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 |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
f6da29 | nt_count_digit_sum_v1_124444284_506 | Let $S$ be the set of all ordered pairs $(x,y)$ of positive integers such that $x + y = 10$. Define $P$ to be the maximum value of $xy$ over all such pairs. Let $N$ be the number of positive integers $n$ such that $1 \le n \le 17956$ and the sum of the digits of $n$ is equal to $P$. Compute $N$. | 618 | graphs = [
Graph(
let={
"upper": Const(17956),
"target_sum": 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(10)))), expr=Mul(Var("x"), V... | NT | null | COUNT | sympy | B1 | [
"B1"
] | 5b950e | nt_count_digit_sum_v1 | null | 4 | 0 | [
"B1"
] | 1 | 0.642 | 2026-02-08T03:20:10.234025Z | {
"verified": true,
"answer": 618,
"timestamp": "2026-02-08T03:20:10.876180Z"
} | f7ec5e | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 206,
"completion_tokens": 5241
},
"timestamp": "2026-02-09T02:46:31.926Z",
"answer": 618
},
{
"i... | 1 | [
{
"lemma": "B1",
"status": "ok"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"
}
] | {
"lo": -3.49,
"mid": 1.84,
"hi": 7.55
} | ||
57c4c9 | comb_binomial_compute_v1_458359167_1353 | Let $S$ be the set of all ordered pairs $(x,y)$ of positive integers such that $x + y$ equals the number of integers $t$ in the interval $5 \leq t \leq 14$ for which there exist integers $a$ and $b$ satisfying $1 \leq a \leq 4$, $1 \leq b \leq 2$, and $t = 2a + 3b$. Let $n$ be the maximum value of $xy$ over all such pa... | 11,440 | 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")), CountOverSet(set=SolutionsSet(var=Var("t"), condition=Exists(var=Var(name='a')... | ALG | COMB | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM/B1"
] | b32639 | comb_binomial_compute_v1 | null | 4 | 0 | [
"B1",
"LIN_FORM"
] | 2 | 0.003 | 2026-02-08T04:33:37.332544Z | {
"verified": true,
"answer": 11440,
"timestamp": "2026-02-08T04:33:37.335114Z"
} | fa0816 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 241,
"completion_tokens": 1261
},
"timestamp": "2026-02-24T01:00:23.892Z",
"answer": 11440
},
{
"... | 1 | [
{
"lemma": "B1",
"status": "ok_later"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
}
] | {
"lo": -2.46,
"mid": 0.47,
"hi": 3.59
} | ||
35ef42 | nt_count_coprime_v1_1918700295_2657 | Let $n = 9$ and $u = 25921$. Define $k = \sum_{d=1}^{9} \varphi(d) \left\lfloor \frac{n}{d} \right\rfloor$. Determine the number of positive integers $m$ such that $1 \leq m \leq u$ and $\gcd(m, k) = 1$. | 13,825 | graphs = [
Graph(
let={
"_n": Const(9),
"upper": Const(25921),
"k": Summation(var="k", start=Const(1), end=Const(9), expr=Mul(EulerPhi(n=Var("k")), Floor(Div(Ref("_n"), Var("k"))))),
"result": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("... | NT | null | COUNT | sympy | K2 | [
"K2"
] | 6897ab | nt_count_coprime_v1 | null | 5 | 0 | [
"K2"
] | 1 | 2.065 | 2026-02-08T08:09:03.878201Z | {
"verified": true,
"answer": 13825,
"timestamp": "2026-02-08T08:09:05.942817Z"
} | 141672 | 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": 1258
},
"timestamp": "2026-02-13T14:56:58.105Z",
"answer": 13825
},
... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "K2",
"status": "ok"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "VAL_SUM_EQ",
"status": "no"
... | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
cc6833 | diophantine_fbi2_min_v1_458359167_4666 | Let $k = 16$ and $U = 26$. Let $D$ be the set of integers $d$ such that $5 \leq d \leq U$, $d$ divides $k$, and $\frac{k}{d} \geq 2$. Compute the minimum value of $D$. | 8 | graphs = [
Graph(
let={
"_n": Const(2),
"k": Const(16),
"upper": Const(26),
"result": MinOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Const(5)), Leq(Var("d"), Ref("upper")), Divides(divisor=Var("d"), dividend=Ref("k")), Geq(Div(Ref("k"), ... | NT | null | EXTREMUM | sympy | COPRIME_PAIRS | [
"COPRIME_PAIRS"
] | 2bb3aa | diophantine_fbi2_min_v1 | null | 3 | 0 | [
"COPRIME_PAIRS"
] | 1 | 0.007 | 2026-02-08T11:58:06.261253Z | {
"verified": true,
"answer": 8,
"timestamp": "2026-02-08T11:58:06.268374Z"
} | 351c9a | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 124,
"completion_tokens": 389
},
"timestamp": "2026-02-16T03:28:59.341Z",
"answer": 8
},
{
"id": 11,
"... | 2 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
}
] | {
"lo": -10,
"mid": -7.71,
"hi": -5.43
} | ||
35d8d3 | geo_count_lattice_rect_v1_124444284_2228 | Let $a = 200$ and $b = 141$. Define a lattice point as a point in the plane with integer coordinates. Consider the rectangle with vertices at $(0,0)$, $(a,0)$, $(0,b)$, and $(a,b)$, including its boundary. Compute the number of lattice points contained in this rectangle. | 28,542 | graphs = [
Graph(
let={
"a": Const(200),
"b": Const(141),
"result": LatticePointsRect(a=Ref(name='a'), b=Ref(name='b')),
},
goal=Ref("result"),
)
] | GEOM | null | COUNT | sympy | [] | geo_count_lattice_rect_v1 | null | 4 | 0 | null | null | 0.002 | 2026-02-08T04:31:43.247591Z | {
"verified": true,
"answer": 28542,
"timestamp": "2026-02-08T04:31:43.249255Z"
} | 483249 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 182,
"completion_tokens": 286
},
"timestamp": "2026-02-24T00:55:53.015Z",
"answer": 28542
},
{
"i... | 1 | [] | {
"lo": -5.97,
"mid": -3.96,
"hi": -1.93
} | ||||
e02592 | alg_poly_orbit_count_v1_1218484723_4310 | Let $T_a$ be the result of iterating the function $f(x) = x^2 - 41 \bmod 97$ five times starting from $a$, so that $N = f(a)$, $M = f(N)$, $R = f(M)$, $S = f(R)$, $T = f(S)$. Find the number of non-negative integers $a$ with $0 \le a \le 14161$ such that $T = a$, but $N \ne a$, $M \ne a$, $R \ne a$, and $S \ne a$. | 730 | graphs = [
Graph(
let={
"p1": Mod(value=Sum(Pow(Var("a"), Const(2)), Const(-41)), modulus=Const(97)),
"p2": Mod(value=Sum(Pow(Ref("p1"), Const(2)), Const(-41)), modulus=Const(97)),
"p3": Mod(value=Sum(Pow(Ref("p2"), Const(2)), Const(-41)), modulus=Const(97)),
... | ALG | null | COUNT | sympy | POLY_ORBIT_COUNT | [
"POLY_ORBIT_COUNT"
] | 4ad965 | alg_poly_orbit_count_v1 | null | 6 | null | [
"POLY_ORBIT_COUNT"
] | 1 | 0.018 | 2026-02-25T05:56:17.636760Z | {
"verified": true,
"answer": 730,
"timestamp": "2026-02-25T05:56:17.655071Z"
} | 544b88 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 239,
"completion_tokens": 20065
},
"timestamp": "2026-03-29T14:57:04.847Z",
"answer": 730
},
{
"i... | 1 | [
{
"lemma": "POLY_ORBIT_COUNT",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
}
] | {
"lo": 3.81,
"mid": 6.33,
"hi": 9.49
} | ||
350ca1 | geo_count_lattice_rect_v1_1520064083_5343 | Let $a = 70$ and $b = 125$. Define $R$ as the rectangle in the coordinate plane with vertices at $(0,0)$, $(70,0)$, $(0,125)$, and $(70,125)$. Compute the number of lattice points contained in $R$, including all boundary and interior points. | 8,946 | graphs = [
Graph(
let={
"a": Const(70),
"b": Const(125),
"result": LatticePointsRect(a=Ref(name='a'), b=Ref(name='b')),
},
goal=Ref("result"),
)
] | GEOM | null | COUNT | sympy | [] | geo_count_lattice_rect_v1 | null | 3 | 0 | null | null | 0.001 | 2026-02-08T06:44:53.442805Z | {
"verified": true,
"answer": 8946,
"timestamp": "2026-02-08T06:44:53.443334Z"
} | b220f8 | 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": 270
},
"timestamp": "2026-02-24T06:57:19.059Z",
"answer": 8946
},
{
"id... | 1 | [] | {
"lo": -4.93,
"mid": -2.91,
"hi": -0.71
} | ||||
12f1d5 | alg_poly3_min_v1_601307018_4892 | Let $Q$ be the minimum value of
$$
7375a^3 + \left|\left\{ (a_1, b_1) \in \mathbb{Z}^2 : 1 \leq a_1, b_1 \leq 40,\ -12a_1b_1 + 41a_1^2 + 20b_1^2 \leq 63504 \right\}\right| \cdot b^3 + 13275a^2b + 7965ab^2
$$
over all ordered pairs $(a, b)$ of positive integers with $1 \leq a, b \leq 356$. Find $Q$. | 30,149 | graphs = [
Graph(
let={
"_n": Const(7375),
"result": MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("a"), Var("b")]), condition=And(Geq(Var("a"), Const(1)), Leq(Var("a"), Const(356)), Geq(Var("b"), Const(1)), Leq(Var("b"), Const(356)))), expr=Sum(Mul(Ref("_n"), Po... | ALG | null | COMPUTE | sympy | QF_PSD_COUNT_LEQ | [
"QF_PSD_COUNT_LEQ"
] | 009d0f | alg_poly3_min_v1 | null | 4 | 0 | [
"QF_PSD_COUNT_LEQ"
] | 1 | 1.04 | 2026-03-10T05:36:58.305229Z | {
"verified": true,
"answer": 30149,
"timestamp": "2026-03-10T05:36:59.345568Z"
} | 4888d6 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 263,
"completion_tokens": 12429
},
"timestamp": "2026-03-29T13:48:57.032Z",
"answer": null
},
{
... | 0 | [
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "QF_PSD_COUNT_LEQ",
"status": "ok"
}
] | {
"lo": 3.34,
"mid": 5.77,
"hi": 8.89
} | ||
198ef4 | geo_count_lattice_rect_v1_1978505735_6690 | Let $a = 21$ and $b = 51$. Compute the number of lattice points in the rectangle $[0, a] \times [0, b]$, including the boundary. | 1,144 | graphs = [
Graph(
let={
"a": Const(21),
"b": Const(51),
"result": LatticePointsRect(a=Ref(name='a'), b=Ref(name='b')),
},
goal=Ref("result"),
)
] | GEOM | null | COUNT | sympy | [] | geo_count_lattice_rect_v1 | null | 2 | 0 | null | null | 0.004 | 2026-02-08T19:44:59.312383Z | {
"verified": true,
"answer": 1144,
"timestamp": "2026-02-08T19:44:59.316046Z"
} | 02f2b6 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 88,
"completion_tokens": 467
},
"timestamp": "2026-02-25T01:49:33.969Z",
"answer": 1144
},
{
... | 1 | [] | {
"lo": -8.48,
"mid": -5.37,
"hi": -3.03
} | ||||
a62d54 | diophantine_fbi2_count_v1_1520064083_4403 | Let $k = 420$. Let $d$ be a positive integer such that $4 \le d \le 154$, $d$ divides $k$, $\frac{k}{d} \ge 6$, and $\frac{k}{d} \le s$, where $s$ is the minimum value of $x + y$ over all ordered pairs $(x, y)$ of positive integers satisfying $xy = 6084$. Let $r$ be the number of such integers $d$. Compute $\sum_{i=1}^... | 50 | graphs = [
Graph(
let={
"k": Const(420),
"result": CountOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Const(4)), Leq(Var("d"), Const(154)), Divides(divisor=Var("d"), dividend=Ref("k")), Geq(Div(Ref("k"), Var("d")), Const(6)), Leq(Div(Ref("k"), Var("d")), MinOverS... | NT | null | COUNT | sympy | ONE_PHI_2 | [
"B3"
] | 0cd20d | diophantine_fbi2_count_v1 | null | 6 | 0 | [
"B3",
"ONE_PHI_2"
] | 2 | 0.076 | 2026-02-08T06:15:43.509274Z | {
"verified": true,
"answer": 50,
"timestamp": "2026-02-08T06:15:43.584789Z"
} | 6ed239 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 179,
"completion_tokens": 1354
},
"timestamp": "2026-02-12T22:05:09.499Z",
"answer": 50
},
{
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "V1",
"status": "no"
}
] | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
6ac775 | modular_modexp_compute_v1_601307018_6837 | Let $e = \sum_{k=0}^{5} 6^{k}$. Compute $17^{e} \bmod 16641$. | 4,121 | graphs = [
Graph(
let={
"a": Const(17),
"e": Summation(var="k", start=Const(0), end=Const(5), expr=Pow(Const(6), Var("k"))),
"m": Const(16641),
"result": ModExp(base=Ref("a"), exp=Ref("e"), mod=Ref("m")),
},
goal=Ref("result"),
)
] | NT | null | COMPUTE | sympy | SUM_GEOM | [
"SUM_GEOM"
] | 04214c | modular_modexp_compute_v1 | null | 3 | 0 | [
"SUM_GEOM"
] | 1 | 0.001 | 2026-03-10T07:28:28.472203Z | {
"verified": true,
"answer": 4121,
"timestamp": "2026-03-10T07:28:28.473539Z"
} | b616b8 | 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": 3976
},
"timestamp": "2026-04-19T05:26:27.630Z",
"answer": 4121
},
{
"... | 1 | [
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "SUM_GEOM",
"status": "ok"
},
{
"lemma": "V1",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "VAL_SUM_EQ",
"status": "no"
}
] | {
"lo": -5.34,
"mid": 1.1,
"hi": 7.53
} | ||
3ccd01 | antilemma_sum_equals_v1_153355830_2926 | Let $n = 101$. Consider the set of all ordered pairs $(i, j)$ of positive integers such that $1 \le i \le 99$, $1 \le j \le 99$, and $i + j = n$. Let $x$ be the number of such ordered pairs. Find the remainder when $12844x$ is divided by 81333. | 38,717 | graphs = [
Graph(
let={
"_n": Const(101),
"x": 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(99)), right=IntegerRange(start=Const(1), end=Co... | COMB | GEOM | COMPUTE | sympy | COUNT_SUM_EQUALS | [
"COUNT_SUM_EQUALS"
] | 75ab0f | antilemma_sum_equals_v1 | null | 2 | 0 | [
"COUNT_SUM_EQUALS"
] | 1 | 0.004 | 2026-02-08T07:28:50.038476Z | {
"verified": true,
"answer": 38717,
"timestamp": "2026-02-08T07:28:50.042374Z"
} | 9542a9 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 190,
"completion_tokens": 1145
},
"timestamp": "2026-02-24T08:05:33.474Z",
"answer": 38717
},
{
"... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "ok"
},
{
"lemma": "V8",
"status": "no"
},
{
"lemma": "V8_SUM",
"status":... | {
"lo": -2.35,
"mid": 1.22,
"hi": 4.84
} | ||
37ff37 | lin_form_endings_v1_677425708_2488 | Let $S$ be the set of all integers $t$ such that $63 \leq t \leq 2133$ and there exist positive integers $a$ and $b$ with $1 \leq a \leq 29$, $1 \leq b \leq 46$, and $t = 45a + 18b$. Let $c$ be the number of elements in $S$. Compute the remainder when $19767 \cdot c$ is divided by $79151$. | 54,653 | graphs = [
Graph(
let={
"_inner_result": CountOverSet(set=SolutionsSet(var=Var("t"), condition=Exists(var=Var(name='a'), condition=Exists(var=Var(name='b'), condition=And(Geq(left=Var(name='a'), right=Const(value=1)), Leq(left=Var(name='a'), right=Const(value=29)), Geq(left=Var(name='b'), right=... | COMB | null | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | lin_form_endings_v1 | null | 4 | null | [
"LIN_FORM"
] | 1 | 0.001 | 2026-02-08T05:04:43.302188Z | {
"verified": true,
"answer": 54653,
"timestamp": "2026-02-08T05:04:43.303353Z"
} | 2b1f41 | 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": 7972
},
"timestamp": "2026-02-24T02:40:59.693Z",
"answer": 54653
},
{
"... | 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": -2.46,
"mid": 0.47,
"hi": 3.59
} | ||
e640d0 | comb_count_surjections_v1_601307018_3690 | Let $f(x) = x^3 - 2x^2 + 2x + 2$. For each integer $a$ with $0 \le a \le 9408$, define $N = f(a) \bmod 9409$, $M = f(N) \bmod 9409$, $R = f(M) \bmod 9409$, and $S = f(R) \bmod 9409$. Let $n$ be the number of such $a$ for which $S = a$, but $N \ne a$, $M \ne a$, and $R \ne a$. Compute $6 \cdot S(n, 3)$, where $S(n, 3)$ ... | 36 | graphs = [
Graph(
let={
"n": CountOverSet(set=SolutionsSet(var=Var("a"), condition=And(Geq(Var("a"), Const(0)), Leq(Var("a"), Const(9408)), Eq(Ref("_po_p4"), Var("a")), Neq(Ref("_po_p1"), Var("a")), Neq(Ref("_po_p2"), Var("a")), Neq(Ref("_po_p3"), Var("a"))))),
"k": Const(3),
... | COMB | null | COUNT | sympy | POLY_ORBIT_LEGENDRE | [
"POLY_ORBIT_HENSEL"
] | 53b6eb | comb_count_surjections_v1 | null | 7 | 0 | [
"POLY_ORBIT_HENSEL",
"POLY_ORBIT_LEGENDRE"
] | 2 | 0.095 | 2026-03-10T04:17:49.023040Z | {
"verified": true,
"answer": 36,
"timestamp": "2026-03-10T04:17:49.118092Z"
} | 533e3d | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 1,
"correct": {
"strict": false,
"boxed": false,
"relaxed": true
},
"usage": {
"prompt_tokens": 275,
"completion_tokens": 32768
},
"timestamp": "2026-03-29T09:40:15.283Z",
"answer": null
},
{
... | 0 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "POLY_ORBIT_HENSEL",
"status": "ok"
},
{
"lemma": "V8",
"status": "no"
},
{
"lemma": "V8_SUM",
"statu... | {
"lo": 3.34,
"mid": 5.77,
"hi": 8.89
} | ||
a1074b | nt_sum_divisors_compute_v1_1520064083_2422 | Let $n=67161$. Let $Q$ be the sum of all positive divisors of $n$.
Find the value of $Q$. | 91,264 | graphs = [
Graph(
let={
"n": Const(67161),
"result": SumDivisors(n=Ref("n")),
},
goal=Ref("result"),
)
] | NT | null | COMPUTE | sympy | C4 | [
"C4/ONE_PHI_2/BIG_OMEGA_ZERO",
"LIN_FORM/MOBIUS_SUM"
] | 6b9a6e | nt_sum_divisors_compute_v1 | null | 3 | 0 | [
"BIG_OMEGA_ZERO",
"C4",
"LIN_FORM",
"MOBIUS_SUM",
"ONE_PHI_2"
] | 5 | 0.006 | 2026-02-08T04:43:31.175158Z | {
"verified": true,
"answer": 91264,
"timestamp": "2026-02-08T04:43:31.180980Z"
} | bba96a | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 141,
"completion_tokens": 1125
},
"timestamp": "2026-02-11T21:50:14.789Z",
"answer": 91264
},
{
... | 1 | [
{
"lemma": "BIG_OMEGA_ZERO",
"status": "ok_later"
},
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "C4",
"status": "ok"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"l... | {
"lo": -3.42,
"mid": 1.86,
"hi": 7.55
} | ||
678124 | lin_form_endings_v1_48377204_914 | Let $a = 56$ and $b = 24$. Define $g$ to be the greatest common divisor of $a$ and $b$, and let $r = \left\lfloor \frac{56}{g} \right\rfloor$. Let $k = 11796$ and $s = k \cdot r$. Compute the remainder when $s$ is divided by $60607$. | 21,965 | graphs = [
Graph(
let={
"a_coeff": Const(56),
"b_coeff": Const(24),
"_inner_result": Floor(Div(Const(56), GCD(a=Ref("a_coeff"), b=Ref("b_coeff")))),
"_scale_k": Const(11796),
"_scaled": Mul(Ref("_scale_k"), Ref("_inner_result")),
"_mod_... | COMB | NT | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | lin_form_endings_v1 | null | 2 | null | [
"LIN_FORM"
] | 1 | 0.001 | 2026-02-08T15:45:34.550234Z | {
"verified": true,
"answer": 21965,
"timestamp": "2026-02-08T15:45:34.551472Z"
} | 48c555 | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 151,
"completion_tokens": 305
},
"timestamp": "2026-02-16T06:20:21.656Z",
"answer": 21965
},
{
"id": 11,
... | 2 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
}
] | {
"lo": -10,
"mid": -7.27,
"hi": -4.54
} | ||
b02fd9 | antilemma_k2_v1_865884756_4124 | Compute $$\sum_{k=1}^{100} \phi(k) \left\lfloor \frac{100}{k} \right\rfloor.$$ | 5,050 | graphs = [
Graph(
let={
"_n": Const(100),
"x": Summation(var="k", start=Pow(Const(45), Sub(Const(30), Const(30))), end=Ref("_n"), expr=Mul(EulerPhi(n=Var("k")), Floor(Div(Const(100), Var("k"))))),
},
goal=Ref("x"),
)
] | NT | COMB | COMPUTE | sympy | IDENTITY_POW_ZERO | [
"IDENTITY_POW_ZERO",
"IDENTITY_SUB_SELF",
"K2"
] | fe633d | antilemma_k2_v1 | null | 3 | 0 | [
"IDENTITY_POW_ZERO",
"IDENTITY_SUB_SELF",
"K2"
] | 3 | 0.002 | 2026-02-08T17:45:40.155806Z | {
"verified": true,
"answer": 5050,
"timestamp": "2026-02-08T17:45:40.157663Z"
} | 384439 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 78,
"completion_tokens": 795
},
"timestamp": "2026-02-18T06:57:23.306Z",
"answer": 5050
},
{
... | 1 | [
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "IDENTITY_POW_ZERO",
"status": "ok"
},
{
"lemma": "IDENTITY_SUB_SELF",
"status": "ok"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K2",
"status": "ok"
},
{
"lemma": "L3b",
"status": "no"
},
{... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
589df2 | nt_sum_gcd_range_mod_v1_1431428450_316 | Let $N$ be the minimum value of $x + y$ over all ordered pairs $(x, y)$ of positive integers such that $xy = 7496644$. Let $k = 96$ and $M = 11287$. Define $\text{sum} = \sum_{n=1}^{N} \gcd(n, k)$. Let $\text{result}$ be the remainder when $\text{sum}$ is divided by $M$. Compute $30276 - \text{result}$. | 20,920 | 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(7496644)))), expr=Sum(Var("x"), Var("y")))),
"k": Const(96),... | NT | null | COMPUTE | sympy | B3 | [
"B3"
] | 0cd20d | nt_sum_gcd_range_mod_v1 | null | 5 | 0 | [
"B3"
] | 1 | 0.29 | 2026-02-08T13:23:24.886469Z | {
"verified": true,
"answer": 20920,
"timestamp": "2026-02-08T13:23:25.176537Z"
} | 0ba0ab | 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": 2177
},
"timestamp": "2026-02-15T14:01:42.588Z",
"answer": 20920
},
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
}
] | {
"lo": -5.49,
"mid": 0.22,
"hi": 6.51
} | ||
65e9d5 | diophantine_fbi2_count_v1_655260480_3749 | Let $m = 20$ and $n = 507$. Define $A$ as the set of all positive integers $a$ such that $1 \leq a \leq n$ and $\gcd(a, m) = 1$. Let $M = |A|$. Define $B$ as the set of all positive integers $b$ such that $1 \leq b \leq 1421$ and $13$ divides the $b$-th Fibonacci number. Let $K = 480$ and $L = |B|$. Determine the numbe... | 18 | graphs = [
Graph(
let={
"_m": Const(20),
"_n": Const(507),
"k": Const(480),
"result": CountOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Const(4)), Leq(Var("d"), CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const... | NT | null | COUNT | sympy | K13 | [
"COUNT_FIB_DIVISIBLE",
"C4"
] | b10525 | diophantine_fbi2_count_v1 | null | 6 | 0 | [
"C4",
"COUNT_FIB_DIVISIBLE",
"K13"
] | 3 | 0.196 | 2026-02-08T17:31:43.341837Z | {
"verified": true,
"answer": 18,
"timestamp": "2026-02-08T17:31:43.537960Z"
} | 2cb55f | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 202,
"completion_tokens": 2764
},
"timestamp": "2026-02-18T03:31:45.998Z",
"answer": 18
},
{
... | 1 | [
{
"lemma": "C4",
"status": "ok"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "ok"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"
... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
278c67 | nt_count_intersection_v1_151522320_1808 | Let $ N = 100000 $ and $ a = 5 $. Let $ S $ be the set of all ordered pairs $ (x, y) $ of positive integers such that $ xy = 49 $. Define $ b $ to be the minimum value of $ x + y $ as $ (x, y) $ ranges over $ S $. Let $ T $ be the set of all integers $ n $ such that $ 1 \leq n \leq N $, $ a $ divides $ n $, and $ \gcd(... | 8,571 | graphs = [
Graph(
let={
"N": Const(100000),
"a": Const(5),
"b": MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(Mul(Var("x"), Var("y")), Const(49)))), expr=... | NT | null | COUNT | sympy | B3 | [
"B3"
] | 0cd20d | nt_count_intersection_v1 | null | 4 | 0 | [
"B3"
] | 1 | 4.626 | 2026-02-08T04:23:17.913137Z | {
"verified": true,
"answer": 8571,
"timestamp": "2026-02-08T04:23:22.538775Z"
} | 9c926a | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 238,
"completion_tokens": 1210
},
"timestamp": "2026-02-10T16:33:18.779Z",
"answer": 8571
},
{
"... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
}
] | {
"lo": -3.42,
"mid": 1.86,
"hi": 7.55
} | ||
ba4677 | sequence_count_fib_divisible_v1_397696148_2034 | Let $n$ be a positive integer. Let $d$ be the largest prime number less than or equal to 7. Determine the number of positive integers $n$ not exceeding 497 for which $d$ divides the $n$th Fibonacci number. Compute this number. | 62 | graphs = [
Graph(
let={
"_n": Const(7),
"upper": Const(497),
"d": MaxOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(2)), Leq(Var("n"), Ref("_n")), IsPrime(Var("n"))))),
"result": CountOverSet(set=SolutionsSet(var=Var("n"), condition=A... | NT | null | COUNT | sympy | MAX_PRIME_BELOW | [
"MAX_PRIME_BELOW"
] | dc3ad3 | sequence_count_fib_divisible_v1 | null | 6 | 0 | [
"MAX_PRIME_BELOW"
] | 1 | 0.041 | 2026-02-08T12:54:33.745898Z | {
"verified": true,
"answer": 62,
"timestamp": "2026-02-08T12:54:33.786679Z"
} | 859fbd | 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": 1578
},
"timestamp": "2026-02-15T07:35:16.745Z",
"answer": 62
},
{
... | 1 | [
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "V3",
"status": "no"
}
] | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
c2a9ed | antilemma_k3_v1_865884756_571 | Let $n = 92598$. Compute the sum of $\phi(d)$ over all positive divisors $d$ of $n$. | 92,598 | graphs = [
Graph(
let={
"_n": Const(92598),
"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 | 2 | 0 | [
"K3"
] | 1 | 0.001 | 2026-02-08T15:31:02.268925Z | {
"verified": true,
"answer": 92598,
"timestamp": "2026-02-08T15:31:02.269591Z"
} | e29fa3 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 74,
"completion_tokens": 902
},
"timestamp": "2026-02-16T07:40:39.827Z",
"answer": 92598
},
{
... | 1 | [
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "K3",
"status": "ok"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
902447 | nt_count_coprime_and_v1_1248542787_921 | Let $k_1$ be the largest prime number $n$ such that $2 \leq n \leq 6$, and let $k_2 = 9$. Compute the number of positive integers $n$ such that $1 \leq n \leq 35598$, $\gcd(n, k_1) = 1$, and $\gcd(n, k_2) = 1$. | 18,986 | graphs = [
Graph(
let={
"_n": Const(6),
"upper": Const(35598),
"k1": MaxOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(2)), Leq(Var("n"), Ref("_n")), IsPrime(Var("n"))))),
"k2": Const(9),
"result": CountOverSet(set=Solutio... | NT | null | COUNT | sympy | MAX_PRIME_BELOW | [
"MAX_PRIME_BELOW"
] | dc3ad3 | nt_count_coprime_and_v1 | null | 4 | 0 | [
"MAX_PRIME_BELOW"
] | 1 | 4.013 | 2026-02-08T03:29:02.114322Z | {
"verified": true,
"answer": 18986,
"timestamp": "2026-02-08T03:29:06.127147Z"
} | 302656 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 203,
"completion_tokens": 2757
},
"timestamp": "2026-02-09T10:04:35.652Z",
"answer": 18986
},
{
"... | 1 | [
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
}
] | {
"lo": -3.46,
"mid": 0.96,
"hi": 5.17
} | ||
36d5a4 | nt_sum_gcd_range_mod_v1_784195855_3399 | Let $k$ be the number of positive integers $t$ such that $5 \leq t \leq 606$ and there exist positive integers $a \leq 18$ and $b \leq 190$ for which $t = 2a + 3b$. Let $N = 2311$. Define $s = \sum_{n=1}^{N} \gcd(n, k)$. Let $M = 10459$, and let $r = s \bmod M$. Let $P$ be the set of all prime numbers $p$ such that $2 ... | 203 | graphs = [
Graph(
let={
"_n": Const(2),
"N": Const(2311),
"k": 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=Co... | NT | COMB | COMPUTE | sympy | MIN_PRIME_FACTOR | [
"MAX_PRIME_BELOW",
"LIN_FORM"
] | 4b337f | nt_sum_gcd_range_mod_v1 | bell_mod | 7 | 0 | [
"LIN_FORM",
"MAX_PRIME_BELOW",
"MIN_PRIME_FACTOR"
] | 3 | 0.599 | 2026-02-08T06:24:44.470900Z | {
"verified": true,
"answer": 203,
"timestamp": "2026-02-08T06:24:45.070035Z"
} | b7561d | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 206,
"completion_tokens": 5013
},
"timestamp": "2026-02-13T00:01:06.333Z",
"answer": 203
},
{
... | 1 | [
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "MOD_SUB"... | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
501f44 | comb_count_derangements_v1_1470522791_1140 | Let $\_c = 16$. Let $\_m$ be the number of ordered pairs $(x_1, x_2)$ of positive odd integers such that $x_1 + x_2 = \_c$. Let $\_n$ be the number of ordered pairs $(i,j)$ with $1 \leq i \leq 8$ and $1 \leq j \leq 8$ such that $i + j = \_m$. Let $n_1$ be the number of ordered pairs $(i,j)$ with $1 \leq i \leq 13$ and ... | 3,110 | graphs = [
Graph(
let={
"_c": Const(16),
"_m": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x1"), Var("x2")]), condition=And(IsPositive(arg=Var(name='x1')), IsPositive(arg=Var(name='x2')), IsOdd(arg=Var(name='x1')), IsOdd(arg=Var(name='x2')), Eq(Sum(Var("x1"), Var("x2")), R... | COMB | NT | COUNT | sympy | COUNT_SUM_EQUALS | [
"COUNT_SUM_EQUALS/COUNT_SUM_EQUALS/BINOMIAL_ALTERNATING",
"COMB1/COUNT_SUM_EQUALS/BINOMIAL_ALTERNATING"
] | 83dbde | comb_count_derangements_v1 | null | 7 | 2 | [
"BINOMIAL_ALTERNATING",
"COMB1",
"COUNT_SUM_EQUALS"
] | 3 | 0.025 | 2026-02-08T13:26:50.855585Z | {
"verified": true,
"answer": 3110,
"timestamp": "2026-02-08T13:26:50.880180Z"
} | f985fc | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 322,
"completion_tokens": 2147
},
"timestamp": "2026-02-15T15:41:03.827Z",
"answer": 3110
},
{... | 1 | [
{
"lemma": "BINOMIAL_ALTERNATING",
"status": "ok_later"
},
{
"lemma": "COMB1",
"status": "ok"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "ok"
},
{
"lemm... | {
"lo": -5.49,
"mid": 0.22,
"hi": 6.51
} | ||
5dacd8 | lin_form_endings_v1_1742523217_3284 | Compute the value of $\left\lfloor \frac{15}{\gcd(21, 15)} \right\rfloor$, multiply the result by $7801$, and then find the remainder when this product is divided by $98431$. | 39,005 | graphs = [
Graph(
let={
"a_coeff": Const(21),
"b_coeff": Const(15),
"_inner_result": Floor(Div(Const(15), GCD(a=Ref("a_coeff"), b=Ref("b_coeff")))),
"_scale_k": Const(7801),
"_scaled": Mul(Ref("_scale_k"), Ref("_inner_result")),
"_mod_M... | COMB | NT | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | lin_form_endings_v1 | null | 2 | null | [
"LIN_FORM"
] | 1 | 0 | 2026-02-08T05:45:48.567773Z | {
"verified": true,
"answer": 39005,
"timestamp": "2026-02-08T05:45:48.568224Z"
} | 493a75 | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 115,
"completion_tokens": 283
},
"timestamp": "2026-02-11T23:03:38.750Z",
"answer": 39005
},
{
"id": 11,
... | 2 | [
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8_SUM",
"st... | {
"lo": -10,
"mid": -7.73,
"hi": -5.46
} | ||
6829b3 | sequence_fibonacci_compute_v1_1520064083_8599 | Let $n$ be the sum of all positive integers at most 23 that are divisible by 23. Compute the $n$-th Fibonacci number. | 28,657 | graphs = [
Graph(
let={
"_n": Const(23),
"n": SumOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Ref("_n")), Eq(Mod(value=Var("n"), modulus=Const(23)), Const(0))))),
"result": Fibonacci(arg=Ref(name='n')),
},
goa... | NT | null | COMPUTE | sympy | SUM_DIVISIBLE | [
"SUM_DIVISIBLE"
] | 02dbe3 | sequence_fibonacci_compute_v1 | null | 2 | 0 | [
"SUM_DIVISIBLE"
] | 1 | 0.001 | 2026-02-08T10:15:55.875747Z | {
"verified": true,
"answer": 28657,
"timestamp": "2026-02-08T10:15:55.877126Z"
} | 1158d1 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 78,
"completion_tokens": 451
},
"timestamp": "2026-02-14T06:54:39.029Z",
"answer": 28657
},
{
... | 1 | [
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "SUM_DIVISIBLE",
"status": "ok"
},
{
"lemma": "V8_SUM",
"status"... | {
"lo": -6.96,
"mid": -4.56,
"hi": -1.46
} | ||
4ad69f | nt_gcd_compute_v1_601307018_466 | Let $N = \gcd(154826, 287534)$. Find the remainder when $18002N$ is divided by $75901$. | 67,491 | graphs = [
Graph(
let={
"a": Const(154826),
"b": Const(287534),
"result": GCD(a=Ref("a"), b=Ref("b")),
"Q": Mod(value=Mul(Const(18002), Ref("result")), modulus=Const(75901)),
},
goal=Ref("Q"),
)
] | NT | null | COMPUTE | sympy | POLY_ORBIT_LEGENDRE | [
"POLY_ORBIT_LEGENDRE/EULER_TOTIENT_SUM",
"SUM_GEOM/LIOUVILLE_ONE",
"BIG_OMEGA_ONE"
] | d1e750 | nt_gcd_compute_v1 | null | 2 | 0 | [
"BIG_OMEGA_ONE",
"EULER_TOTIENT_SUM",
"LIOUVILLE_ONE",
"POLY_ORBIT_LEGENDRE",
"SUM_GEOM"
] | 5 | 0.013 | 2026-03-10T00:57:57.056010Z | {
"verified": true,
"answer": 67491,
"timestamp": "2026-03-10T00:57:57.069256Z"
} | 62f758 | CC BY 4.0 | null | null | [
{
"lemma": "BIG_OMEGA_ONE",
"status": "ok"
},
{
"lemma": "EULER_TOTIENT_SUM",
"status": "ok_later"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "LIOUVILLE_ONE",
"status": "ok_later"
},
{
"lemma": "MAX_VAL",
... | {
"lo": -10,
"mid": 0,
"hi": 10
} | ||
87fdb1 | alg_poly3_min_v1_1419126231_1024 | Let $S$ be the set of pairs $(a_1, b_1)$ of positive integers with $1 \le a_1, b_1 \le 25$ satisfying $-12a_1b_1 + 20b_1^2 + 41a_1^2 \le 15193$. Let $A = |S|$. Find the remainder when $$\min\left\{ -9a^3 -27a^2b -81ab^2 \mid 1 \le a \le A,\ 1 \le b \le 436 \right\}$$ is divided by $99905$. | 1,768 | graphs = [
Graph(
let={
"_n": Const(2),
"result": Mod(value=MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("a"), Var("b")]), condition=And(Geq(Var("a"), Const(1)), Leq(Var("a"), CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("a1"), Var("b1")]), condition=An... | ALG | null | COMPUTE | sympy | QF_PSD_COUNT_LEQ | [
"QF_PSD_COUNT_LEQ"
] | 009d0f | alg_poly3_min_v1 | null | 4 | 0 | [
"QF_PSD_COUNT_LEQ"
] | 1 | 0.223 | 2026-02-25T10:32:09.655688Z | {
"verified": true,
"answer": 1768,
"timestamp": "2026-02-25T10:32:09.878255Z"
} | 99541c | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 247,
"completion_tokens": 7109
},
"timestamp": "2026-03-30T11:07:47.277Z",
"answer": 1768
},
{
"i... | 1 | [
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "QF_PSD_COUNT_LEQ",
"status": "ok"
}
] | {
"lo": -5.37,
"mid": 0.23,
"hi": 5.22
} | ||
1f1709 | nt_lcm_compute_v1_865884756_296 | Let $a = 2111$. Let $b$ be the number of positive integers $j$ such that $1 \leq j \leq 1169$ and $j^5 \leq 2183094602096849$. Let $L = \mathrm{lcm}(a, b)$. Compute the remainder when $71289 - L$ is divided by 99609. | 93,755 | graphs = [
Graph(
let={
"_n": Const(99609),
"a": Const(2111),
"b": CountOverSet(set=SolutionsSet(var=Var("j"), condition=And(Geq(Var("j"), Const(1)), Leq(Var("j"), Const(1169)), Leq(Pow(Var("j"), Const(5)), Const(2183094602096849))), domain='positive_integers')),
... | NT | null | COMPUTE | sympy | C3 | [
"C3"
] | 8a214c | nt_lcm_compute_v1 | null | 2 | 0 | [
"C3"
] | 1 | 0.003 | 2026-02-08T15:18:32.525799Z | {
"verified": true,
"answer": 93755,
"timestamp": "2026-02-08T15:18:32.528793Z"
} | 222838 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 194,
"completion_tokens": 3384
},
"timestamp": "2026-02-10T06:45:49.217Z",
"answer": 93755
},
{
"... | 1 | [
{
"lemma": "C3",
"status": "ok"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
}
] | {
"lo": -7.09,
"mid": -0.49,
"hi": 6.1
} | ||
516126 | nt_num_divisors_compute_v1_1820931509_451 | Let $n = 12996$. Let $d_{\text{min}}$ be the smallest divisor of $14742701$ that is at least $2$. Compute the value of $\tau(n)^2 + d_{\text{min}} \cdot \tau(n) + 24$, where $\tau(n)$ denotes the number of positive divisors of $n$. | 1,374 | graphs = [
Graph(
let={
"n": Const(12996),
"result": NumDivisors(n=Ref("n")),
"Q": Sum(Pow(Ref("result"), Const(2)), Mul(MinOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Const(2)), Divides(divisor=Var("d"), dividend=Const(14742701))))), Ref("result"))... | NT | null | COMPUTE | sympy | MIN_PRIME_FACTOR | [
"MIN_PRIME_FACTOR"
] | 76121b | nt_num_divisors_compute_v1 | quadratic_mod | 3 | 0 | [
"MIN_PRIME_FACTOR"
] | 1 | 0.001 | 2026-02-08T11:35:59.141008Z | {
"verified": true,
"answer": 1374,
"timestamp": "2026-02-08T11:35:59.142102Z"
} | d91faf | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 121,
"completion_tokens": 1055
},
"timestamp": "2026-02-14T17:53:05.010Z",
"answer": 1374
},
{... | 1 | [
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "MIN_PRIME_FACTOR",
"status": "ok"
},
{
"lemma": "MOD_MUL",
"status": "n... | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
1eb1bf | comb_bell_compute_v1_1520064083_4865 | Let $m$ be the minimum value of $x + y$ over all ordered pairs $(x,y)$ of positive integers such that $xy = 1936$. Let $n$ be the number of integers $n'$ in the range $1 \leq n' \leq m$ such that $n' \equiv \left\lfloor \frac{n'}{2} \right\rfloor \pmod{11}$. Compute the remainder when $44121 \cdot B_n$ is divided by $5... | 9,743 | graphs = [
Graph(
let={
"_m": Const(58411),
"_n": MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(Mul(Var("x"), Var("y")), Const(1936)))), expr=Sum(Var("x"), Var("y")))... | NT | COMB | COMPUTE | sympy | B3 | [
"B3/L3C"
] | 345f3b | comb_bell_compute_v1 | null | 7 | 0 | [
"B3",
"L3C"
] | 2 | 0.002 | 2026-02-08T06:27:57.036271Z | {
"verified": true,
"answer": 9743,
"timestamp": "2026-02-08T06:27:57.038026Z"
} | 672e60 | 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": 2286
},
"timestamp": "2026-02-13T00:25:04.201Z",
"answer": 9743
},
{... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "L3C",
"status": "ok_later"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
... | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
a5c0d8 | diophantine_product_count_v1_2051736721_799 | Let $n = 44$ and $k = 60$. Define $\text{upper}$ to be the sum of all positive integers $n$ such that $n \leq 44$ and $n \equiv 0 \pmod{44}$. Let $S$ be the set of all positive integers $x$ such that $x \leq \text{upper}$, $x$ divides $60$, and $\frac{60}{x} \leq \text{upper}$. Let $\text{result}$ be the number of elem... | 13,446 | graphs = [
Graph(
let={
"_n": Const(44),
"k": Const(60),
"upper": SumOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Ref("_n")), Eq(Mod(value=Var("n"), modulus=Const(44)), Const(0))))),
"result": CountOverSet(set=Sol... | NT | null | COUNT | sympy | SUM_DIVISIBLE | [
"SUM_DIVISIBLE"
] | 02dbe3 | diophantine_product_count_v1 | null | 4 | 0 | [
"SUM_DIVISIBLE"
] | 1 | 0.029 | 2026-02-08T15:41:19.544784Z | {
"verified": true,
"answer": 13446,
"timestamp": "2026-02-08T15:41:19.573608Z"
} | b76c38 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 172,
"completion_tokens": 979
},
"timestamp": "2026-02-16T11:13:08.082Z",
"answer": 13446
},
{... | 1 | [
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "SUM_DIVISIBLE",
"status": "ok"
},
{
"lemma": "V7",
"status": ... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
cabff6 | diophantine_fbi2_min_v1_124444284_4343 | Let $S$ be the set of all ordered pairs of positive integers $(x, y)$ such that $xy = 81$. Let $s_{\min}$ be the minimum value of $x + y$ over all such pairs. Let $T$ be the set of all ordered pairs of positive integers $(x, y)$ such that $x + y = s_{\min}$. Let $k$ be the maximum value of $xy$ over all pairs in $T$. D... | 3 | graphs = [
Graph(
let={
"_n": Const(2),
"k": MaxOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(Sum(Var("x"), Var("y")), MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tup... | NT | null | EXTREMUM | sympy | B3 | [
"B3/B1"
] | 7f76f7 | diophantine_fbi2_min_v1 | null | 5 | 0 | [
"B1",
"B3"
] | 2 | 0.013 | 2026-02-08T05:56:27.870703Z | {
"verified": true,
"answer": 3,
"timestamp": "2026-02-08T05:56:27.883571Z"
} | 770d61 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 186,
"completion_tokens": 918
},
"timestamp": "2026-02-12T16:40:27.826Z",
"answer": 3
},
{
... | 1 | [
{
"lemma": "B1",
"status": "ok_later"
},
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
... | {
"lo": -5.55,
"mid": -3.01,
"hi": 0.32
} | ||
18e1e3 | algebra_quadratic_discriminant_v1_1218484723_2025 | Let $M$ be the number of ordered pairs $(a_1, b_1)$ of positive integers with $1 \leq a_1, b_1 \leq 30$ such that $257a_1^4 - 1028a_1^3b_1 + 1542a_1^2b_1^2 - 1028a_1b_1^3 + 257b_1^4 = 160625$. Let $b$ be the minimum value of $M b_2^2 - 20a_2 b_2 + 4a_2^2$ over all ordered pairs $(a_2, b_2)$ with $1 \leq a_2, b_2 \leq 5... | 88,242 | graphs = [
Graph(
let={
"_m": Const(3),
"_n": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("a1"), Var("b1")]), condition=And(Geq(Var("a1"), Const(1)), Leq(Var("a1"), Const(30)), Geq(Var("b1"), Const(1)), Leq(Var("b1"), Const(30)), Eq(Sum(Mul(Const(-1028), Pow(Var("a1"), Cons... | ALG | null | COMPUTE | sympy | POLY4_COUNT | [
"POLY4_COUNT/QF_PSD_MIN"
] | dce3a4 | algebra_quadratic_discriminant_v1 | null | 5 | 0 | [
"POLY4_COUNT",
"QF_PSD_MIN"
] | 2 | 0.005 | 2026-02-25T03:43:42.175794Z | {
"verified": true,
"answer": 88242,
"timestamp": "2026-02-25T03:43:42.181284Z"
} | bd56ac | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 317,
"completion_tokens": 3069
},
"timestamp": "2026-03-29T02:35:07.150Z",
"answer": 0
},
{
"i... | 1 | [
{
"lemma": "POLY4_COUNT",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "QF_PSD_MIN",
"status": "ok_later"
}
] | {
"lo": 3.14,
"mid": 5.37,
"hi": 7.61
} | ||
cab696 | geo_count_lattice_triangle_v1_1978505735_8432 | Let $A$ be the set of all integers $t$ such that $7 \leq t \leq 123$ and there exist positive integers $a$ and $b$ with $1 \leq a \leq 27$, $1 \leq b \leq 5$, and $t = 4a + 3b$. Let $b_0$ be the number of elements in $A$. Consider the triangle with vertices at $(0,0)$, $(100,21)$, and $(7,111)$. The area of this triang... | 5,475 | graphs = [
Graph(
let={
"_m": Const(7),
"_n": Const(111),
"area_2x": Abs(arg=Sum(Mul(Const(value=100), Ref(name='_n')), Mul(Const(value=7), Sub(left=Const(value=0), right=Const(value=21))))),
"boundary": Sum(GCD(a=Abs(arg=Const(value=100)), b=Abs(arg=Const(val... | NT | null | COUNT | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | geo_count_lattice_triangle_v1 | null | 6 | 0 | [
"LIN_FORM"
] | 1 | 0.016 | 2026-02-08T20:49:42.998154Z | {
"verified": true,
"answer": 5475,
"timestamp": "2026-02-08T20:49:43.014134Z"
} | 6fe248 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 282,
"completion_tokens": 3254
},
"timestamp": "2026-02-19T01:14:14.101Z",
"answer": 5475
},
{... | 1 | [
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "V1",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
06ac8e | antilemma_k3_v1_1918700295_1137 | Let $ n = 83868 $. Compute the sum of $ \phi(d) $ over all positive divisors $ d $ of $ n $. | 83,868 | graphs = [
Graph(
let={
"x": SumOverDivisors(n=Const(value=83868), 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 | 2026-02-08T05:36:27.057809Z | {
"verified": true,
"answer": 83868,
"timestamp": "2026-02-08T05:36:27.058168Z"
} | 5630ae | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 76,
"completion_tokens": 951
},
"timestamp": "2026-02-12T11:01:09.730Z",
"answer": 83868
},
{
... | 1 | [
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "K3",
"status": "ok"
},
{
"lemma": "LTE_DIFF_P2",
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{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
}
] | {
"lo": -5.55,
"mid": -3.01,
"hi": 0.32
} | ||
b9f2d9_l | modular_product_range_v1_50713871_17 | Let $m = 10181$ and $n = 65536$. Let $S$ be the set of all positive integers $t$ such that there exist integers $a$ and $b$ satisfying $1 \le a \le 4$, $1 \le b \le 3$, $5 \le t \le 18$, and $t = 3a + 2b$. Let $P$ be the product $\prod_{i = |S|}^{T} i$, where $T$ is the minimum value of $x + y$ over all ordered pairs $... | 1 | NT | ALG | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM",
"B3"
] | 688dbe | modular_product_range_v1 | null | 6 | 0 | [
"B3",
"LIN_FORM"
] | 2 | 0.004 | 2026-02-08T02:43:12.890185Z | {
"verified": false,
"answer": 938,
"timestamp": "2026-02-08T02:43:12.894101Z"
} | bbe3df | b9f2d9 | legacy_text | CC BY 4.0 | [
{
"id": 1,
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"score": 0,
"correct": {
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"usage": {
"prompt_tokens": 261,
"completion_tokens": 32768
},
"timestamp": "2026-02-23T15:48:04.581Z",
"answer": null
},
{
... | 0 | [
{
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},
{
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{
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{
"lemma": "MOD_SUB",
"status": "no... | {
"lo": 5.02,
"mid": 7.3,
"hi": 10
} | |
355721 | modular_sum_quadratic_residues_v1_153355830_1100 | Let $n = 4$. Let $p$ be the smallest prime divisor of $3234356647$. Define $\text{result} = \frac{p(p-1)}{n}$. Let $Q$ be the remainder when $39227 \cdot \text{result}$ is divided by $61258$. Compute $Q$. | 48,204 | graphs = [
Graph(
let={
"_n": Const(4),
"p": MinOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Const(2)), Divides(divisor=Var("d"), dividend=Const(3234356647))))),
"result": Div(Mul(Ref("p"), Sub(Ref("p"), Const(1))), Ref("_n")),
"_c": Cons... | NT | null | SUM | sympy | MIN_PRIME_FACTOR | [
"MIN_PRIME_FACTOR"
] | bc3776 | modular_sum_quadratic_residues_v1 | null | 3 | 0 | [
"MIN_PRIME_FACTOR"
] | 1 | 0.001 | 2026-02-08T04:23:59.367145Z | {
"verified": true,
"answer": 48204,
"timestamp": "2026-02-08T04:23:59.368611Z"
} | 3bbbfc | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 115,
"completion_tokens": 2355
},
"timestamp": "2026-02-12T20:26:24.251Z",
"answer": 48204
},
... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "MIN_PRIME_FACTOR",
"status": "ok"
},
{
"lemma": "V8",
"status": "no"
}
] | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
7f4fad | nt_count_gcd_equals_v1_397696148_1340 | Let $n$ be the number of integers $t$ such that $12 \leq t \leq 269$ and there exist positive integers $a \leq 60$ and $b \leq 17$ satisfying $t = 3a + 5b + 4$. Let $S$ be the set of all nonnegative integers $j \leq n$ for which
$$
\binom{\min\{x+y \mid x, y \text{ are positive integers with } xy = 15625\}}{j} \equiv 1... | 83,248 | 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=60)), Geq(left=Var(name='b'), right=Const(value... | NT | null | COUNT | sympy | LIN_FORM | [
"LIN_FORM/V8",
"B3/V8"
] | 3f10a4 | nt_count_gcd_equals_v1 | null | 7 | 0 | [
"B3",
"LIN_FORM",
"V8"
] | 3 | 1.126 | 2026-02-08T12:30:58.137057Z | {
"verified": true,
"answer": 83248,
"timestamp": "2026-02-08T12:30:59.262745Z"
} | 6eb3b4 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 241,
"completion_tokens": 4630
},
"timestamp": "2026-02-15T01:37:13.034Z",
"answer": 83248
},
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},... | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
34ac5a | diophantine_fbi2_count_v1_1915831931_1028 | Let $k$ be the number of ordered pairs $(a, b)$ such that $1 \leq a \leq 35$ and $1 \leq b \leq 36$. Determine the number of integers $d$ such that $2 \leq d \leq 181$, $d$ divides $k$, and the quotient $k/d$ satisfies $6 \leq k/d \leq 185$. Compute the remainder when $92089$ times this count is divided by $50250$. | 49,386 | graphs = [
Graph(
let={
"_n": Const(185),
"k": CountOverSet(set=CartesianProduct(left=IntegerRange(start=Const(1), end=Const(35)), right=IntegerRange(start=Const(1), end=Const(36)))),
"result": CountOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Const(... | NT | null | COUNT | sympy | COUNT_CARTESIAN | [
"COUNT_CARTESIAN"
] | 409d7d | diophantine_fbi2_count_v1 | null | 3 | 0 | [
"COUNT_CARTESIAN"
] | 1 | 0.035 | 2026-02-08T15:50:48.075208Z | {
"verified": true,
"answer": 49386,
"timestamp": "2026-02-08T15:50:48.110325Z"
} | 717f07 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 149,
"completion_tokens": 1546
},
"timestamp": "2026-02-16T14:29:43.988Z",
"answer": 49386
},
... | 1 | [
{
"lemma": "COUNT_CARTESIAN",
"status": "ok"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
d5d511 | comb_count_permutations_fixed_v1_1520064083_8217 | Let $n$ be the sum of $\phi(d)$ over all positive divisors $d$ of $7$, where $\phi$ denotes Euler's totient function. Compute the value of
$$
\binom{n}{4} \cdot !(n - 4),
$$where $!k$ denotes the number of derangements of $k$ elements. | 70 | graphs = [
Graph(
let={
"_n": Const(7),
"n": SumOverDivisors(n=Ref(name='_n'), var='d', expr=EulerPhi(n=Var(name='d'))),
"k": Const(4),
"result": Mul(Binom(n=Ref("n"), k=Ref("k")), Subfactorial(arg=Sub(left=Ref(name='n'), right=Ref(name='k')))),
},
... | NT | COMB | COUNT | sympy | MIN_PRIME_FACTOR | [
"K3"
] | 54c41e | comb_count_permutations_fixed_v1 | null | 4 | 0 | [
"K3",
"MIN_PRIME_FACTOR"
] | 2 | 0.01 | 2026-02-08T10:04:52.204283Z | {
"verified": true,
"answer": 70,
"timestamp": "2026-02-08T10:04:52.214460Z"
} | 4e06c0 | 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": 570
},
"timestamp": "2026-02-14T06:19:10.485Z",
"answer": 70
},
{
... | 1 | [
{
"lemma": "K3",
"status": "ok"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "V1",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
}
] | {
"lo": -9.12,
"mid": -6.02,
"hi": -3.62
} | ||
f55fcd | nt_gcd_compute_v1_397696148_711 | Let $a = 610821$ and $b = 1153773$. Define $\text{result} = \gcd(a, b)$. Let $P$ be the set of all prime numbers $n$ such that $2 \leq n \leq 11$, and let $m$ be the maximum element of $P$. Compute the Bell number of $|\text{result}| \mod m$, and let $Q$ be the remainder when this Bell number is divided by $88374$. Det... | 27,601 | graphs = [
Graph(
let={
"_n": Const(2),
"a": Const(610821),
"b": Const(1153773),
"result": GCD(a=Ref("a"), b=Ref("b")),
"Q": Mod(value=Bell(Mod(value=Abs(arg=Ref(name='result')), modulus=MaxOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(V... | NT | COMB | COMPUTE | sympy | COPRIME_PAIRS | [
"MAX_PRIME_BELOW"
] | 88ea9c | nt_gcd_compute_v1 | bell_mod | 4 | 0 | [
"COPRIME_PAIRS",
"MAX_PRIME_BELOW"
] | 2 | 0.027 | 2026-02-08T11:42:53.067445Z | {
"verified": true,
"answer": 27601,
"timestamp": "2026-02-08T11:42:53.094594Z"
} | 9cbb7a | 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": 687
},
"timestamp": "2026-02-14T17:23:55.894Z",
"answer": 27601
},
{... | 1 | [
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "V1",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
}
] | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
742862 | sequence_fibonacci_compute_v1_1440796553_686 | Let $S$ be the set of all integers $t$ such that $7 \le t \le 30$ and there exist positive integers $a$ and $b$ with $1 \le a \le 10$, $1 \le b \le 2$, and $t = 2a + 5b$. Let $n$ be the number of elements in $S$. Compute the $n$-th Fibonacci number, where the Fibonacci sequence is defined by $F_1 = 1$, $F_2 = 1$, and $... | 6,765 | 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=10)), Geq(left=Var(name='b'), right=Const(value=... | NT | null | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | sequence_fibonacci_compute_v1 | null | 4 | 0 | [
"LIN_FORM"
] | 1 | 0.001 | 2026-02-08T11:55:18.585461Z | {
"verified": true,
"answer": 6765,
"timestamp": "2026-02-08T11:55:18.586564Z"
} | 562fb0 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 188,
"completion_tokens": 1111
},
"timestamp": "2026-02-14T20:43:56.257Z",
"answer": 6765
},
{... | 1 | [
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
}
] | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
6f7984 | nt_gcd_compute_v1_1431428450_78 | Let $m=63877$. Let $n$ be the number of positive integers $p$ for which there exists a positive integer $q$ such that
\begin{itemize}
\item $pq=72$,
\item $\gcd(p,q)=1$, and
\item $p<q$.
\end{itemize}
Let $a=490296$ and $b=919305$, and let $d=\gcd(a,b)$.
For each integer $k$ with $1\le k\le 5$, let $\varphi(k)$ denot... | 65,383 | graphs = [
Graph(
let={
"_m": Const(63877),
"_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=72)), Eq(left=GCD(a=Var(name='p'), b=Var(nam... | NT | null | COMPUTE | sympy | MAX_PRIME_BELOW | [
"MAX_PRIME_BELOW/K2",
"COPRIME_PAIRS/K2"
] | 3570c9 | nt_gcd_compute_v1 | mod_exp | 6 | 0 | [
"COPRIME_PAIRS",
"K2",
"MAX_PRIME_BELOW"
] | 3 | 0.004 | 2026-02-08T13:10:49.955177Z | {
"verified": true,
"answer": 65383,
"timestamp": "2026-02-08T13:10:49.959479Z"
} | 27a7ae | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 312,
"completion_tokens": 2399
},
"timestamp": "2026-02-15T11:06:08.290Z",
"answer": 65383
},
... | 1 | [
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "K2",
"status": "ok_later"
},
{
"lemma": "K5",
"status": "no"
},
... | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
b51efe | geo_visible_lattice_v1_1431428450_284 | Let $n = 171$. Define $\text{result}$ to be the number of lattice points $(x, y)$ with $1 \le x, y \le n$ such that $\gcd(x, y) = 1$. Compute the smallest positive integer $k$ such that the $k$th Fibonacci number is divisible by $\text{result} + 2$. | 2,900 | graphs = [
Graph(
let={
"n": Const(171),
"result": VisibleLatticePoints(n=Ref(name='n')),
"Q": FibonacciEntryPoint(modulus=Sum(Abs(arg=Ref(name='result')), Const(value=2))),
},
goal=Ref("Q"),
)
] | GEOM | NT | COUNT | sympy | [] | geo_visible_lattice_v1 | null | 3 | 0 | null | null | 0.776 | 2026-02-08T13:22:40.117902Z | {
"verified": true,
"answer": 2900,
"timestamp": "2026-02-08T13:22:40.893984Z"
} | 332733 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 189,
"completion_tokens": 8550
},
"timestamp": "2026-02-24T17:55:25.476Z",
"answer": 504
},
{
... | 1 | [] | {
"lo": 3.25,
"mid": 5.68,
"hi": 8.81
} | ||||
11d962 | nt_count_with_divisor_count_v1_458359167_4423 | Let $r$ be the number of positive integers $n$ such that $1 \leq n \leq 65536$ and $n$ has exactly 15 positive divisors. Let $c$ be the number of nonnegative integers $j$ such that $0 \leq j \leq 30175$ and $\binom{30175}{j}$ is odd. Compute $r^2 + 49r + c$. | 6,802 | graphs = [
Graph(
let={
"_n": Const(2),
"upper": Const(65536),
"div_count": Const(15),
"result": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Ref("upper")), Eq(NumDivisors(n=Var("n")), Ref("div_count"))))),
... | NT | null | COUNT | sympy | V8 | [
"V8"
] | 4109e4 | nt_count_with_divisor_count_v1 | quadratic_mod | 6 | 0 | [
"V8"
] | 1 | 3.459 | 2026-02-08T11:45:56.623781Z | {
"verified": true,
"answer": 6802,
"timestamp": "2026-02-08T11:46:00.083010Z"
} | f0878e | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 135,
"completion_tokens": 2402
},
"timestamp": "2026-02-14T18:40:02.074Z",
"answer": 6802
},
{... | 1 | [
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
},
{
"lemma": "V8",
"status": "ok"
},
{
"lemma": "V8_SUM",
"status": "no"
}
] | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
c78ffa | diophantine_fbi2_min_v1_124444284_99 | Let $n = 6$, $k = 26$, and $u = 36$. Define $d$ to be an integer such that $d \geq n$, $d \leq u$, $d$ divides $k$, and $\frac{k}{d} \geq 2$. Let $A$ be the smallest such $d$.
Let $B$ be the smallest integer $d' \geq 2$ that divides $48841$.
Compute the value of $3^{|A|} + B$ modulo $99991$. If the result is nonnegat... | 94,471 | graphs = [
Graph(
let={
"_n": Const(6),
"k": Const(26),
"upper": Const(36),
"result": MinOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Ref("_n")), Leq(Var("d"), Ref("upper")), Divides(divisor=Var("d"), dividend=Ref("k")), Geq(Div(Ref("k"),... | NT | null | EXTREMUM | sympy | MIN_PRIME_FACTOR | [
"MIN_PRIME_FACTOR"
] | 3a66af | diophantine_fbi2_min_v1 | two_stage_modexp | 4 | 0 | [
"MIN_PRIME_FACTOR"
] | 1 | 0.008 | 2026-02-08T02:58:55.150245Z | {
"verified": true,
"answer": 94471,
"timestamp": "2026-02-08T02:58:55.158103Z"
} | 23643e | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 250,
"completion_tokens": 1193
},
"timestamp": "2026-02-09T13:41:56.442Z",
"answer": 94471
},
{
"... | 1 | [
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "MIN_PRIME_FACTOR",
"status": "ok"
},
{
"lemma": "V3",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
... | {
"lo": -3.47,
"mid": 0.81,
"hi": 4.81
} | ||
60dde9 | comb_count_surjections_v1_1470522791_1202 | Let $n$ be the number of ordered pairs $(x_1, x_2)$ of positive odd integers such that $x_1 + x_2 = 14$. Let $S(n, k)$ denote the Stirling number of the second kind, and let $k = 3$. Define $T = k! \cdot S(n, k)$. Compute the remainder when $35117 \cdot T$ is divided by $97308$. | 73,794 | graphs = [
Graph(
let={
"n": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x1"), Var("x2")]), condition=And(IsPositive(arg=Var(name='x1')), IsPositive(arg=Var(name='x2')), IsOdd(arg=Var(name='x1')), IsOdd(arg=Var(name='x2')), Eq(Sum(Var("x1"), Var("x2")), Const(14))))),
"k":... | COMB | null | COUNT | sympy | COMB1 | [
"COMB1"
] | 567f58 | comb_count_surjections_v1 | null | 4 | 0 | [
"COMB1"
] | 1 | 0.003 | 2026-02-08T13:30:44.879233Z | {
"verified": true,
"answer": 73794,
"timestamp": "2026-02-08T13:30:44.882430Z"
} | ff1bc8 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 206,
"completion_tokens": 2175
},
"timestamp": "2026-02-24T18:31:33.954Z",
"answer": 73794
},
{
"... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COMB1",
"status": "ok"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
}
] | {
"lo": -2.35,
"mid": 1.22,
"hi": 4.84
} | ||
4519e6 | nt_sum_divisors_mod_v1_2051736721_88 | Let $k$ be a positive integer such that $1 \leq k \leq 1118880$ and $k$ is divisible by the minimum value of $x + y$ over all positive integers $x, y$ such that $xy = 49284$. Let $n$ be the number of such integers $k$. Let $\sigma$ be the sum of the positive divisors of $n$. Let $M = 11311$, and let $r$ be the remainde... | 150 | graphs = [
Graph(
let={
"_n": Const(49284),
"n": CountOverSet(set=SolutionsSet(var=Var("k"), condition=And(Geq(Var("k"), Const(1)), Leq(Var("k"), Const(1118880)), Divides(divisor=MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPosi... | NT | null | COMPUTE | sympy | B3 | [
"B3/C2"
] | dcbe93 | nt_sum_divisors_mod_v1 | null | 6 | 0 | [
"B3",
"C2"
] | 2 | 0.006 | 2026-02-08T15:11:55.194470Z | {
"verified": true,
"answer": 150,
"timestamp": "2026-02-08T15:11:55.200083Z"
} | 0ebda6 | 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": 3343
},
"timestamp": "2026-02-16T01:11:38.391Z",
"answer": 150
},
{
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "C2",
"status": "ok_later"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
846397 | nt_count_divisors_in_range_v1_784195855_5707 | Let $T$ be the set of all integers $t$ such that $7 \leq t \leq 47$ and there exist positive integers $a$, $b$ with $1 \leq a \leq 8$, $1 \leq b \leq 5$, satisfying $t = 4a + 3b$. Let $d_0$ be the smallest divisor of $|T|$ that is at least $2$. Let $m = 5$. Define $a = \sum_{k=1}^{m} \phi(k) \left\lfloor \frac{d_0}{k} ... | 172 | graphs = [
Graph(
let={
"_m": Const(5),
"_n": MinOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Const(2)), Divides(divisor=Var("d"), dividend=CountOverSet(set=SolutionsSet(var=Var("t"), condition=Exists(var=Var(name='a'), condition=Exists(var=Var(name='b'), condit... | NT | null | COUNT | sympy | B3 | [
"LIN_FORM/MIN_PRIME_FACTOR/K2"
] | db5ec0 | nt_count_divisors_in_range_v1 | null | 7 | 0 | [
"B3",
"K2",
"LIN_FORM",
"MIN_PRIME_FACTOR"
] | 4 | 1.166 | 2026-02-08T08:04:06.990234Z | {
"verified": true,
"answer": 172,
"timestamp": "2026-02-08T08:04:08.156118Z"
} | d0e878 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 237,
"completion_tokens": 3286
},
"timestamp": "2026-02-13T14:26:52.303Z",
"answer": 172
},
{
... | 1 | [
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "K2",
"status": "ok_later"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "MIN_PRIME_FACTOR",
"status": "ok_later"
},
{
"lemma": "MOD_ADD",
"status": "no"
... | {
"lo": -3.51,
"mid": 1.33,
"hi": 6.56
} | ||
5d237c | modular_sum_quadratic_residues_v1_601307018_5273 | Let $p$ be the largest prime number $n$ such that $2 \leq n \leq 281$. Let $R = \frac{p(p-1)}{4}$. Find the remainder when $46672 \cdot R$ is divided by $64767$. | 30,782 | graphs = [
Graph(
let={
"_n": Const(281),
"p": MaxOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(2)), Leq(Var("n"), Ref("_n")), IsPrime(Var("n"))))),
"result": Div(Mul(Ref("p"), Sub(Ref("p"), Const(1))), Const(4)),
"_c": Const(46672),... | NT | null | SUM | sympy | MAX_PRIME_BELOW | [
"MAX_PRIME_BELOW"
] | dc3ad3 | modular_sum_quadratic_residues_v1 | null | 3 | 0 | [
"MAX_PRIME_BELOW"
] | 1 | 0.003 | 2026-03-10T05:56:41.020172Z | {
"verified": true,
"answer": 30782,
"timestamp": "2026-03-10T05:56:41.023172Z"
} | da0ac9 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 171,
"completion_tokens": 1822
},
"timestamp": "2026-04-19T01:41:05.824Z",
"answer": 30782
},
{
... | 1 | [
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok"
},
{
"lemma": "V8_SUM",
"status": "no"
}
] | {
"lo": -3.31,
"mid": 1.32,
"hi": 5.87
} | ||
b54f4e | nt_count_coprime_v1_1915831931_1870 | Let $n$ be a positive integer. Define $A$ as the number of integers $n$ with $1 \leq n \leq 10731$ such that $\gcd(n, 26) = 1$. Let $B$ be the number of integers $n_1$ with $1 \leq n_1 \leq 131$ such that $n_1 \equiv \left\lfloor \frac{n_1}{2} \right\rfloor \pmod{3}$. Compute the remainder when $B - A$ is divided by $6... | 55,178 | graphs = [
Graph(
let={
"upper": Const(10731),
"k": Const(26),
"result": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Ref("upper")), Eq(GCD(a=Var("n"), b=Ref("k")), Const(1))))),
"_c": CountOverSet(set=Soluti... | NT | null | COUNT | sympy | L3C | [
"L3C"
] | fba717 | nt_count_coprime_v1 | negation_mod | 4 | 0 | [
"L3C"
] | 1 | 12.979 | 2026-02-08T16:29:26.305574Z | {
"verified": true,
"answer": 55178,
"timestamp": "2026-02-08T16:29:39.284224Z"
} | 481040 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 166,
"completion_tokens": 1457
},
"timestamp": "2026-02-17T04:48:18.126Z",
"answer": 55178
},
... | 1 | [
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "L3C",
"status": "ok"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
268885 | modular_sum_quadratic_residues_v1_1978505735_5711 | Let $m = 7744$ and $n = 2$. Consider the set of all ordered pairs $(x, y)$ of positive integers such that $xy = m$. For each such pair, compute the sum $x + y$, and let $s_{\min}$ be the minimum of these sums. Let $p$ be the largest prime number such that $n \leq p \leq s_{\min}$. Compute $\frac{p(p-1)}{4}$. | 7,439 | graphs = [
Graph(
let={
"_m": Const(7744),
"_n": Const(2),
"p": MaxOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Ref("_n")), Leq(Var("n"), MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(ar... | NT | null | SUM | sympy | B3 | [
"B3/MAX_PRIME_BELOW"
] | f253c0 | modular_sum_quadratic_residues_v1 | null | 7 | 0 | [
"B3",
"MAX_PRIME_BELOW"
] | 2 | 0.18 | 2026-02-08T19:11:37.030311Z | {
"verified": true,
"answer": 7439,
"timestamp": "2026-02-08T19:11:37.210198Z"
} | eba651 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 143,
"completion_tokens": 3063
},
"timestamp": "2026-02-18T21:33:14.255Z",
"answer": 7439
},
{... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok_later"
},
{
"lemma": "V1",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
},
{
"lemma":... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
9ab671 | antilemma_k3_v1_2051736721_1658 | Let $n = 44410$. Compute the remainder when $44121$ times the sum $\sum_{d \mid n} \phi(d)$ is divided by $68029$, where $\phi$ denotes Euler's totient function. | 42,352 | graphs = [
Graph(
let={
"_n": Const(44410),
"x": SumOverDivisors(n=Ref(name='_n'), var='d', expr=EulerPhi(n=Var(name='d'))),
"Q": Mod(value=Mul(Const(44121), Ref("x")), modulus=Const(68029)),
},
goal=Ref("Q"),
)
] | NT | COMB | COMPUTE | sympy | K3 | [
"K3"
] | 54c41e | antilemma_k3_v1 | null | 2 | 0 | [
"K3"
] | 1 | 0.001 | 2026-02-08T16:08:54.037984Z | {
"verified": true,
"answer": 42352,
"timestamp": "2026-02-08T16:08:54.038642Z"
} | 7f6571 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 95,
"completion_tokens": 1475
},
"timestamp": "2026-02-16T21:20:32.516Z",
"answer": 42352
},
{... | 1 | [
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "K3",
"status": "ok"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
22f116 | modular_sum_quadratic_residues_v1_1470522791_1470 | Let $n = 423$. Define $p$ to be the largest prime number less than or equal to $n$. Compute $\frac{p(p-1)}{4}$. | 44,205 | graphs = [
Graph(
let={
"_n": Const(423),
"p": MaxOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(2)), Leq(Var("n"), Ref("_n")), IsPrime(Var("n"))))),
"result": Div(Mul(Ref("p"), Sub(Ref("p"), Const(1))), Const(4)),
},
goal=Ref("re... | NT | null | SUM | sympy | MAX_PRIME_BELOW | [
"MAX_PRIME_BELOW"
] | dc3ad3 | modular_sum_quadratic_residues_v1 | null | 3 | 0 | [
"MAX_PRIME_BELOW"
] | 1 | 0.002 | 2026-02-08T13:40:56.415662Z | {
"verified": true,
"answer": 44205,
"timestamp": "2026-02-08T13:40:56.417687Z"
} | d946d6 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 82,
"completion_tokens": 927
},
"timestamp": "2026-02-15T19:22:43.668Z",
"answer": 44205
},
{
... | 1 | [
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "VAL_SUM_EQ",
"status": "no"
... | {
"lo": -8.26,
"mid": -5.01,
"hi": -1.76
} | ||
365074 | comb_factorial_compute_v1_601307018_8860 | Let $n$ be the number of positive integers $v$ with $20 \le v \le 1280$ for which there exist integers $a, b$ such that $1 \le a \le 8$, $1 \le b \le 8$, and $20a^2 = v$. Compute $n!$. | 40,320 | graphs = [
Graph(
let={
"_n": Const(1280),
"n": CountOverSet(set=SolutionsSet(var=Var("v"), condition=And(Geq(Var("v"), Const(20)), Leq(Var("v"), Ref("_n")), Exists(var=Tuple(elements=[Var(name='a'), Var(name='b')]), condition=And(Geq(left=Var(name='a'), right=Const(value=1)), Leq(le... | COMB | null | COMPUTE | sympy | QF_PSD_DISTINCT | [
"QF_PSD_DISTINCT"
] | a8f9cb | comb_factorial_compute_v1 | null | 3 | 0 | [
"QF_PSD_DISTINCT"
] | 1 | 0.007 | 2026-03-10T09:18:40.698227Z | {
"verified": true,
"answer": 40320,
"timestamp": "2026-03-10T09:18:40.704928Z"
} | 2a1580 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 181,
"completion_tokens": 641
},
"timestamp": "2026-04-19T09:59:41.649Z",
"answer": 40320
},
{
"... | 2 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "QF_PSD_DISTINCT",
"status": "ok"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
... | {
"lo": -10,
"mid": -5.89,
"hi": -1.79
} | ||
bb3c1f | comb_count_surjections_v1_677425708_3641 | Let $n = 6$ and $k = 6$. Compute $k! \cdot S(n, k)$, where $S(n, k)$ denotes the Stirling number of the second kind, the number of ways to partition a set of $n$ elements into $k$ nonempty subsets. | 720 | graphs = [
Graph(
let={
"n": Const(6),
"k": Const(6),
"result": Mul(Factorial(Ref("k")), Stirling2(n=Ref(name='n'), k=Ref(name='k'))),
},
goal=Ref("result"),
)
] | COMB | null | COUNT | sympy | COUNT_SUM_EQUALS | [
"COUNT_SUM_EQUALS",
"COMB1"
] | 938829 | comb_count_surjections_v1 | null | 2 | 0 | [
"COMB1",
"COUNT_SUM_EQUALS"
] | 2 | 0.019 | 2026-02-08T05:52:00.619351Z | {
"verified": true,
"answer": 720,
"timestamp": "2026-02-08T05:52:00.638836Z"
} | 6e0991 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 175,
"completion_tokens": 277
},
"timestamp": "2026-02-24T04:45:55.673Z",
"answer": 720
},
{
"id"... | 2 | [
{
"lemma": "COMB1",
"status": "ok"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "ok"
},
{
"lemma": "V7... | {
"lo": -9.23,
"mid": -6.18,
"hi": -4.06
} | ||
8e8455 | algebra_quadratic_discriminant_v1_124444284_9962 | Let $a = -8$, $b = 9$, and $c = 7$. Define the discriminant $D = b^2 - 4ac$. Compute $2$ if $D > 0$, $1$ if $D = 0$, and $0$ if $D < 0$. | 2 | graphs = [
Graph(
let={
"a": Const(-8),
"b": Const(9),
"c": Const(7),
"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"), Const... | NT | null | COMPUTE | sympy | K2 | [
"COPRIME_PAIRS"
] | 2bb3aa | algebra_quadratic_discriminant_v1 | null | 3 | 0 | [
"COPRIME_PAIRS",
"K2"
] | 2 | 0.019 | 2026-02-08T12:44:36.916493Z | {
"verified": true,
"answer": 2,
"timestamp": "2026-02-08T12:44:36.935647Z"
} | 7ae783 | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 1,
"correct": {
"strict": false,
"boxed": false,
"relaxed": true
},
"usage": {
"prompt_tokens": 123,
"completion_tokens": 164
},
"timestamp": "2026-02-16T04:03:29.428Z",
"answer": 0
},
{
"id": 11,
... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "V1",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
}
] | {
"lo": -9.12,
"mid": -6.02,
"hi": -3.62
} | ||
95ba35 | nt_count_digit_sum_v1_124444284_4249 | Let $n = 2$. Let $\text{result}$ be the number of positive integers $n$ such that $1 \leq n \leq 57291$ and the sum of the decimal digits of $n$ is $25$. Let $d_{\text{min}}$ be the smallest integer $d \geq n$ such that $d$ divides $41327$. Compute the Bell number $B_k$, where $k = \text{result} \bmod d_{\text{min}}$. | 203 | graphs = [
Graph(
let={
"_n": Const(2),
"upper": Const(57291),
"target_sum": Const(25),
"result": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Ref("upper")), Eq(DigitSum(Var("n")), Ref("target_sum"))))),
... | NT | COMB | COUNT | sympy | MIN_PRIME_FACTOR | [
"MIN_PRIME_FACTOR"
] | 58d7e9 | nt_count_digit_sum_v1 | bell_mod | 7 | 0 | [
"MIN_PRIME_FACTOR"
] | 1 | 2.63 | 2026-02-08T05:52:19.592637Z | {
"verified": true,
"answer": 203,
"timestamp": "2026-02-08T05:52:22.222191Z"
} | ace962 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 152,
"completion_tokens": 3210
},
"timestamp": "2026-02-12T15:35:46.267Z",
"answer": 203
},
{
... | 1 | [
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "MIN_PRIME_FACTOR",
"stat... | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
842601 | nt_count_gcd_equals_v1_124444284_5697 | Let $P$ be the set of all ordered pairs $(x, y)$ of positive integers such that $xy = 14288400$. Define $S$ as the set of all values $x + y$ where $(x, y) \in P$. Let $u$ be the minimum element of $S$. Determine the number of positive integers $n$ such that $1 \leq n \leq u$ and $\gcd(n, 105) = 5$. Let this number be $... | 60,504 | graphs = [
Graph(
let={
"_n": Const(83465),
"upper": MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(Mul(Var("x"), Var("y")), Const(14288400)))), expr=Sum(Var("x"), Var... | NT | null | COUNT | sympy | B3 | [
"B3"
] | 0cd20d | nt_count_gcd_equals_v1 | null | 5 | 0 | [
"B3"
] | 1 | 4.879 | 2026-02-08T06:46:34.714436Z | {
"verified": true,
"answer": 60504,
"timestamp": "2026-02-08T06:46:39.593673Z"
} | c7d918 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 170,
"completion_tokens": 2145
},
"timestamp": "2026-02-13T04:27:14.339Z",
"answer": 60504
},
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
}
] | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
0d8cc6 | modular_mod_compute_v1_2051736721_3775 | Let $n_0 = 2$. Let $a = 32768$. Let $S$ be the set of all integers $t$ such that there exist integers $a$ and $b$ satisfying $1 \leq a \leq 93$, $1 \leq b \leq 249$, $26 \leq t \leq 1138$, and $t = 4a + 3b + 19$. Let $m$ be the largest prime number $n$ such that $n_0 \leq n \leq |S|$. Compute the remainder when $a$ is ... | 781 | graphs = [
Graph(
let={
"_n": Const(2),
"a": Const(32768),
"m": MaxOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Ref("_n")), Leq(Var("n"), CountOverSet(set=SolutionsSet(var=Var("t"), condition=Exists(var=Var(name='a'), condition=Exists(var=Var(name='b... | NT | null | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM/MAX_PRIME_BELOW"
] | 47006e | modular_mod_compute_v1 | null | 5 | 0 | [
"LIN_FORM",
"MAX_PRIME_BELOW"
] | 2 | 0.003 | 2026-02-08T17:31:58.799778Z | {
"verified": true,
"answer": 781,
"timestamp": "2026-02-08T17:31:58.803082Z"
} | 2fe5a9 | 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": 5492
},
"timestamp": "2026-02-18T04:23:01.725Z",
"answer": 781
},
{
... | 1 | [
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "MAX_PRIME_BELOW",
"status"... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
0a3da3 | comb_catalan_compute_v1_168721529_560 | Let $n$ be the number of integers $t$ such that $7 \leq t \leq 20$ and there exist integers $a$ and $b$ with $1 \leq a \leq 5$, $1 \leq b \leq 2$, and $t = 2a + 5b$. Define $r = C_n$, where $C_n$ denotes the $n$-th Catalan number. Compute the value of $$ Q = r + \phi(|r| + \binom{11}{11}) + \tau(|r| + 1), $$ where $\ph... | 26,964 | graphs = [
Graph(
let={
"_n": Const(11),
"n": CountOverSet(set=SolutionsSet(var=Var("t"), condition=Exists(var=Var(name='a'), condition=Exists(var=Var(name='b'), condition=And(Geq(left=Var(name='a'), right=Const(value=1)), Leq(left=Var(name='a'), right=Const(value=5)), Geq(left=Var(n... | COMB | NT | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM",
"ONE_BINOM_N"
] | c318da | comb_catalan_compute_v1 | null | 5 | 0 | [
"LIN_FORM",
"ONE_BINOM_N"
] | 2 | 0.173 | 2026-02-08T13:08:31.896988Z | {
"verified": true,
"answer": 26964,
"timestamp": "2026-02-08T13:08:32.070368Z"
} | d9b98e | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 278,
"completion_tokens": 1400
},
"timestamp": "2026-02-09T06:21:00.461Z",
"answer": 26964
},
{
"... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "ONE_BINOM_N",
"status": "ok"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
},
{
... | {
"lo": -1.2,
"mid": 1.93,
"hi": 4.95
} | ||
90028c | nt_count_coprime_and_v1_717093673_1496 | Let $k_1$ be the number of positive integers $n$ such that $1 \leq n \leq 5$ and $\gcd(n, 14) = 1$. Let $k_2 = 7$. Determine the number of positive integers $n_1$ such that $1 \leq n_1 \leq 10004$, $\gcd(n_1, k_1) = 1$, and $\gcd(n_1, k_2) = 1$. | 5,717 | graphs = [
Graph(
let={
"_n": Const(14),
"upper": Const(10004),
"k1": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Const(5)), Eq(GCD(a=Var("n"), b=Ref("_n")), Const(1))))),
"k2": Const(7),
"result... | NT | null | COUNT | sympy | C4 | [
"C4"
] | 08d162 | nt_count_coprime_and_v1 | null | 4 | 0 | [
"C4"
] | 1 | 4.912 | 2026-02-08T16:06:37.749969Z | {
"verified": true,
"answer": 5717,
"timestamp": "2026-02-08T16:06:42.662293Z"
} | d8f593 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 150,
"completion_tokens": 883
},
"timestamp": "2026-02-16T21:57:53.011Z",
"answer": 5717
},
{
... | 1 | [
{
"lemma": "C4",
"status": "ok"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "V3",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
e2f4ba | alg_qf_psd_min_v1_1218484723_2531 | Let $S$ be the set of integers $t$ such that there exist integers $a, b$ with $1 \leq a \leq 1040$, $1 \leq b \leq 67$, $t = 21a + 6b$, and $27 \leq t \leq 22242$. Let $k = |S|$. Let $m = \left|\{ (a_1, b_1) : 1 \leq a_1, b_1 \leq 20,\ -189a_1^3 = -12096 \}\right|$. Find the minimum value of
\[
-44400bc + 22200c^2 + 3... | 36,260 | graphs = [
Graph(
let={
"_m": Const(2),
"_n": Const(30340),
"result": MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("a"), Var("b"), Var("c")]), condition=And(Geq(Var("a"), Const(1)), Leq(Var("a"), CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var(... | ALG | null | COMPUTE | sympy | POLY3_COUNT | [
"POLY3_COUNT",
"LIN_FORM"
] | ef20a0 | alg_qf_psd_min_v1 | null | 6 | 0 | [
"LIN_FORM",
"POLY3_COUNT"
] | 2 | 0.034 | 2026-02-25T04:16:50.015635Z | {
"verified": true,
"answer": 36260,
"timestamp": "2026-02-25T04:16:50.049544Z"
} | 4557cc | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 334,
"completion_tokens": 10854
},
"timestamp": "2026-03-29T05:15:33.201Z",
"answer": 36263
},
{
... | 1 | [
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "POLY3_COUNT",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
}
] | {
"lo": 3.81,
"mid": 6.33,
"hi": 9.49
} | ||
09d06f | comb_count_surjections_v1_1218484723_2948 | Let $k = 6$ and $n = \sum_{k_1 = \binom{18}{18} - 1}^{2} 2^{k_1}$. Compute $k! \cdot S(n, k)$, where $S(n, k)$ denotes the Stirling number of the second kind. | 15,120 | graphs = [
Graph(
let={
"_n": Const(2),
"n": Summation(var="k1", start=Sub(Binom(n=Const(18), k=Const(18)), Const(1)), end=Ref("_n"), expr=Pow(Const(2), Var("k1"))),
"k": Const(6),
"result": Mul(Factorial(Ref("k")), Stirling2(n=Ref(name='n'), k=Ref(name='k')))... | COMB | null | COUNT | sympy | SUM_GEOM | [
"SUM_GEOM",
"ZERO_BINOM_N"
] | 4e18d8 | comb_count_surjections_v1 | null | 3 | 0 | [
"SUM_GEOM",
"ZERO_BINOM_N"
] | 2 | 0.002 | 2026-02-25T04:41:25.244888Z | {
"verified": true,
"answer": 15120,
"timestamp": "2026-02-25T04:41:25.246888Z"
} | df6dd0 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 180,
"completion_tokens": 2411
},
"timestamp": "2026-03-29T07:25:25.851Z",
"answer": 15120
},
{
"... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "SUM_GEOM",
"status": "ok"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
},... | {
"lo": -2.45,
"mid": 1.37,
"hi": 5.29
} | ||
020707 | nt_count_with_divisor_count_v1_1125832087_2372 | Let $T$ be the set of all integers $t$ such that $22 \leq t \leq 12856$ and $t = 14a + 8b$ for some positive integers $a \leq 748$ and $b \leq 298$. Let $N$ be the number of positive integers $n \leq |T|$ such that $n$ has exactly $7$ positive divisors. Compute $25845 \cdot N$. | 51,690 | graphs = [
Graph(
let={
"upper": CountOverSet(set=SolutionsSet(var=Var("t"), condition=Exists(var=Var(name='a'), condition=Exists(var=Var(name='b'), condition=And(Geq(left=Var(name='a'), right=Const(value=1)), Leq(left=Var(name='a'), right=Const(value=748)), Geq(left=Var(name='b'), right=Const(v... | NT | null | COUNT | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | nt_count_with_divisor_count_v1 | null | 5 | 0 | [
"LIN_FORM"
] | 1 | 1.67 | 2026-02-08T04:34:30.447489Z | {
"verified": true,
"answer": 51690,
"timestamp": "2026-02-08T04:34:32.117986Z"
} | 07179b | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 213,
"completion_tokens": 3070
},
"timestamp": "2026-02-10T17:06:39.946Z",
"answer": 51690
},
{
... | 1 | [
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
... | {
"lo": -3.42,
"mid": 1.86,
"hi": 7.55
} | ||
5f3455 | modular_mod_compute_v1_865884756_6290 | Let $S$ be the set of all integers $t$ such that $21 \le t \le 240$ and there exist positive integers $a \in \{1,2\}$ and $b \in \{1,2,\dots,35\}$ for which $t = 15a + 6b$. Let $a = |S|$, the number of elements in $S$. Compute $a \mod 25281$. | 70 | graphs = [
Graph(
let={
"a": CountOverSet(set=SolutionsSet(var=Var("t"), condition=Exists(var=Var(name='a'), condition=Exists(var=Var(name='b'), condition=And(Geq(left=Var(name='a'), right=Const(value=1)), Leq(left=Var(name='a'), right=Const(value=2)), Geq(left=Var(name='b'), right=Const(value=1... | NT | null | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | modular_mod_compute_v1 | null | 4 | 0 | [
"LIN_FORM"
] | 1 | 0.001 | 2026-02-08T19:08:03.005781Z | {
"verified": true,
"answer": 70,
"timestamp": "2026-02-08T19:08:03.006860Z"
} | 9f72a5 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 140,
"completion_tokens": 2051
},
"timestamp": "2026-02-18T21:17:39.229Z",
"answer": 70
},
{
... | 1 | [
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "MAX_PRIME_BELOW",
"status"... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
2ca178 | antilemma_sum_equals_v1_1915831931_2705 | Let $x$ be the number of ordered pairs $(i, j)$ of positive integers such that $i + j = 49$ and $1 \leq i, j \leq 49$. Compute $4096 - x$. | 4,048 | graphs = [
Graph(
let={
"_n": Const(49),
"x": 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(49)), right=IntegerRange(start=Const(1), end=Con... | COMB | GEOM | COMPUTE | sympy | COUNT_SUM_EQUALS | [
"COUNT_SUM_EQUALS"
] | 75ab0f | antilemma_sum_equals_v1 | null | 3 | 0 | [
"COUNT_SUM_EQUALS"
] | 1 | 0.007 | 2026-02-08T17:04:03.543169Z | {
"verified": true,
"answer": 4048,
"timestamp": "2026-02-08T17:04:03.550290Z"
} | 37a2e5 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 95,
"completion_tokens": 568
},
"timestamp": "2026-02-24T22:11:47.909Z",
"answer": 4048
},
{
... | 1 | [
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "ok"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8",
... | {
"lo": -8.52,
"mid": -5.43,
"hi": -3.2
} | ||
881778 | algebra_vieta_sum_v1_784195855_451 | Let $m$ be the number of integers $t$ such that $14 \leq t \leq 64$ and $t = 8a + 6b$ for some positive integers $a, b$ with $1 \leq a \leq 5$ and $1 \leq b \leq 4$. Let $n$ be the number of ordered pairs $(i, j)$ of positive integers with $1 \leq i \leq 5$, $1 \leq j \leq 15$, and $\gcd(i, j) = 1$. Determine the sum o... | 14 | graphs = [
Graph(
let={
"_m": Const(4),
"_n": CountOverSet(set=SolutionsSet(var=Var("t"), condition=Exists(var=Var(name='a'), condition=Exists(var=Var(name='b'), condition=And(Geq(left=Var(name='a'), right=Const(value=1)), Leq(left=Var(name='a'), right=Const(value=5)), Geq(left=Var(n... | NT | null | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM/COUNT_COPRIME_GRID"
] | fe0223 | algebra_vieta_sum_v1 | null | 7 | 0 | [
"COUNT_COPRIME_GRID",
"LIN_FORM"
] | 2 | 0.017 | 2026-02-08T04:23:47.761931Z | {
"verified": true,
"answer": 14,
"timestamp": "2026-02-08T04:23:47.779386Z"
} | 3b2eac | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 280,
"completion_tokens": 2022
},
"timestamp": "2026-02-11T09:07:27.112Z",
"answer": 14
},
{
"id"... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "ok_later"
},
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "MOD_ADD",
... | {
"lo": -5.55,
"mid": -3.02,
"hi": 0.31
} | ||
8b2e60 | geo_count_lattice_rect_v1_1520064083_8544 | Let $a = 128$ and $b = 309$. Define the rectangle in the coordinate plane with vertices at $(0,0)$, $(a,0)$, $(0,b)$, and $(a,b)$. Compute the number of lattice points contained in this rectangle, including the boundary. | 39,990 | graphs = [
Graph(
let={
"a": Const(128),
"b": Const(309),
"result": LatticePointsRect(a=Ref(name='a'), b=Ref(name='b')),
},
goal=Ref("result"),
)
] | GEOM | null | COUNT | sympy | [] | geo_count_lattice_rect_v1 | null | 3 | 0 | null | null | 0.003 | 2026-02-08T10:15:02.365111Z | {
"verified": true,
"answer": 39990,
"timestamp": "2026-02-08T10:15:02.367958Z"
} | 40c6a8 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 172,
"completion_tokens": 276
},
"timestamp": "2026-02-24T11:53:30.832Z",
"answer": 39990
},
{
"i... | 1 | [] | {
"lo": -4.92,
"mid": -2.91,
"hi": -0.68
} | ||||
93cffd | nt_min_coprime_above_v1_238844314_114 | Let $a$ be the smallest integer $n$ such that $54289 < n \leq 54303$ and $\gcd(n, 4) = 1$. Let $b$ be the largest positive divisor of $14810932$ that does not exceed $3844$. Compute the remainder when $b - a$ is divided by $88008$. | 37,561 | graphs = [
Graph(
let={
"start": Const(54289),
"upper": Const(54303),
"modulus": Const(4),
"result": MinOverSet(set=SolutionsSet(var=Var("n"), condition=And(Gt(Var("n"), Ref("start")), Leq(Var("n"), Ref("upper")), Eq(GCD(a=Var("n"), b=Ref("modulus")), Const(1)... | NT | null | EXTREMUM | sympy | MAX_DIVISOR | [
"MAX_DIVISOR"
] | ad1a9b | nt_min_coprime_above_v1 | negation_mod | 4 | 0 | [
"MAX_DIVISOR"
] | 1 | 0.005 | 2026-02-08T13:07:42.277817Z | {
"verified": true,
"answer": 37561,
"timestamp": "2026-02-08T13:07:42.282702Z"
} | d9995e | 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": 5628
},
"timestamp": "2026-02-15T10:05:01.194Z",
"answer": 37561
},
... | 1 | [
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "MAX_DIVISOR",
"status": "ok"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "V1",
"status... | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
6c134b | nt_sum_divisors_range_v1_124444284_5787 | Let $n = 4$. Consider the set of all ordered pairs $(x,y)$ of positive integers such that $xy = 6250000$. Let $S$ be the set of all values of $x + y$ as $(x,y)$ ranges over these pairs. Define $u$ to be the minimum element of $S$. Let $T$ be the set of all positive integers $n$ such that $1 \leq n \leq u$. Compute the ... | 25,768 | graphs = [
Graph(
let={
"_n": Const(4),
"upper": MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(Mul(Var("x"), Var("y")), Const(6250000)))), expr=Sum(Var("x"), Var("y")... | NT | null | SUM | sympy | LIN_FORM | [
"B3"
] | 0cd20d | nt_sum_divisors_range_v1 | null | 6 | 0 | [
"B3",
"LIN_FORM"
] | 2 | 0.793 | 2026-02-08T06:51:10.209088Z | {
"verified": true,
"answer": 25768,
"timestamp": "2026-02-08T06:51:11.001985Z"
} | 8e6049 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 186,
"completion_tokens": 3735
},
"timestamp": "2026-02-13T05:10:05.455Z",
"answer": 25768
},
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"
}
] | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
bff756 | sequence_fibonacci_compute_v1_1125832087_59 | Let $n$ be the minimum value of $x + y$ over all ordered pairs $(x, y)$ of positive integers such that $xy = 144$. Let $F_n$ denote the $n$th Fibonacci number, where $F_1 = F_2 = 1$ and $F_k = F_{k-1} + F_{k-2}$ for $k \geq 3$. Compute the remainder when $|F_n|$ is divided by $67321$. | 46,368 | graphs = [
Graph(
let={
"_n": Const(67321),
"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(144)))), expr=Sum(Var("x"), Var("y")))),... | NT | null | COMPUTE | sympy | B3 | [
"B3"
] | 0cd20d | sequence_fibonacci_compute_v1 | null | 4 | 0 | [
"B3"
] | 1 | 0.001 | 2026-02-08T02:51:09.666668Z | {
"verified": true,
"answer": 46368,
"timestamp": "2026-02-08T02:51:09.668039Z"
} | c552c6 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 215,
"completion_tokens": 570
},
"timestamp": "2026-02-10T11:41:28.147Z",
"answer": 46368
},
{
"i... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "V1",
"status": "no"
},
{
"lemma": "V3",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
}
] | {
"lo": -7.05,
"mid": -4.76,
"hi": -2.5
} | ||
1418ff | modular_count_residue_v1_48377204_2137 | Let $S$ be the set of all ordered pairs $(x,y)$ of positive integers such that $xy = 36$. Define $m$ to be the minimum value of $x + y$ as $(x,y)$ ranges over $S$. Find the number of positive integers $n$ such that $1 \leq n \leq 71824$ and $n \equiv 3 \pmod{m}$. | 5,986 | graphs = [
Graph(
let={
"upper": Const(71824),
"m": MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(Mul(Var("x"), Var("y")), Const(36)))), expr=Sum(Var("x"), Var("y")))... | NT | null | COUNT | sympy | B3 | [
"B3"
] | 0cd20d | modular_count_residue_v1 | null | 4 | 0 | [
"B3"
] | 1 | 3.84 | 2026-02-08T16:37:08.782289Z | {
"verified": true,
"answer": 5986,
"timestamp": "2026-02-08T16:37:12.622389Z"
} | 4bf8ab | 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": 856
},
"timestamp": "2026-02-17T07:24:38.707Z",
"answer": 5986
},
{
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "V1",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
a1470b | antilemma_sum_equals_v1_124444284_9754 | Let $t$ be a positive integer. Define $n$ as the number of values of $t$ in the range $7 \leq t \leq 76$ for which there exist positive integers $a$ and $b$ such that $1 \leq a \leq 7$, $1 \leq b \leq 16$, and $t = 4a + 3b$. Now let $x$ be the number of ordered pairs $(i, j)$ of positive integers such that $1 \leq i \l... | 7,531 | graphs = [
Graph(
let={
"_m": Const(44121),
"_n": CountOverSet(set=SolutionsSet(var=Var("t"), condition=Exists(var=Var(name='a'), condition=Exists(var=Var(name='b'), condition=And(Geq(left=Var(name='a'), right=Const(value=1)), Leq(left=Var(name='a'), right=Const(value=7)), Geq(left=V... | COMB | GEOM | COMPUTE | sympy | COMB1 | [
"LIN_FORM/COUNT_SUM_EQUALS",
"COUNT_SUM_EQUALS"
] | ada383 | antilemma_sum_equals_v1 | null | 5 | 0 | [
"COMB1",
"COUNT_SUM_EQUALS",
"LIN_FORM"
] | 3 | 0.054 | 2026-02-08T12:39:49.414061Z | {
"verified": true,
"answer": 7531,
"timestamp": "2026-02-08T12:39:49.468414Z"
} | 5980dc | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 270,
"completion_tokens": 4315
},
"timestamp": "2026-02-24T16:05:25.528Z",
"answer": 7531
},
{
"i... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "ok"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "V8",
"status... | {
"lo": -2.35,
"mid": 1.22,
"hi": 4.84
} | ||
a8cd8b | nt_num_divisors_compute_v1_153355830_434 | Let $n$ be the number of integers $t$ with $24 \le t \le 1876$ for which there exist positive integers $a \le 427$ and $b \le 201$ such that $t = 2a + 5b + 17$. Determine the number of positive divisors of $n$. | 3 | 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=427)), Geq(left=Var(name='b'), right=Const(value... | NT | null | COMPUTE | sympy | L3B | [
"LIN_FORM"
] | 7b2633 | nt_num_divisors_compute_v1 | null | 6 | 0 | [
"L3B",
"LIN_FORM"
] | 2 | 0.043 | 2026-02-08T03:06:03.430911Z | {
"verified": true,
"answer": 3,
"timestamp": "2026-02-08T03:06:03.473848Z"
} | 28c8a9 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 182,
"completion_tokens": 2862
},
"timestamp": "2026-02-10T12:39:19.719Z",
"answer": 3
},
{
"id"... | 1 | [
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
}
] | {
"lo": 1.96,
"mid": 5.23,
"hi": 8.52
} | ||
9591da | v7_endings_v1_1874849503_412 | Let $ S = \sum_{k=0}^{850} e_k $, where $ e_k $ is the largest integer $ e $ such that $ 5^e $ divides $ \binom{850}{k} $. Compute $ S $. | 2,039 | graphs = [
Graph(
let={
"total": Summation(var="k", start=Const(0), end=Const(850), expr=MaxKDivides(target=Binom(n=Const(850), k=Var("k")), base=Const(5))),
},
goal=Ref("total"),
)
] | NT | null | COMPUTE | sympy | V7 | [
"V7"
] | 0672d4 | v7_endings_v1 | null | 6 | null | [
"V7"
] | 1 | 0.002 | 2026-02-08T13:03:11.753823Z | {
"verified": true,
"answer": 2039,
"timestamp": "2026-02-08T13:03:11.755407Z"
} | 59e217 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 161,
"completion_tokens": 3562
},
"timestamp": "2026-02-09T16:32:37.737Z",
"answer": 2039
},
{
"i... | 1 | [
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "V7",
"status": "ok"
},
{
"lemma": "VAL_SUM_EQ",
"status": "no"
}
] | {
"lo": -6.5,
"mid": -0.2,
"hi": 6.11
} | ||
f1f891 | antilemma_sum_equals_v1_1742523217_4508 | Let $S$ be the set of all ordered pairs $(i, j)$ of positive integers such that $i + j = 96$, $1 \leq i \leq 94$, and $1 \leq j \leq 94$. Let $N$ be the number of elements in $S$. Define $m = N + 2$. The Fibonacci sequence is defined by $F_1 = 1$, $F_2 = 1$, and $F_k = F_{k-1} + F_{k-2}$ for $k \geq 3$. Let $k$ be the ... | 90 | graphs = [
Graph(
let={
"x": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("i"), Var("j")]), condition=Eq(Sum(Var("i"), Var("j")), Const(96)), domain=CartesianProduct(left=IntegerRange(start=Const(1), end=Const(94)), right=IntegerRange(start=Const(1), end=Const(94))))),
"Q": ... | COMB | GEOM | COMPUTE | sympy | COUNT_CARTESIAN | [
"COUNT_SUM_EQUALS"
] | 75ab0f | antilemma_sum_equals_v1 | null | 3 | 0 | [
"COUNT_CARTESIAN",
"COUNT_SUM_EQUALS"
] | 2 | 0.086 | 2026-02-08T08:53:25.790638Z | {
"verified": true,
"answer": 90,
"timestamp": "2026-02-08T08:53:25.876172Z"
} | 099229 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 263,
"completion_tokens": 2704
},
"timestamp": "2026-02-24T10:10:17.023Z",
"answer": 90
},
{
"id"... | 1 | [
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "ok"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
},
{
"lemma": "V8_SUM",
"stat... | {
"lo": -2.35,
"mid": 1.22,
"hi": 4.84
} | ||
8a527f | nt_lcm_compute_v1_655260480_4280 | Let $a = 2707$. Let $b$ be the number of integers $t$ with $8 \leq t \leq 551$ such that there exist positive integers $a_1$ and $b_1$, with $1 \leq a_1 \leq 61$ and $1 \leq b_1 \leq 82$, satisfying $t = 5a_1 + 3b_1$. Define $\text{result} = \text{lcm}(a, b)$. Let $Q$ be the remainder when $42624 \cdot \text{result}$ i... | 19,473 | graphs = [
Graph(
let={
"_n": Const(97955),
"a": Const(2707),
"b": 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'), righ... | NT | null | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | nt_lcm_compute_v1 | null | 5 | 0 | [
"LIN_FORM"
] | 1 | 0.002 | 2026-02-08T17:50:57.006334Z | {
"verified": true,
"answer": 19473,
"timestamp": "2026-02-08T17:50:57.008639Z"
} | 6eb644 | 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": 6573
},
"timestamp": "2026-02-18T08:52:36.012Z",
"answer": 19473
},
... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
7cf129 | comb_count_permutations_fixed_v1_1742523217_5115 | Let $T$ be the set of all integers $t$ with $5 \leq t \leq 14$ for which there exist integers $a$ and $b$ such that $1 \leq a \leq 2$, $1 \leq b \leq 4$, and $t = 3a + 2b$. Let $n$ be the number of elements in $T$. Define $r = \binom{n}{0} \cdot !\!(n - 0)$, where $!k$ denotes the number of derangements of $k$ elements... | 33,889 | graphs = [
Graph(
let={
"_n": Const(92874),
"n": CountOverSet(set=SolutionsSet(var=Var("t"), condition=Exists(var=Var(name='a'), condition=Exists(var=Var(name='b'), condition=And(Geq(left=Var(name='a'), right=Const(value=1)), Leq(left=Var(name='a'), right=Const(value=2)), Geq(left=Va... | COMB | null | COUNT | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | comb_count_permutations_fixed_v1 | null | 4 | 0 | [
"LIN_FORM"
] | 1 | 0.003 | 2026-02-08T10:48:56.728820Z | {
"verified": true,
"answer": 33889,
"timestamp": "2026-02-08T10:48:56.731999Z"
} | 6a2fdc | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 259,
"completion_tokens": 3367
},
"timestamp": "2026-02-24T12:19:42.895Z",
"answer": 33889
},
{
"... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "V8_SUM",
"st... | {
"lo": -2.35,
"mid": 1.22,
"hi": 4.84
} | ||
e8fea9 | nt_count_digit_sum_v1_1742523217_2654 | Let $T$ be the set of all integers $t$ such that $9 \leq t \leq 40$ and $t = 5a + 4b$ for some positive integers $a \leq 4$ and $b \leq 5$. Let $s$ be the number of elements in $T$. Compute the number of positive integers $n \leq 50000$ such that the sum of the decimal digits of $n$ is equal to $s$. Determine the value... | 3,256 | graphs = [
Graph(
let={
"upper": Const(50000),
"target_sum": CountOverSet(set=SolutionsSet(var=Var("t"), condition=Exists(var=Var(name='a'), condition=Exists(var=Var(name='b'), condition=And(Geq(left=Var(name='a'), right=Const(value=1)), Leq(left=Var(name='a'), right=Const(value=4)),... | NT | null | COUNT | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | nt_count_digit_sum_v1 | null | 5 | 0 | [
"LIN_FORM"
] | 1 | 5.674 | 2026-02-08T04:53:59.350484Z | {
"verified": true,
"answer": 3256,
"timestamp": "2026-02-08T04:54:05.024692Z"
} | 0e0087 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 223,
"completion_tokens": 3260
},
"timestamp": "2026-02-11T22:20:49.841Z",
"answer": 3256
},
{
"... | 1 | [
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
}
] | {
"lo": -3.42,
"mid": 1.86,
"hi": 7.55
} | ||
989fdb | geo_visible_lattice_v1_1440796553_357 | Let $n = 105$. A lattice point $(x, y)$ is called visible if $1 \leq x, y \leq n$ and $\gcd(x, y) = 1$. Compute the number of visible lattice points. | 6,747 | graphs = [
Graph(
let={
"n": Const(105),
"result": VisibleLatticePoints(n=Ref(name='n')),
},
goal=Ref("result"),
)
] | GEOM | null | COUNT | sympy | [] | geo_visible_lattice_v1 | null | 3 | 0 | null | null | 0.243 | 2026-02-08T11:45:05.077971Z | {
"verified": true,
"answer": 6747,
"timestamp": "2026-02-08T11:45:05.321031Z"
} | c5799d | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 162,
"completion_tokens": 6221
},
"timestamp": "2026-02-24T14:38:25.743Z",
"answer": 6747
},
{
"i... | 1 | [] | {
"lo": -2.35,
"mid": 1.22,
"hi": 4.84
} | ||||
f8c9fe | alg_poly4_count_v1_1218484723_294 | Let $C = \left|\{ p > 0 : \exists\, q \in \mathbb{Z} \text{ such that } pq = 13677313650,\ \gcd(p, q) = 1,\ p < q \}\right|$. Find the number of ordered pairs $(a, b)$ of positive integers with $1 \le a, b \le 330$ such that $C \cdot b^4 = 1310720000$. | 330 | graphs = [
Graph(
let={
"_n": Const(330),
"result": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("a"), Var("b")]), condition=And(Geq(Var("a"), Const(1)), Leq(Var("a"), Const(330)), Geq(Var("b"), Const(1)), Leq(Var("b"), Ref("_n")), Eq(Mul(CountOverSet(set=SolutionsSet(var=Va... | NT | null | COUNT | sympy | COPRIME_PAIRS | [
"COPRIME_PAIRS"
] | 2bb3aa | alg_poly4_count_v1 | null | 6 | 0 | [
"COPRIME_PAIRS"
] | 1 | 0.299 | 2026-02-25T01:59:17.872071Z | {
"verified": true,
"answer": 330,
"timestamp": "2026-02-25T01:59:18.170601Z"
} | 57bd90 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 1,
"correct": {
"strict": false,
"boxed": false,
"relaxed": true
},
"usage": {
"prompt_tokens": 212,
"completion_tokens": 32768
},
"timestamp": "2026-03-10T09:27:16.561Z",
"answer": null
},
{
... | 1 | [
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "V1",
"status": "no"
},
{
"lemma": "V5",
"status": "no"... | {
"lo": -0.93,
"mid": 2.04,
"hi": 4.6
} | ||
1d99b9 | alg_poly3_count_v1_601307018_10026 | Find the number of ordered pairs $(a, b)$ of positive integers with $1 \le a, b \le 400$ such that $$152b^3 + \left|\left\{ (a_1, b_1) : 1 \le a_1, b_1 \le 35,\ -18a_1b_1 + 25b_1^2 + 10a_1^2 \le 1954 \right\}\right| \cdot a^3 + 456ab^2 + 456a^2b = 40977092672.$$ | 155 | graphs = [
Graph(
let={
"_n": Const(3),
"result": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("a"), Var("b")]), condition=And(Geq(Var("a"), Const(1)), Leq(Var("a"), Const(400)), Geq(Var("b"), Const(1)), Leq(Var("b"), Const(400)), Eq(Sum(Mul(Const(152), Pow(Var("b"), Ref("_n... | ALG | null | COUNT | sympy | QF_PSD_COUNT | [
"QF_PSD_COUNT_LEQ"
] | 009d0f | alg_poly3_count_v1 | null | 6 | 0 | [
"QF_PSD_COUNT",
"QF_PSD_COUNT_LEQ"
] | 2 | 2.318 | 2026-03-10T10:30:08.487083Z | {
"verified": true,
"answer": 155,
"timestamp": "2026-03-10T10:30:10.805500Z"
} | f984a5 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 238,
"completion_tokens": 4173
},
"timestamp": "2026-04-19T12:48:16.222Z",
"answer": 155
},
{
"i... | 1 | [
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "QF_PSD_COUNT_LEQ",
"status": "ok"
}
] | {
"lo": -5.34,
"mid": 1.1,
"hi": 7.53
} | ||
cc05d6 | comb_catalan_compute_v1_397696148_1547 | Let $C_{11}$ denote the 11th Catalan number. Let $c$ be the number of positive integers $t$ such that $15 \le t \le 16683$ and there exist positive integers $a$ and $b$ with $1 \le a \le 233$, $1 \le b \le 2431$, and $t = 9a + 6b$. Compute the remainder when $c - C_{11}$ is divided by $68482$. | 15,251 | graphs = [
Graph(
let={
"n": Const(11),
"result": Catalan(Ref("n")),
"_c": 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... | COMB | null | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM"
] | 324ba4 | comb_catalan_compute_v1 | negation_mod | 5 | 0 | [
"LIN_FORM"
] | 1 | 0.004 | 2026-02-08T12:38:36.226736Z | {
"verified": true,
"answer": 15251,
"timestamp": "2026-02-08T12:38:36.230494Z"
} | 8a4b5a | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 215,
"completion_tokens": 5096
},
"timestamp": "2026-02-24T16:00:27.191Z",
"answer": 15251
},
{
"... | 1 | [
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
}
... | {
"lo": 1.15,
"mid": 4.18,
"hi": 6.61
} | ||
82004e | comb_count_derangements_v1_1419126231_1661 | Let $D_n$ denote the number of derangements of $n$ elements and $B_n$ the $n$-th Bell number. Let $N = D_7$. Let $T = \{ t : \text{there exist integers } a, b \text{ with } 1 \leq a \leq 3,\ 1 \leq b \leq 4,\ t = 9a + 6b,\ 15 \leq t \leq 51 \}$. Define $Q = B_{N \bmod |T|}$. Compute $Q$. | 203 | graphs = [
Graph(
let={
"n": Const(7),
"result": Subfactorial(arg=Ref(name='n')),
"Q": Bell(Mod(value=Abs(arg=Ref(name='result')), modulus=CountOverSet(set=SolutionsSet(var=Var("t"), condition=Exists(var=Var(name='a'), condition=Exists(var=Var(name='b'), condition=And(Geq... | COMB | null | COUNT | sympy | HALFPLANE_COUNT | [
"LIN_FORM"
] | 1ae498 | comb_count_derangements_v1 | bell_mod | 4 | 0 | [
"HALFPLANE_COUNT",
"LIN_FORM"
] | 2 | 0.012 | 2026-02-25T11:12:45.923872Z | {
"verified": true,
"answer": 203,
"timestamp": "2026-02-25T11:12:45.936113Z"
} | a6005f | 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": 755
},
"timestamp": "2026-03-30T13:25:39.479Z",
"answer": 203
},
{
"id"... | 1 | [
{
"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"
},
{
"lemma": "V8_SUM",
"status": "no"
... | {
"lo": -5.37,
"mid": 0.23,
"hi": 5.22
} | ||
470dbe | comb_sum_binomial_row_v1_168721529_63 | Let $n = 2^{12}$. Compute the decimal representation of $n$. Let $D$ be the number of digits in $n$. For each digit position $i$ from $0$ to $D-1$, let $d_i$ be the $i$-th digit of $n$ (with $i=0$ being the units digit). Define $S = \sum_{i=0}^{D-1} d_i \cdot (i + 1)^2$. Let $p$ be the largest prime number such that $2... | 149 | graphs = [
Graph(
let={
"_n": Const(2),
"n": Const(12),
"result": Pow(Ref("_n"), Ref("n")),
"Q": Sum(Summation(var="i", start=Const(0), end=Sub(NumDigits(x=Abs(arg=Ref(name='result')), base=None), Const(1)), expr=Mul(Digit(x=Abs(arg=Ref(name='result')), k=Var(... | NT | null | SUM | sympy | MAX_PRIME_BELOW | [
"MAX_PRIME_BELOW"
] | 38b8fc | comb_sum_binomial_row_v1 | digits_weighted_mod | 3 | 0 | [
"MAX_PRIME_BELOW"
] | 1 | 0.002 | 2026-02-08T12:47:36.857729Z | {
"verified": true,
"answer": 149,
"timestamp": "2026-02-08T12:47:36.860158Z"
} | 206ed3 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 248,
"completion_tokens": 465
},
"timestamp": "2026-02-08T20:59:38.976Z",
"answer": 149
},
{
"id"... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok"
},
{
"lemma": "V8_SUM",
"status": "no"
},
{
"lemma": "VAL_SUM_EQ",
"status": "no"
}
] | {
"lo": -5.3,
"mid": -2.05,
"hi": 1.82
} | ||
317074_n | geo_count_lattice_rect_v1_1419126231_903 | A grid artist paints dots at every lattice point $(x,y)$ within a rectangle bounded by $x = 0$ to $x = 324$ and $y = 0$ to $y = b$, where $b$ is the sum of the first $18$ positive integers. How many dots does the artist paint? | 55,900 | GEOM | GEOM | COUNT | sympy | SUM_ARITHMETIC | [
"SUM_ARITHMETIC"
] | eb34f0 | geo_count_lattice_rect_v1 | null | 2 | null | [
"SUM_ARITHMETIC"
] | 1 | 0.001 | 2026-02-25T10:23:03.603838Z | null | 378d7d | 317074 | narrative | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 178,
"completion_tokens": 537
},
"timestamp": "2026-03-31T04:05:52.114Z",
"answer": 55900
},
{
"i... | 1 | [
{
"lemma": "SUM_ARITHMETIC",
"status": "ok"
}
] | {
"lo": -5.37,
"mid": 0.23,
"hi": 5.22
} | |
70b83e | nt_sum_divisors_mod_v1_397696148_2266 | Let $n$ be the minimum value of $x + y$ over all ordered pairs $(x,y)$ of positive integers such that $xy = 705600$. Let $\sigma$ denote the sum of all positive divisors of $n$. Find the remainder when $\sigma$ is divided by $10867$. | 5,952 | 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(705600)))), expr=Sum(Var("x"), Var("y")))),
"M": Const(10867... | NT | null | COMPUTE | sympy | B3 | [
"B3"
] | 0cd20d | nt_sum_divisors_mod_v1 | null | 6 | 0 | [
"B3"
] | 1 | 0.003 | 2026-02-08T13:04:35.736786Z | {
"verified": true,
"answer": 5952,
"timestamp": "2026-02-08T13:04:35.740119Z"
} | 30bae5 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 110,
"completion_tokens": 1527
},
"timestamp": "2026-02-15T09:11:31.716Z",
"answer": 5952
},
{... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "VAL_SUM_EQ",
"status": "no"
}
] | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
f72636 | antilemma_k2_v1_124444284_710 | Let $x = \sum_{k=1}^{70} \phi(k) \left\lfloor \frac{70}{k} \right\rfloor$, where $\phi(k)$ denotes Euler's totient function. Let $Q = 33411 - x$. Compute the value of $Q$. | 30,926 | graphs = [
Graph(
let={
"x": Summation(var="k", start=Div(Const(53), Const(53)), end=Const(70), expr=Mul(EulerPhi(n=Var("k")), Floor(Div(Const(70), Var("k"))))),
"_c": Const(33411),
"Q": Sub(Ref("_c"), Ref("x")),
},
goal=Ref("Q"),
)
] | NT | COMB | COMPUTE | sympy | IDENTITY_DIV_SELF | [
"IDENTITY_DIV_SELF",
"K2"
] | 39e678 | antilemma_k2_v1 | null | 5 | 0 | [
"IDENTITY_DIV_SELF",
"K2"
] | 2 | 0.001 | 2026-02-08T03:27:55.937648Z | {
"verified": true,
"answer": 30926,
"timestamp": "2026-02-08T03:27:55.938398Z"
} | cd1471 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 174,
"completion_tokens": 586
},
"timestamp": "2026-02-09T20:53:00.632Z",
"answer": 30926
},
{
"i... | 1 | [
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "IDENTITY_DIV_SELF",
"status": "ok"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "K2",
"status": "ok"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
... | {
"lo": -3.53,
"mid": 1.02,
"hi": 5.49
} | ||
bdadd4 | sequence_lucas_compute_v1_655260480_1603 | Let $m$ be the number of integers $t$ such that $10 \leq t \leq 30$ and there exist integers $a$ and $b$ with $1 \leq a \leq 3$, $1 \leq b \leq 3$, and $t = 4a + 6b$. Let $n$ be the minimum value of $x + y$ over all ordered pairs of positive integers $(x, y)$ such that $xy = m$. Define $s = \sum_{k=1}^{n} k$. Compute t... | 24,476 | graphs = [
Graph(
let={
"_m": 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=... | NT | null | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM/B3/SUM_ARITHMETIC"
] | d586f5 | sequence_lucas_compute_v1 | null | 5 | 0 | [
"B3",
"LIN_FORM",
"SUM_ARITHMETIC"
] | 3 | 0.004 | 2026-02-08T16:15:00.333440Z | {
"verified": true,
"answer": 24476,
"timestamp": "2026-02-08T16:15:00.337210Z"
} | f73798 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 222,
"completion_tokens": 1022
},
"timestamp": "2026-02-17T00:01:10.280Z",
"answer": 24476
},
... | 1 | [
{
"lemma": "B3",
"status": "ok_later"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "SUM_ARITHMETIC",
"status": "ok_later"
},
{
"lemma": "V8",
"status":... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
8e565b | lin_form_endings_v1_349078426_774 | Let $a = 70$, $b = 40$, $A = 25$, and $B = 57$. Let $g = \gcd(a, b)$, and define $a' = \left\lfloor \frac{a}{g} \right\rfloor$ and $b' = \left\lfloor \frac{b}{g} \right\rfloor$. Let $r = a'A + b'B - a'b'$. Multiply $r$ by $6837$, and compute the remainder when this product is divided by $55455$. Determine the value of ... | 12,945 | graphs = [
Graph(
let={
"a_coeff": Const(70),
"b_coeff": Const(40),
"A_val": Const(25),
"B_val": Const(57),
"g_step": GCD(a=Ref("a_coeff"), b=Ref("b_coeff")),
"ap_node": Floor(Div(Ref("a_coeff"), Ref("g_step"))),
"bp_node": ... | COMB | NT | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | lin_form_endings_v1 | null | 3 | null | [
"LIN_FORM"
] | 1 | 0.002 | 2026-02-08T13:17:32.027104Z | {
"verified": true,
"answer": 12945,
"timestamp": "2026-02-08T13:17:32.029487Z"
} | 1fcd58 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 169,
"completion_tokens": 1078
},
"timestamp": "2026-02-15T12:22:58.799Z",
"answer": 12945
},
... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "V8",
"status... | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
083aff | lin_form_endings_v1_677425708_3397 | Determine the number of integers $t$ with $42 \leq t \leq 1422$ for which there exist positive integers $a$ and $b$ such that $1 \leq a \leq 39$, $1 \leq b \leq 21$, and $t = 30a + 12b$. Let $N$ be this number. Compute the remainder when $14264 \cdot N$ is divided by $53661$. | 18,268 | graphs = [
Graph(
let={
"_inner_result": CountOverSet(set=SolutionsSet(var=Var("t"), condition=Exists(var=Var(name='a'), condition=Exists(var=Var(name='b'), condition=And(Geq(left=Var(name='a'), right=Const(value=1)), Leq(left=Var(name='a'), right=Const(value=39)), Geq(left=Var(name='b'), right=... | COMB | null | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | lin_form_endings_v1 | null | 3 | null | [
"LIN_FORM"
] | 1 | 0.002 | 2026-02-08T05:41:21.382537Z | {
"verified": true,
"answer": 18268,
"timestamp": "2026-02-08T05:41:21.384045Z"
} | 55d3a6 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 210,
"completion_tokens": 2191
},
"timestamp": "2026-02-24T04:14:35.690Z",
"answer": 22263
},
{
... | 1 | [
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "V8",
"status": "no"
},
{
"lemma": "V8_SUM",
"st... | {
"lo": 1.97,
"mid": 4.36,
"hi": 6.69
} | ||
108227 | modular_inverse_v1_2051736721_274 | Let $a = 443$ and $m = 953$. Let $S$ be the set of all integers $t$ such that there exist integers $a$ and $b$ satisfying $1 \le a \le 40$, $1 \le b \le 175$, $11 \le t \le 980$, and $t = 7a + 4b$. Let $T$ be the set of all positive integers $x$ such that $1 \le x \le |S|$ and $ax \equiv 1 \pmod{m}$. Determine the valu... | 256 | graphs = [
Graph(
let={
"a": Const(443),
"m": Const(953),
"upper": CountOverSet(set=SolutionsSet(var=Var("t"), condition=Exists(var=Var(name='a'), condition=Exists(var=Var(name='b'), condition=And(Geq(left=Var(name='a'), right=Const(value=1)), Leq(left=Var(name='a'), righ... | NT | null | EXTREMUM | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | modular_inverse_v1 | null | 5 | 0 | [
"LIN_FORM"
] | 1 | 0.074 | 2026-02-08T15:19:24.991929Z | {
"verified": true,
"answer": 256,
"timestamp": "2026-02-08T15:19:25.065946Z"
} | a5f468 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 179,
"completion_tokens": 4360
},
"timestamp": "2026-02-16T04:22:38.149Z",
"answer": 256
},
{
... | 1 | [
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "V1",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
25b21f | nt_count_with_divisor_count_v1_1520064083_1187 | Let $s$ be the minimum value of $x + y$ over all ordered pairs $(x,y)$ of positive integers such that $xy = 49$. Let $N$ be the number of positive integers $n$ such that $1 \le n \le 47089$ and the number of positive divisors of $n$ is exactly $s$. Compute the value of $N$. | 149 | graphs = [
Graph(
let={
"_n": Const(49),
"upper": Const(47089),
"div_count": MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(Mul(Var("x"), Var("y")), Ref("_... | NT | null | COUNT | sympy | B3 | [
"B3"
] | 0cd20d | nt_count_with_divisor_count_v1 | null | 5 | 0 | [
"B3"
] | 1 | 2.237 | 2026-02-08T03:49:49.708808Z | {
"verified": true,
"answer": 149,
"timestamp": "2026-02-08T03:49:51.945922Z"
} | 6df581 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 192,
"completion_tokens": 3004
},
"timestamp": "2026-02-10T14:40:14.187Z",
"answer": 149
},
{
"i... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "V1",
"status": "no"
},
{
"lemma": "V3",
"status": "no"
}
] | {
"lo": -3.49,
"mid": 1.84,
"hi": 7.55
} | ||
dd529f_l | modular_product_range_v1_1125832087_1206 | Let $c$ be the number of positive integers $p$ for which there exists a positive integer $q$ such that $pq = 36$, $\gcd(p, q) = 1$, and $p < q$. Let $n$ be the largest prime number that is at least $c$ and at most 4. Let $t_0$ be the number of integers $t$ with $12 \leq t \leq 218$ for which there exist integers $a$ an... | 1 | NT | null | COMPUTE | sympy | MAX_PRIME_BELOW | [
"MAX_PRIME_BELOW/MAX_PRIME_BELOW/LIN_FORM",
"COPRIME_PAIRS/MAX_PRIME_BELOW/LIN_FORM"
] | 510d65 | modular_product_range_v1 | null | 7 | 0 | [
"COPRIME_PAIRS",
"LIN_FORM",
"MAX_PRIME_BELOW"
] | 3 | 0.006 | 2026-02-08T03:36:47.516470Z | {
"verified": false,
"answer": 5578,
"timestamp": "2026-02-08T03:36:47.522072Z"
} | 9d831b | dd529f | legacy_text | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 280,
"completion_tokens": 17373
},
"timestamp": "2026-02-23T20:58:05.261Z",
"answer": 5578
},
{
... | 1 | [
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "K5",
"status": ... | {
"lo": -3.42,
"mid": 1.86,
"hi": 7.55
} | |
159d56 | diophantine_fbi2_min_v1_397696148_784 | Let $k = 27$ and let $u = 37$. Let $D$ be the set of all integers $d$ such that $4 \le d \le 37$, $d$ divides 27, and $\frac{27}{d} \ge N$, where $N$ is the number of positive integers $p$ for which there exists a positive integer $q > p$ such that $pq = 24$ and $\gcd(p,q) = 1$. Let $d_{\min}$ be the smallest element o... | 25,947 | graphs = [
Graph(
let={
"k": Const(27),
"upper": Const(37),
"result": MinOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Const(4)), Leq(Var("d"), Ref("upper")), Divides(divisor=Var("d"), dividend=Ref("k")), Geq(Div(Ref("k"), Var("d")), CountOverSet(set=... | NT | null | EXTREMUM | sympy | COPRIME_PAIRS | [
"COPRIME_PAIRS"
] | 2bb3aa | diophantine_fbi2_min_v1 | null | 4 | 0 | [
"COPRIME_PAIRS"
] | 1 | 0.007 | 2026-02-08T11:44:14.393541Z | {
"verified": true,
"answer": 25947,
"timestamp": "2026-02-08T11:44:14.400236Z"
} | ab8820 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 173,
"completion_tokens": 1165
},
"timestamp": "2026-02-14T18:07:47.110Z",
"answer": 25947
},
... | 1 | [
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
}
] | {
"lo": -9.12,
"mid": -6.02,
"hi": -3.62
} | ||
9bcf74 | modular_min_linear_v1_1742523217_400 | Let $a = 47784$, $b = 47508$, and $m = 64695$. Let $S$ be the set of all integers $x$ such that $$x \geq \sum_{d\mid \gcd(7,11)} \mu(d),$$ $$x \leq m,$$ and $$ax \equiv b \pmod{m}.$$ Let $r$ be the smallest element of $S$. Compute the remainder when $80039r$ is divided by $87097$. | 39,611 | graphs = [
Graph(
let={
"a": Const(47784),
"b": Const(47508),
"m": Const(64695),
"result": MinOverSet(set=SolutionsSet(var=Var("x"), condition=And(Geq(Var("x"), SumOverDivisors(n=GCD(a=Const(value=7), b=Const(value=11)), var='d', expr=MoebiusMu(n=Var(name='d')... | NT | null | EXTREMUM | sympy | MOBIUS_COPRIME | [
"MOBIUS_COPRIME"
] | ac54ac | modular_min_linear_v1 | null | 5 | 0 | [
"MOBIUS_COPRIME"
] | 1 | 3.168 | 2026-02-08T03:01:38.477957Z | {
"verified": true,
"answer": 39611,
"timestamp": "2026-02-08T03:01:41.645542Z"
} | a22186 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 222,
"completion_tokens": 7998
},
"timestamp": "2026-02-09T17:31:21.326Z",
"answer": 39611
},
{
"... | 1 | [
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "MOBIUS_COPRIME",
"status": "ok"
},
{
"lemma": "V3",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
}
] | {
"lo": -6.51,
"mid": -0.31,
"hi": 5.43
} | ||
8a2f40 | antilemma_coprime_grid_v1_124444284_941 | Let $S$ be the set of all ordered pairs $(i, j)$ of positive integers with $1 \leq i \leq 12$ and $1 \leq j \leq 95$ such that
$$
\gcd(i, j) = \sum_{d \mid \gcd(4,9)} \mu(d),
$$
where $\mu$ denotes the M\"obius function. Determine the value of $|S|$. | 714 | graphs = [
Graph(
let={
"x": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("i"), Var("j")]), condition=Eq(GCD(a=Var("i"), b=Var("j")), SumOverDivisors(n=GCD(a=Const(value=4), b=Const(value=9)), var='d', expr=MoebiusMu(n=Var(name='d')))), domain=CartesianProduct(left=IntegerRange(start=Co... | NT | null | COMPUTE | sympy | MOBIUS_COPRIME | [
"MOBIUS_COPRIME",
"COUNT_COPRIME_GRID"
] | db308f | antilemma_coprime_grid_v1 | null | 4 | 0 | [
"COUNT_COPRIME_GRID",
"MOBIUS_COPRIME"
] | 2 | 0.001 | 2026-02-08T03:36:24.721496Z | {
"verified": true,
"answer": 714,
"timestamp": "2026-02-08T03:36:24.722226Z"
} | eb600a | 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": 2987
},
"timestamp": "2026-02-10T00:18:44.226Z",
"answer": 714
},
{
"id... | 1 | [
{
"lemma": "COUNT_COPRIME_GRID",
"status": "ok"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{... | {
"lo": -6.51,
"mid": -0.31,
"hi": 5.43
} |
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