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 |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
295a94 | nt_count_gcd_equals_v1_458359167_5554 | Let $d = 67$, $k = 469$, and $N = 45796$. Compute the number of positive integers $n$ such that $1 \leq n \leq N$ and $\gcd(n, k) = d$. | 586 | graphs = [
Graph(
let={
"upper": Const(45796),
"k": Const(469),
"d": Const(67),
"result": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Ref("upper")), Eq(GCD(a=Var("n"), b=Ref("k")), Ref("d"))))),
},
... | NT | null | COUNT | sympy | C2 | [
"B3"
] | 0cd20d | nt_count_gcd_equals_v1 | null | 3 | 0 | [
"B3",
"C2"
] | 2 | 13.647 | 2026-02-08T12:35:24.034155Z | {
"verified": true,
"answer": 586,
"timestamp": "2026-02-08T12:35:37.681212Z"
} | e66e97 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 99,
"completion_tokens": 881
},
"timestamp": "2026-02-15T02:32:14.659Z",
"answer": 586
},
{
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "VAL_SUM_EQ",
"status": "no"
}
] | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
31cde7 | antilemma_k3_v1_865884756_3599 | Let $x = \sum_{d \mid 62003} \phi(d)$ and let $c = 29$. Find the remainder when $c - x$ is divided by $58038$. | 54,102 | graphs = [
Graph(
let={
"x": SumOverDivisors(n=Const(value=62003), var='d', expr=EulerPhi(n=Var(name='d'))),
"_c": Const(29),
"Q": Mod(value=Sub(Ref("_c"), Ref("x")), modulus=Const(58038)),
},
goal=Ref("Q"),
)
] | NT | COMB | COMPUTE | sympy | K3 | [
"K3"
] | 54c41e | antilemma_k3_v1 | null | 3 | 0 | [
"K3"
] | 1 | 0.001 | 2026-02-08T17:30:50.448429Z | {
"verified": true,
"answer": 54102,
"timestamp": "2026-02-08T17:30:50.449121Z"
} | fa0713 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 89,
"completion_tokens": 1817
},
"timestamp": "2026-02-18T02:49:37.196Z",
"answer": 54102
},
{... | 1 | [
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "K3",
"status": "ok"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "V1",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
2aecc3 | comb_sum_binomial_row_v1_124444284_3908 | Let $n$ be the smallest divisor of $2431$ that is greater than or equal to $2$. Compute $2^n$. | 2,048 | graphs = [
Graph(
let={
"_n": Const(2431),
"n": MinOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Const(2)), Divides(divisor=Var("d"), dividend=Ref("_n"))))),
"result": Pow(Const(2), Ref("n")),
},
goal=Ref("result"),
)
] | NT | null | SUM | sympy | MIN_PRIME_FACTOR | [
"MIN_PRIME_FACTOR"
] | bc3776 | comb_sum_binomial_row_v1 | null | 3 | 0 | [
"MIN_PRIME_FACTOR"
] | 1 | 0.001 | 2026-02-08T05:39:51.124749Z | {
"verified": true,
"answer": 2048,
"timestamp": "2026-02-08T05:39:51.125454Z"
} | 4d9184 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 75,
"completion_tokens": 433
},
"timestamp": "2026-02-12T11:58:31.438Z",
"answer": 2048
},
{
... | 1 | [
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "MIN_PRIME_FACTOR",
"status": "ok"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "V1",
"status": "no"
}
] | {
"lo": -7.01,
"mid": -4.68,
"hi": -2.15
} | ||
f4fda0 | nt_count_coprime_v1_124444284_498 | Let $P$ be the set of all positive integers $p$ for which there exists a positive integer $q$ such that $pq = 73500$, $\gcd(p, q) = 1$, and $p < q$. Let $k$ be the number of elements in $P$. Compute the number of positive integers $n \leq 65536$ such that $\gcd(n, k) = 1$. Let this count be $r$. Find the remainder when... | 31,722 | graphs = [
Graph(
let={
"_n": Const(97977),
"upper": Const(65536),
"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=73500)), E... | NT | null | COUNT | sympy | COPRIME_PAIRS | [
"COPRIME_PAIRS"
] | 2bb3aa | nt_count_coprime_v1 | null | 6 | 0 | [
"COPRIME_PAIRS"
] | 1 | 8.896 | 2026-02-08T03:19:57.136531Z | {
"verified": true,
"answer": 31722,
"timestamp": "2026-02-08T03:20:06.032519Z"
} | 361f9d | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 231,
"completion_tokens": 2115
},
"timestamp": "2026-02-09T02:41:46.786Z",
"answer": 31722
},
{
... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
}
] | {
"lo": -3.42,
"mid": 1.86,
"hi": 7.55
} | ||
a36709 | sequence_lucas_compute_v1_809748730_363 | Let $m = 81$. Define $s = \sum_{d \mid m} \phi(d)$. Let $n$ be the minimum value of $x + y$ over all ordered pairs $(x,y)$ of positive integers such that $xy = s$. Compute the $n$-th Lucas number, where the Lucas sequence is defined by $L_1 = 1$, $L_2 = 3$, and $L_k = L_{k-1} + L_{k-2}$ for $k \geq 3$. | 5,778 | graphs = [
Graph(
let={
"_m": Const(81),
"_n": SumOverDivisors(n=Ref(name='_m'), var='d', expr=EulerPhi(n=Var(name='d'))),
"n": MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg... | NT | null | COMPUTE | sympy | K3 | [
"K3/B3"
] | f0a0b3 | sequence_lucas_compute_v1 | null | 6 | 0 | [
"B3",
"K3"
] | 2 | 0.001 | 2026-02-08T11:29:16.991726Z | {
"verified": true,
"answer": 5778,
"timestamp": "2026-02-08T11:29:16.993185Z"
} | 0e3d50 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 160,
"completion_tokens": 890
},
"timestamp": "2026-02-14T14:55:53.096Z",
"answer": 5778
},
{
... | 1 | [
{
"lemma": "B3",
"status": "ok_later"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K3",
"status": "ok"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"l... | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
318c9d | antilemma_cartesian_v1_151522320_750 | Let $x$ be the number of ordered pairs $(i, j)$ such that $1 \leq i \leq 18$ and $1 \leq j \leq 29$. Compute the remainder when $31453 \cdot x$ is divided by $67536$. | 7,218 | graphs = [
Graph(
let={
"x": CountOverSet(set=CartesianProduct(left=IntegerRange(start=Const(1), end=Const(18)), right=IntegerRange(start=Const(1), end=Const(29)))),
"_c": Const(31453),
"Q": Mod(value=Mul(Ref("_c"), Ref("x")), modulus=Const(67536)),
},
goa... | COMB | GEOM | COMPUTE | sympy | COUNT_CARTESIAN | [
"COUNT_CARTESIAN"
] | 409d7d | antilemma_cartesian_v1 | null | 2 | 0 | [
"COUNT_CARTESIAN"
] | 1 | 0.001 | 2026-02-08T03:29:36.378971Z | {
"verified": true,
"answer": 7218,
"timestamp": "2026-02-08T03:29:36.380018Z"
} | 20dbc1 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 171,
"completion_tokens": 6251
},
"timestamp": "2026-02-10T15:00:15.952Z",
"answer": 7218
},
{
"i... | 1 | [
{
"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",
"status": "no"
},
{
"lemma": "V8_SU... | {
"lo": -0.05,
"mid": 2.89,
"hi": 5.27
} | ||
5d67a9 | alg_poly4_min_v1_601307018_8509 | Find the minimum value of $13143a^4 + 3120a^3b + 48672a^2b^2 - 24960ab^3 + 10608b^4$ over all ordered pairs $(a, b)$ of positive integers with $1 \le a, b \le 419$. | 50,583 | graphs = [
Graph(
let={
"result": MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("a"), Var("b")]), condition=And(Geq(Var("a"), Const(1)), Leq(Var("a"), Const(419)), Geq(Var("b"), Const(1)), Leq(Var("b"), Const(419)))), expr=Sum(Mul(Const(13143), Pow(Var("a"), Const(4))), Mul(... | ALG | null | COMPUTE | sympy | POLY_ORBIT_HENSEL | [
"POLY_ORBIT_COUNT",
"QF_PSD_COUNT_LEQ"
] | e22c28 | alg_poly4_min_v1 | null | 4 | null | [
"POLY_ORBIT_COUNT",
"POLY_ORBIT_HENSEL",
"QF_PSD_COUNT_LEQ"
] | 3 | 1.676 | 2026-03-10T08:59:16.928027Z | {
"verified": true,
"answer": 50583,
"timestamp": "2026-03-10T08:59:18.603849Z"
} | f540d8 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 179,
"completion_tokens": 10568
},
"timestamp": "2026-04-19T09:11:39.823Z",
"answer": 50583
},
{
... | 1 | [
{
"lemma": "POLY_ORBIT_COUNT",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "QF_PSD_COUNT_LEQ",
"status": "ok"
}
] | {
"lo": -5.34,
"mid": 1.1,
"hi": 7.53
} | ||
559f2c | modular_count_residue_v1_784195855_5161 | Determine the number of integers $n$ such that $1 \le n \le 34596$ and $n \equiv 2 \pmod{3}$. | 11,532 | graphs = [
Graph(
let={
"upper": Const(34596),
"m": Const(3),
"r": Const(2),
"result": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), EulerPhi(n=Const(2))), Leq(Var("n"), Ref("upper")), Eq(Mod(value=Var("n"), modulus=Ref("m")), Ref("r"... | NT | null | COUNT | sympy | ONE_PHI_2 | [
"ONE_PHI_2"
] | e19278 | modular_count_residue_v1 | null | 3 | 0 | [
"ONE_PHI_2"
] | 1 | 1.133 | 2026-02-08T07:42:28.818765Z | {
"verified": true,
"answer": 11532,
"timestamp": "2026-02-08T07:42:29.951725Z"
} | 656739 | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 130,
"completion_tokens": 405
},
"timestamp": "2026-02-20T04:51:06.022Z",
"answer": 11532
}
] | 2 | [
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "ONE_PHI_2",
"status": "ok"
},
{
"lemma": "V3",
"status": "no"... | {
"lo": -10,
"mid": -6.47,
"hi": -2.95
} | ||
9a026c | modular_mod_compute_v1_153355830_255 | Let $S$ be the set of all ordered pairs $(x, y)$ of positive integers such that $xy = 10000$. Let $m$ be the minimum value of $x + y$ over all pairs $(x, y) \in S$. Now, let $T$ be the set of all ordered pairs $(x, y)$ of positive integers such that $x + y = m$. Let $a$ be the maximum value of $xy$ over all pairs $(x, ... | 4,071 | graphs = [
Graph(
let={
"_n": Const(10000),
"a": 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")), MinOverSet(set=MapOverSet(set=SolutionsSet(var... | NT | null | COMPUTE | sympy | B3 | [
"B3/B1"
] | 7f76f7 | modular_mod_compute_v1 | null | 5 | 0 | [
"B1",
"B3"
] | 2 | 0.002 | 2026-02-08T02:59:23.437530Z | {
"verified": true,
"answer": 4071,
"timestamp": "2026-02-08T02:59:23.439788Z"
} | a57106 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 232,
"completion_tokens": 1204
},
"timestamp": "2026-02-10T12:25:36.212Z",
"answer": 4071
},
{
"i... | 1 | [
{
"lemma": "B1",
"status": "ok_later"
},
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma... | {
"lo": -7.01,
"mid": -4.68,
"hi": -2.15
} | ||
4e2704 | geo_count_lattice_rect_v1_1439011603_1345 | Let $a = 111$ and $b = 79$. Define $L$ to be the number of lattice points $(x, y)$ such that $0 \leq x \leq a$ and $0 \leq y \leq b$. Let $m = L + 2$. The Fibonacci sequence is defined by $F_1 = 1$, $F_2 = 1$, and $F_k = F_{k-1} + F_{k-2}$ for $k \geq 3$. Find the smallest positive integer $k$ such that $F_k$ is divisi... | 192 | graphs = [
Graph(
let={
"a": Const(111),
"b": Const(79),
"result": LatticePointsRect(a=Ref(name='a'), b=Ref(name='b')),
"Q": FibonacciEntryPoint(modulus=Sum(Abs(arg=Ref(name='result')), Const(value=2))),
},
goal=Ref("Q"),
)
] | GEOM | NT | COUNT | sympy | [] | geo_count_lattice_rect_v1 | null | 3 | 0 | null | null | 0.009 | 2026-02-08T16:02:35.447697Z | {
"verified": true,
"answer": 192,
"timestamp": "2026-02-08T16:02:35.456653Z"
} | 19bfd4 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 243,
"completion_tokens": 6635
},
"timestamp": "2026-02-24T19:40:43.359Z",
"answer": 192
},
{
"i... | 1 | [] | {
"lo": 1.98,
"mid": 5.23,
"hi": 8.52
} | ||||
040ca4 | nt_count_intersection_v1_151522320_2371 | Let $N = 20000$. Let $a$ be the smallest divisor of $41327$ that is at least $2$, and let $b = 15$. Define $r$ to be the number of integers $n$ with $1 \leq n \leq N$ such that $a$ divides $n$ and $\gcd(n, 15) = 1$. Compute the remainder when $|r|$ is divided by $95562$. | 970 | graphs = [
Graph(
let={
"N": Const(20000),
"a": MinOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Const(2)), Divides(divisor=Var("d"), dividend=Const(41327))))),
"b": Const(15),
"result": CountOverSet(set=SolutionsSet(var=Var("n"), conditio... | NT | null | COUNT | sympy | MIN_PRIME_FACTOR | [
"MIN_PRIME_FACTOR"
] | bc3776 | nt_count_intersection_v1 | null | 4 | 0 | [
"MIN_PRIME_FACTOR"
] | 1 | 0.64 | 2026-02-08T04:46:53.272526Z | {
"verified": true,
"answer": 970,
"timestamp": "2026-02-08T04:46:53.912120Z"
} | 6fa3c8 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 209,
"completion_tokens": 1458
},
"timestamp": "2026-02-11T21:55:55.709Z",
"answer": 970
},
{
"i... | 1 | [
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "MIN_PRIME_FACTOR",
"status": "ok"
},
{
"lemma": "V5",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
}... | {
"lo": -5.55,
"mid": -3.01,
"hi": 0.33
} | ||
54b5f2 | nt_gcd_compute_v1_655260480_3533 | Let $p$ be a positive integer. Define $n$ to be the number of such $p$ for which there exists a positive integer $q$ such that $p \cdot q = 54$, $\gcd(p, q) = 1$, and $p < q$. Let $a = 275824$ and $b = 620604$, and define $r = \gcd(a, b)$. Let $d_0$ be the smallest integer $d$ such that $d \ge n$ and $d$ divides $38239... | 4,140 | graphs = [
Graph(
let={
"_n": CountOverSet(set=SolutionsSet(var=Var("p"), condition=And(IsPositive(arg=Var(name='p')), Exists(var=Var(name='q'), condition=And(Eq(left=Mul(Var(name='p'), Var(name='q')), right=Const(value=54)), Eq(left=GCD(a=Var(name='p'), b=Var(name='q')), right=Const(value=1)), ... | NT | COMB | COMPUTE | sympy | COPRIME_PAIRS | [
"COPRIME_PAIRS/MIN_PRIME_FACTOR"
] | c17aaa | nt_gcd_compute_v1 | bell_mod | 6 | 0 | [
"COPRIME_PAIRS",
"MIN_PRIME_FACTOR"
] | 2 | 0.003 | 2026-02-08T17:25:07.189885Z | {
"verified": true,
"answer": 4140,
"timestamp": "2026-02-08T17:25:07.192817Z"
} | ae685c | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 190,
"completion_tokens": 2111
},
"timestamp": "2026-02-18T01:39:07.305Z",
"answer": 4140
},
{... | 1 | [
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "MIN_PRIME_FACTOR",
"status": "o... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
d6902d | geo_visible_lattice_v1_238844314_1029 | Let $n = 90$. Define a visible lattice point as an ordered pair $(x, y)$ of positive integers such that $1 \leq x, y \leq n$ and $\gcd(x, y) = 1$. Let $R$ be the number of visible lattice points for this $n$. Compute $72361 - R$. Determine the value of this difference. | 67,402 | graphs = [
Graph(
let={
"n": Const(90),
"result": VisibleLatticePoints(n=Ref(name='n')),
"Q": Sub(Const(72361), Ref("result")),
},
goal=Ref("Q"),
)
] | GEOM | null | COUNT | sympy | [] | geo_visible_lattice_v1 | null | 3 | 0 | null | null | 0.185 | 2026-02-08T13:51:33.100284Z | {
"verified": true,
"answer": 67402,
"timestamp": "2026-02-08T13:51:33.285580Z"
} | 56a3ed | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 1,
"correct": {
"strict": false,
"boxed": false,
"relaxed": true
},
"usage": {
"prompt_tokens": 191,
"completion_tokens": 32768
},
"timestamp": "2026-02-24T19:16:40.516Z",
"answer": null
},
{
... | 1 | [] | {
"lo": 3.25,
"mid": 5.68,
"hi": 8.81
} | ||||
e7e28b | comb_catalan_compute_v1_1470522791_1369 | Let $n$ be the number of integers $t$ with $10 \leq t \leq 34$ for which there exist positive integers $a$ and $b$, with $1 \leq a \leq 3$ and $1 \leq b \leq 4$, such that $t = 6a + 4b$. Let $c = 19809$. Compute the remainder when $c$ times the $n$-th Catalan number is divided by $69568$. | 62,690 | 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 | 2026-02-08T13:36:22.214240Z | {
"verified": true,
"answer": 62690,
"timestamp": "2026-02-08T13:36:22.216453Z"
} | 266d32 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 219,
"completion_tokens": 2243
},
"timestamp": "2026-02-24T18:43:29.527Z",
"answer": 62690
},
{
"... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
}
... | {
"lo": -2.35,
"mid": 1.22,
"hi": 4.84
} | ||
90cdf5 | comb_count_permutations_fixed_v1_784195855_3013 | Let $n = 1 + 2 + 3 + 4$ and $k = 5$. Define
$$
\text{result} = \binom{n}{k} \cdot !(n - k),
$$
where $!m$ denotes the number of derangements of $m$ elements.
Let $Q$ be the remainder when $44121 \cdot \text{result}$ is divided by $55151$.
Find the value of $Q$. | 24,278 | graphs = [
Graph(
let={
"_n": Const(4),
"n": Summation(var="k", start=Const(1), end=Ref("_n"), expr=Var("k")),
"k": Const(5),
"result": Mul(Binom(n=Ref("n"), k=Ref("k")), Subfactorial(arg=Sub(left=Ref(name='n'), right=Ref(name='k')))),
"Q": Mod(val... | COMB | null | COUNT | sympy | MIN_PRIME_FACTOR | [
"SUM_ARITHMETIC"
] | eb34f0 | comb_count_permutations_fixed_v1 | null | 3 | 0 | [
"MIN_PRIME_FACTOR",
"SUM_ARITHMETIC"
] | 2 | 0.043 | 2026-02-08T06:11:37.605830Z | {
"verified": true,
"answer": 24278,
"timestamp": "2026-02-08T06:11:37.648828Z"
} | 4e74ea | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 212,
"completion_tokens": 3563
},
"timestamp": "2026-02-24T05:35:25.213Z",
"answer": 24278
},
{
"... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "SUM_ARITHMETIC",
"status": "ok"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8_SUM",
"status... | {
"lo": -2.46,
"mid": 0.47,
"hi": 3.59
} | ||
8f6446 | nt_count_divisors_in_range_v1_1439011603_2064 | Let $c=2$, and let $m$ be the greatest prime number less than or equal to $1012$. Let $n=27720$ and $a=1$.
Let $b$ be the number of integers $t$ for which there exist integers $a_1$ and $b_1$ satisfying $1\le a_1\le 1001$, $1\le b_1\le 70$, $10\le t\le 3493$, and
$$t=3a_1+7b_1.$$
Let $r$ be the number of positive divi... | 89,890 | graphs = [
Graph(
let={
"_c": Const(2),
"_m": MaxOverSet(set=SolutionsSet(var=Var("n1"), condition=And(Geq(Var("n1"), Const(2)), Leq(Var("n1"), Const(1012)), IsPrime(Var("n1"))))),
"_n": Const(2),
"n": Const(27720),
"a": Const(1),
"b": ... | NT | null | COUNT | sympy | MIN_PRIME_FACTOR | [
"MIN_PRIME_FACTOR/MAX_PRIME_BELOW",
"MAX_PRIME_BELOW/LIN_FORM"
] | 9ecc92 | nt_count_divisors_in_range_v1 | two_moduli | 6 | 0 | [
"LIN_FORM",
"MAX_PRIME_BELOW",
"MIN_PRIME_FACTOR"
] | 3 | 0.042 | 2026-02-08T16:29:05.959022Z | {
"verified": true,
"answer": 89890,
"timestamp": "2026-02-08T16:29:06.001489Z"
} | f0e8c8 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 394,
"completion_tokens": 5673
},
"timestamp": "2026-02-17T05:52:16.132Z",
"answer": 89890
},
... | 1 | [
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok_later"
... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
ef3bf8 | nt_max_prime_below_v1_1520064083_4143 | Let $a$ and $b$ be positive integers such that $ab = 216$ and $\gcd(a, b) = 1$, with $a < b$. Let $S$ be the set of all such integers $a$. Compute the number of elements in $S$. Let $T$ be the set of prime numbers $n$ such that $n \geq |S|$ and $n \leq 15876$. Let $M$ be the largest element of $T$. Compute the remainde... | 2,721 | graphs = [
Graph(
let={
"upper": Const(15876),
"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 | 3.117 | 2026-02-08T06:06:35.543310Z | {
"verified": true,
"answer": 2721,
"timestamp": "2026-02-08T06:06:38.660508Z"
} | fdfac0 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 168,
"completion_tokens": 4296
},
"timestamp": "2026-02-12T20:11:04.713Z",
"answer": 2721
},
{... | 1 | [
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "K16",
"status":... | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
610001 | antilemma_k2_v1_1915831931_3071 | Let $x = \sum_{k=1}^{243} \phi(k) \left\lfloor \frac{243}{k} \right\rfloor$, where $\phi(k)$ denotes Euler's totient function. Let $Q$ be the remainder when $8281 - x$ is divided by $75184$. Compute $Q$. | 53,819 | graphs = [
Graph(
let={
"x": Summation(var="k", start=Const(1), end=Const(243), expr=Mul(EulerPhi(n=Var("k")), Floor(Div(Const(243), Var("k"))))),
"Q": Mod(value=Sub(Const(8281), Ref("x")), modulus=Const(75184)),
},
goal=Ref("Q"),
)
] | NT | COMB | COMPUTE | sympy | K13 | [
"K2"
] | 6897ab | antilemma_k2_v1 | null | 3 | 0 | [
"K13",
"K2"
] | 2 | 0.005 | 2026-02-08T17:20:25.251436Z | {
"verified": true,
"answer": 53819,
"timestamp": "2026-02-08T17:20:25.256746Z"
} | 46b875 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 116,
"completion_tokens": 850
},
"timestamp": "2026-02-18T01:07:21.717Z",
"answer": 53819
},
{... | 1 | [
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K2",
"status": "ok"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
5c66e1 | comb_count_permutations_fixed_v1_2051736721_3590 | Let $n$ be the largest prime number satisfying $2 \leq n \leq 11$. Let $k = 8$. Compute $\binom{n}{k} \cdot !(n - k)$, where $!m$ denotes the number of derangements of $m$ elements. | 330 | graphs = [
Graph(
let={
"n": MaxOverSet(set=SolutionsSet(var=Var("n1"), condition=And(Geq(Var("n1"), Const(2)), Leq(Var("n1"), Const(11)), IsPrime(Var("n1"))))),
"k": Const(8),
"result": Mul(Binom(n=Ref("n"), k=Ref("k")), Subfactorial(arg=Sub(left=Ref(name='n'), right=Ref... | NT | COMB | COUNT | sympy | MAX_PRIME_BELOW | [
"MAX_PRIME_BELOW"
] | dc3ad3 | comb_count_permutations_fixed_v1 | null | 3 | 0 | [
"MAX_PRIME_BELOW"
] | 1 | 0.003 | 2026-02-08T17:24:50.769131Z | {
"verified": true,
"answer": 330,
"timestamp": "2026-02-08T17:24:50.771788Z"
} | 7d6b18 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 106,
"completion_tokens": 553
},
"timestamp": "2026-02-18T01:25:17.013Z",
"answer": 330
},
{
... | 1 | [
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "V1",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
9c4079 | comb_factorial_compute_v1_1915831931_1338 | Let $n$ be the number of positive integers $p$ for which there exists a positive integer $q$ such that $p \cdot q = 257250$, $\gcd(p, q) = 1$, and $p < q$. Compute $n!$. | 40,320 | graphs = [
Graph(
let={
"n": CountOverSet(set=SolutionsSet(var=Var("p"), condition=And(IsPositive(arg=Var(name='p')), Exists(var=Var(name='q'), condition=And(Eq(left=Mul(Var(name='p'), Var(name='q')), right=Const(value=257250)), Eq(left=GCD(a=Var(name='p'), b=Var(name='q')), right=Const(value=1)... | NT | null | COMPUTE | sympy | COPRIME_PAIRS | [
"COPRIME_PAIRS"
] | 2bb3aa | comb_factorial_compute_v1 | null | 5 | 0 | [
"COPRIME_PAIRS"
] | 1 | 0.003 | 2026-02-08T16:00:31.644779Z | {
"verified": true,
"answer": 40320,
"timestamp": "2026-02-08T16:00:31.647313Z"
} | f6b74a | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 103,
"completion_tokens": 1463
},
"timestamp": "2026-02-16T19:33:23.469Z",
"answer": 40320
},
... | 1 | [
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "V1",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
9e6dd2 | antilemma_product_of_sums_v1_1116507919_417 | Let $S_1$ be the sum of $ij$ over all ordered pairs $(i, j)$ with $1 \leq i \leq 3$ and $1 \leq j \leq 7$. Let $S_2$ be the sum of all integers $k$ from $1$ to the largest prime number less than or equal to $24$. Let $x = S_1 \cdot S_2$. Let $c$ be the number of nonnegative integers $j$ with $0 \leq j \leq 53717$ such ... | 47,544 | graphs = [
Graph(
let={
"_m": Const(2),
"_n": Const(93400),
"S1": SumOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("i"), Var("j")]), condition=Const(1), domain=CartesianProduct(left=IntegerRange(start=Const(1), end=Const(3)), right=IntegerRange(start=Con... | NT | null | COMPUTE | sympy | MAX_PRIME_BELOW | [
"MAX_PRIME_BELOW/SUM_ARITHMETIC",
"V8",
"PRODUCT_OF_SUMS"
] | 7ae8e6 | antilemma_product_of_sums_v1 | negation_mod | 5 | 0 | [
"MAX_PRIME_BELOW",
"PRODUCT_OF_SUMS",
"SUM_ARITHMETIC",
"V8"
] | 4 | 0.003 | 2026-02-08T02:34:05.574805Z | {
"verified": true,
"answer": 47544,
"timestamp": "2026-02-08T02:34:05.577498Z"
} | 0d9f11 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 266,
"completion_tokens": 1371
},
"timestamp": "2026-02-08T19:31:38.841Z",
"answer": 47544
},
{
"... | 1 | [
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "PRODUCT_OF_SUMS",
... | {
"lo": -4.6,
"mid": 0.18,
"hi": 4.74
} | ||
2bc855 | nt_count_divisible_v1_655260480_3986 | Let $A$ be the number of positive integers $n$ such that $1 \leq n \leq 540$ and $20$ divides the $n$th Fibonacci number. Let $B$ be the number of positive integers $n_1$ such that $1 \leq n_1 \leq 73984$ and $n_1$ is divisible by $A$. Compute the remainder when $36367 \cdot B$ is divided by $81624$. | 14,826 | graphs = [
Graph(
let={
"_n": Const(540),
"upper": Const(73984),
"divisor": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Ref("_n")), Divides(divisor=Const(20), dividend=Fibonacci(arg=Var(name='n')))))),
"resu... | ALG | NT | COUNT | sympy | COUNT_FIB_DIVISIBLE | [
"COUNT_FIB_DIVISIBLE"
] | 66de3c | nt_count_divisible_v1 | null | 6 | 0 | [
"COUNT_FIB_DIVISIBLE"
] | 1 | 2.395 | 2026-02-08T17:38:45.408698Z | {
"verified": true,
"answer": 14826,
"timestamp": "2026-02-08T17:38:47.803961Z"
} | aa9c4c | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 145,
"completion_tokens": 2052
},
"timestamp": "2026-02-18T05:12:42.834Z",
"answer": 14826
},
... | 1 | [
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "ok"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "V3",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
6029c9 | modular_min_modexp_v1_1439011603_2025 | Let $m = 131$. Let $s$ be the minimum value of $x + y$ over all ordered pairs $(x, y)$ of positive integers such that $xy = 4225$. Let $r$ be the smallest positive integer $x_1$ such that $1 \leq x_1 \leq s$ and $2^{x_1} \equiv 98 \pmod{m}$. Compute the Bell number $B_k$, where $k$ is the absolute value of $r$ modulo $... | 4,140 | graphs = [
Graph(
let={
"a": Const(2),
"b": Const(98),
"m": Const(131),
"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"), V... | NT | COMB | EXTREMUM | sympy | B3 | [
"B3"
] | 0cd20d | modular_min_modexp_v1 | null | 6 | 0 | [
"B3"
] | 1 | 0.021 | 2026-02-08T16:28:11.948961Z | {
"verified": true,
"answer": 4140,
"timestamp": "2026-02-08T16:28:11.969571Z"
} | 4a8ab4 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 157,
"completion_tokens": 2358
},
"timestamp": "2026-02-17T04:03:35.066Z",
"answer": 4140
},
{... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "VAL_SUM_EQ",
"status": "no"
}
... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
366914 | algebra_quadratic_discriminant_v1_865884756_5575 | Let $S$ be the set of all positive integers $t$ between 15 and 45 inclusive that can be written in the form $6a + 9b$ for positive integers $a \leq 3$ and $b \leq 3$. Let $b$ be the minimum value of $x + y$ over all pairs of positive integers $(x, y)$ such that $xy = |S|$. Let $c$ be the number of prime numbers between... | 196 | graphs = [
Graph(
let={
"_n": Const(2),
"a": Const(-1),
"b": MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(Mul(Var("x"), Var("y")), CountOverSet(set=Solut... | NT | null | COMPUTE | sympy | MOBIUS_SUM | [
"LIN_FORM/B3",
"COUNT_PRIMES"
] | f413ae | algebra_quadratic_discriminant_v1 | null | 5 | 0 | [
"B3",
"COUNT_PRIMES",
"LIN_FORM",
"MOBIUS_SUM"
] | 4 | 0.021 | 2026-02-08T18:42:15.507193Z | {
"verified": true,
"answer": 196,
"timestamp": "2026-02-08T18:42:15.527950Z"
} | ce55ca | 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": 1666
},
"timestamp": "2026-02-18T18:46:44.761Z",
"answer": 196
},
{
... | 1 | [
{
"lemma": "B3",
"status": "ok_later"
},
{
"lemma": "COUNT_PRIMES",
"status": "ok"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": ... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
eb39bc | nt_sum_divisors_mod_v1_1520064083_2172 | Let $n$ be the minimum possible value of $x + y$ where $x$ and $y$ are positive integers such that $xy = 14400$. Let $\sigma$ be the sum of all positive divisors of $n$. Compute the remainder when $\sigma$ is divided by $11801$. | 744 | graphs = [
Graph(
let={
"_n": Const(14400),
"n": MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(Mul(Var("x"), Var("y")), Ref("_n")))), expr=Sum(Var("x"), Var("y")))),
... | NT | null | COMPUTE | sympy | B3 | [
"B3"
] | 0cd20d | nt_sum_divisors_mod_v1 | null | 6 | 0 | [
"B3"
] | 1 | 0.002 | 2026-02-08T04:33:06.206949Z | {
"verified": true,
"answer": 744,
"timestamp": "2026-02-08T04:33:06.208615Z"
} | 6cc986 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 175,
"completion_tokens": 571
},
"timestamp": "2026-02-10T17:07:47.041Z",
"answer": 744
},
{
"id... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
}
] | {
"lo": -5.55,
"mid": -3.01,
"hi": 0.33
} | ||
df979f | nt_count_intersection_v1_865884756_3892 | Let $a = 7$. Let $b$ be the minimum value of $x + y$ over all ordered pairs $(x, y)$ of positive integers such that $xy = 81$. Determine the number of positive integers $n$, with $1 \leq n \leq 100000$, such that $7$ divides $n$ and $\gcd(n, b) = 1$. Let $Q$ be the remainder when $180$ minus this count is divided by $5... | 54,817 | graphs = [
Graph(
let={
"_n": Const(59399),
"N": Const(100000),
"a": Const(7),
"b": MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(Mul(Var("x")... | NT | null | COUNT | sympy | B3 | [
"B3"
] | 0cd20d | nt_count_intersection_v1 | null | 4 | 0 | [
"B3"
] | 1 | 3.808 | 2026-02-08T17:39:27.290841Z | {
"verified": true,
"answer": 54817,
"timestamp": "2026-02-08T17:39:31.098640Z"
} | fde2c6 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 157,
"completion_tokens": 1025
},
"timestamp": "2026-02-18T05:29:22.257Z",
"answer": 54817
},
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "V3",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
efdbc3 | comb_binomial_compute_v1_1116507919_306 | Let $n = 13$. Define $k$ to be the value of the sum
$$
\sum_{k=1}^{3} \phi(k) \left\lfloor \frac{3}{k} \right\rfloor,
$$
where $\phi$ denotes Euler's totient function. Let $\binom{n}{k}$ denote the binomial coefficient. Compute the remainder when $79663 \cdot \binom{n}{k}$ is divided by $57383$. | 15,402 | graphs = [
Graph(
let={
"_n": Const(79663),
"n": Const(13),
"k": Summation(var="k", start=Const(1), end=Const(3), expr=Mul(EulerPhi(n=Var("k")), Floor(Div(Const(3), Var("k"))))),
"result": Binom(n=Ref("n"), k=Ref("k")),
"Q": Mod(value=Mul(Ref("_n")... | NT | null | COMPUTE | sympy | K2 | [
"K2"
] | 6897ab | comb_binomial_compute_v1 | null | 3 | 0 | [
"K2"
] | 1 | 0.001 | 2026-02-08T02:30:45.148623Z | {
"verified": true,
"answer": 15402,
"timestamp": "2026-02-08T02:30:45.149661Z"
} | 2d6080 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 219,
"completion_tokens": 1972
},
"timestamp": "2026-02-08T19:21:31.573Z",
"answer": 15402
},
{
"... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "K2",
"status": "ok"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "V3",
"status": "no"
}
] | {
"lo": -0.93,
"mid": 0.84,
"hi": 2.38
} | ||
4ebc65 | comb_bell_compute_v1_1520064083_339 | Let $S$ be the set of all ordered pairs $(x,y)$ of positive integers such that $xy = 16$. Let $T$ be the set of all values $x + y$ where $(x,y) \in S$. Define $n$ to be the minimum element of $T$. Compute the remainder when $39813 \cdot B_n$ is divided by 63629, where $B_n$ denotes the $n$-th Bell number. | 26,710 | graphs = [
Graph(
let={
"n": MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(Mul(Var("x"), Var("y")), Const(16)))), expr=Sum(Var("x"), Var("y")))),
"result": Bell(Ref("... | COMB | null | COMPUTE | sympy | C3 | [
"B3"
] | 0cd20d | comb_bell_compute_v1 | null | 3 | 0 | [
"B3",
"C3"
] | 2 | 0.01 | 2026-02-08T03:16:50.580840Z | {
"verified": true,
"answer": 26710,
"timestamp": "2026-02-08T03:16:50.590872Z"
} | 0209d8 | 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": 1169
},
"timestamp": "2026-02-10T13:50:10.869Z",
"answer": 26710
},
{
"... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8_SUM",
"statu... | {
"lo": -2.46,
"mid": 0.47,
"hi": 3.59
} | ||
91b800 | antilemma_k2_v1_717093673_3032 | Let $c = 401$ and $m = 401$. Define $n$ to be the sum of $\phi(d)$ over all positive divisors $d$ of $m$, where $\phi$ is the Euler totient function. Define $C$ to be the sum of $\phi(d_1)$ over all positive divisors $d_1$ of $c$.
Now define
$$
x = \sum_{k=1}^{n} \phi(k) \left\lfloor \frac{C}{k} \right\rfloor.
$$
Comp... | 7,652 | graphs = [
Graph(
let={
"_c": Const(401),
"_m": Const(401),
"_n": SumOverDivisors(n=Ref(name='_m'), var='d', expr=EulerPhi(n=Var(name='d'))),
"x": Summation(var="k", start=Const(1), end=Ref("_n"), expr=Mul(EulerPhi(n=Var("k")), Floor(Div(SumOverDivisors(n=Ref(... | NT | COMB | COMPUTE | sympy | K13 | [
"K3/K2",
"K2"
] | c7f244 | antilemma_k2_v1 | null | 5 | 0 | [
"K13",
"K2",
"K3"
] | 3 | 0.005 | 2026-02-08T17:20:43.836699Z | {
"verified": true,
"answer": 7652,
"timestamp": "2026-02-08T17:20:43.842141Z"
} | c00c9a | 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": 1307
},
"timestamp": "2026-02-18T00:25:53.568Z",
"answer": 7652
},
{... | 1 | [
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K2",
"status": "ok"
},
{
"lemma": "K3",
"status": "ok"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lem... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
6b8bd8 | antilemma_sum_primes_v1_168721529_122 | Let $x$ be the sum of all prime numbers $n$ such that $2 \leq n \leq 3$. Let $S$ be the set of all positive integers $p$ for which there exists a positive integer $q$ such that $p \cdot q = 72$, $\gcd(p, q) = 1$, and $p < q$. Let $Q$ be the remainder when the number of elements in $S$ minus $x$ is divided by $69804$. F... | 69,801 | graphs = [
Graph(
let={
"_n": Const(2),
"x": SumOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Ref("_n")), Leq(Var("n"), Const(3)), IsPrime(Var("n"))))),
"Q": Mod(value=Sub(CountOverSet(set=SolutionsSet(var=Var("p"), condition=And(IsPositive(arg=Var(na... | NT | null | COMPUTE | sympy | COPRIME_PAIRS | [
"COPRIME_PAIRS",
"SUM_PRIMES"
] | 2e4a7d | antilemma_sum_primes_v1 | negation_mod | 4 | 0 | [
"COPRIME_PAIRS",
"SUM_PRIMES"
] | 2 | 0.003 | 2026-02-08T12:50:01.357351Z | {
"verified": true,
"answer": 69801,
"timestamp": "2026-02-08T12:50:01.360308Z"
} | df88bb | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 229,
"completion_tokens": 1384
},
"timestamp": "2026-02-08T21:03:57.885Z",
"answer": 69801
},
{
"... | 1 | [
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "SUM_PRIMES",
"status": "ok"
},
{
"lemma": "V1",
"status": "no"
},
{
"lemma": "V5",
"st... | {
"lo": -2.06,
"mid": 1.85,
"hi": 5.2
} | ||
b799ab | sequence_fibonacci_compute_v1_1125832087_86 | Let $n$ be the minimum value of $x + y$ over all pairs of positive integers $(x, y)$ such that $xy = 100$. Compute the $n$-th Fibonacci number, where $F_1 = 1$, $F_2 = 1$, and $F_m = F_{m-1} + F_{m-2}$ for $m \geq 3$. | 6,765 | graphs = [
Graph(
let={
"_n": Const(100),
"n": MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(Mul(Var("x"), Var("y")), Ref("_n")))), expr=Sum(Var("x"), Var("y")))),
... | NT | null | COMPUTE | sympy | B3 | [
"B3"
] | 0cd20d | sequence_fibonacci_compute_v1 | null | 4 | 0 | [
"B3"
] | 1 | 0.001 | 2026-02-08T02:51:29.802854Z | {
"verified": true,
"answer": 6765,
"timestamp": "2026-02-08T02:51:29.804116Z"
} | 88368b | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 197,
"completion_tokens": 585
},
"timestamp": "2026-02-10T11:42:20.981Z",
"answer": 6765
},
{
"id... | 2 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
}
] | {
"lo": -10,
"mid": -7.33,
"hi": -4.66
} | ||
5eb26b | modular_inverse_v1_124444284_9045 | Let $a$ be the largest positive integer $d$ such that $d \leq 979$ and $d$ divides 976063. Let $m$ be the largest prime number $n$ such that $2 \leq n \leq 1152$. Let $S$ be the set of all positive integers $x$ such that $1 \leq x \leq 1150$ and
$$
ax \equiv 1 \pmod{m}.
$$Let $r$ be the smallest element of $S$. Compute... | 46,204 | graphs = [
Graph(
let={
"a": MaxOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Const(1)), Leq(Var("d"), Const(979)), Divides(divisor=Var("d"), dividend=Const(976063))))),
"m": MaxOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(2)), Leq(Var... | NT | null | EXTREMUM | sympy | MAX_PRIME_BELOW | [
"MAX_PRIME_BELOW",
"MAX_DIVISOR"
] | beffb0 | modular_inverse_v1 | null | 5 | 0 | [
"MAX_DIVISOR",
"MAX_PRIME_BELOW"
] | 2 | 0.053 | 2026-02-08T12:10:10.485571Z | {
"verified": true,
"answer": 46204,
"timestamp": "2026-02-08T12:10:10.538469Z"
} | 0a8027 | 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": 4761
},
"timestamp": "2026-02-14T22:41:35.979Z",
"answer": 46204
},
... | 1 | [
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "MAX_DIVISOR",
"status": "ok"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok"
},
{
"lemma": "V3",
"status": "no"
},
... | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
898cc2 | antilemma_k3_v1_655260480_5694 | Let $x = \sum_{d \mid 60482} \phi(d)$, where $\phi$ denotes Euler's totient function. Compute $x + 2^{x \bmod 15} \bmod 80755$. | 60,486 | graphs = [
Graph(
let={
"x": SumOverDivisors(n=Const(value=60482), var='d', expr=EulerPhi(n=Var(name='d'))),
"Q": Sum(Ref("x"), Mod(value=Pow(Const(2), Mod(value=Ref("x"), modulus=Const(15))), modulus=Const(80755))),
},
goal=Ref("Q"),
)
] | NT | COMB | COMPUTE | sympy | K3 | [
"K3"
] | 54c41e | antilemma_k3_v1 | null | 3 | 0 | [
"K3"
] | 1 | 0 | 2026-02-08T18:37:48.699904Z | {
"verified": true,
"answer": 60486,
"timestamp": "2026-02-08T18:37:48.700365Z"
} | f205dd | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 115,
"completion_tokens": 790
},
"timestamp": "2026-02-16T13:27:50.000Z",
"answer": 30305
},
{
"id": 11... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K3",
"status": "ok"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
}
] | {
"lo": -8.26,
"mid": -5.01,
"hi": -1.76
} | ||
d274d4 | geo_count_lattice_rect_v1_1978505735_6446 | Let $a = 222$ and $b = 147$. Compute the number of lattice points in the rectangle $[0, a] \times [0, b]$, including the boundaries. Let $m$ be this number plus 2. Find the smallest positive integer $k$ such that the $k$-th Fibonacci number is divisible by $m$. | 16,500 | graphs = [
Graph(
let={
"a": Const(222),
"b": Const(147),
"result": LatticePointsRect(a=Ref(name='a'), b=Ref(name='b')),
"Q": FibonacciEntryPoint(modulus=Sum(Abs(arg=Ref(name='result')), Const(value=2))),
},
goal=Ref("Q"),
)
] | GEOM | NT | COUNT | sympy | [] | geo_count_lattice_rect_v1 | null | 4 | 0 | null | null | 0.003 | 2026-02-08T19:36:09.722204Z | {
"verified": true,
"answer": 16500,
"timestamp": "2026-02-08T19:36:09.725522Z"
} | 3ea27d | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 122,
"completion_tokens": 5659
},
"timestamp": "2026-02-18T22:58:27.017Z",
"answer": 16500
},
... | 1 | [] | {
"lo": -3.12,
"mid": 1.47,
"hi": 6.57
} | ||||
3faa0c | antilemma_k2_v1_1742523217_2233 | Let $m = 2$ and let $n$ be the sum of all real solutions $x$ to the equation $x^2 - 106x - 4080 = 0$. Compute the value of $$
\sum_{k=1}^{106} \phi(k) \left\lfloor \frac{n}{k} \right\rfloor,
$$ where $\phi$ denotes Euler's totient function. | 5,671 | graphs = [
Graph(
let={
"_m": Const(2),
"_n": SumOverSet(set=SolutionsSet(var=Var("x"), condition=Eq(Sum(Pow(Var("x"), Ref("_m")), Mul(Const(-106), Var("x")), Const(-4080)), Const(0)))),
"x": Summation(var="k", start=Const(1), end=Const(106), expr=Mul(EulerPhi(n=Var("k"))... | NT | COMB | COMPUTE | sympy | VIETA_SUM | [
"VIETA_SUM/K2",
"K2"
] | 6be084 | antilemma_k2_v1 | null | 6 | 0 | [
"K2",
"VIETA_SUM"
] | 2 | 0.003 | 2026-02-08T04:36:55.852080Z | {
"verified": true,
"answer": 5671,
"timestamp": "2026-02-08T04:36:55.855548Z"
} | 328657 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 200,
"completion_tokens": 646
},
"timestamp": "2026-02-11T21:42:42.848Z",
"answer": 5671
},
{
"i... | 1 | [
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "K2",
"status": "ok"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "V1",
"status": "no"
},
{
"lemma": "VIETA_SUM"... | {
"lo": -3.42,
"mid": 1.86,
"hi": 7.55
} | ||
3b9cd7 | nt_min_coprime_above_v1_1978505735_7714 | Let $A$ be the number of integers $n$ with $1 \leq n \leq 60236$ such that $n \equiv \left\lfloor \frac{n}{2} \right\rfloor \pmod{11}$. Let $B$ be the number of integers $n$ with $1 \leq n \leq 14529$ such that $\gcd(n, 20) = 1$. Let $T$ be the set of all ordered pairs of positive integers $(x, y)$ such that $xy = 2656... | 7,133 | graphs = [
Graph(
let={
"_m": Const(14529),
"_n": Const(60236),
"start": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Ref("_n")), Congruent(a=Var(name='n'), b=Floor(arg=Div(left=Var(name='n'), right=Const(value=2))), mod... | NT | null | EXTREMUM | sympy | L3C | [
"L3C",
"B3",
"C4"
] | 5142f7 | nt_min_coprime_above_v1 | null | 7 | 0 | [
"B3",
"C4",
"L3C"
] | 3 | 0.031 | 2026-02-08T20:24:13.623818Z | {
"verified": true,
"answer": 7133,
"timestamp": "2026-02-08T20:24:13.654547Z"
} | 8679bf | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 277,
"completion_tokens": 2906
},
"timestamp": "2026-02-19T00:31:20.654Z",
"answer": 7133
},
{... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "C4",
"status": "ok"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "L3C",
"status": "ok"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "MOD_A... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
a9e6d9 | nt_count_divisors_in_range_v1_124444284_2721 | Let $a$ be the number of positive integers $p$ for which there exists a positive integer $q$ such that $pq = 6$, $\gcd(p, q) = 1$, and $p < q$. Let $n = 27720$. Let $S$ be the set of all positive divisors $d$ of $n$ such that $a \le d \le 27725$. Compute the remainder when $44359 \cdot |S|$ is divided by $73571$. | 20,558 | graphs = [
Graph(
let={
"_n": Const(73571),
"n": Const(27720),
"a": 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=6)), Eq(left=G... | NT | null | COUNT | sympy | COPRIME_PAIRS | [
"COPRIME_PAIRS"
] | 2bb3aa | nt_count_divisors_in_range_v1 | null | 4 | 0 | [
"COPRIME_PAIRS"
] | 1 | 0.476 | 2026-02-08T04:54:02.619476Z | {
"verified": true,
"answer": 20558,
"timestamp": "2026-02-08T04:54:03.095112Z"
} | 877974 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 219,
"completion_tokens": 2962
},
"timestamp": "2026-02-11T22:42:27.782Z",
"answer": 20558
},
{
"... | 1 | [
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "V8_SUM",
"sta... | {
"lo": -3.52,
"mid": 1.14,
"hi": 6.18
} | ||
d5d5ae | alg_poly4_min_v1_1218484723_2017 | Let $T$ be the number of positive integers $p$ such that $p < q$, $pq = 4898589994206014701336942200$, and $\gcd(p, q) = 1$. Find the minimum value of $128a^4 + 12288a^2b^2 + 32768ab^3 + 32768b^4 + T a^3 b$ over all ordered pairs $(a, b)$ of positive integers with $1 \le a, b \le 83$. | 80,000 | graphs = [
Graph(
let={
"_n": Const(32768),
"result": MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("a"), Var("b")]), condition=And(Geq(Var("a"), Const(1)), Leq(Var("a"), Const(83)), Geq(Var("b"), Const(1)), Leq(Var("b"), Const(83)))), expr=Sum(Mul(Const(12288), ... | NT | null | COMPUTE | sympy | COPRIME_PAIRS | [
"COPRIME_PAIRS"
] | 2bb3aa | alg_poly4_min_v1 | null | 6 | 0 | [
"COPRIME_PAIRS"
] | 1 | 0.026 | 2026-02-25T03:43:32.528867Z | {
"verified": true,
"answer": 80000,
"timestamp": "2026-02-25T03:43:32.555361Z"
} | 4eca66 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 223,
"completion_tokens": 32768
},
"timestamp": "2026-03-29T02:34:50.499Z",
"answer": null
},
{
... | 1 | [
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"
}
] | {
"lo": 3.14,
"mid": 5.37,
"hi": 7.61
} | ||
519c45_n | modular_modexp_compute_v1_601307018_1789 | A security system uses a two-stage code. The first stage selects the largest prime number between 2 and 30, denoted $a$. The second stage calculates a length $L$ equal to the number of integers from 1 to 224 satisfying $n_1 \equiv \lfloor n_1/2 \rfloor \pmod{7}$. Then it finds the maximum possible product $e = x \cdot ... | 16,321 | NT | null | COMPUTE | sympy | MAX_PRIME_BELOW | [
"MAX_PRIME_BELOW",
"L3C/B1"
] | 5af77e | modular_modexp_compute_v1 | null | 6 | null | [
"B1",
"L3C",
"MAX_PRIME_BELOW"
] | 3 | 0.004 | 2026-03-10T02:32:21.924541Z | null | e479c9 | 519c45 | narrative | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 232,
"completion_tokens": 3791
},
"timestamp": "2026-03-29T15:27:21.287Z",
"answer": 16321
},
{
"... | 1 | [
{
"lemma": "B1",
"status": "ok_later"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "L3C",
"status": "ok"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
... | {
"lo": -5.36,
"mid": 0.27,
"hi": 5.45
} | |
522f9f | nt_min_crt_v1_1353956133_469 | Let $m = 3$ and $k = 7$. Define $a = 2$ and $b = 2$. Let $S$ be the set of all integers $n$ such that $1 \leq n \leq \sum_{i=1}^{6} i$, $n \equiv a \pmod{m}$, and $n \equiv b \pmod{k}$. Compute the minimum value of $S$. | 2 | graphs = [
Graph(
let={
"m": Const(3),
"k": Const(7),
"a": Const(2),
"b": Const(2),
"upper": Summation(var="k", start=Const(1), end=Const(6), expr=Var("k")),
"result": MinOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n")... | NT | null | EXTREMUM | sympy | SUM_ARITHMETIC | [
"SUM_ARITHMETIC"
] | eb34f0 | nt_min_crt_v1 | null | 3 | 0 | [
"SUM_ARITHMETIC"
] | 1 | 0.005 | 2026-02-08T11:27:58.887998Z | {
"verified": true,
"answer": 2,
"timestamp": "2026-02-08T11:27:58.892935Z"
} | a03cf4 | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 148,
"completion_tokens": 685
},
"timestamp": "2026-02-15T22:05:43.837Z",
"answer": 2
},
{
"id": 11,
"... | 2 | [
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "SUM_ARITHMETIC",
"status": "ok"
},
{
"lemma": "V8_SUM",
"stat... | {
"lo": -9.12,
"mid": -6.02,
"hi": -3.62
} | ||
986b1f | modular_count_residue_v1_1915831931_3382 | Let $m$ be the number of positive integers $p$ for which there exists a positive integer $q$ such that $p < q$, $\gcd(p, q) = 1$, and $p \cdot q = 1067220$. Compute the number of positive integers $n \leq 55225$ such that the remainder when $n$ is divided by $m$ is $11$. | 3,451 | graphs = [
Graph(
let={
"upper": Const(55225),
"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=1067220)), Eq(left=GCD(a=Var(name='p'), b=... | NT | null | COUNT | sympy | COPRIME_PAIRS | [
"COPRIME_PAIRS"
] | 2bb3aa | modular_count_residue_v1 | null | 5 | 0 | [
"COPRIME_PAIRS"
] | 1 | 2.155 | 2026-02-08T17:36:47.470244Z | {
"verified": true,
"answer": 3451,
"timestamp": "2026-02-08T17:36:49.625476Z"
} | fb6a74 | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 151,
"completion_tokens": 543
},
"timestamp": "2026-02-16T11:27:44.170Z",
"answer": 173
},
{
"id": 11,
... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "VAL_SUM_EQ",
"status": "no"
}
] | {
"lo": -8.26,
"mid": -5.01,
"hi": -1.76
} | ||
2e48f9 | comb_count_derangements_v1_124444284_6477 | Let $m=75668$ and $n=44121$. Define
$$h=\sum_{k=0}^{0}(-1)^k\binom{0}{k}$$
and let $u$ be the number of integers $t$ for which there exist integers $a$ and $b$ satisfying $1\le a\le3$, $1\le b\le3$, $5\le t\le15$, and
$$t=2a+3b.$$
Let $n_1=u+1$.
Let $T$ be the set of all ordered pairs $(x_1,x_2)$ of positive odd integ... | 3,226 | graphs = [
Graph(
let={
"_m": Const(75668),
"_n": Const(44121),
"n2": Const(0),
"h": Summation(var="k", start=Const(0), end=Ref("n2"), expr=Mul(Pow(Const(-1), Var("k")), Binom(n=Ref("n2"), k=Var("k")))),
"u": CountOverSet(set=SolutionsSet(var=Var("... | COMB | null | COUNT | sympy | COMB1 | [
"COMB1/ZERO_BINOM_0/BINOMIAL_ALTERNATING",
"LIN_FORM/BINOMIAL_ALTERNATING"
] | 0aac41 | comb_count_derangements_v1 | null | 6 | 2 | [
"BINOMIAL_ALTERNATING",
"COMB1",
"LIN_FORM",
"ZERO_BINOM_0"
] | 4 | 0.005 | 2026-02-08T08:28:47.750297Z | {
"verified": true,
"answer": 3226,
"timestamp": "2026-02-08T08:28:47.754863Z"
} | 6b5c3f | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 383,
"completion_tokens": 8890
},
"timestamp": "2026-02-24T09:34:49.805Z",
"answer": 3226
},
{
"i... | 1 | [
{
"lemma": "BINOMIAL_ALTERNATING",
"status": "ok_later"
},
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COMB1",
"status": "ok"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "LIN_FORM",
... | {
"lo": -2.35,
"mid": 1.22,
"hi": 4.84
} | ||
abf434 | comb_count_surjections_v1_1915831931_3545 | Let $k$ be the number of ordered pairs $(i, j)$ of positive integers such that $1 \leq i \leq 3$, $1 \leq j \leq 4$, and $i + j = 4$. Compute $k! \cdot S(7, k)$, where $S(7, k)$ denotes the Stirling number of the second kind. | 1,806 | graphs = [
Graph(
let={
"n": Const(7),
"k": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("i"), Var("j")]), condition=Eq(Sum(Var("i"), Var("j")), Const(4)), domain=CartesianProduct(left=IntegerRange(start=Const(1), end=Const(3)), right=IntegerRange(start=Const(1), end=Const(4... | COMB | null | COUNT | sympy | COUNT_SUM_EQUALS | [
"COUNT_SUM_EQUALS"
] | 75ab0f | comb_count_surjections_v1 | null | 3 | 0 | [
"COUNT_SUM_EQUALS"
] | 1 | 0.017 | 2026-02-08T17:43:59.308037Z | {
"verified": true,
"answer": 1806,
"timestamp": "2026-02-08T17:43:59.324908Z"
} | ea5883 | 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": 871
},
"timestamp": "2026-02-18T07:04:33.802Z",
"answer": 1806
},
{
... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "ok"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
}
] | {
"lo": -5.64,
"mid": -3.17,
"hi": -0.81
} | ||
62caec | comb_bell_compute_v1_717093673_1086 | Let $S$ be the set of all ordered pairs $(x_1, y_1)$ of positive integers such that $x_1 + y_1 = 8$. Define $M$ to be the maximum value of $x_1 y_1$ over all such pairs.
Now let $T$ be the set of all ordered pairs $(x, y)$ of positive integers such that $xy = M$. Define $n$ to be the minimum value of $x + y$ over all ... | 27,156 | graphs = [
Graph(
let={
"_n": Const(44121),
"n": MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(Mul(Var("x"), Var("y")), MaxOverSet(set=MapOverSet(set=SolutionsSet(var... | COMB | null | COMPUTE | sympy | B1 | [
"B1/B3"
] | 80b49d | comb_bell_compute_v1 | null | 6 | 0 | [
"B1",
"B3"
] | 2 | 0.003 | 2026-02-08T15:51:10.646055Z | {
"verified": true,
"answer": 27156,
"timestamp": "2026-02-08T15:51:10.648779Z"
} | 0cf940 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 270,
"completion_tokens": 1253
},
"timestamp": "2026-02-24T18:52:36.389Z",
"answer": 27156
},
{
... | 1 | [
{
"lemma": "B1",
"status": "ok"
},
{
"lemma": "B3",
"status": "ok_later"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
},
{... | {
"lo": -2.4,
"mid": 1.57,
"hi": 5.75
} | ||
ed3382 | nt_sum_gcd_range_mod_v1_1520064083_3331 | Let $N$ be the maximum value of $xy$ over all pairs of positive integers $(x, y)$ such that $x + y = 108$. Let $k = 60$ and $M = 11779$. Define $\text{sum} = \sum_{n=1}^{N} \gcd(n, k)$. Compute the remainder when $\text{sum}$ is divided by $M$. | 5,693 | graphs = [
Graph(
let={
"_n": Const(108),
"N": MaxOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(Sum(Var("x"), Var("y")), Ref("_n")))), expr=Mul(Var("x"), Var("y")))),
... | NT | null | COMPUTE | sympy | B1 | [
"B1"
] | 5b950e | nt_sum_gcd_range_mod_v1 | null | 5 | 0 | [
"B1"
] | 1 | 0.19 | 2026-02-08T05:35:45.880490Z | {
"verified": true,
"answer": 5693,
"timestamp": "2026-02-08T05:35:46.070866Z"
} | a8a853 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 132,
"completion_tokens": 2273
},
"timestamp": "2026-02-12T10:51:09.686Z",
"answer": 5693
},
{... | 1 | [
{
"lemma": "B1",
"status": "ok"
},
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
}
] | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
26ff1b | nt_count_digit_sum_v1_1978505735_7178 | Let $S$ be the set of all positive integers $n_1$ such that $1 \leq n_1 \leq 344$, $8$ divides $n_1$, and $\gcd(n_1, 35) = 1$. Let $N$ be the number of elements in $S$. Define $s$ to be the largest prime number $n$ such that $2 \leq n \leq N$.
Compute the number of positive integers $n_2$ such that $1 \leq n_2 \leq 22... | 290 | graphs = [
Graph(
let={
"_n": Const(35),
"upper": Const(22801),
"target_sum": MaxOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(2)), Leq(Var("n"), CountOverSet(set=SolutionsSet(var=Var("n1"), condition=And(Geq(Var("n1"), Const(1)), Leq(Var("n1"),... | NT | null | COUNT | sympy | C5 | [
"C5/MAX_PRIME_BELOW"
] | e03314 | nt_count_digit_sum_v1 | null | 6 | 0 | [
"C5",
"MAX_PRIME_BELOW"
] | 2 | 0.769 | 2026-02-08T20:06:16.376167Z | {
"verified": true,
"answer": 290,
"timestamp": "2026-02-08T20:06:17.145220Z"
} | 6d09f8 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 182,
"completion_tokens": 5430
},
"timestamp": "2026-02-18T23:59:56.919Z",
"answer": 290
},
{
... | 1 | [
{
"lemma": "C5",
"status": "ok"
},
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "LTE_SUM",
"statu... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
c4d57b | modular_count_residue_v1_784195855_3326 | Let $m$ be the number of integers $j$ with $0 \le j \le 34304$ such that $\binom{34304}{j}$ is odd. Let $r = 7$. Define $s$ to be the number of positive integers $n$ at most $66049$ such that $n \equiv r \pmod{m}$. Let $Q$ be the remainder when $30233 \cdot s$ is divided by $72750$. Compute $Q$. | 71,148 | graphs = [
Graph(
let={
"upper": Const(66049),
"m": CountOverSet(set=SolutionsSet(var=Var("j"), condition=And(Geq(Var("j"), Const(0)), Leq(Var("j"), Const(34304)), Eq(Mod(value=Binom(n=Const(34304), k=Var("j")), modulus=Const(2)), Const(1))), domain='nonnegative_integers')),
... | ALG | COMB | COUNT | sympy | V8 | [
"V8"
] | 86348e | modular_count_residue_v1 | null | 6 | 0 | [
"V8"
] | 1 | 2.355 | 2026-02-08T06:20:30.775530Z | {
"verified": true,
"answer": 71148,
"timestamp": "2026-02-08T06:20:33.130455Z"
} | a910f5 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 217,
"completion_tokens": 2531
},
"timestamp": "2026-02-24T06:05:26.657Z",
"answer": 71148
},
{
"... | 1 | [
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
},
{
"lemma": "V8",
"status": "ok"
},
{
"lemma": "VAL_SUM_EQ",
"status": "no"
}
] | {
"lo": -2.46,
"mid": 0.47,
"hi": 3.59
} | ||
67168f | nt_count_gcd_equals_v1_898971024_567 | Let $x_1$ and $y_1$ be positive integers such that $x_1 y_1 = 5476$. Let $T$ be the set of all values of $x_1 + y_1$ for such pairs $(x_1, y_1)$, and let $s$ be the minimum value in $T$. Now let $x$ and $y$ be positive integers such that $x + y = s$. Let $U$ be the set of all values of $xy$ for such pairs $(x, y)$, and... | 48,123 | graphs = [
Graph(
let={
"_m": Const(5476),
"_n": Const(73424),
"upper": 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")), MinOverSet(... | NT | null | COUNT | sympy | B3 | [
"B3/B1"
] | 7f76f7 | nt_count_gcd_equals_v1 | null | 6 | 0 | [
"B1",
"B3"
] | 2 | 0.426 | 2026-02-08T15:32:30.508452Z | {
"verified": true,
"answer": 48123,
"timestamp": "2026-02-08T15:32:30.934575Z"
} | f61b6f | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 234,
"completion_tokens": 1734
},
"timestamp": "2026-02-16T08:03:14.754Z",
"answer": 48123
},
... | 1 | [
{
"lemma": "B1",
"status": "ok_later"
},
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma":... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
994265 | alg_poly4_sum_v1_601307018_3016 | Let $M$ be the largest positive integer $d$ such that $d^2 \leq 590592$ and $d \mid 590592$. Find the remainder when $$\sum_{\substack{1 \leq a \leq 451 \\ 1 \leq b \leq 451}} \left( 32b^4 + M a^2 b^2 - 256a b^3 - 1024a^3 b + \left|\left\{ p > 0 \mid \exists\, q \in \mathbb{Z},\ pq = 243443756644778890200,\ \gcd(p,q)=1... | 4,816 | graphs = [
Graph(
let={
"_m": Const(58438),
"_n": MaxOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Const(1)), Divides(divisor=Var("d"), dividend=Const(590592)), Leq(Mul(Var("d"), Var("d")), Const(590592))))),
"result": Mod(value=SumOverSet(set=MapOver... | NT | null | COMPUTE | sympy | B3_CLOSEST | [
"B3_CLOSEST/COPRIME_PAIRS"
] | da9c44 | alg_poly4_sum_v1 | null | 7 | 0 | [
"B3_CLOSEST",
"COPRIME_PAIRS"
] | 2 | 0.633 | 2026-03-10T03:38:18.913591Z | {
"verified": true,
"answer": 4816,
"timestamp": "2026-03-10T03:38:19.546942Z"
} | 2e32ed | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 280,
"completion_tokens": 32768
},
"timestamp": "2026-03-29T07:15:37.172Z",
"answer": null
},
{
... | 1 | [
{
"lemma": "B3_CLOSEST",
"status": "ok"
},
{
"lemma": "COPRIME_PAIRS",
"status": "ok_later"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
... | {
"lo": 3.34,
"mid": 5.77,
"hi": 8.89
} | ||
a1f496 | modular_product_range_v1_124444284_1850 | Let $N$ be the sum of all integers $x$ such that $x^2-48x-1105=0$. Let $M$ be the minimum of the set of all values of $x+y$ as $(x,y)$ ranges over all ordered pairs of positive integers satisfying $xy=144$. Let $S$ be the set of all integers $n$ such that $1\le n\le N$ and $n\equiv 0\pmod{M}$. Let
$$P=\prod_{i=6}^{\,\s... | 8,538 | graphs = [
Graph(
let={
"_c": Const(2),
"_m": Const(11779),
"_n": Const(6),
"prod": MathProduct(expr=Var("i"), var="i", start=Ref("_n"), end=SumOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), SumOverSet(set=Solutions... | NT | null | COMPUTE | sympy | VIETA_SUM | [
"VIETA_SUM/SUM_DIVISIBLE",
"B3/SUM_DIVISIBLE"
] | 617187 | modular_product_range_v1 | null | 8 | 0 | [
"B3",
"SUM_DIVISIBLE",
"VIETA_SUM"
] | 3 | 0.004 | 2026-02-08T04:11:04.259318Z | {
"verified": true,
"answer": 8538,
"timestamp": "2026-02-08T04:11:04.263258Z"
} | 3fcefc | CC BY 4.0 | [
{
"id": 4,
"model": "NousResearch/Hermes-4-405B",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 200,
"completion_tokens": 489
},
"timestamp": "2026-02-12T02:05:43.913Z",
"answer": 1
},
{... | 0 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "SUM_DIVISIBLE",
"status":... | {
"lo": 1.6,
"mid": 4.12,
"hi": 7.38
} | ||
9bfd0c | antilemma_k3_v1_238844314_196 | Compute the value of $\sum_{d \mid 30050} \phi(d)$, where $\phi$ denotes Euler's totient function. | 30,050 | graphs = [
Graph(
let={
"_n": Const(30050),
"x": SumOverDivisors(n=Ref(name='_n'), var='d', expr=EulerPhi(n=Var(name='d'))),
},
goal=Ref("x"),
)
] | NT | COMB | COMPUTE | sympy | K3 | [
"K3"
] | 54c41e | antilemma_k3_v1 | null | 3 | 0 | [
"K3"
] | 1 | 0.002 | 2026-02-08T13:10:08.290161Z | {
"verified": true,
"answer": 30050,
"timestamp": "2026-02-08T13:10:08.292358Z"
} | 11c8c2 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 75,
"completion_tokens": 435
},
"timestamp": "2026-02-15T10:11:32.576Z",
"answer": 30050
},
{
... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "K3",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "V1",
"status": "no"
},
{
"lemma": "VAL_SUM_EQ",
"status": "no"
}
] | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
cadcc4 | comb_sum_binomial_row_v1_1470522791_442 | Let $w = \sum_{k=0}^{0} (-1)^k \binom{0}{k}$, $c = \sum_{k=0}^{7} (-1)^k \binom{7}{k}$, and $n = 15$. Let $\text{result} = (2 + c)^n$. Compute the remainder when $99175 \cdot \text{result}$ is divided by $58856 \cdot w$. | 32,360 | graphs = [
Graph(
let={
"n2": Const(0),
"w": 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(7),
"c": Summation(var="k", start=Const(0), end=Ref("n1"), expr=Mul(Pow(Const(-1), V... | COMB | null | SUM | sympy | BINOMIAL_ALTERNATING | [
"BINOMIAL_ALTERNATING"
] | c21569 | comb_sum_binomial_row_v1 | null | 5 | 2 | [
"BINOMIAL_ALTERNATING"
] | 1 | 0.001 | 2026-02-08T13:01:15.811978Z | {
"verified": true,
"answer": 32360,
"timestamp": "2026-02-08T13:01:15.812968Z"
} | 798e59 | 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": 2768
},
"timestamp": "2026-02-24T16:59:06.430Z",
"answer": 32360
},
{
"... | 1 | [
{
"lemma": "BINOMIAL_ALTERNATING",
"status": "ok"
},
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_CARTESIAN",
"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
} | ||
faacac | nt_count_intersection_v1_349078426_1219 | Let $N = 50000$ and $a = 11$. Let $s$ be the sum $\sum_{k=1}^5 k$. Let $B$ be the set of all positive integers $j$ such that $1 \leq j \leq s$ and $j^2 \leq 225$. Let $b$ be the number of elements in $B$. Let $R$ be the set of all positive integers $n$ such that $1 \leq n \leq N$, $a$ divides $n$, and $\gcd(n, b) = 1$.... | 46,498 | graphs = [
Graph(
let={
"N": Const(50000),
"a": Const(11),
"b": CountOverSet(set=SolutionsSet(var=Var("j"), condition=And(Geq(Var("j"), Const(1)), Leq(Var("j"), Summation(var="k", start=Const(1), end=Const(5), expr=Var("k"))), Leq(Pow(Var("j"), Const(2)), Const(225))), do... | NT | null | COUNT | sympy | SUM_ARITHMETIC | [
"SUM_ARITHMETIC/C3"
] | 540975 | nt_count_intersection_v1 | null | 4 | 0 | [
"C3",
"SUM_ARITHMETIC"
] | 2 | 1.633 | 2026-02-08T13:31:15.541250Z | {
"verified": true,
"answer": 46498,
"timestamp": "2026-02-08T13:31:17.173968Z"
} | 74d141 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 199,
"completion_tokens": 1347
},
"timestamp": "2026-02-15T16:49:23.082Z",
"answer": 46498
},
... | 1 | [
{
"lemma": "C3",
"status": "ok_later"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "SUM_ARITHMETIC",
"status": "ok"
},
{
"lemma": "V5",
"status": "n... | {
"lo": -5.49,
"mid": 0.22,
"hi": 6.51
} | ||
4084f4 | comb_sum_binomial_row_v1_2051736721_2929 | Let $n$ be the largest prime number such that $2 \leq n \leq 12$. Compute $2^n$. | 2,048 | graphs = [
Graph(
let={
"_n": Const(2),
"n": MaxOverSet(set=SolutionsSet(var=Var("n1"), condition=And(Geq(Var("n1"), Const(2)), Leq(Var("n1"), Const(12)), IsPrime(Var("n1"))))),
"result": Pow(Ref("_n"), Ref("n")),
},
goal=Ref("result"),
)
] | NT | null | SUM | sympy | MAX_PRIME_BELOW | [
"MAX_PRIME_BELOW"
] | dc3ad3 | comb_sum_binomial_row_v1 | null | 2 | 0 | [
"MAX_PRIME_BELOW"
] | 1 | 0.001 | 2026-02-08T17:00:29.521549Z | {
"verified": true,
"answer": 2048,
"timestamp": "2026-02-08T17:00:29.522860Z"
} | bde38c | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 83,
"completion_tokens": 157
},
"timestamp": "2026-02-16T08:42:07.367Z",
"answer": 2048
},
{
"id": 11,
... | 2 | [
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
}
] | {
"lo": -10,
"mid": -7.27,
"hi": -4.54
} | ||
d0a0d5_n | comb_count_derangements_v1_1218484723_1493 | A game developer designs a level where players collect coins in amounts that are linear combinations of two power-ups: one gives $5a$ coins and the other $2b$ coins, with $a$ from $1$ to $964$ and $b$ from $1$ to $1691$. Only totals between $7$ and $8202$ are valid. Let $T$ be the number of distinct valid coin totals. ... | 6,338 | COMB | null | COUNT | sympy | LIN_FORM | [
"LIN_FORM",
"SUM_GEOM",
"ZERO_BINOM_N"
] | b578f8 | comb_count_derangements_v1 | negation_mod | 4 | null | [
"LIN_FORM",
"SUM_GEOM",
"ZERO_BINOM_N"
] | 3 | 0.004 | 2026-02-25T03:11:59.611946Z | null | 7f5607 | d0a0d5 | narrative | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 265,
"completion_tokens": 32768
},
"timestamp": "2026-03-30T17:01:00.768Z",
"answer": null
},
{
... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "SUM_GEOM",
"status": "ok"
},
{
"lemma": "V7",
"status": "no"... | {
"lo": 3.8,
"mid": 6.33,
"hi": 9.49
} | |
ed540f | comb_count_surjections_v1_1520064083_6249 | Let $n$ be the number of integers $t$ with $19 \leq t \leq 40$ for which there exist positive integers $a$ and $b$ such that $1 \leq a \leq 3$, $1 \leq b \leq 2$, and $t = 6a + 9b + 4$. Let $k = 3$. Define $\text{result} = k! \cdot S(n, k)$, where $S(n, k)$ denotes the Stirling number of the second kind. Compute $57121... | 56,581 | 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 | COUNT | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | comb_count_surjections_v1 | null | 6 | 0 | [
"LIN_FORM"
] | 1 | 0.002 | 2026-02-08T07:58:29.886719Z | {
"verified": true,
"answer": 56581,
"timestamp": "2026-02-08T07:58:29.889178Z"
} | e51d16 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 242,
"completion_tokens": 1363
},
"timestamp": "2026-02-24T08:43:30.566Z",
"answer": 56581
},
{
"... | 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": -3.84,
"mid": -1.67,
"hi": 1.32
} | ||
78a374 | comb_count_derangements_v1_1419126231_1257 | Let $n = \sum_{k=\binom{6}{6} - 1}^{2} 2^{k}$. Compute the number of derangements of $n$ elements. | 1,854 | graphs = [
Graph(
let={
"_n": Const(2),
"n": Summation(var="k", start=Sub(Binom(n=Const(6), k=Const(6)), Const(1)), end=Ref("_n"), expr=Pow(Const(2), Var("k"))),
"result": Subfactorial(arg=Ref(name='n')),
},
goal=Ref("result"),
)
] | COMB | null | COUNT | sympy | SUM_GEOM | [
"SUM_GEOM",
"ZERO_BINOM_N"
] | 4e18d8 | comb_count_derangements_v1 | null | 2 | 0 | [
"SUM_GEOM",
"ZERO_BINOM_N"
] | 2 | 0.001 | 2026-02-25T10:43:23.965764Z | {
"verified": true,
"answer": 1854,
"timestamp": "2026-02-25T10:43:23.967002Z"
} | 9c48a2 | 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": 906
},
"timestamp": "2026-03-30T11:54:54.204Z",
"answer": 1854
},
{
"id... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "SUM_GEOM",
"status": "ok"
},
{
"lemma": "V8_SUM",
"st... | {
"lo": -5.37,
"mid": 0.23,
"hi": 5.22
} | ||
7b073a | nt_max_prime_below_v1_1248542787_431 | Let $S$ be the set of all positive integers $p$ for which there exists a positive integer $q$ such that $pq = 36$, $\gcd(p, q) = 1$, and $p < q$. Let $m$ be the number of elements in $S$. Determine the largest prime number $n$ such that $m \leq n \leq 46656$. | 46,649 | graphs = [
Graph(
let={
"upper": Const(46656),
"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 | 3.024 | 2026-02-08T03:07:13.852175Z | {
"verified": true,
"answer": 46649,
"timestamp": "2026-02-08T03:07:16.875754Z"
} | eed8cc | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 1,
"correct": {
"strict": false,
"boxed": false,
"relaxed": true
},
"usage": {
"prompt_tokens": 199,
"completion_tokens": 6633
},
"timestamp": "2026-02-09T04:06:01.285Z",
"answer": 46651
},
{
... | 1 | [
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
},
{
"lemma": "V7",
"statu... | {
"lo": 1.1,
"mid": 4.17,
"hi": 6.61
} | ||
63a964 | diophantine_fbi2_min_v1_1520064083_6084 | Let $S$ be the set of all ordered pairs of positive integers $(x, y)$ such that $x \cdot y = 144$. Let $k$ be the minimum value of $x + y$ as $(x, y)$ ranges over $S$. Let $d$ be the smallest integer with $5 \le d \le 34$ such that $d$ divides $k$ and $\frac{k}{d} \ge 4$. Compute the remainder when $31474 \cdot d$ is d... | 56,594 | graphs = [
Graph(
let={
"_n": Const(66125),
"k": MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(Mul(Var("x"), Var("y")), Const(144)))), expr=Sum(Var("x"), Var("y")))),... | NT | null | EXTREMUM | sympy | B3 | [
"B3"
] | 0cd20d | diophantine_fbi2_min_v1 | null | 4 | 0 | [
"B3"
] | 1 | 0.004 | 2026-02-08T07:50:44.603977Z | {
"verified": true,
"answer": 56594,
"timestamp": "2026-02-08T07:50:44.608413Z"
} | fee4d9 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 160,
"completion_tokens": 843
},
"timestamp": "2026-02-13T12:57:13.822Z",
"answer": 56594
},
{... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "V1",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
}
] | {
"lo": -5.55,
"mid": -3.01,
"hi": 0.32
} | ||
b80833 | nt_count_coprime_and_v1_717093673_4107 | Let $k_1$ be the number of integers $t$ with $10 \leq t \leq 30$ for which there exist integers $a$ and $b$, each between $1$ and $3$ inclusive, such that $t = 4a + 6b$. Let $k_2 = 11$. Let $S$ be the set of all positive integers $n$ such that $1 \leq n \leq 18052$, $\gcd(n, k_1) = 1$, and $\gcd(n, k_2) = 1$. Compute t... | 10,941 | graphs = [
Graph(
let={
"upper": Const(18052),
"k1": 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(lef... | NT | null | COUNT | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | nt_count_coprime_and_v1 | null | 5 | 0 | [
"LIN_FORM"
] | 1 | 1.871 | 2026-02-08T18:02:34.934678Z | {
"verified": true,
"answer": 10941,
"timestamp": "2026-02-08T18:02:36.805348Z"
} | 329d4a | 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": 1191
},
"timestamp": "2026-02-18T12:24:50.165Z",
"answer": 10941
},
... | 1 | [
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "V7",
"status": "no... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
e7b0a0 | sequence_count_fib_divisible_v1_1439011603_3053 | Let $u = \sum_{d\mid 695} \phi(d)$, where $\phi$ denotes Euler's totient function. Determine the number of positive integers $n$ such that $1 \leq n \leq u$ and the $n$th Fibonacci number is even. | 231 | graphs = [
Graph(
let={
"upper": SumOverDivisors(n=Const(value=695), var='d1', expr=EulerPhi(n=Var(name='d1'))),
"d": Const(2),
"result": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Ref("upper")), Divides(divisor=Ref("d... | NT | null | COUNT | sympy | K3 | [
"K3"
] | 54c41e | sequence_count_fib_divisible_v1 | null | 6 | 0 | [
"K3"
] | 1 | 0.071 | 2026-02-08T17:11:35.182719Z | {
"verified": true,
"answer": 231,
"timestamp": "2026-02-08T17:11:35.253360Z"
} | 41e454 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 104,
"completion_tokens": 692
},
"timestamp": "2026-02-17T22:02:17.880Z",
"answer": 231
},
{
... | 1 | [
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "K3",
"status": "ok"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
7b97e0 | comb_binomial_compute_v1_865884756_504 | Let $a = 2$ and $b = 2$. Define $n_2 = a + b$. Let $$ f = \sum_{k_1=0}^{n_2} (-1)^{k_1} \binom{n_2}{k_1}. $$ Now let $n_1 = f$, and define $$ v = \sum_{k_2=0}^{n_1} (-1)^{k_2} \binom{n_1}{k_2}. $$ Set $n = 12v$ and $k = 7$. Compute $\binom{n}{k}$. | 792 | graphs = [
Graph(
let={
"a": Const(2),
"b": Const(2),
"n2": Sum(Ref("a"), Ref("b")),
"f": Summation(var="k1", start=Const(0), end=Ref("n2"), expr=Mul(Pow(Const(-1), Var("k1")), Binom(n=Ref("n2"), k=Var("k1")))),
"n1": Ref("f"),
"v": Sum... | COMB | null | COMPUTE | sympy | BINOMIAL_ALTERNATING | [
"BINOMIAL_ALTERNATING"
] | c21569 | comb_binomial_compute_v1 | null | 4 | 2 | [
"BINOMIAL_ALTERNATING"
] | 1 | 0.002 | 2026-02-08T15:27:32.424412Z | {
"verified": true,
"answer": 792,
"timestamp": "2026-02-08T15:27:32.426243Z"
} | 72a0ff | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 245,
"completion_tokens": 613
},
"timestamp": "2026-02-24T20:56:42.484Z",
"answer": 792
},
{
"id"... | 1 | [
{
"lemma": "BINOMIAL_ALTERNATING",
"status": "ok"
},
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8_SUM",
"... | {
"lo": -8,
"mid": -4.75,
"hi": -2.29
} | ||
f2213f | algebra_poly_eval_v1_458359167_717 | Let $n_1$ be the number of positive integers $k$ such that $1 \leq k \leq 8100$ and $27$ divides $k$. Let $n_2$ be the number of positive integers $n$ such that $1 \leq n \leq 2359$, $7$ divides $n$, and $\gcd(n, 15) = 1$. Compute the value of
$$
\frac{n_1 \cdot 23^4 + n_2 \cdot 23^{\sum_{k=1}^{2} \phi(k) \left\lfloor ... | 5,069 | graphs = [
Graph(
let={
"_m": Const(16974),
"_n": CountOverSet(set=SolutionsSet(var=Var("k"), condition=And(Geq(Var("k"), Const(1)), Leq(Var("k"), Const(8100)), Divides(divisor=Const(27), dividend=Var("k"))), domain='positive_integers')),
"z": Const(23),
"resu... | NT | null | COMPUTE | sympy | C2 | [
"C2/K2",
"C5"
] | dce945 | algebra_poly_eval_v1 | null | 6 | 0 | [
"C2",
"C5",
"K2"
] | 3 | 0.007 | 2026-02-08T03:31:16.786289Z | {
"verified": true,
"answer": 5069,
"timestamp": "2026-02-08T03:31:16.793315Z"
} | bb23c4 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 282,
"completion_tokens": 1769
},
"timestamp": "2026-02-10T14:41:59.026Z",
"answer": 5069
},
{
"i... | 1 | [
{
"lemma": "C2",
"status": "ok"
},
{
"lemma": "C5",
"status": "ok"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "K2",
"status": "ok_later"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "M... | {
"lo": -3.46,
"mid": 1.03,
"hi": 5.49
} | ||
5f86a7 | antilemma_v1_legendre_1248542787_402 | Let $x$ be the largest integer $k$ such that $7^k$ divides $19901!$. Find the value of $x$. | 3,316 | graphs = [
Graph(
let={
"_n": Const(7),
"x": MaxKDivides(target=Factorial(Const(19901)), base=Ref("_n")),
},
goal=Ref("x"),
)
] | NT | null | COMPUTE | sympy | V1 | [
"V1"
] | dae96f | antilemma_v1_legendre | null | 5 | 0 | [
"V1"
] | 1 | 0 | 2026-02-08T03:06:52.007308Z | {
"verified": true,
"answer": 3316,
"timestamp": "2026-02-08T03:06:52.007733Z"
} | 0f6849 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 145,
"completion_tokens": 872
},
"timestamp": "2026-02-09T03:40:19.640Z",
"answer": 3316
},
{
"id... | 2 | [
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "K5",
"status": "same_pattern_wrong"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_... | {
"lo": -10,
"mid": -6.47,
"hi": -2.95
} | ||
3ef3e0 | sequence_fibonacci_compute_v1_601307018_8377 | Let $F_n$ denote the $n$-th Fibonacci number. Let $n$ be the number of ordered pairs $(a, b)$ of positive integers with $1 \le a, b \le 30$ such that $5a^2 + 5b^2 + 10ab = 2420$. Compute $F_n$. | 10,946 | graphs = [
Graph(
let={
"_n": Const(30),
"n": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("a"), Var("b")]), condition=And(Geq(Var("a"), Const(1)), Leq(Var("a"), Ref("_n")), Geq(Var("b"), Const(1)), Leq(Var("b"), Const(30)), Eq(Sum(Mul(Const(5), Pow(Var("b"), Const(2))), Mul... | ALG | null | COMPUTE | sympy | QF_PSD_COUNT | [
"QF_PSD_COUNT"
] | 09ce67 | sequence_fibonacci_compute_v1 | null | 5 | 0 | [
"QF_PSD_COUNT"
] | 1 | 0.002 | 2026-03-10T08:51:26.757842Z | {
"verified": true,
"answer": 10946,
"timestamp": "2026-03-10T08:51:26.759711Z"
} | c67db1 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 183,
"completion_tokens": 729
},
"timestamp": "2026-04-19T08:54:57.925Z",
"answer": 10946
},
{
"... | 1 | [
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "QF_PSD_COUNT",
"status": "ok"
}
] | {
"lo": -5.34,
"mid": 1.1,
"hi": 7.53
} | ||
bc7cf1 | nt_count_coprime_v1_655260480_1204 | Let $k$ be the number of nonnegative integers $j$ such that $0 \leq j \leq 40961$ and $\binom{40961}{j}$ is odd. Determine the number of positive integers $n$ such that $1 \leq n \leq 11449$ and $\gcd(n, k) = 1$. | 5,725 | graphs = [
Graph(
let={
"upper": Const(11449),
"k": CountOverSet(set=SolutionsSet(var=Var("j"), condition=And(Geq(Var("j"), Const(0)), Leq(Var("j"), Const(40961)), Eq(Mod(value=Binom(n=Const(40961), k=Var("j")), modulus=Const(2)), Const(1))), domain='nonnegative_integers')),
... | NT | null | COUNT | sympy | V8 | [
"V8"
] | 86348e | nt_count_coprime_v1 | null | 6 | 0 | [
"V8"
] | 1 | 1.17 | 2026-02-08T15:59:11.973555Z | {
"verified": true,
"answer": 5725,
"timestamp": "2026-02-08T15:59:13.143270Z"
} | 047e21 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 119,
"completion_tokens": 1478
},
"timestamp": "2026-02-16T19:14:52.479Z",
"answer": 5725
},
{... | 1 | [
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "V8",
"status": "ok"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
7eb6ba | diophantine_fbi2_count_v1_1918700295_4034 | Let $d_0$ be the number of positive integers $p$ for which there exists a positive integer $q$ such that $pq = 24$, $\gcd(p, q) = 1$, and $p < q$. Let $m$ be the smallest divisor of $11635567$ that is at least $d_0$. Let $k = 60$. Determine the number of integers $d$ such that $4 \leq d \leq 53$, $d$ divides $k$, $\fra... | 6 | graphs = [
Graph(
let={
"_m": Const(4),
"_n": Const(4),
"k": Const(60),
"result": CountOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Ref("_m")), Leq(Var("d"), Const(53)), Divides(divisor=Var("d"), dividend=Ref("k")), Geq(Div(Ref("k"), Var(... | NT | null | COUNT | sympy | COPRIME_PAIRS | [
"COPRIME_PAIRS/MIN_PRIME_FACTOR"
] | 52cee2 | diophantine_fbi2_count_v1 | null | 6 | 0 | [
"COPRIME_PAIRS",
"MIN_PRIME_FACTOR"
] | 2 | 0.013 | 2026-02-08T09:06:06.422861Z | {
"verified": true,
"answer": 6,
"timestamp": "2026-02-08T09:06:06.436078Z"
} | 57ec1e | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 175,
"completion_tokens": 2135
},
"timestamp": "2026-02-14T00:07:46.024Z",
"answer": 6
},
{
... | 1 | [
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "MIN_PRIME_FACTOR",
"status": "ok_later"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
... | {
"lo": -5.55,
"mid": -3.01,
"hi": 0.32
} | ||
6c95c7 | alg_poly4_min_v1_1419126231_1184 | Let $m = \min\{ x + y : x, y > 0,\ xy = 589824 \}$. Find the minimum value of $$7872a^4 + m a^3b + 9216a^2b^2 + 24576ab^3 + 24576b^4$$ over all positive integers $a, b$ with $1 \le a, b \le 153$. | 67,776 | graphs = [
Graph(
let={
"_n": Const(24576),
"result": MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("a"), Var("b")]), condition=And(Geq(Var("a"), Const(1)), Leq(Var("a"), Const(153)), Geq(Var("b"), Const(1)), Leq(Var("b"), Const(153)))), expr=Sum(Mul(Const(24576)... | ALG | null | COMPUTE | sympy | B3 | [
"B3"
] | 0cd20d | alg_poly4_min_v1 | null | 5 | 0 | [
"B3"
] | 1 | 0.065 | 2026-02-25T10:39:59.684048Z | {
"verified": true,
"answer": 67776,
"timestamp": "2026-02-25T10:39:59.748605Z"
} | f09959 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 201,
"completion_tokens": 6445
},
"timestamp": "2026-03-30T11:40:37.475Z",
"answer": 67776
},
{
"... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
}
] | {
"lo": -5.37,
"mid": 0.23,
"hi": 5.22
} | ||
300757 | antilemma_sum_equals_v1_2051736721_4658 | Let $t$ be an integer. Suppose there exist integers $a$ and $b$ such that $1 \leq a \leq 9$, $1 \leq b \leq 4$, and $t = 9a + 12b + 1$, with $22 \leq t \leq 130$. Let $n$ be the number of such integers $t$. Let $x$ be the number of ordered pairs $(i, j)$ of positive integers such that $i \leq 30$, $j \leq 31$, and $i +... | 11,905 | 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=9)), Geq(left=Var(name='b'), right=Const(value=... | COMB | GEOM | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM/COUNT_SUM_EQUALS",
"COUNT_SUM_EQUALS"
] | ada383 | antilemma_sum_equals_v1 | null | 3 | 0 | [
"COUNT_SUM_EQUALS",
"LIN_FORM"
] | 2 | 0.061 | 2026-02-08T18:05:55.281897Z | {
"verified": true,
"answer": 11905,
"timestamp": "2026-02-08T18:05:55.343174Z"
} | ec2d5f | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 183,
"completion_tokens": 2436
},
"timestamp": "2026-02-18T13:20:20.892Z",
"answer": 11905
},
... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "ok"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "V7",
"st... | {
"lo": -2.38,
"mid": 1.74,
"hi": 6.59
} | ||
ad83cc | nt_sum_divisors_compute_v1_260342960_178 | Let $n = 44121$. Define $s = \Omega(1)$, where $\Omega(k)$ is the number of prime factors of $k$ counted with multiplicity. Let $p$ be the sum of $s$ and the number of integers $t$ in the range $15 \leq t \leq 85$ for which there exist integers $a$ and $b$ such that $1 \leq a \leq 6$, $1 \leq b \leq 8$, and $t = 7a + 5... | 32,953 | graphs = [
Graph(
let={
"_n": Const(44121),
"n1": Const(1),
"s": BigOmega(n=Ref(name='n1')),
"p": 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'), righ... | NT | null | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM/BIG_OMEGA_ZERO/BIG_OMEGA_ONE"
] | 65e135 | nt_sum_divisors_compute_v1 | null | 6 | 2 | [
"BIG_OMEGA_ONE",
"BIG_OMEGA_ZERO",
"LIN_FORM"
] | 3 | 0.002 | 2026-02-08T11:17:22.591650Z | {
"verified": true,
"answer": 32953,
"timestamp": "2026-02-08T11:17:22.593668Z"
} | 7681b9 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 302,
"completion_tokens": 5344
},
"timestamp": "2026-02-08T20:32:48.233Z",
"answer": 32953
},
{
"... | 1 | [
{
"lemma": "BIG_OMEGA_ONE",
"status": "ok_later"
},
{
"lemma": "BIG_OMEGA_ZERO",
"status": "ok_later"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "M... | {
"lo": -6.69,
"mid": -2.4,
"hi": 1.76
} | ||
657063 | nt_lcm_compute_v1_898971024_2393 | Let $a = 561$ and $b = 1921$. Compute the least common multiple of $a$ and $b$. | 63,393 | graphs = [
Graph(
let={
"a": Const(561),
"b": Const(1921),
"result": LCM(a=Ref("a"), b=Ref("b")),
},
goal=Ref("result"),
)
] | NT | null | COMPUTE | sympy | K13 | [
"LIN_FORM",
"V5"
] | 6f82b2 | nt_lcm_compute_v1 | null | 2 | 0 | [
"K13",
"LIN_FORM",
"V5"
] | 3 | 0.02 | 2026-02-08T16:43:01.690704Z | {
"verified": true,
"answer": 63393,
"timestamp": "2026-02-08T16:43:01.711143Z"
} | 9da5b9 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 75,
"completion_tokens": 903
},
"timestamp": "2026-02-17T10:49:06.285Z",
"answer": 63393
},
{
... | 1 | [
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "V5",
"status": "ok"
},
{
... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
11d8d2 | comb_bell_compute_v1_1520064083_8407 | Let $a = 1$ and $b = 3$. Define $n_2 = a + b$. Let
$$
m = \sum_{k=0}^{n_2} (-1)^k \binom{n_2}{k}.
$$
Set $n_1 = m$, and define
$$
h = \sum_{k=0}^{n_1} (-1)^k \binom{n_1}{k}.
$$
Let $n = 9h$. Compute the Bell number $B_n$, the number of partitions of a set of $n$ elements. | 21,147 | graphs = [
Graph(
let={
"a": Const(1),
"b": Const(3),
"n2": Sum(Ref("a"), Ref("b")),
"m": Summation(var="k", start=Const(0), end=Ref("n2"), expr=Mul(Pow(Const(-1), Var("k")), Binom(n=Ref("n2"), k=Var("k")))),
"n1": Ref("m"),
"h": Summat... | COMB | null | COMPUTE | sympy | BINOMIAL_ALTERNATING | [
"BINOMIAL_ALTERNATING"
] | c21569 | comb_bell_compute_v1 | null | 6 | 2 | [
"BINOMIAL_ALTERNATING"
] | 1 | 0.001 | 2026-02-08T10:10:23.387710Z | {
"verified": true,
"answer": 21147,
"timestamp": "2026-02-08T10:10:23.388682Z"
} | 1a8d39 | 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": 523
},
"timestamp": "2026-02-24T11:50:58.829Z",
"answer": 21147
},
{
"i... | 1 | [
{
"lemma": "BINOMIAL_ALTERNATING",
"status": "ok"
},
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8_SUM",
"sta... | {
"lo": -3.84,
"mid": -1.67,
"hi": 1.32
} | ||
18c9e2_l | comb_count_derangements_v1_677425708_180 | Let $n$ be the number of nonnegative integers $j \leq 16424$ such that $\binom{16424}{j}$ is odd. Compute the remainder when $44121$ times the subfactorial of $n$ is divided by $79598$. | 0 | COMB | null | COUNT | sympy | V8 | [
"V8"
] | 86348e | comb_count_derangements_v1 | null | 7 | 0 | [
"V8"
] | 1 | 0.001 | 2026-02-08T03:06:59.133289Z | {
"verified": false,
"answer": 71635,
"timestamp": "2026-02-08T03:06:59.134423Z"
} | 526105 | 18c9e2 | 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": 168,
"completion_tokens": 2130
},
"timestamp": "2026-02-23T21:37:14.266Z",
"answer": 71635
},
{
"... | 1 | [
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "V1",
"status": "no"
},
{
"lemma": "V8",... | {
"lo": 1.42,
"mid": 3.03,
"hi": 4.44
} | |
059a29 | alg_telescope_v1_601307018_1068 | Let $S = \sum_{k=0}^{T} \left((k+1)^2 - k^2\right) \bmod d$, where $T = \left|\{ (a, b) : 1 \leq a, b \leq 40,\, -2ab + 13a^2 + 2b^m \leq 15733 \}\right|$, $m = \min\{ 98b_1^3 - 96a_1b_1^2 + 24a_1^2b_1 : 1 \leq a_1, b_1 \leq 14 \}$, and $d = \min\{ |x - y| : x, y > 0,\, xy = 123276394 \}$. Find the remainder when $3225... | 64,989 | graphs = [
Graph(
let={
"_c": Const(2),
"_m": Const(40),
"_n": Const(32259),
"result": Mod(value=Summation(var="k", start=Const(0), end=CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("a"), Var("b")]), condition=And(Geq(Var("a"), Const(1)), Leq(Var("a"),... | ALG | null | COMPUTE | sympy | POLY3_MIN | [
"POLY3_MIN/QF_PSD_COUNT_LEQ",
"B3_DIFF"
] | d12526 | alg_telescope_v1 | null | 7 | 0 | [
"B3_DIFF",
"POLY3_MIN",
"QF_PSD_COUNT_LEQ"
] | 3 | 0.145 | 2026-03-10T01:39:01.591997Z | {
"verified": true,
"answer": 64989,
"timestamp": "2026-03-10T01:39:01.737089Z"
} | 6bd751 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 302,
"completion_tokens": 15940
},
"timestamp": "2026-03-29T01:06:04.292Z",
"answer": 64989
},
{
... | 1 | [
{
"lemma": "B3_DIFF",
"status": "ok"
},
{
"lemma": "POLY3_MIN",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "QF_PSD_COUNT_LEQ",
"status": "ok_later"
}
] | {
"lo": 4.01,
"mid": 6.11,
"hi": 9.15
} | ||
344faa | modular_count_residue_v1_349078426_788 | Let $S$ be the set of all positive integers $p$ for which there exists a positive integer $q$ such that $p \cdot q = 24$, $\gcd(p, q) = 1$, and $p < q$. Let $k$ be the largest integer such that the number of elements in $S$ raised to the power $k$ is at most 38835890057. Let $n$ be this value of $k$. Let $m$ be the sma... | 17,641 | graphs = [
Graph(
let={
"_n": MaxOverSet(set=SolutionsSet(var=Var("k"), condition=Leq(Pow(CountOverSet(set=SolutionsSet(var=Var("p"), condition=And(IsPositive(arg=Var(name='p')), Exists(var=Var(name='q'), condition=And(Eq(left=Mul(Var(name='p'), Var(name='q')), right=Const(value=24)), Eq(left=GC... | NT | null | COUNT | sympy | B3 | [
"COPRIME_PAIRS/MAX_VAL/MIN_PRIME_FACTOR"
] | 7062f0 | modular_count_residue_v1 | null | 6 | 0 | [
"B3",
"COPRIME_PAIRS",
"MAX_VAL",
"MIN_PRIME_FACTOR"
] | 4 | 8.013 | 2026-02-08T13:17:45.521467Z | {
"verified": true,
"answer": 17641,
"timestamp": "2026-02-08T13:17:53.534440Z"
} | 06dd20 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 198,
"completion_tokens": 1067
},
"timestamp": "2026-02-15T12:24:57.320Z",
"answer": 17641
},
... | 1 | [
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "ok_later"
},
{
"lemma": "MIN_PRIME_FACTOR",
"status"... | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
3d9643 | nt_num_divisors_compute_v1_1470522791_1746 | Let $n$ be the smallest integer $d \geq 2$ that divides the number of integers $n$ in the range $1 \leq n \leq 7435$ such that $n \equiv \left\lfloor \frac{n}{2} \right\rfloor \pmod{11}$. Compute $44121$ multiplied by the number of positive divisors of $n$. | 88,242 | graphs = [
Graph(
let={
"_m": Const(2),
"_n": Const(44121),
"n": MinOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Ref("_m")), Divides(divisor=Var("d"), dividend=CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var... | NT | null | COMPUTE | sympy | L3C | [
"L3C/MIN_PRIME_FACTOR"
] | eb2a9a | nt_num_divisors_compute_v1 | null | 6 | 0 | [
"L3C",
"MIN_PRIME_FACTOR"
] | 2 | 0.004 | 2026-02-08T13:55:16.214536Z | {
"verified": true,
"answer": 88242,
"timestamp": "2026-02-08T13:55:16.218895Z"
} | c042c4 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 127,
"completion_tokens": 1254
},
"timestamp": "2026-02-15T22:26:04.768Z",
"answer": 88242
},
... | 1 | [
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "L3C",
"status": "ok"
},
{
"lemma": "MIN_PRIME_FACTOR",
"status": "ok_later"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "V5",
"statu... | {
"lo": -5.49,
"mid": 0.22,
"hi": 6.51
} | ||
8c9889 | nt_sum_divisors_compute_v1_238844314_515 | Let $n = 55225$. Let $R$ be the sum of all positive divisors of $n$. Let $c$ be the number of positive integers $n$ with $1 \leq n \leq 6999$ such that $n \equiv \left\lfloor \frac{n}{2} \right\rfloor \pmod{7}$. Compute the remainder when $c - R$ is divided by $70834$. | 1,866 | graphs = [
Graph(
let={
"_n": Const(70834),
"n": Const(55225),
"result": SumDivisors(n=Ref("n")),
"_c": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Const(6999)), Congruent(a=Var(name='n'), b=Floor(arg=Div(le... | NT | null | COMPUTE | sympy | L3C | [
"L3C"
] | fba717 | nt_sum_divisors_compute_v1 | negation_mod | 6 | 0 | [
"L3C"
] | 1 | 0.003 | 2026-02-08T13:23:09.125176Z | {
"verified": true,
"answer": 1866,
"timestamp": "2026-02-08T13:23:09.127811Z"
} | cf96e6 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 137,
"completion_tokens": 1218
},
"timestamp": "2026-02-15T13:49:02.760Z",
"answer": 1866
},
{... | 1 | [
{
"lemma": "L3C",
"status": "ok"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "VAL_SUM_EQ",
"status": "no"
}
] | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
dab3c5 | comb_bell_compute_v1_2051736721_1701 | Let $j$ be a nonnegative integer. Define $n$ to be the number of integers $j$ such that $0 \leq j \leq 2320$ and $\binom{2320}{j}$ is odd. Let $\text{result} = B_n$, the $n$th Bell number, which counts the number of partitions of a set of $n$ elements. Find the value of $\text{result}$. | 4,140 | graphs = [
Graph(
let={
"_n": Const(2),
"n": CountOverSet(set=SolutionsSet(var=Var("j"), condition=And(Geq(Var("j"), Const(0)), Leq(Var("j"), Const(2320)), Eq(Mod(value=Binom(n=Const(2320), k=Var("j")), modulus=Ref("_n")), Const(1))), domain='nonnegative_integers')),
"res... | COMB | null | COMPUTE | sympy | V8 | [
"V8"
] | 86348e | comb_bell_compute_v1 | null | 5 | 0 | [
"V8"
] | 1 | 0.002 | 2026-02-08T16:10:28.528425Z | {
"verified": true,
"answer": 4140,
"timestamp": "2026-02-08T16:10:28.530173Z"
} | 7f45d3 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 204,
"completion_tokens": 671
},
"timestamp": "2026-02-24T20:05:49.718Z",
"answer": 4140
},
{
"i... | 1 | [
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "V8",
"status": "ok"
}
] | {
"lo": -2.4,
"mid": 1.57,
"hi": 5.75
} | ||
cc8b8c | comb_count_surjections_v1_677425708_272 | Let $k$ be the number of ordered pairs $(i,j)$ of positive integers such that $1 \leq i \leq 3$, $1 \leq j \leq 4$, and $i + j = 5$. Compute the remainder when $85055 \cdot k! \cdot S(4, k)$ is divided by 89112, where $S(n,k)$ denotes the Stirling number of the second kind. | 32,172 | graphs = [
Graph(
let={
"n": Const(4),
"k": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("i"), Var("j")]), condition=Eq(Sum(Var("i"), Var("j")), Const(5)), domain=CartesianProduct(left=IntegerRange(start=Const(1), end=Const(3)), right=IntegerRange(start=Const(1), end=Const(4... | COMB | null | COUNT | sympy | COUNT_SUM_EQUALS | [
"COUNT_SUM_EQUALS"
] | 75ab0f | comb_count_surjections_v1 | null | 5 | 0 | [
"COUNT_SUM_EQUALS"
] | 1 | 0.015 | 2026-02-08T03:12:21.278865Z | {
"verified": true,
"answer": 32172,
"timestamp": "2026-02-08T03:12:21.293836Z"
} | 00e678 | 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": 1790
},
"timestamp": "2026-02-08T20:26:16.232Z",
"answer": 32172
},
{
"... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "ok"
},
{
"lemma": "V8",
"status": "no"
},
{
"lemma": "V8_SUM",
"status"... | {
"lo": -2.46,
"mid": 0.47,
"hi": 3.59
} | ||
70fab2 | sequence_lucas_compute_v1_2051736721_4678 | Let $n = 2$. Define $S$ as the set of all real numbers $x$ such that $x^n - 18x - 648 = 0$. Let $s$ be the sum of all elements in $S$. The Lucas sequence is defined by $L_0 = 2$, $L_1 = 1$, and $L_k = L_{k-1} + L_{k-2}$ for $k \geq 2$. Compute $L_s$. | 5,778 | graphs = [
Graph(
let={
"_n": Const(2),
"n": SumOverSet(set=SolutionsSet(var=Var("x"), condition=Eq(Sum(Pow(Var("x"), Ref("_n")), Mul(Const(-18), Var("x")), Const(-648)), Const(0)))),
"result": Lucas(arg=Ref(name='n')),
},
goal=Ref("result"),
)
] | NT | null | COMPUTE | sympy | VIETA_SUM | [
"VIETA_SUM"
] | b33a7a | sequence_lucas_compute_v1 | null | 3 | 0 | [
"VIETA_SUM"
] | 1 | 0.001 | 2026-02-08T18:06:16.891933Z | {
"verified": true,
"answer": 5778,
"timestamp": "2026-02-08T18:06:16.893295Z"
} | a6619b | 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": 713
},
"timestamp": "2026-02-18T13:24:26.837Z",
"answer": 5778
},
{
... | 1 | [
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "V3",
"status": "no"
},
{
"lemma": "VIETA_SUM",
"status": "ok"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
ceb7c3 | comb_sum_binomial_row_v1_458359167_1728 | Let $n$ be the number of ordered pairs $(i, j)$ of integers such that $1 \leq i \leq 17$, $1 \leq j \leq 17$, and $i + j = 19$. Compute $2^n$. | 65,536 | graphs = [
Graph(
let={
"_n": Const(19),
"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(17)), right=IntegerRange(start=Const(1), end=Con... | NT | null | SUM | sympy | COUNT_SUM_EQUALS | [
"COUNT_SUM_EQUALS"
] | 75ab0f | comb_sum_binomial_row_v1 | null | 3 | 0 | [
"COUNT_SUM_EQUALS"
] | 1 | 0.01 | 2026-02-08T04:49:25.860857Z | {
"verified": true,
"answer": 65536,
"timestamp": "2026-02-08T04:49:25.870845Z"
} | 1260e0 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 168,
"completion_tokens": 382
},
"timestamp": "2026-02-11T22:10:56.648Z",
"answer": 65536
},
{
"... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "ok"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
},
{
"lemma": "VAL_SUM_EQ",
"status": "no"
}
] | {
"lo": -5.55,
"mid": -3.01,
"hi": 0.33
} | ||
8668ed | modular_sum_quadratic_residues_v1_1470522791_829 | Let $c = 14562$, $m = 4$, and $n = 78536$. Let $S$ be the set of all positive integers $x_1, x_2$ such that $x_1$ and $x_2$ are odd, $x_1 + x_2 = c$, and both $x_1$ and $x_2$ are at least 1. Let $N_1$ be the number of elements in $S$. Let $T$ be the set of all integers $n$ such that $1 \leq n \leq N_1$, $9$ divides $n$... | 77,755 | graphs = [
Graph(
let={
"_c": Const(14562),
"_m": Const(4),
"_n": Const(78536),
"p": MaxOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(2)), Leq(Var("n"), CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)... | NT | null | SUM | sympy | COMB1 | [
"COMB1/C5/MAX_PRIME_BELOW"
] | 7fdd64 | modular_sum_quadratic_residues_v1 | null | 7 | 0 | [
"C5",
"COMB1",
"MAX_PRIME_BELOW"
] | 3 | 0.008 | 2026-02-08T13:16:09.724853Z | {
"verified": true,
"answer": 77755,
"timestamp": "2026-02-08T13:16:09.732974Z"
} | a6932b | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 279,
"completion_tokens": 4102
},
"timestamp": "2026-02-15T11:57:20.441Z",
"answer": 77755
},
... | 1 | [
{
"lemma": "C5",
"status": "ok_later"
},
{
"lemma": "COMB1",
"status": "ok"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok_later"
... | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
4415b0 | comb_count_permutations_fixed_v1_677425708_4334 | Let $n$ be the smallest prime divisor of 847, and let $k$ be the number of positive integers $p$ for which there exists a positive integer $q$ such that $p \cdot q = 36$, $\gcd(p, q) = 1$, and $p < q$. Compute $$\binom{n}{k} \cdot !(n - k),$$ where $!m$ denotes the subfactorial of $m$. | 924 | 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(847))))),
"k": CountOverSet(set=SolutionsSet(var=Var("p"), condition=And(IsPositive(arg=Var(name='p')), ... | NT | COMB | COUNT | sympy | MIN_PRIME_FACTOR | [
"MIN_PRIME_FACTOR",
"COPRIME_PAIRS"
] | a3b634 | comb_count_permutations_fixed_v1 | null | 5 | 0 | [
"COPRIME_PAIRS",
"MIN_PRIME_FACTOR"
] | 2 | 0.003 | 2026-02-08T06:33:25.823925Z | {
"verified": true,
"answer": 924,
"timestamp": "2026-02-08T06:33:25.826614Z"
} | 4aad8f | 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": 906
},
"timestamp": "2026-02-13T01:36:39.097Z",
"answer": 924
},
{
... | 1 | [
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "MIN_PRIME_FACTOR",
"status": "o... | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
592e62 | modular_mod_compute_v1_1915831931_2695 | Let $\_n$ be the maximum value of $xy$ over all pairs of positive integers $(x, y)$ such that $x + y = 48$. Let $s$ be the minimum value of $x_2 + y_2$ over all pairs of positive integers $(x_2, y_2)$ such that $x_2 y_2 = \_n$. Define $a$ to be the maximum value of $x_1 y_1$ over all pairs of positive integers $(x_1, y... | 576 | graphs = [
Graph(
let={
"_n": MaxOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(Sum(Var("x"), Var("y")), Const(48)))), expr=Mul(Var("x"), Var("y")))),
"a": MaxOverSet(set... | NT | null | COMPUTE | sympy | B1 | [
"B1/B3/B1"
] | 644515 | modular_mod_compute_v1 | null | 6 | 0 | [
"B1",
"B3"
] | 2 | 0.004 | 2026-02-08T17:03:56.164336Z | {
"verified": true,
"answer": 576,
"timestamp": "2026-02-08T17:03:56.168398Z"
} | 63fd2c | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 193,
"completion_tokens": 733
},
"timestamp": "2026-02-17T18:23:16.415Z",
"answer": 576
},
{
... | 1 | [
{
"lemma": "B1",
"status": "ok"
},
{
"lemma": "B3",
"status": "ok_later"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemm... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
dac0aa | modular_inverse_v1_971394319_679 | Let $a = 54$ and $m = 109$. Determine the smallest positive integer $x$ such that $1 \le x \le 108$ and $54x \equiv 1 \pmod{109}$. Compute the value of $x$. | 107 | graphs = [
Graph(
let={
"a": Const(54),
"m": Const(109),
"upper": Const(108),
"result": MinOverSet(set=SolutionsSet(var=Var("x"), condition=And(Geq(Var("x"), Const(1)), Leq(Var("x"), Ref("upper")), Eq(Mod(value=Mul(Ref("a"), Var("x")), modulus=Ref("m")), Const... | NT | null | EXTREMUM | sympy | MAX_PRIME_BELOW | [
"MAX_PRIME_BELOW"
] | dc3ad3 | modular_inverse_v1 | null | 4 | 0 | [
"MAX_PRIME_BELOW"
] | 1 | 0.041 | 2026-02-08T13:15:14.103374Z | {
"verified": true,
"answer": 107,
"timestamp": "2026-02-08T13:15:14.144148Z"
} | 6171fb | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 119,
"completion_tokens": 436
},
"timestamp": "2026-02-16T04:28:56.375Z",
"answer": 107
},
{
"id": 11,
... | 2 | [
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "V8",
"status": "no"... | {
"lo": -9.12,
"mid": -6.02,
"hi": -3.62
} | ||
8ed00e | modular_modexp_compute_v1_865884756_270 | Let $a$ be the smallest divisor of $2904739$ that is greater than 1. Let $e$ be the number of nonnegative integers $j$ such that $0 \leq j \leq 54767$ and $\binom{54767}{j}$ is odd. Compute the remainder when $a^e$ is divided by $44444$. | 34,737 | graphs = [
Graph(
let={
"_n": Const(54767),
"a": MinOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Const(2)), Divides(divisor=Var("d"), dividend=Const(2904739))))),
"e": CountOverSet(set=SolutionsSet(var=Var("j"), condition=And(Geq(Var("j"), Const(0)),... | NT | null | COMPUTE | sympy | MIN_PRIME_FACTOR | [
"MIN_PRIME_FACTOR",
"V8"
] | aeb95e | modular_modexp_compute_v1 | null | 7 | 0 | [
"MIN_PRIME_FACTOR",
"V8"
] | 2 | 0.003 | 2026-02-08T15:17:26.814849Z | {
"verified": true,
"answer": 34737,
"timestamp": "2026-02-08T15:17:26.817543Z"
} | c0504d | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 189,
"completion_tokens": 4010
},
"timestamp": "2026-02-10T06:23:32.538Z",
"answer": 34737
},
{
"... | 1 | [
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "MIN_PRIME_FACTOR",
"status": "ok"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "V8",
"status": "ok"
},
{
... | {
"lo": -7.09,
"mid": -0.49,
"hi": 6.1
} | ||
2c5033 | alg_sum_powers_v1_1218484723_3691 | Let $M$ be the sum $\sum_{k=1}^{1490} k^2$ modulo the minimum value of $x + y$ over all pairs of positive integers $(x, y)$ such that $xy = 2340900$. Find the remainder when $27413 \cdot M$ is divided by $92132$. | 87,101 | graphs = [
Graph(
let={
"result": Mod(value=Summation(var="k", start=Const(1), end=Const(1490), expr=Pow(Var("k"), Const(2))), modulus=MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), ... | ALG | null | COMPUTE | sympy | B3 | [
"B3"
] | 0cd20d | alg_sum_powers_v1 | null | 5 | 0 | [
"B3"
] | 1 | 0.066 | 2026-02-25T05:19:56.586982Z | {
"verified": true,
"answer": 87101,
"timestamp": "2026-02-25T05:19:56.652868Z"
} | 4f2661 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 181,
"completion_tokens": 5474
},
"timestamp": "2026-03-29T11:42:08.449Z",
"answer": 87101
},
{
"... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
}
] | {
"lo": -2.45,
"mid": 1.37,
"hi": 5.29
} | ||
4e12c1 | nt_sum_divisors_mod_v1_168721529_116 | Let $N=75809$ and let $n_1=1$. Let $f$ be the number of distinct prime factors of $n_1$.
Let $a=40$, and let $b$ be the sum of $f$ and the least integer $d\ge2$ that divides $N$.
Let
$$e=\sum_{d\mid \gcd(a,b)} \mu(d),$$
where $\mu$ is the Möbius function.
Let $n$ be the greatest integer $k$ such that $11^k$ divides ... | 1,170 | graphs = [
Graph(
let={
"_n": Const(75809),
"n1": Const(1),
"f": SmallOmega(n=Ref(name='n1')),
"a": Const(40),
"b": Sum(MinOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Const(2)), Divides(divisor=Var("d"), dividend=Ref("_n"))))... | NT | null | COMPUTE | sympy | MIN_PRIME_FACTOR | [
"MIN_PRIME_FACTOR/OMEGA_ZERO/MOBIUS_COPRIME",
"V1"
] | 26841d | nt_sum_divisors_mod_v1 | null | 7 | 2 | [
"MIN_PRIME_FACTOR",
"MOBIUS_COPRIME",
"OMEGA_ZERO",
"V1"
] | 4 | 0.003 | 2026-02-08T12:49:00.240279Z | {
"verified": true,
"answer": 1170,
"timestamp": "2026-02-08T12:49:00.242953Z"
} | b81608 | CC BY 4.0 | [
{
"id": 4,
"model": "NousResearch/Hermes-4-405B",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 233,
"completion_tokens": 649
},
"timestamp": "2026-02-09T13:42:48.082Z",
"answer": 1170
},
{... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "K5",
"status": "same_pattern_wrong"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "MIN_PRIME_FACTOR",
"status": "ok"
},
{
"lemma": "MOBIUS_COPRIME",
... | {
"lo": -6.69,
"mid": -2.39,
"hi": 1.85
} | ||
db0ae3 | algebra_quadratic_discriminant_v1_865884756_5962 | Let $a = -2$, $b = 16$, and $c = -30$. Compute the discriminant $D = b^2 - 4ac$. Define a quantity that equals $2$ if $D > 0$, $1$ if $D = 0$, and $0$ otherwise. Compute this quantity. | 2 | graphs = [
Graph(
let={
"a": Const(-2),
"b": Const(16),
"c": Const(-30),
"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"), Co... | NT | null | COMPUTE | sympy | MAX_PRIME_BELOW | [
"MAX_PRIME_BELOW",
"L3C",
"B1"
] | 9bba55 | algebra_quadratic_discriminant_v1 | null | 2 | 0 | [
"B1",
"L3C",
"MAX_PRIME_BELOW"
] | 3 | 0.015 | 2026-02-08T18:53:45.373517Z | {
"verified": true,
"answer": 2,
"timestamp": "2026-02-08T18:53:45.388061Z"
} | 790948 | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 129,
"completion_tokens": 145
},
"timestamp": "2026-02-16T18:29:24.605Z",
"answer": 2
},
{
"id": 11,
"... | 2 | [
{
"lemma": "B1",
"status": "ok"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "L3C",
"status": "ok"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MAX_P... | {
"lo": -10,
"mid": -7.27,
"hi": -4.54
} | ||
414fdd | nt_num_divisors_compute_v1_1918700295_4568 | Let $n = \sum_{k=1}^{49} \phi(k) \left\lfloor \frac{49}{k} \right\rfloor$, where $\phi$ denotes Euler's totient function. Let $d$ be the number of positive divisors of $n$. Compute $10291 \times d$. | 92,619 | graphs = [
Graph(
let={
"_n": Const(49),
"n": Summation(var="k", start=Const(1), end=Const(49), expr=Mul(EulerPhi(n=Var("k")), Floor(Div(Ref("_n"), Var("k"))))),
"result": NumDivisors(n=Ref("n")),
"Q": Mul(Const(10291), Ref("result")),
},
goal=... | NT | null | COMPUTE | sympy | K2 | [
"K2"
] | 6897ab | nt_num_divisors_compute_v1 | null | 4 | 0 | [
"K2"
] | 1 | 0.001 | 2026-02-08T09:27:58.886528Z | {
"verified": true,
"answer": 92619,
"timestamp": "2026-02-08T09:27:58.887991Z"
} | 880cac | 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": 515
},
"timestamp": "2026-02-14T04:26:31.272Z",
"answer": 92619
},
{... | 1 | [
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "K2",
"status": "ok"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
}
] | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
fa4908 | comb_bell_compute_v1_865884756_1755 | Let $m = 2$. Compute the number of nonnegative integers $j$ such that $0 \leq j \leq 4385$ and $\binom{4385}{j}$ is odd. Let $N$ be this number. Consider the set of all ordered pairs $(x,y)$ of positive integers such that $xy = N$. Let $S$ be the set of all values $x + y$ for such pairs, and let $s$ be the minimum elem... | 4,140 | graphs = [
Graph(
let={
"_m": Const(2),
"_n": CountOverSet(set=SolutionsSet(var=Var("j"), condition=And(Geq(Var("j"), Const(0)), Leq(Var("j"), Const(4385)), Eq(Mod(value=Binom(n=Const(4385), k=Var("j")), modulus=Ref("_m")), Const(1))), domain='nonnegative_integers')),
"n"... | COMB | null | COMPUTE | sympy | V8 | [
"V8/B3"
] | b4fc86 | comb_bell_compute_v1 | null | 6 | 0 | [
"B3",
"V8"
] | 2 | 0.003 | 2026-02-08T16:17:09.349374Z | {
"verified": true,
"answer": 4140,
"timestamp": "2026-02-08T16:17:09.352607Z"
} | b1bf27 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 240,
"completion_tokens": 1185
},
"timestamp": "2026-02-24T20:27:48.149Z",
"answer": 4140
},
{
"... | 1 | [
{
"lemma": "B3",
"status": "ok_later"
},
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
},
{
"lemm... | {
"lo": -2.4,
"mid": 1.57,
"hi": 5.75
} | ||
6c0fdc | antilemma_k2_v1_898971024_137 | Let $M$ be the sum of all integers $x$ satisfying
$$x^2-6000x+17991=0.$$
Let $n=396$, and let $S$ be the sum of all integers $y$ satisfying
$$y^2-396y-19360=0.$$
Define
$$X=\sum_{k=1}^{S} \varphi(k)\left\lfloor\frac{n}{k}\right\rfloor,$$
where $\varphi$ is Euler's totient function.
Let
$$R=X^2+44X+\sum_{d\mid M} \va... | 1,320 | graphs = [
Graph(
let={
"_c": Const(54405),
"_m": SumOverSet(set=SolutionsSet(var=Var("x1"), condition=Eq(Sum(Pow(Var("x1"), Const(2)), Mul(Const(-6000), Var("x1")), Const(17991)), Const(0)))),
"_n": Const(396),
"x": Summation(var="k", start=Const(1), end=SumO... | NT | COMB | COMPUTE | sympy | VIETA_SUM | [
"VIETA_SUM/K3",
"VIETA_SUM/K2",
"K2"
] | f92052 | antilemma_k2_v1 | quadratic_mod | 6 | 0 | [
"K2",
"K3",
"VIETA_SUM"
] | 3 | 0.005 | 2026-02-08T15:13:10.408417Z | {
"verified": true,
"answer": 1320,
"timestamp": "2026-02-08T15:13:10.413800Z"
} | 60a2c1 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 225,
"completion_tokens": 2958
},
"timestamp": "2026-02-16T02:42:33.491Z",
"answer": 1320
},
{... | 1 | [
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K2",
"status": "ok"
},
{
"lemma": "K3",
"status": "ok_later"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma"... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
d37c34 | antilemma_k3_v1_1520064083_857 | Compute the sum of $\phi(d)$ over all positive divisors $d$ of $22070$, where $\phi$ denotes Euler's totient function. | 22,070 | graphs = [
Graph(
let={
"x": SumOverDivisors(n=Const(value=22070), var='d', expr=EulerPhi(n=Var(name='d'))),
},
goal=Ref("x"),
)
] | NT | COMB | COMPUTE | sympy | K3 | [
"K3"
] | 54c41e | antilemma_k3_v1 | null | 3 | 0 | [
"K3"
] | 1 | 0 | 2026-02-08T03:38:16.762410Z | {
"verified": true,
"answer": 22070,
"timestamp": "2026-02-08T03:38:16.762670Z"
} | b0c510 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 142,
"completion_tokens": 273
},
"timestamp": "2026-02-10T14:00:34.149Z",
"answer": 22070
},
{
"... | 1 | [
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K3",
"status": "ok"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
}
] | {
"lo": -5.92,
"mid": -3.14,
"hi": 0.27
} | ||
7e79db | geo_count_lattice_rect_v1_784195855_2929 | Let $a = 256$ and $b = 182$. Define the number of lattice points in the rectangle $[0, a] \times [0, b]$ to be the number of ordered pairs $(x, y)$ of integers such that $0 \leq x \leq a$ and $0 \leq y \leq b$. Let $Q = 54756$ minus the number of such lattice points. Find the value of $Q$. | 7,725 | graphs = [
Graph(
let={
"a": Const(256),
"b": Const(182),
"result": LatticePointsRect(a=Ref(name='a'), b=Ref(name='b')),
"_c": Const(54756),
"Q": Sub(Ref("_c"), Ref("result")),
},
goal=Ref("Q"),
)
] | GEOM | null | COUNT | sympy | [] | geo_count_lattice_rect_v1 | null | 3 | 0 | null | null | 0.001 | 2026-02-08T06:07:39.642448Z | {
"verified": true,
"answer": 7725,
"timestamp": "2026-02-08T06:07:39.643220Z"
} | b015fb | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 209,
"completion_tokens": 456
},
"timestamp": "2026-02-24T05:23:37.217Z",
"answer": 7725
},
{
"id... | 1 | [] | {
"lo": -4.93,
"mid": -2.91,
"hi": -0.71
} | ||||
de0293 | sequence_lucas_compute_v1_784195855_7039 | Let $n$ be the number of integers $t$ such that $5 \leq t \leq 24$ and there exist integers $a$ and $b$ with $1 \leq a \leq 6$, $1 \leq b \leq 3$, and $t = 3a + 2b$. Let $L_n$ denote the $n$th Lucas number, where $L_1 = 1$, $L_2 = 3$, and $L_k = L_{k-1} + L_{k-2}$ for $k \geq 3$. Compute the remainder when $34189 \cdot... | 18,440 | graphs = [
Graph(
let={
"_n": Const(64007),
"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=6)), Geq(left=Va... | NT | null | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | sequence_lucas_compute_v1 | null | 4 | 0 | [
"LIN_FORM"
] | 1 | 0.001 | 2026-02-08T09:03:46.095576Z | {
"verified": true,
"answer": 18440,
"timestamp": "2026-02-08T09:03:46.096607Z"
} | 469daa | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 191,
"completion_tokens": 1705
},
"timestamp": "2026-02-13T23:55:31.777Z",
"answer": 18440
},
... | 1 | [
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "LTE_SUM",
"status": ... | {
"lo": -3.51,
"mid": 1.33,
"hi": 6.56
} | ||
75973c | diophantine_fbi2_count_v1_1915831931_1391 | Let $n = 3$ and $k = 240$. Let $A$ be the set of all positive integers $d$ such that $5 \leq d \leq 54$, $d$ divides $k$, $\frac{k}{d} \geq n$, and $\frac{k}{d} \leq N$, where $N$ is the number of ordered pairs $(x_1, x_2)$ of positive odd integers satisfying $x_1 + x_2 = 104$. Compute the number of elements in $A$. | 12 | graphs = [
Graph(
let={
"_n": Const(3),
"k": Const(240),
"result": CountOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Const(5)), Leq(Var("d"), Const(54)), Divides(divisor=Var("d"), dividend=Ref("k")), Geq(Div(Ref("k"), Var("d")), Ref("_n")), Leq(Div(R... | NT | null | COUNT | sympy | K14 | [
"COMB1"
] | 567f58 | diophantine_fbi2_count_v1 | null | 4 | 0 | [
"COMB1",
"K14"
] | 2 | 0.077 | 2026-02-08T16:03:46.228081Z | {
"verified": true,
"answer": 12,
"timestamp": "2026-02-08T16:03:46.305369Z"
} | d3fec4 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 160,
"completion_tokens": 1580
},
"timestamp": "2026-02-16T21:44:23.581Z",
"answer": 12
},
{
... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COMB1",
"status": "ok"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "V1",
"status": "no"
... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
804117 | alg_poly4_sum_v1_601307018_8311 | Find the remainder when $$\sum_{\substack{a=1 \\ b=1}}^{329} \left( 128a b^3 + 17b^4 + \left|\left\{ j : 0 \leq j \leq 51485,\ \binom{51485}{j} \bmod 2 = 1 \right\}\right| a^4 + 384a^2b^2 + 512a^3b \right)$$ is divided by $50773$. | 8,330 | graphs = [
Graph(
let={
"_n": Const(2),
"result": Mod(value=SumOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("a"), Var("b")]), condition=And(Geq(Var("a"), Const(1)), Leq(Var("a"), Const(329)), Geq(Var("b"), Const(1)), Leq(Var("b"), Const(329)))), expr=Sum(Mul(Const(... | ALG | COMB | COMPUTE | sympy | V8 | [
"V8"
] | 86348e | alg_poly4_sum_v1 | null | 5 | 0 | [
"V8"
] | 1 | 1.483 | 2026-03-10T08:47:57.111618Z | {
"verified": true,
"answer": 8330,
"timestamp": "2026-03-10T08:47:58.595117Z"
} | 77d791 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 222,
"completion_tokens": 8593
},
"timestamp": "2026-04-19T08:46:54.182Z",
"answer": 8330
},
{
"... | 1 | [
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "V8",
"status": "ok"
}
] | {
"lo": -5.34,
"mid": 1.1,
"hi": 7.53
} | ||
126dd2 | nt_sum_divisors_mod_v1_1978505735_7120 | Let $n = 7560$ and $M = 11287$. Let $\sigma$ be the sum of the positive divisors of $n$. Define $\text{result}$ to be the remainder when $\sigma$ is divided by $M$. Let $Q$ be the smallest positive integer $k$ such that the $k$-th Fibonacci number is divisible by $|\text{result}| + 2$. Determine the value of $Q$. | 348 | graphs = [
Graph(
let={
"n": Const(7560),
"M": Const(11287),
"sigma": SumDivisors(n=Ref("n")),
"result": Mod(value=Ref("sigma"), modulus=Ref("M")),
"Q": FibonacciEntryPoint(modulus=Sum(Abs(arg=Ref(name='result')), Const(value=2))),
},
... | NT | null | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | nt_sum_divisors_mod_v1 | null | 4 | 0 | [
"LIN_FORM"
] | 1 | 0.013 | 2026-02-08T20:03:53.964793Z | {
"verified": true,
"answer": 348,
"timestamp": "2026-02-08T20:03:53.977800Z"
} | 80520c | 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": 5758
},
"timestamp": "2026-02-18T23:54:36.016Z",
"answer": 348
},
{
... | 1 | [
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
f41ba8 | lin_form_endings_v1_349078426_43 | Let $a = 70$ and $b = 42$. Compute $\text{lcm}(a, b)$. Multiply this least common multiple by $13192$, and then find the remainder when the result is divided by $88103$. Determine the value of this remainder. | 39,127 | graphs = [
Graph(
let={
"a_coeff": Const(70),
"b_coeff": Const(42),
"_inner_result": LCM(a=Ref("a_coeff"), b=Ref("b_coeff")),
"_scale_k": Const(13192),
"_scaled": Mul(Ref("_scale_k"), Ref("_inner_result")),
"_mod_M": Const(88103),
... | COMB | NT | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | lin_form_endings_v1 | null | 2 | null | [
"LIN_FORM"
] | 1 | 0.001 | 2026-02-08T12:47:29.549544Z | {
"verified": true,
"answer": 39127,
"timestamp": "2026-02-08T12:47:29.550268Z"
} | d9f447 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 103,
"completion_tokens": 668
},
"timestamp": "2026-02-15T05:23:23.776Z",
"answer": 39127
},
{... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
... | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
3cd866 | nt_sum_divisors_mod_v1_124444284_490 | Let $n = \sum_{k=1}^{15} \phi(k) \left\lfloor \frac{15}{k} \right\rfloor$, where $\phi$ denotes Euler's totient function. Let $\sigma$ be the sum of all positive divisors of $n$. Let $M = 10163$.
Compute the remainder when $\sigma$ is divided by $M$, and then compute the absolute value of that remainder. Finally, find... | 360 | graphs = [
Graph(
let={
"_n": Const(15),
"n": Summation(var="k", start=Const(1), end=Const(15), expr=Mul(EulerPhi(n=Var("k")), Floor(Div(Ref("_n"), Var("k"))))),
"M": Const(10163),
"sigma": SumDivisors(n=Ref("n")),
"result": Mod(value=Ref("sigma"),... | NT | null | COMPUTE | sympy | K2 | [
"K2"
] | 6897ab | nt_sum_divisors_mod_v1 | null | 5 | 0 | [
"K2"
] | 1 | 0.002 | 2026-02-08T03:19:55.203946Z | {
"verified": true,
"answer": 360,
"timestamp": "2026-02-08T03:19:55.206077Z"
} | 4ca739 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 217,
"completion_tokens": 1799
},
"timestamp": "2026-02-09T18:22:16.263Z",
"answer": 360
},
{
"id... | 1 | [
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "K2",
"status": "ok"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "V1",
"status": "no"
}
] | {
"lo": -5.55,
"mid": -3.02,
"hi": 0.31
} |
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