1 \le a \le 10$, $1 \le b \le 2$, and $t = 2a + 7b$. Let $k_{\text{max}}$ be the largest integer $k$ such that $3^k \le 43$. Compute $k_{\text{max}} \cdot n^3 + 8n^2 - 3n + 6$. | 27,146 | graphs = [
Graph(
let={
"_c": Const(43),
"_m": Const(3),
"_n": Summation(var="k", start=Const(1), end=Const(3), expr=Var("k")),
"n": CountOverSet(set=SolutionsSet(var=Var("t"), condition=Exists(var=Var(name='a'), condition=Exists(var=Var(name='b'), condition=A... | NT | null | COMPUTE | sympy | SUM_ARITHMETIC | [
"SUM_ARITHMETIC/LIN_FORM",
"MAX_VAL"
] | 519e5a | algebra_poly_eval_v1 | null | 4 | 0 | [
"LIN_FORM",
"MAX_VAL",
"SUM_ARITHMETIC"
] | 3 | 0.006 | 2026-02-08T12:21:06.241772Z | {
"verified": true,
"answer": 27146,
"timestamp": "2026-02-08T12:21:06.247537Z"
} | 91a015 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 169,
"completion_tokens": 1560
},
"timestamp": "2026-02-15T00:37:54.990Z",
"answer": 27146
},
... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K16",
"status": "same_pattern_wrong"
},
{
"lemma": "LIN_FORM",
"status": "ok_later"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status... | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
eacc9c | modular_count_residue_v1_717093673_1840 | Let $r$ be the largest prime number less than or equal to $13$. Determine the number of positive integers $n_1$ such that $1 \leq n_1 \leq 88209$ and $n_1 \equiv r \pmod{21}$. Compute this number. | 4,200 | graphs = [
Graph(
let={
"_n": Const(13),
"upper": Const(88209),
"m": Const(21),
"r": MaxOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(2)), Leq(Var("n"), Ref("_n")), IsPrime(Var("n"))))),
"result": CountOverSet(set=Solutio... | NT | null | COUNT | sympy | MAX_PRIME_BELOW | [
"MAX_PRIME_BELOW"
] | dc3ad3 | modular_count_residue_v1 | null | 3 | 0 | [
"MAX_PRIME_BELOW"
] | 1 | 3.486 | 2026-02-08T16:22:20.769250Z | {
"verified": true,
"answer": 4200,
"timestamp": "2026-02-08T16:22:24.254836Z"
} | be1aae | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 108,
"completion_tokens": 597
},
"timestamp": "2026-02-17T01:31:26.532Z",
"answer": 4200
},
{
... | 1 | [
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "V1",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
453337 | nt_count_intersection_v1_655260480_3475 | Let $N = 50000$. Let $a$ be the largest prime number $n$ such that $2 \leq n \leq 12$. Let $T$ be the set of all positive integers $n_1$ with $1 \leq n_1 \leq N$ such that $a$ divides $n_1$ and $\gcd(n_1, 15) = 1$. Let $r$ be the number of elements in $T$. Compute the remainder when $23460 \cdot r$ is divided by $64177... | 6,218 | graphs = [
Graph(
let={
"N": Const(50000),
"a": MaxOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(2)), Leq(Var("n"), Const(12)), IsPrime(Var("n"))))),
"b": Const(15),
"result": CountOverSet(set=SolutionsSet(var=Var("n1"), condition=An... | NT | null | COUNT | sympy | MAX_PRIME_BELOW | [
"MAX_PRIME_BELOW"
] | dc3ad3 | nt_count_intersection_v1 | null | 4 | 0 | [
"MAX_PRIME_BELOW"
] | 1 | 1.624 | 2026-02-08T17:23:58.446747Z | {
"verified": true,
"answer": 6218,
"timestamp": "2026-02-08T17:24:00.070650Z"
} | cc409d | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 163,
"completion_tokens": 1481
},
"timestamp": "2026-02-18T01:33:06.544Z",
"answer": 6218
},
{... | 1 | [
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok"
... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
5b4015 | lin_form_endings_v1_124444284_4505 | Let $t$ be an integer such that $56 \leq t \leq 1421$. Let $k$ be the number of such $t$ for which there exist positive integers $a$ and $b$ with $1 \leq a \leq 13$, $1 \leq b \leq 46$, and $t = 35a + 21b$. Compute the remainder when $11460 \cdot k$ is divided by $75236$. | 47,872 | graphs = [
Graph(
let={
"_inner_result": CountOverSet(set=SolutionsSet(var=Var("t"), condition=Exists(var=Var(name='a'), condition=Exists(var=Var(name='b'), condition=And(Geq(left=Var(name='a'), right=Const(value=1)), Leq(left=Var(name='a'), right=Const(value=13)), Geq(left=Var(name='b'), right=... | COMB | null | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | lin_form_endings_v1 | null | 4 | null | [
"LIN_FORM"
] | 1 | 0.001 | 2026-02-08T06:03:40.710342Z | {
"verified": true,
"answer": 47872,
"timestamp": "2026-02-08T06:03:40.711459Z"
} | 464292 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 213,
"completion_tokens": 2303
},
"timestamp": "2026-02-24T05:16:27.225Z",
"answer": 47872
},
{
"... | 1 | [
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "V8",
"status": "no"
},
{
"lemma": "V8_SUM",
"s... | {
"lo": 1.97,
"mid": 4.36,
"hi": 6.69
} | ||
da0087 | antilemma_cartesian_v1_397696148_829 | Let $x$ be the number of ordered pairs $(i, j)$ such that $1 \leq i \leq 34$ and $1 \leq j \leq 35$. Define $Q$ to be the smallest positive integer $k$ such that the $k$-th Fibonacci number is divisible by $|x| + 2$. Find the value of $Q$. | 222 | graphs = [
Graph(
let={
"x": CountOverSet(set=CartesianProduct(left=IntegerRange(start=Const(1), end=Const(34)), right=IntegerRange(start=Const(1), end=Const(35)))),
"Q": FibonacciEntryPoint(modulus=Sum(Abs(arg=Ref(name='x')), Const(value=2))),
},
goal=Ref("Q"),
)... | COMB | GEOM | COMPUTE | sympy | COUNT_CARTESIAN | [
"COUNT_CARTESIAN"
] | 409d7d | antilemma_cartesian_v1 | null | 3 | 0 | [
"COUNT_CARTESIAN"
] | 1 | 0.001 | 2026-02-08T11:46:25.150543Z | {
"verified": true,
"answer": 222,
"timestamp": "2026-02-08T11:46:25.151493Z"
} | 25b3c8 | 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": 4831
},
"timestamp": "2026-02-24T14:38:10.565Z",
"answer": 222
},
{
"id... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "ok"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "V7",
... | {
"lo": -2.35,
"mid": 1.22,
"hi": 4.84
} | ||
23551f | nt_num_divisors_compute_v1_865884756_6752 | Let $N$ be the number of positive integers $n_1$ such that $1 \le n_1 \le 1199$ and $\gcd(n_1, 6) = 1$. Let $d(N)$ be the number of positive divisors of $N$. Compute the remainder when $24433 \cdot d(N)$ is divided by $62790$. | 52,545 | graphs = [
Graph(
let={
"_n": Const(6),
"n": CountOverSet(set=SolutionsSet(var=Var("n1"), condition=And(Geq(Var("n1"), Const(1)), Leq(Var("n1"), Const(1199)), Eq(GCD(a=Var("n1"), b=Ref("_n")), Const(1))))),
"result": NumDivisors(n=Ref("n")),
"_c": Const(24433)... | NT | null | COMPUTE | sympy | C4 | [
"C4"
] | 08d162 | nt_num_divisors_compute_v1 | null | 4 | 0 | [
"C4"
] | 1 | 0.002 | 2026-02-08T19:22:54.259038Z | {
"verified": true,
"answer": 52545,
"timestamp": "2026-02-08T19:22:54.260810Z"
} | fd2c8e | 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": 1336
},
"timestamp": "2026-02-18T22:10:39.801Z",
"answer": 52545
},
... | 1 | [
{
"lemma": "C4",
"status": "ok"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
bfcf21 | algebra_vieta_sum_v1_784195855_0 | Let $P(x)$ be the polynomial
$$
P(x) = x^4 + \left(\sum_{k=1}^{2} \phi(k) \left\lfloor \frac{2}{k} \right\rfloor\right) x^3 - 118x^2 - 300x + S,
$$
where $S$ is the minimum value of $x + y$ over all ordered pairs $(x, y)$ of positive integers such that $xy = 810000$.
Compute the product of all real roots of $P(x) = 0$... | 1,800 | graphs = [
Graph(
let={
"_m": Const(3),
"_n": Const(2),
"result": ProductOverSet(set=SolutionsSet(var=Var(name='x'), condition=Eq(left=Sum(Pow(base=Var(name='x'), exp=Const(value=4)), Mul(Summation(expr=Mul(EulerPhi(n=Var(name='k')), Floor(arg=Div(left=Const(value=2), rig... | NT | null | COMPUTE | sympy | COPRIME_PAIRS | [
"B3",
"K2"
] | f1ea07 | algebra_vieta_sum_v1 | null | 6 | 0 | [
"B3",
"COPRIME_PAIRS",
"K2"
] | 3 | 0.625 | 2026-02-08T02:53:22.329011Z | {
"verified": true,
"answer": 1800,
"timestamp": "2026-02-08T02:53:22.954221Z"
} | fe3f30 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 238,
"completion_tokens": 2078
},
"timestamp": "2026-02-08T19:57:37.571Z",
"answer": 1800
},
{
"i... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "K2",
"status": "ok"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "V... | {
"lo": -1.94,
"mid": 0.57,
"hi": 2.67
} | ||
bc8ef8 | nt_sum_gcd_range_mod_v1_1520064083_9377 | Let $S$ be the set of all nonnegative integers $j$ such that
\[
\sum_{k=0}^{8} (-1)^k \binom{8}{k} \leq j \leq 15340
\]
and
\[
\binom{15340}{j} \equiv 1 \pmod{2}.
\]
Let $N$ be the number of elements in $S$. Let $k = 180$ and define
\[
\text{sum} = \sum_{n=1}^{N} \gcd(n, k).
\]
Let $r$ be the remainder when $\text{sum... | 192 | graphs = [
Graph(
let={
"_n": Const(73811),
"N": CountOverSet(set=SolutionsSet(var=Var("j"), condition=And(Geq(Var("j"), Summation(var="k", start=Const(0), end=Const(8), expr=Mul(Pow(Const(-1), Var("k")), Binom(n=Const(8), k=Var("k"))))), Leq(Var("j"), Const(15340)), Eq(Mod(value=Bin... | COMB | NT | COMPUTE | sympy | BINOMIAL_ALTERNATING | [
"BINOMIAL_ALTERNATING",
"V8"
] | efe7d7 | nt_sum_gcd_range_mod_v1 | null | 7 | 0 | [
"BINOMIAL_ALTERNATING",
"V8"
] | 2 | 0.092 | 2026-02-08T10:42:46.546444Z | {
"verified": true,
"answer": 192,
"timestamp": "2026-02-08T10:42:46.638124Z"
} | 0f325a | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 205,
"completion_tokens": 4013
},
"timestamp": "2026-02-14T08:10:59.170Z",
"answer": 192
},
{
... | 1 | [
{
"lemma": "BINOMIAL_ALTERNATING",
"status": "ok"
},
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "V3",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
},
{
... | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
ccf308 | antilemma_k3_v1_1520064083_6723 | Let $n = 64629$. Compute the sum of $\phi(d)$ over all positive divisors $d$ of $n$, where $\phi$ denotes Euler's totient function. | 64,629 | graphs = [
Graph(
let={
"x": SumOverDivisors(n=Const(value=64629), var='d', expr=EulerPhi(n=Var(name='d'))),
},
goal=Ref("x"),
)
] | NT | COMB | COMPUTE | sympy | K3 | [
"K3"
] | 54c41e | antilemma_k3_v1 | null | 4 | 0 | [
"K3"
] | 1 | 0 | 2026-02-08T08:17:17.345794Z | {
"verified": true,
"answer": 64629,
"timestamp": "2026-02-08T08:17:17.346155Z"
} | b1b5e1 | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 1,
"correct": {
"strict": false,
"boxed": false,
"relaxed": true
},
"usage": {
"prompt_tokens": 100,
"completion_tokens": 635
},
"timestamp": "2026-02-15T19:59:09.815Z",
"answer": 6480
},
{
"id": 11,
... | 1 | [
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "K3",
"status": "ok"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "V1",
"status": "no"
}
] | {
"lo": -5.92,
"mid": -3.14,
"hi": 0.27
} | ||
688ae7 | algebra_quadratic_discriminant_v1_2051736721_5542 | Let $a = -2$, $b = 6$, and $c = 140$. Compute the discriminant $D = b^2 - 4ac$. Define $\alpha = 1$ if $D > 0$, and $\alpha = 0$ otherwise. Define $\beta = 1$ if $D = 0$, and $\beta = 0$ otherwise. Compute the value of $2\alpha + \beta$. | 2 | graphs = [
Graph(
let={
"a": Const(-2),
"b": Const(6),
"c": Const(140),
"D": Sub(Pow(Ref("b"), Const(2)), Mul(Const(4), Ref("a"), Ref("c"))),
"result": Sum(Mul(Const(2), Iverson(condition=Gt(Ref("D"), Const(0)))), Iverson(condition=Eq(Ref("D"), Con... | NT | null | COMPUTE | sympy | COPRIME_PAIRS | [
"C4/K3"
] | 97ada4 | algebra_quadratic_discriminant_v1 | null | 2 | 0 | [
"C4",
"COPRIME_PAIRS",
"K3"
] | 3 | 0.045 | 2026-02-08T18:39:44.784249Z | {
"verified": true,
"answer": 2,
"timestamp": "2026-02-08T18:39:44.829481Z"
} | e632fb | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 152,
"completion_tokens": 278
},
"timestamp": "2026-02-16T13:59:48.933Z",
"answer": 2
},
{
"id": 11,
"... | 2 | [
{
"lemma": "C4",
"status": "ok"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "K3",
"status": "ok_later"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma... | {
"lo": -10,
"mid": -7.27,
"hi": -4.54
} | ||
1c6f0e | nt_count_coprime_and_v1_784195855_3388 | Let $k_1$ be the minimum value of $x + y$ over all pairs of positive integers $(x, y)$ such that $xy = 4$. Let $k_2 = 9$. Let $r$ be the number of positive integers $n$ such that $1 \le n \le 84954$, $\gcd(n, k_1) = 1$, and $\gcd(n, k_2) = 1$. Let $Q = (44121 \cdot r) \bmod 77108$. Find the value of $Q$. | 37,554 | graphs = [
Graph(
let={
"_n": Const(44121),
"upper": Const(84954),
"k1": MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(Mul(Var("x"), Var("y")), Const(4)))... | NT | null | COUNT | sympy | B3 | [
"B3"
] | 0cd20d | nt_count_coprime_and_v1 | null | 5 | 0 | [
"B3"
] | 1 | 17.011 | 2026-02-08T06:24:14.300327Z | {
"verified": true,
"answer": 37554,
"timestamp": "2026-02-08T06:24:31.311748Z"
} | 42cf5a | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 167,
"completion_tokens": 5247
},
"timestamp": "2026-02-12T23:59:05.957Z",
"answer": 37554
},
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
}
... | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
93ae0a | geo_count_lattice_triangle_v1_601307018_6080 | Let $M = (a^3 - a) \bmod 9409$, where $a$ is an integer satisfying $0 \le a \le 9408$. Let $R = (M^3 - M) \bmod 9409$. Define $S = \left|128 \cdot 100 + 22 \cdot \left(\sum_{k=0}^{2} (-1)^k \binom{2}{k} - 23\right)\right|$ and $T = \gcd(128, 23) + \gcd(|22 - 128|, |100 - 23|) + \gcd(|0 - 22|, |0 - N|)$, where $N$ is th... | 6,146 | graphs = [
Graph(
let={
"_n": Const(2),
"area_2x": Abs(arg=Sum(Mul(Const(value=128), Const(value=100)), Mul(Const(value=22), Sub(left=Summation(expr=Mul(Pow(base=Const(value=-1), exp=Var(name='k')), Binom(n=Const(value=2), k=Var(name='k'))), var='k', start=Const(value=0), end=Const(v... | GEOM | COMB | COUNT | sympy | BINOMIAL_ALTERNATING | [
"BINOMIAL_ALTERNATING",
"POLY_ORBIT_HENSEL"
] | 845c0d | geo_count_lattice_triangle_v1 | null | 6 | 0 | [
"BINOMIAL_ALTERNATING",
"POLY_ORBIT_HENSEL"
] | 2 | 0.011 | 2026-03-10T06:40:05.799974Z | {
"verified": true,
"answer": 6146,
"timestamp": "2026-03-10T06:40:05.810609Z"
} | 122bf4 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 314,
"completion_tokens": 7946
},
"timestamp": "2026-04-19T03:34:51.496Z",
"answer": 6146
},
{
"... | 1 | [
{
"lemma": "BINOMIAL_ALTERNATING",
"status": "ok"
},
{
"lemma": "POLY_ORBIT_HENSEL",
"status": "ok"
}
] | {
"lo": -5.35,
"mid": 0.52,
"hi": 5.84
} | ||
87a6b0_l | antilemma_sum_equals_v1_168721529_141 | Let $n = 61$. Compute the number of ordered pairs $(i, j)$ of integers such that $1 \leq i \leq 61$, $1 \leq j \leq 61$, and $i + j = 61$. | 61 | COMB | GEOM | COMPUTE | sympy | COMB1 | [
"COUNT_SUM_EQUALS"
] | 75ab0f | antilemma_sum_equals_v1 | null | 2 | 0 | [
"COMB1",
"COUNT_SUM_EQUALS"
] | 2 | 0.074 | 2026-02-08T12:50:11.135120Z | {
"verified": false,
"answer": 60,
"timestamp": "2026-02-08T12:50:11.209158Z"
} | 9b8acb | 87a6b0 | 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": 169,
"completion_tokens": 208
},
"timestamp": "2026-02-08T21:06:41.766Z",
"answer": 60
},
{
"id":... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "ok"
},
{
"lemma": "V7",
... | {
"lo": -5.98,
"mid": -3.99,
"hi": -2
} | |
6ceafa | comb_catalan_compute_v1_1742523217_411 | Let $n$ be the number of integers $t$ such that $11 \leq t \leq 23$ and there exist positive integers $a$ and $b$ with $1 \leq a \leq 3$, $1 \leq b \leq 4$, and $t = 3a + 2b + 6$. Compute the $n$th Catalan number, defined by $C_n = \frac{1}{n+1} \binom{2n}{n}$. | 58,786 | graphs = [
Graph(
let={
"n": CountOverSet(set=SolutionsSet(var=Var("t"), condition=Exists(var=Var(name='a'), condition=Exists(var=Var(name='b'), condition=And(Geq(left=Var(name='a'), right=Const(value=1)), Leq(left=Var(name='a'), right=Const(value=3)), Geq(left=Var(name='b'), right=Const(value=1... | COMB | null | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | comb_catalan_compute_v1 | null | 4 | 0 | [
"LIN_FORM"
] | 1 | 0.002 | 2026-02-08T03:01:49.507221Z | {
"verified": true,
"answer": 58786,
"timestamp": "2026-02-08T03:01:49.509308Z"
} | af07ef | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 223,
"completion_tokens": 2007
},
"timestamp": "2026-02-09T17:35:17.500Z",
"answer": 58786
},
{
"... | 1 | [
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "V8",
"status": "no"
},
{
"lemma": "V8_SUM",
"st... | {
"lo": -3.83,
"mid": -1.68,
"hi": 1.09
} | ||
b42242 | comb_binomial_compute_v1_865884756_2740 | Let $n = 16$. Let $k$ be the maximum value of $xy$ over all ordered pairs $(x, y)$ of positive integers such that $x + y = 6$. Compute $\binom{n}{k}$. | 11,440 | graphs = [
Graph(
let={
"_n": Const(6),
"n": Const(16),
"k": MaxOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(Sum(Var("x"), Var("y")), Ref("_n")))), expr=Mul... | ALG | COMB | COMPUTE | sympy | B1 | [
"B1"
] | 5b950e | comb_binomial_compute_v1 | null | 4 | 0 | [
"B1"
] | 1 | 0.002 | 2026-02-08T16:55:14.428342Z | {
"verified": true,
"answer": 11440,
"timestamp": "2026-02-08T16:55:14.430141Z"
} | 75408c | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 95,
"completion_tokens": 1400
},
"timestamp": "2026-02-17T14:45:18.777Z",
"answer": 11440
},
{... | 1 | [
{
"lemma": "B1",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
}
] | {
"lo": -8,
"mid": -4.75,
"hi": -2.28
} | ||
a3c644 | nt_sum_divisors_mod_v1_1742523217_2283 | Let $P$ be the set of all positive integers $p$ for which there exists a positive integer $q$ such that $pq = 1600830$, $\gcd(p, q) = 1$, and $p < q$. Let $\nu$ be the number of elements in $P$. Define $n$ to be the number of positive integers $k$ such that $1 \le k \le 120960$ and $\nu$ divides $k$. Let $\sigma$ be th... | 8,158 | 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=1600830)), Eq(left=GCD(a=Var(name='p'), b=Var(name='q')), right=Const(value=... | NT | null | COMPUTE | sympy | COPRIME_PAIRS | [
"COPRIME_PAIRS/C2"
] | 7a1379 | nt_sum_divisors_mod_v1 | null | 6 | 0 | [
"C2",
"COPRIME_PAIRS"
] | 2 | 0.004 | 2026-02-08T04:40:42.531994Z | {
"verified": true,
"answer": 8158,
"timestamp": "2026-02-08T04:40:42.536317Z"
} | ae0138 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 239,
"completion_tokens": 2424
},
"timestamp": "2026-02-11T21:43:32.169Z",
"answer": 8158
},
{
"... | 1 | [
{
"lemma": "C2",
"status": "ok_later"
},
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "V1",
"status": "no"
... | {
"lo": -3.42,
"mid": 1.86,
"hi": 7.55
} | ||
567773 | geo_count_lattice_rect_v1_865884756_3104 | Let $a = 25$ and $b = 54$. Let $R$ be the number of lattice points in the rectangle $[0, a] \times [0, b]$, including the boundary. Compute the remainder when $22427 \cdot R$ is divided by $60282$. | 586 | graphs = [
Graph(
let={
"a": Const(25),
"b": Const(54),
"result": LatticePointsRect(a=Ref(name='a'), b=Ref(name='b')),
"Q": Mod(value=Mul(Const(22427), Ref("result")), modulus=Const(60282)),
},
goal=Ref("Q"),
)
] | GEOM | null | COUNT | sympy | [] | geo_count_lattice_rect_v1 | null | 3 | 0 | null | null | 0.001 | 2026-02-08T17:10:47.656811Z | {
"verified": true,
"answer": 586,
"timestamp": "2026-02-08T17:10:47.657882Z"
} | d99835 | 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": 722
},
"timestamp": "2026-02-17T20:55:11.486Z",
"answer": 586
},
{
... | 1 | [] | {
"lo": -2.38,
"mid": 1.74,
"hi": 6.59
} | ||||
209558 | nt_min_coprime_above_v1_677425708_2528 | Let $n$ be an integer. Define $\mathcal{P}$ as the set of all integers $n$ such that $2 \leq n \leq 3$ and $n$ is prime. Let $S$ be the set of all positive integers $d$ such that $d$ divides 478661 and $d \geq |\mathcal{P}|$. Let $m$ be the smallest element of $S$. Determine the value of the smallest integer $n$ such t... | 28,901 | graphs = [
Graph(
let={
"_n": Const(2),
"start": Const(28900),
"upper": Const(28983),
"modulus": MinOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Ref("_n")), Leq(Var("... | NT | null | EXTREMUM | sympy | COUNT_PRIMES | [
"COUNT_PRIMES/MIN_PRIME_FACTOR",
"ONE_PHI_2"
] | 84f657 | nt_min_coprime_above_v1 | null | 5 | 0 | [
"COUNT_PRIMES",
"MIN_PRIME_FACTOR",
"ONE_PHI_2"
] | 3 | 0.05 | 2026-02-08T05:06:30.953646Z | {
"verified": true,
"answer": 28901,
"timestamp": "2026-02-08T05:06:31.003908Z"
} | 2d295f | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 244,
"completion_tokens": 588
},
"timestamp": "2026-02-18T15:10:46.118Z",
"answer": 28901
}
] | 2 | [
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_PRIMES",
"status": "ok"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "MIN_PRIME_FACTOR",
"status": "ok_later"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "ON... | {
"lo": -10,
"mid": -6.47,
"hi": -2.95
} | ||
dc11f9 | modular_mod_compute_v1_784195855_2180 | Let $n = 156$. Consider the set of all ordered pairs $(x, y)$ of positive integers such that $x + y = n$. Let $m$ be the maximum value of $xy$ over all such pairs. Compute the remainder when $-128$ is divided by $m$. | 5,956 | graphs = [
Graph(
let={
"_n": Const(156),
"a": Const(-128),
"m": MaxOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(Sum(Var("x"), Var("y")), Ref("_n")))), expr... | NT | null | COMPUTE | sympy | B1 | [
"B1"
] | 5b950e | modular_mod_compute_v1 | null | 4 | 0 | [
"B1"
] | 1 | 0.002 | 2026-02-08T05:32:08.351007Z | {
"verified": true,
"answer": 5956,
"timestamp": "2026-02-08T05:32:08.353077Z"
} | 15b5ed | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 121,
"completion_tokens": 521
},
"timestamp": "2026-02-11T22:53:13.874Z",
"answer": 6014
},
{
"id": 11,... | 1 | [
{
"lemma": "B1",
"status": "ok"
},
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "V1",
"status": "no"
}
] | {
"lo": -7.01,
"mid": -4.68,
"hi": -2.15
} | ||
c23d2a | lin_form_endings_v1_1918700295_3494 | Let $a = 35$ and $b = 15$. Let $A = 9$ and $B = 44$. Let $g = \gcd(a, b)$. Define $N = aA + bB - a - b$. Let $s = \left\lfloor \frac{N}{g} \right\rfloor + 1$. Compute the remainder when $14610 \cdot s$ is divided by 97140. | 94,680 | graphs = [
Graph(
let={
"a_coeff": Const(35),
"b_coeff": Const(15),
"A_val": Const(9),
"B_val": Const(44),
"g_step": GCD(a=Ref("a_coeff"), b=Ref("b_coeff")),
"numerator": Sub(Sum(Mul(Ref("a_coeff"), Ref("A_val")), Mul(Ref("b_coeff"), Re... | COMB | NT | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | lin_form_endings_v1 | null | 4 | null | [
"LIN_FORM"
] | 1 | 0.001 | 2026-02-08T08:40:03.074675Z | {
"verified": true,
"answer": 94680,
"timestamp": "2026-02-08T08:40:03.075790Z"
} | 518361 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 139,
"completion_tokens": 1365
},
"timestamp": "2026-02-13T20:24:44.429Z",
"answer": 94680
},
... | 1 | [
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "V8",
"status": "no"
},
{
"lemma": "V8_SUM",
"st... | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
ec62cb | comb_catalan_compute_v1_1915831931_1556 | Let $n$ be the number of positive integers $t$ such that $7 \leq t \leq 20$ and there exist positive integers $a$, $b$ with $1 \leq a \leq 5$, $1 \leq b \leq 2$, and $t = 2a + 5b$. Define $\text{result}$ to be the $n$-th Catalan number. Compute the remainder when $46681 \cdot \text{result}$ is divided by $58817$. Find ... | 23,466 | graphs = [
Graph(
let={
"_n": Const(58817),
"n": CountOverSet(set=SolutionsSet(var=Var("t"), condition=Exists(var=Var(name='a'), condition=Exists(var=Var(name='b'), condition=And(Geq(left=Var(name='a'), right=Const(value=1)), Leq(left=Var(name='a'), right=Const(value=5)), Geq(left=Va... | COMB | null | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | comb_catalan_compute_v1 | null | 4 | 0 | [
"LIN_FORM"
] | 1 | 0.002 | 2026-02-08T16:14:38.018102Z | {
"verified": true,
"answer": 23466,
"timestamp": "2026-02-08T16:14:38.020548Z"
} | 0a2716 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 232,
"completion_tokens": 1357
},
"timestamp": "2026-02-24T20:29:08.127Z",
"answer": 23466
},
{
... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "V7",
"status... | {
"lo": -2.4,
"mid": 1.57,
"hi": 5.75
} | ||
0460f3 | comb_count_permutations_fixed_v1_1526740231_133 | Let $n$ be the smallest divisor of $9625$ that is at least $2$. Let $k = 1$. Define $\text{result} = \binom{n}{k} \cdot !(n - k)$, where $!m$ denotes the number of derangements of $m$ elements. Compute the remainder when $44121 \cdot \text{result}$ is divided by $79108$. | 7,745 | graphs = [
Graph(
let={
"_n": Const(79108),
"n": MinOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Const(2)), Divides(divisor=Var("d"), dividend=Const(9625))))),
"k": Const(1),
"result": Mul(Binom(n=Ref("n"), k=Ref("k")), Subfactorial(arg=S... | NT | COMB | COUNT | sympy | MIN_PRIME_FACTOR | [
"MIN_PRIME_FACTOR"
] | bc3776 | comb_count_permutations_fixed_v1 | null | 4 | 0 | [
"MIN_PRIME_FACTOR"
] | 1 | 0.001 | 2026-02-08T11:22:02.734397Z | {
"verified": true,
"answer": 7745,
"timestamp": "2026-02-08T11:22:02.735874Z"
} | 60e11d | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 133,
"completion_tokens": 879
},
"timestamp": "2026-02-14T13:01:32.981Z",
"answer": 7745
},
{
... | 1 | [
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "MIN_PRIME_FACTOR",
"status": "ok"
},
{
"lemma": "V5",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
}
] | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
4772ec | nt_min_phi_inverse_v1_971394319_474 | Let $n = 888$. Let $S$ be the set of all positive integers $t$ such that $15 \leq t \leq 318$ and there exist positive integers $a$, $b$ with $1 \leq a \leq 14$, $1 \leq b \leq 32$, satisfying $t = 9a + 6b$. Let $u$ be the number of elements in $S$. Let $k = 24$. Let $T$ be the set of all positive integers $n$ with $1 ... | 853 | graphs = [
Graph(
let={
"_n": Const(888),
"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=14)), Geq(left... | NT | null | EXTREMUM | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | nt_min_phi_inverse_v1 | null | 6 | 0 | [
"LIN_FORM"
] | 1 | 0.015 | 2026-02-08T13:06:46.731011Z | {
"verified": true,
"answer": 853,
"timestamp": "2026-02-08T13:06:46.745772Z"
} | ed2ec3 | 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": 5000
},
"timestamp": "2026-02-15T09:47:50.375Z",
"answer": 853
},
{
... | 1 | [
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
}
] | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
216863 | nt_sum_divisors_compute_v1_898971024_808 | Let $m = 1521$. Let $S$ be the set of all ordered pairs $(x, y)$ of positive integers such that $xy = m$. Let $P$ be the set of all values $x + y$ as $(x, y)$ ranges over $S$. Let $s$ be the minimum value in $P$. Now let $T$ be the set of all ordered pairs $(x, y)$ of positive integers such that $x + y = s$. Let $R$ be... | 55,429 | graphs = [
Graph(
let={
"_m": Const(1521),
"_n": Const(59036),
"n": Const(58996),
"result": SumDivisors(n=Ref("n")),
"Q": Mod(value=Sub(MaxOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(ar... | NT | null | COMPUTE | sympy | B3 | [
"B3/B1"
] | 6cdf3d | nt_sum_divisors_compute_v1 | negation_mod | 7 | 0 | [
"B1",
"B3"
] | 2 | 0.004 | 2026-02-08T15:40:13.988040Z | {
"verified": true,
"answer": 55429,
"timestamp": "2026-02-08T15:40:13.991900Z"
} | b0d8ad | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 226,
"completion_tokens": 1365
},
"timestamp": "2026-02-16T11:53:02.243Z",
"answer": 55429
},
... | 1 | [
{
"lemma": "B1",
"status": "ok_later"
},
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
15503a | modular_sum_quadratic_residues_v1_677425708_159 | Let $p$ be the number of ordered pairs $(i, j)$ of positive integers such that $1 \leq i \leq 11$, $1 \leq j \leq 57$, and $\gcd(i, j) = 1$. Compute the value of $\frac{p(p - 1)}{4}$. | 41,718 | graphs = [
Graph(
let={
"_n": Const(4),
"p": 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(11)), right=IntegerRange(start=Const(1), end=C... | NT | null | SUM | sympy | COUNT_COPRIME_GRID | [
"COUNT_COPRIME_GRID",
"ONE_PHI_1"
] | 3d404c | modular_sum_quadratic_residues_v1 | null | 5 | 0 | [
"COUNT_COPRIME_GRID",
"ONE_PHI_1"
] | 2 | 0.003 | 2026-02-08T03:06:49.710291Z | {
"verified": true,
"answer": 41718,
"timestamp": "2026-02-08T03:06:49.713132Z"
} | a38fb8 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 187,
"completion_tokens": 927
},
"timestamp": "2026-02-08T20:20:09.421Z",
"answer": 41718
},
{
"i... | 1 | [
{
"lemma": "COUNT_COPRIME_GRID",
"status": "ok"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "ONE_PHI_1",
"status": "ok"
},
{
"lemma": "V3",
"status": "no"
},
{
"lemma": "V7",
"status": "... | {
"lo": -6.51,
"mid": -0.53,
"hi": 4.75
} | ||
dd4c87 | lin_form_endings_v1_124444284_3724 | Let $T$ be the set of all integers $t$ such that $156 \leq t \leq 3906$ and there exist positive integers $a \leq 29$, $b \leq 19$ satisfying $t = 105a + 45b + 6$. Let $r$ be the number of elements in $T$. Compute the remainder when $11061 \cdot r$ is divided by $90215$. | 27,344 | graphs = [
Graph(
let={
"_inner_result": CountOverSet(set=SolutionsSet(var=Var("t"), condition=Exists(var=Var(name='a'), condition=Exists(var=Var(name='b'), condition=And(Geq(left=Var(name='a'), right=Const(value=1)), Leq(left=Var(name='a'), right=Const(value=29)), Geq(left=Var(name='b'), right=... | COMB | null | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | lin_form_endings_v1 | null | 3 | null | [
"LIN_FORM"
] | 1 | 0.002 | 2026-02-08T05:34:23.672637Z | {
"verified": true,
"answer": 27344,
"timestamp": "2026-02-08T05:34:23.674847Z"
} | 6d56c4 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 206,
"completion_tokens": 5459
},
"timestamp": "2026-02-24T03:56:33.117Z",
"answer": 27344
},
{
"... | 1 | [
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": ... | {
"lo": -0.06,
"mid": 2.89,
"hi": 5.27
} | ||
d01a2a | nt_lcm_compute_v1_1353956133_811 | Let $n = 53256$. Let $a$ be the largest prime number $p$ such that $2 \leq p \leq 656$. Let $b = 889$, and let $L$ be the least common multiple of $a$ and $b$. Let $T$ be the set of all integers $t$ such that $16 \leq t \leq 148$ and there exist positive integers $a$ and $b$ with $1 \leq a \leq 4$, $1 \leq b \leq 18$, ... | 6,895 | graphs = [
Graph(
let={
"_n": Const(53256),
"a": MaxOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(2)), Leq(Var("n"), Const(656)), IsPrime(Var("n"))))),
"b": Const(889),
"result": LCM(a=Ref("a"), b=Ref("b")),
"Q": Mod(valu... | NT | null | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM",
"MAX_PRIME_BELOW"
] | a71ada | nt_lcm_compute_v1 | affine_mod | 5 | 0 | [
"LIN_FORM",
"MAX_PRIME_BELOW"
] | 2 | 0.005 | 2026-02-08T11:52:17.116563Z | {
"verified": true,
"answer": 6895,
"timestamp": "2026-02-08T11:52:17.121070Z"
} | dfc3dc | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 210,
"completion_tokens": 3811
},
"timestamp": "2026-02-14T19:58:05.802Z",
"answer": 6895
},
{... | 1 | [
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok"
},
{
"lemma": "V7",
"stat... | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
df6f81 | nt_min_crt_v1_1978505735_1604 | Find the smallest positive integer $n \leq 88$ such that $n \equiv 3 \pmod{8}$ and $n \equiv 0 \pmod{11}$. Let $d_0, d_1, \dots, d_{k-1}$ be the decimal digits of $n$, listed from least significant to most. Compute $\sum_{i=0}^{k-1} d_i (i+1)^2 + 12$. | 17 | graphs = [
Graph(
let={
"m": Const(8),
"k": Const(11),
"a": Const(3),
"b": Const(0),
"upper": Const(88),
"result": MinOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Ref("upper")), Eq(Mod(valu... | NT | null | EXTREMUM | sympy | B3 | [
"B3",
"ONE_PHI_2"
] | c8ff86 | nt_min_crt_v1 | digits_weighted_mod | 4 | 0 | [
"B3",
"ONE_PHI_2"
] | 2 | 0.056 | 2026-02-08T16:16:57.848781Z | {
"verified": true,
"answer": 17,
"timestamp": "2026-02-08T16:16:57.904984Z"
} | dddca7 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 144,
"completion_tokens": 595
},
"timestamp": "2026-02-16T23:50:57.475Z",
"answer": 17
},
{
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "ONE_PHI_2",
"status": "ok"
},
{
"lemma": "V3",
"status": "no"
},
{
"lemma": "V... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
4617e3 | modular_min_linear_v1_677425708_1221 | Let $a = 16529$, $b = 17752$, and $m = 25207$. Let $r$ be the smallest integer $x$ such that $$
x \ge \sum_{d \mid \gcd(5,7)} \mu(d),
$$ $x \le m$, and $$
16529x \equiv 17752 \pmod{25207}.
$$ Compute the value of $$
r + 2^{r \bmod 15} \bmod 72874.
$$ | 39,393 | graphs = [
Graph(
let={
"a": Const(16529),
"b": Const(17752),
"m": Const(25207),
"result": MinOverSet(set=SolutionsSet(var=Var("x"), condition=And(Geq(Var("x"), SumOverDivisors(n=GCD(a=Const(value=5), b=Const(value=7)), var='d', expr=MoebiusMu(n=Var(name='d'))... | NT | null | EXTREMUM | sympy | MOBIUS_COPRIME | [
"MOBIUS_COPRIME"
] | ac54ac | modular_min_linear_v1 | null | 6 | 0 | [
"MOBIUS_COPRIME"
] | 1 | 0.983 | 2026-02-08T04:02:15.631371Z | {
"verified": true,
"answer": 39393,
"timestamp": "2026-02-08T04:02:16.614733Z"
} | 189168 | 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": 1334
},
"timestamp": "2026-02-09T17:11:08.821Z",
"answer": 39393
},
{
"... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "MOBIUS_COPRIME",
"status": "ok"
},
{
"lemma": "V5",
"status": "no"
},
{
"lemma": "VAL_SUM_EQ",
"status": "no"... | {
"lo": -6.5,
"mid": -0.2,
"hi": 6.11
} | ||
2f4f09 | antilemma_sum_equals_v1_2051736721_2832 | Let $m = 97269$. Let $n$ be the number of integers $t$ such that $5 \leq t \leq 23$ and there exist integers $a$ and $b$ with $1 \leq a \leq 4$, $1 \leq b \leq 5$, and $t = 2a + 3b$. Let $x$ be the number of ordered pairs $(i,j)$ of positive integers such that $1 \leq i \leq 15$, $1 \leq j \leq 16$, and $i + j = n$. Le... | 67,239 | graphs = [
Graph(
let={
"_m": Const(97269),
"_n": CountOverSet(set=SolutionsSet(var=Var("t"), condition=Exists(var=Var(name='a'), condition=Exists(var=Var(name='b'), condition=And(Geq(left=Var(name='a'), right=Const(value=1)), Leq(left=Var(name='a'), right=Const(value=4)), Geq(left=V... | COMB | GEOM | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM/COUNT_SUM_EQUALS",
"COUNT_SUM_EQUALS"
] | ada383 | antilemma_sum_equals_v1 | null | 4 | 0 | [
"COUNT_SUM_EQUALS",
"LIN_FORM"
] | 2 | 0.014 | 2026-02-08T16:55:34.791554Z | {
"verified": true,
"answer": 67239,
"timestamp": "2026-02-08T16:55:34.805142Z"
} | f9315f | 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": 1688
},
"timestamp": "2026-02-17T14:53:16.445Z",
"answer": 67239
},
... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "ok"
},
{
"lemma": "LIN_F... | {
"lo": -4.1,
"mid": -1.76,
"hi": 1.32
} | ||
4939c7 | sequence_lucas_compute_v1_1431428450_277 | Let $c = 9$. Let $m$ be the minimum value of $x + y$ over all ordered pairs $(x, y)$ of positive integers such that $xy = c$. Let $n'$ be the number of positive integers $n$ such that $1 \leq n \leq 59$ and $\gcd(n, m) = 1$. Let $n$ be the sum of $\phi(d)$ over all positive divisors $d$ of $n'$, where $\phi$ is Euler's... | 15,127 | graphs = [
Graph(
let={
"_c": Const(9),
"_m": MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(Mul(Var("x"), Var("y")), Ref("_c")))), expr=Sum(Var("x"), Var("y")))),
... | NT | null | COMPUTE | sympy | B3 | [
"B3/C4/K3"
] | b3e17d | sequence_lucas_compute_v1 | null | 6 | 0 | [
"B3",
"C4",
"K3"
] | 3 | 0.004 | 2026-02-08T13:22:17.086708Z | {
"verified": true,
"answer": 15127,
"timestamp": "2026-02-08T13:22:17.090677Z"
} | fff089 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 167,
"completion_tokens": 1119
},
"timestamp": "2026-02-15T13:55:27.816Z",
"answer": 15127
},
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "C4",
"status": "ok_later"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "K3",
"status": "ok_later"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "L3c"... | {
"lo": -5.49,
"mid": 0.22,
"hi": 6.51
} | ||
10d73b | comb_sum_binomial_row_v1_124444284_5760 | Let $m = 46863$. Let $p$ and $q$ be positive integers such that $pq = 18$, $\gcd(p, q) = 1$, and $p < q$. Let $n_1$ be the number of such integers $p$. Let $a$ and $b$ be integers satisfying $1 \le a \le 2$, $1 \le b \le 6$, and define $t = 5a + 2b$. Let $n_2$ be the number of distinct values of $t$ such that $7 \le t ... | 21,873 | graphs = [
Graph(
let={
"_m": Const(46863),
"_n": CountOverSet(set=SolutionsSet(var=Var("p"), condition=And(IsPositive(arg=Var(name='p')), Exists(var=Var(name='q'), condition=And(Eq(left=Mul(Var(name='p'), Var(name='q')), right=Const(value=18)), Eq(left=GCD(a=Var(name='p'), b=Var(nam... | NT | null | SUM | sympy | COPRIME_PAIRS | [
"COPRIME_PAIRS/LIN_FORM"
] | a1eac8 | comb_sum_binomial_row_v1 | null | 4 | 0 | [
"COPRIME_PAIRS",
"LIN_FORM"
] | 2 | 0.005 | 2026-02-08T06:49:43.721254Z | {
"verified": true,
"answer": 21873,
"timestamp": "2026-02-08T06:49:43.726539Z"
} | 6f1ad5 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 206,
"completion_tokens": 2642
},
"timestamp": "2026-02-13T05:07:37.613Z",
"answer": 21873
},
... | 1 | [
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok_later"
},
{
"lemma": "MOD_ADD",
"status":... | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
d043a5 | nt_sum_over_divisible_v1_1742523217_4418 | Let $S$ be the set of all positive integers $n$ at most 74529 that are divisible by 68. Compute the sum of all elements in $S$. Let $T$ be the set of all pairs of positive integers $(x, y)$ such that $x + y = 74$. Let $c$ be the maximum value of $xy$ over all such pairs. Let $Q$ be the remainder when $c$ minus the sum ... | 66,121 | graphs = [
Graph(
let={
"_n": Const(70592),
"upper": Const(74529),
"divisor": Const(68),
"result": SumOverSet(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")), Con... | NT | null | SUM | sympy | B1 | [
"B1"
] | d2b6e1 | nt_sum_over_divisible_v1 | negation_mod | 3 | 0 | [
"B1"
] | 1 | 5.113 | 2026-02-08T07:17:06.876357Z | {
"verified": true,
"answer": 66121,
"timestamp": "2026-02-08T07:17:11.988956Z"
} | f04872 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 162,
"completion_tokens": 1228
},
"timestamp": "2026-02-13T09:16:09.546Z",
"answer": 66121
},
... | 1 | [
{
"lemma": "B1",
"status": "ok"
},
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "V1",
"status": "no"
},
{
"lemma": "V3",
"status": "no"
}
] | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
524fb3 | comb_binomial_compute_v1_784195855_8985 | Let $\mathcal{P}$ be the set of all prime numbers $n$ such that $2 \leq n \leq 151$. Define $S$ to be the set of all ordered pairs $(x, y)$ of positive integers such that $xy = |\mathcal{P}|$. Let $n$ be the minimum value of $x + y$ over all such pairs $(x, y) \in S$. Let $k = 6$. Compute the binomial coefficient $\bin... | 1,392 | graphs = [
Graph(
let={
"_n": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(2)), Leq(Var("n"), Const(151)), IsPrime(Var("n"))))),
"n": MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var... | NT | null | COMPUTE | sympy | COUNT_PRIMES | [
"COUNT_PRIMES/B3"
] | 3caaca | comb_binomial_compute_v1 | null | 7 | 0 | [
"B3",
"COUNT_PRIMES"
] | 2 | 0.004 | 2026-02-08T16:26:41.748749Z | {
"verified": true,
"answer": 1392,
"timestamp": "2026-02-08T16:26:41.752261Z"
} | ef2edd | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 188,
"completion_tokens": 2560
},
"timestamp": "2026-02-17T03:54:19.168Z",
"answer": 1392
},
{... | 1 | [
{
"lemma": "B3",
"status": "ok_later"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "COUNT_PRIMES",
"status": "ok"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "MOD_MUL",
"statu... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
5b112c | comb_binomial_compute_v1_1918700295_2735 | Let $n = 16$ and $k = 8$. Let $A$ be the set of all positive integers $n$ such that $1 \leq n \leq 48$ and $n \equiv 0 \pmod{16}$. Let $s$ be the sum of all elements of $A$. Let $P$ be the set of all ordered pairs $(x,y)$ of positive integers such that $x + y = s$. Define $c$ to be the maximum value of $xy$ over all pa... | 55,471 | graphs = [
Graph(
let={
"n": Const(16),
"k": Const(8),
"result": Binom(n=Ref("n"), k=Ref("k")),
"_c": MaxOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')... | ALG | COMB | COMPUTE | sympy | SUM_DIVISIBLE | [
"SUM_DIVISIBLE/B1"
] | 174767 | comb_binomial_compute_v1 | negation_mod | 5 | 0 | [
"B1",
"SUM_DIVISIBLE"
] | 2 | 0.003 | 2026-02-08T08:11:08.291463Z | {
"verified": true,
"answer": 55471,
"timestamp": "2026-02-08T08:11:08.294223Z"
} | 399840 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 250,
"completion_tokens": 1046
},
"timestamp": "2026-02-24T09:00:29.101Z",
"answer": 55471
},
{
"... | 1 | [
{
"lemma": "B1",
"status": "ok_later"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "SUM_DIVISIBLE",
"status": "ok"
}
] | {
"lo": -5.97,
"mid": -3.97,
"hi": -1.93
} | ||
374ac7 | antilemma_k2_v1_124444284_7810 | Let $S$ be the set of real solutions $x$ to the equation $x^2 - 268x + T = 0$, where $T$ is the sum of all real solutions $x$ to the equation $x^2 - 2580x + 35924 = 0$. Let $N$ be the sum of all elements of $S$. Define
$$
x = \sum_{k=1}^{268} \phi(k) \left\lfloor \frac{N}{k} \right\rfloor,
$$
where $\phi(k)$ denotes Eu... | 51,440 | graphs = [
Graph(
let={
"_n": SumOverSet(set=SolutionsSet(var=Var("x"), condition=Eq(Sum(Pow(Var("x"), Const(2)), Mul(Const(-268), Var("x")), SumOverSet(set=SolutionsSet(var=Var("x"), condition=Eq(Sum(Pow(Var("x"), Const(2)), Mul(Const(-2580), Var("x")), Const(35924)), Const(0))))), Const(0)))),... | NT | COMB | COMPUTE | sympy | VIETA_SUM | [
"VIETA_SUM/VIETA_SUM/K2",
"K2"
] | f0fb5f | antilemma_k2_v1 | null | 7 | 0 | [
"K2",
"VIETA_SUM"
] | 2 | 0.002 | 2026-02-08T09:22:59.229568Z | {
"verified": true,
"answer": 51440,
"timestamp": "2026-02-08T09:22:59.231451Z"
} | 72ad72 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 188,
"completion_tokens": 1717
},
"timestamp": "2026-02-14T03:36:44.289Z",
"answer": 51440
},
... | 1 | [
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K2",
"status": "ok"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
},
{
"lemma": "VAL_SUM_EQ",
"status": "no"
},
{
... | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
315d80 | antilemma_sum_factor_cartesian_v1_168721529_350 | Let $S$ be the set of all ordered pairs $(i,j)$ of positive integers such that $1 \leq i \leq 21$ and $1 \leq j \leq 5$. Define $x$ to be the sum of $i \cdot j$ over all pairs $(i,j)$ in $S$. Compute the remainder when $39867 \cdot x$ is divided by $55982$. | 31,561 | 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(21)), 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 | 3 | 0 | [
"SUM_FACTOR_CARTESIAN"
] | 1 | 0.001 | 2026-02-08T13:00:23.402139Z | {
"verified": true,
"answer": 31561,
"timestamp": "2026-02-08T13:00:23.403009Z"
} | e9bc84 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 205,
"completion_tokens": 1562
},
"timestamp": "2026-02-09T04:04:42.190Z",
"answer": 31561
},
{
"... | 1 | [
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "SUM_FACTOR_CARTESIAN",
"status": "ok"
},
{
"lemma": "V1",
"status": "no"
}
] | {
"lo": -6.69,
"mid": -2.4,
"hi": 1.77
} | ||
87472f | modular_count_residue_v1_784195855_3754 | Let $d_{\text{min}}$ be the smallest integer $d \geq 2$ that divides 1001. Compute the number of positive integers $n$ such that $1 \leq n \leq 85264$ and $n \equiv d_{\text{min}} \pmod{9}$. | 9,474 | graphs = [
Graph(
let={
"_n": Const(2),
"upper": Const(85264),
"m": Const(9),
"r": MinOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Ref("_n")), Divides(divisor=Var("d"), dividend=Const(1001))))),
"result": CountOverSet(set=Solu... | NT | null | COUNT | sympy | MIN_PRIME_FACTOR | [
"MIN_PRIME_FACTOR"
] | bc3776 | modular_count_residue_v1 | null | 3 | 0 | [
"MIN_PRIME_FACTOR"
] | 1 | 3.336 | 2026-02-08T06:36:53.565455Z | {
"verified": true,
"answer": 9474,
"timestamp": "2026-02-08T06:36:56.901940Z"
} | 0eb20a | 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": 952
},
"timestamp": "2026-02-13T02:43:08.859Z",
"answer": 9474
},
{
... | 1 | [
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "MIN_PRIME_FACTOR",
"status": "ok"
},
{
"lemma": "V8",
"status": "no"
},
{
"lemma": "VAL_SUM_EQ",
"status": "no"
... | {
"lo": -5.55,
"mid": -3.01,
"hi": 0.32
} | ||
309d79 | modular_sum_quadratic_residues_v1_898971024_2675 | Let $p=173$ and define
\[R=\frac{p(p-1)}{4}.
\]
Let $A$ be the set of all positive integers $p_1$ for which there exists a positive integer $q$ such that
\[p_1q=24,\quad \gcd(p_1,q)=1,\quad p_1<q.
\]
Let $S$ be the set of all prime numbers $n$ such that
\[n\ge |A|\quad\text{and}\quad n\le \sum_{k=1}^{8} k.
\]
Let $T$... | 58,367 | graphs = [
Graph(
let={
"_c": Const(8),
"_m": Const(4),
"_n": Const(65775),
"p": Const(173),
"result": Div(Mul(Ref("p"), Sub(Ref("p"), Const(1))), Ref("_m")),
"Q": Mod(value=Sub(MaxOverSet(set=SolutionsSet(var=Var("n"), condition=And(Ge... | NT | null | SUM | sympy | SUM_ARITHMETIC | [
"SUM_ARITHMETIC/MAX_PRIME_BELOW",
"COPRIME_PAIRS/MAX_PRIME_BELOW"
] | 8e0128 | modular_sum_quadratic_residues_v1 | negation_mod | 6 | 0 | [
"COPRIME_PAIRS",
"MAX_PRIME_BELOW",
"SUM_ARITHMETIC"
] | 3 | 0.006 | 2026-02-08T16:54:31.538274Z | {
"verified": true,
"answer": 58367,
"timestamp": "2026-02-08T16:54:31.544770Z"
} | 14fdc3 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 204,
"completion_tokens": 1388
},
"timestamp": "2026-02-17T14:16:19.348Z",
"answer": 58367
},
... | 1 | [
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok_later"
},
{
"lemma": "MOD_MUL",
"s... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
182034 | nt_count_divisible_v1_124444284_8875 | Let $D$ be the number of ordered pairs $(i, j)$ with $1 \leq i \leq 4$ and $1 \leq j \leq 4$ such that $\gcd(i, j) = 1$. Let $U = 52441$. Determine the number of positive integers $n \leq U$ such that $n$ is divisible by $D$. Let $Q$ be the remainder when $41465$ times this count is divided by $96786$. Find the value o... | 26,643 | graphs = [
Graph(
let={
"_n": Const(96786),
"upper": Const(52441),
"divisor": 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(4... | NT | null | COUNT | sympy | COUNT_COPRIME_GRID | [
"COUNT_COPRIME_GRID"
] | 20ec03 | nt_count_divisible_v1 | null | 3 | 0 | [
"COUNT_COPRIME_GRID"
] | 1 | 4.949 | 2026-02-08T11:56:29.623856Z | {
"verified": true,
"answer": 26643,
"timestamp": "2026-02-08T11:56:34.573263Z"
} | 62bfae | 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": 1077
},
"timestamp": "2026-02-14T20:36:51.550Z",
"answer": 26643
},
... | 1 | [
{
"lemma": "COUNT_COPRIME_GRID",
"status": "ok"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "V5",
"sta... | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
6c9f98 | sequence_fibonacci_compute_v1_809748730_1202 | Let $n = 21$ and let $F_n$ denote the $n$th Fibonacci number, where $F_1 = 1$, $F_2 = 1$, and $F_k = F_{k-1} + F_{k-2}$ for $k \geq 3$. Let $S$ be the set of all ordered pairs $(x, y)$ of positive integers such that $xy = 3721$. For each pair $(x, y)$ in $S$, compute $x + y$, and let $m$ be the minimum value among all ... | 52,531 | graphs = [
Graph(
let={
"_n": Const(55974),
"n": Const(21),
"result": Fibonacci(arg=Ref(name='n')),
"Q": Mod(value=Sub(Summation(var="k", start=Const(1), end=MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsP... | NT | null | COMPUTE | sympy | LTE_SUM | [
"B3/SUM_ARITHMETIC"
] | 8f97ac | sequence_fibonacci_compute_v1 | negation_mod | 4 | 0 | [
"B3",
"LTE_SUM",
"SUM_ARITHMETIC"
] | 3 | 0.01 | 2026-02-08T12:16:11.394299Z | {
"verified": true,
"answer": 52531,
"timestamp": "2026-02-08T12:16:11.403834Z"
} | f201d7 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 219,
"completion_tokens": 840
},
"timestamp": "2026-02-14T23:37:23.440Z",
"answer": 52531
},
{... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"stat... | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} |
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