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 |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
978efd | nt_max_prime_below_v1_1431428450_1137 | Let $p$ and $q$ be positive integers such that $pq = 108$, $\gcd(p, q) = 1$, and $p < q$. Let $d$ be the number of such integers $p$. Let $k = 2026$. Let $m$ be the number of positive integers $j$ such that $1 \le j \le k$ and $j^4 \le 16848365064976$. Let $r$ be the largest prime number at most $32768$. Compute the re... | 8,040 | graphs = [
Graph(
let={
"_m": Const(37),
"_n": Const(95060),
"upper": Const(32768),
"result": MaxOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(2)), Leq(Var("n"), Ref("upper")), IsPrime(Var("n"))))),
"Q": Mod(value=Sum(Pow... | NT | null | EXTREMUM | sympy | COPRIME_PAIRS | [
"COPRIME_PAIRS",
"C3"
] | a85c3e | nt_max_prime_below_v1 | quadratic_mod | 4 | 0 | [
"C3",
"COPRIME_PAIRS"
] | 2 | 1.018 | 2026-02-08T13:55:14.620899Z | {
"verified": true,
"answer": 8040,
"timestamp": "2026-02-08T13:55:15.638689Z"
} | b96b56 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 178,
"completion_tokens": 3219
},
"timestamp": "2026-02-15T21:54:09.843Z",
"answer": 8040
},
{... | 1 | [
{
"lemma": "C3",
"status": "ok"
},
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "LTE_SUM",
... | {
"lo": -5.49,
"mid": 0.22,
"hi": 6.51
} | ||
751fe8_n | algebra_quadratic_discriminant_v1_1218484723_2799 | A bakery sells gift boxes that each contain either 12 croissants or 15 muffins. Each day, they prepare between 1 and 740 croissant boxes and between 1 and 612 muffin boxes. At the end of the day, they combine the contents into large gift sets, each containing exactly $t$ pastries. Only values of $t$ between 27 and 1806... | 5,996 | ALG | null | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM"
] | 324ba4 | algebra_quadratic_discriminant_v1 | negation_mod | 2 | null | [
"LIN_FORM"
] | 1 | 0.002 | 2026-02-25T04:31:53.875036Z | null | 4890f7 | 751fe8 | narrative | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 247,
"completion_tokens": 32768
},
"timestamp": "2026-03-30T19:06:48.043Z",
"answer": 10004
},
{
... | 1 | [
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
}
] | {
"lo": 3.8,
"mid": 6.33,
"hi": 9.49
} | |
55eaa2 | comb_count_derangements_v1_865884756_6780 | Let $m = 2$ and $n_0 = 2$. Define $n$ to be the largest prime number $n_1$ such that $n_1 \geq n_0$ and $n_1$ is less than or equal to the smallest divisor $d$ of $41503$ satisfying $d \geq m$. Compute the subfactorial of $n$, denoted $!n$. | 1,854 | graphs = [
Graph(
let={
"_m": Const(2),
"_n": Const(2),
"n": MaxOverSet(set=SolutionsSet(var=Var("n1"), condition=And(Geq(Var("n1"), Ref("_n")), Leq(Var("n1"), MinOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Ref("_m")), Divides(divisor=Var("d"), divi... | NT | COMB | COUNT | sympy | MIN_PRIME_FACTOR | [
"MIN_PRIME_FACTOR/MAX_PRIME_BELOW"
] | e4e16c | comb_count_derangements_v1 | null | 4 | 0 | [
"MAX_PRIME_BELOW",
"MIN_PRIME_FACTOR"
] | 2 | 0.002 | 2026-02-08T19:23:11.688258Z | {
"verified": true,
"answer": 1854,
"timestamp": "2026-02-08T19:23:11.689984Z"
} | 5b66f0 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 134,
"completion_tokens": 1140
},
"timestamp": "2026-02-18T22:13:22.119Z",
"answer": 1854
},
{... | 1 | [
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok_later"
},
{
"lemma": "MIN_PRIME_FACTOR",
"status": "ok"
},
{
"lemma": "V5",
"status": "no"
... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
6cc2f5 | nt_sum_divisors_mod_v1_1918700295_2803 | Let $n$ be the smallest possible value of $x + y$ where $x$ and $y$ are positive integers such that $xy = 32400$. Let $\sigma(n)$ denote the sum of all positive divisors of $n$. Compute the remainder when $\sigma(n)$ is divided by $10597$. | 1,170 | graphs = [
Graph(
let={
"_n": Const(32400),
"n": MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(Mul(Var("x"), Var("y")), Ref("_n")))), expr=Sum(Var("x"), Var("y")))),
... | NT | null | COMPUTE | sympy | B3 | [
"B3"
] | 0cd20d | nt_sum_divisors_mod_v1 | null | 5 | 0 | [
"B3"
] | 1 | 0.001 | 2026-02-08T08:13:13.526970Z | {
"verified": true,
"answer": 1170,
"timestamp": "2026-02-08T08:13:13.528177Z"
} | a329e3 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 113,
"completion_tokens": 941
},
"timestamp": "2026-02-13T16:37:04.491Z",
"answer": 1170
},
{
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
},
{
"lemma": "VAL_SUM_EQ",
"status": "no"
}
] | {
"lo": -5.55,
"mid": -3.01,
"hi": 0.32
} | ||
24533e | nt_num_divisors_compute_v1_784195855_5006 | Let $n = 2024$. The number of positive divisors of $n$ is denoted by $d(n)$. Let $p$ be the largest prime number less than or equal to 6161. Compute the value of $p \cdot d(2024)$. | 98,416 | graphs = [
Graph(
let={
"_n": Const(2),
"n": Const(2024),
"result": NumDivisors(n=Ref("n")),
"_c": MaxOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Ref("_n")), Leq(Var("n"), Const(6161)), IsPrime(Var("n"))))),
"Q": Mul(Ref("_c"... | NT | null | COMPUTE | sympy | MAX_PRIME_BELOW | [
"MAX_PRIME_BELOW"
] | 183c11 | nt_num_divisors_compute_v1 | affine_mod | 3 | 0 | [
"MAX_PRIME_BELOW"
] | 1 | 0.001 | 2026-02-08T07:32:54.552376Z | {
"verified": true,
"answer": 98416,
"timestamp": "2026-02-08T07:32:54.553408Z"
} | 28b6c4 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 102,
"completion_tokens": 2409
},
"timestamp": "2026-02-13T11:15:32.401Z",
"answer": 98416
},
... | 1 | [
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "V3",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
}
] | {
"lo": -5.55,
"mid": -3.01,
"hi": 0.32
} | ||
c0674b | comb_count_partitions_v1_655260480_5897 | Let $n$ be the minimum value of $x + y$ over all ordered pairs of positive integers $(x, y)$ such that $xy = 484$. Let $p(n)$ denote the number of integer partitions of $n$. Compute the remainder when $44121 \cdot p(n)$ is divided by $67462$. | 26,945 | graphs = [
Graph(
let={
"_n": Const(484),
"n": MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(Mul(Var("x"), Var("y")), Ref("_n")))), expr=Sum(Var("x"), Var("y")))),
... | COMB | null | COUNT | sympy | B3 | [
"B3"
] | 0cd20d | comb_count_partitions_v1 | null | 4 | 0 | [
"B3"
] | 1 | 0.001 | 2026-02-08T18:42:04.874520Z | {
"verified": true,
"answer": 26945,
"timestamp": "2026-02-08T18:42:04.875494Z"
} | 926fbe | 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": 2170
},
"timestamp": "2026-02-18T19:02:37.133Z",
"answer": 26945
},
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "V8",
"status":... | {
"lo": -3.12,
"mid": 1.47,
"hi": 6.57
} | ||
e7feb4 | alg_poly4_sum_v1_1218484723_2298 | Compute the remainder when
\[
\sum_{\substack{1 \le a \le 261\\1 \le b \le 261}} \Bigl(257a^{4} + \bigl|\{(a1, b1) : 1 \le a1 \le 40,\, 1 \le b1 \le 40,\, 25b1^{2} + 34a1^{2} + 22a1b1 \le 118480\}\bigr|\, a^{2}b^{2} + 337b^{4} - 1132ab^{3} - 1036a^{3}b\Bigr)
\]
is divided by $63006$. | 31,584 | graphs = [
Graph(
let={
"_n": Const(4),
"result": Mod(value=SumOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("a"), Var("b")]), condition=And(Geq(Var("a"), Const(1)), Leq(Var("a"), Const(261)), Geq(Var("b"), Const(1)), Leq(Var("b"), Const(261)))), expr=Sum(Mul(Const(... | ALG | null | COMPUTE | sympy | QF_PSD_COUNT_LEQ | [
"QF_PSD_COUNT_LEQ"
] | 009d0f | alg_poly4_sum_v1 | null | 7 | 0 | [
"QF_PSD_COUNT_LEQ"
] | 1 | 0.161 | 2026-02-25T04:08:14.732484Z | {
"verified": true,
"answer": 31584,
"timestamp": "2026-02-25T04:08:14.893665Z"
} | 29a9f4 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 266,
"completion_tokens": 15485
},
"timestamp": "2026-03-29T03:59:02.488Z",
"answer": 31584
},
{
... | 1 | [
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "QF_PSD_COUNT_LEQ",
"status": "ok"
}
] | {
"lo": 1.55,
"mid": 4.7,
"hi": 7.23
} | ||
f74cd6 | diophantine_product_count_v1_865884756_4878 | Find the number of positive integers $x$ such that $x \leq 48$, $x$ divides $480$, and $\frac{480}{x} \leq 48$. | 10 | graphs = [
Graph(
let={
"k": Const(480),
"upper": Const(48),
"result": CountOverSet(set=SolutionsSet(var=Var("x"), condition=And(Geq(Var("x"), Const(1)), Leq(Var("x"), Ref("upper")), Divides(divisor=Var("x"), dividend=Ref("k")), Leq(Div(Ref("k"), Var("x")), Ref("upper")))... | NT | null | COUNT | sympy | COUNT_FIB_DIVISIBLE | [
"COUNT_FIB_DIVISIBLE/B3"
] | 3b8dd4 | diophantine_product_count_v1 | null | 3 | 0 | [
"B3",
"COUNT_FIB_DIVISIBLE"
] | 2 | 0.032 | 2026-02-08T18:14:25.585020Z | {
"verified": true,
"answer": 10,
"timestamp": "2026-02-08T18:14:25.617370Z"
} | ed29f8 | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 100,
"completion_tokens": 575
},
"timestamp": "2026-02-16T12:15:21.533Z",
"answer": 10
},
{
"id": 11,
... | 2 | [
{
"lemma": "B3",
"status": "ok_later"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "ok"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
},
... | {
"lo": -10,
"mid": -7.27,
"hi": -4.54
} | ||
a8c73c | diophantine_fbi2_min_v1_124444284_7022 | Let $k = 33$ and the upper bound be $43$. Find the smallest integer $d \geq 2$ such that $d \leq 43$, $d$ divides $k$, and $\frac{k}{d} \geq 7$. | 3 | graphs = [
Graph(
let={
"_n": Const(7),
"k": Const(33),
"upper": Const(43),
"result": MinOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Const(2)), Leq(Var("d"), Ref("upper")), Divides(divisor=Var("d"), dividend=Ref("k")), Geq(Div(Ref("k"), ... | NT | null | EXTREMUM | sympy | C4 | [
"C4"
] | 08d162 | diophantine_fbi2_min_v1 | null | 3 | 0 | [
"C4"
] | 1 | 0.005 | 2026-02-08T08:46:12.010413Z | {
"verified": true,
"answer": 3,
"timestamp": "2026-02-08T08:46:12.015216Z"
} | 4b9d54 | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 113,
"completion_tokens": 388
},
"timestamp": "2026-02-15T20:21:40.515Z",
"answer": 3
},
{
"id": 11,
"... | 2 | [
{
"lemma": "C4",
"status": "ok"
},
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
}... | {
"lo": -9.14,
"mid": -6.05,
"hi": -3.73
} | ||
93324c | nt_num_divisors_compute_v1_151522320_859 | Let $m = 14$. Define $s$ to be the sum of all positive integers $n$ with $1 \leq n \leq 14$ such that $n$ is divisible by $m$. Let $t$ be the number of positive integers $n$ with $1 \leq n \leq s$ such that $n \equiv \left\lfloor \frac{n}{2} \right\rfloor \pmod{7}$. Compute the number of positive divisors of $t$. | 2 | graphs = [
Graph(
let={
"_m": Const(14),
"_n": SumOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Const(14)), Eq(Mod(value=Var("n"), modulus=Ref("_m")), Const(0))))),
"n": CountOverSet(set=SolutionsSet(var=Var("n"), condition=An... | NT | null | COMPUTE | sympy | SUM_DIVISIBLE | [
"SUM_DIVISIBLE/L3C"
] | 1f6f30 | nt_num_divisors_compute_v1 | null | 6 | 0 | [
"L3C",
"SUM_DIVISIBLE"
] | 2 | 0.004 | 2026-02-08T03:36:36.937528Z | {
"verified": true,
"answer": 2,
"timestamp": "2026-02-08T03:36:36.941619Z"
} | f2102e | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 223,
"completion_tokens": 782
},
"timestamp": "2026-02-10T15:11:42.835Z",
"answer": 2
},
{
"id": ... | 1 | [
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "L3C",
"status": "ok_later"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status... | {
"lo": -5.55,
"mid": -3.02,
"hi": 0.31
} | ||
aed1c0 | comb_count_surjections_v1_1915831931_1982 | Let $n = 4$ and let $k$ be the number of ordered pairs $(i, j)$ of positive integers such that $i + j = 6$, where $1 \leq i \leq 4$ and $1 \leq j \leq 5$. Define $\text{result} = k! \cdot S(n, k)$, where $S(n, k)$ denotes the Stirling number of the second kind. Let $Q$ be the remainder when $27315 \cdot \text{result}$ ... | 73,182 | graphs = [
Graph(
let={
"_n": Const(6),
"n": Const(4),
"k": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("i"), Var("j")]), condition=Eq(Sum(Var("i"), Var("j")), Ref("_n")), domain=CartesianProduct(left=IntegerRange(start=Const(1), end=Const(4)), right=IntegerRang... | COMB | null | COUNT | sympy | COUNT_SUM_EQUALS | [
"COUNT_SUM_EQUALS"
] | 75ab0f | comb_count_surjections_v1 | null | 5 | 0 | [
"COUNT_SUM_EQUALS"
] | 1 | 0.012 | 2026-02-08T16:33:18.241607Z | {
"verified": true,
"answer": 73182,
"timestamp": "2026-02-08T16:33:18.253578Z"
} | 265747 | 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": 956
},
"timestamp": "2026-02-24T21:44:21.842Z",
"answer": 73182
},
{... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "ok"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8_SUM",
"status":... | {
"lo": -8.52,
"mid": -5.43,
"hi": -3.2
} | ||
7c3fec | geo_count_lattice_rect_v1_1520064083_9636 | Let $a = 337$ and $b = 208$. Compute the number of lattice points $(x, y)$ such that $0 \leq x \leq a$ and $0 \leq y \leq b$. | 70,642 | graphs = [
Graph(
let={
"a": Const(337),
"b": Const(208),
"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 | 2026-02-08T10:56:13.947179Z | {
"verified": true,
"answer": 70642,
"timestamp": "2026-02-08T10:56:13.947675Z"
} | d5367d | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 160,
"completion_tokens": 279
},
"timestamp": "2026-02-24T12:30:06.257Z",
"answer": 70642
},
{
"i... | 1 | [] | {
"lo": -3.84,
"mid": -1.67,
"hi": 1.32
} | ||||
c6a3f0 | sequence_lucas_compute_v1_1116507919_458 | Let $m = 3$ and $k_0 = \sum_{k=1}^{3} k$. Define $n = \sum_{k=1}^{s} \varphi(k) \left\lfloor \frac{k_0}{k} \right\rfloor$, where $s = \sum_{k=1}^{m} \varphi(k) \left\lfloor \frac{3}{k} \right\rfloor$. Compute the $n$-th Lucas number. | 24,476 | graphs = [
Graph(
let={
"_m": Const(3),
"_n": Summation(var="k", start=Const(1), end=Const(3), expr=Var("k")),
"n": Summation(var="k", start=Const(1), end=Summation(var="k", start=Const(1), end=Ref("_m"), expr=Mul(EulerPhi(n=Var("k")), Floor(Div(Const(3), Var("k"))))), ex... | NT | null | COMPUTE | sympy | SUM_ARITHMETIC | [
"SUM_ARITHMETIC/K2",
"K2/K2"
] | 81ad28 | sequence_lucas_compute_v1 | null | 7 | 0 | [
"K2",
"SUM_ARITHMETIC"
] | 2 | 0.002 | 2026-02-08T02:34:39.359066Z | {
"verified": true,
"answer": 24476,
"timestamp": "2026-02-08T02:34:39.361182Z"
} | ed02ad | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 221,
"completion_tokens": 1249
},
"timestamp": "2026-02-08T19:34:45.481Z",
"answer": 24476
},
{
"... | 1 | [
{
"lemma": "K2",
"status": "ok"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "SUM_ARITHMETIC",
"status": "ok"
}... | {
"lo": -2.84,
"mid": -0.85,
"hi": 1.08
} | ||
c8f654 | lin_form_endings_v1_1978505735_433 | Let $a = 48$, $b = 60$, $A = 9$, and $B = 18$. 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 $T$ be the value of $a'A + b'B - a'b'$. Define $S = aA + bB - a - b + 1$. Compute $S - T$. | 1,299 | graphs = [
Graph(
let={
"a_coeff": Const(48),
"b_coeff": Const(60),
"A_val": Const(9),
"B_val": Const(18),
"g_step": GCD(a=Ref("a_coeff"), b=Ref("b_coeff")),
"ap_node": Floor(Div(Ref("a_coeff"), Ref("g_step"))),
"bp_node": F... | COMB | NT | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | lin_form_endings_v1 | null | 6 | null | [
"LIN_FORM"
] | 1 | 0.002 | 2026-02-08T15:22:37.616245Z | {
"verified": true,
"answer": 1299,
"timestamp": "2026-02-08T15:22:37.618171Z"
} | 23d691 | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 188,
"completion_tokens": 317
},
"timestamp": "2026-02-16T05:40:37.185Z",
"answer": 1355
},
{
"id": 11,... | 1 | [
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8_SUM",
"st... | {
"lo": -8.26,
"mid": -5.01,
"hi": -1.76
} | ||
3bb208_l | antilemma_cartesian_v1_124444284_10146 | Let $A$ be the set of all ordered pairs $(x_1, x_2)$ of positive integers such that $x_1$ is odd, $x_2$ is odd, and $x_1 + x_2 = 8$. Compute the number of elements in $A$. Let $B$ be the Cartesian product of the sets $\{1, 2, \dots, 10\}$ and $\{1, 2, \dots, 29\}$, and let $x$ be the number of elements in $B$. Let $C$ ... | 290 | COMB | GEOM | COMPUTE | sympy | COMB1 | [
"COMB1/COMB1",
"COUNT_CARTESIAN",
"COUNT_CARTESIAN"
] | c3ecc5 | antilemma_cartesian_v1 | mod_exp | 4 | 0 | [
"COMB1",
"COUNT_CARTESIAN"
] | 2 | 0.002 | 2026-02-08T12:50:40.668243Z | {
"verified": false,
"answer": 294,
"timestamp": "2026-02-08T12:50:40.670591Z"
} | 76ee41 | 3bb208 | legacy_text | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 370,
"completion_tokens": 890
},
"timestamp": "2026-02-24T16:30:46.792Z",
"answer": 294
},
{
"id"... | 1 | [
{
"lemma": "COMB1",
"status": "ok"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "ok"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "V8... | {
"lo": -3.84,
"mid": -1.67,
"hi": 1.32
} | |
c9a433 | lin_form_endings_v1_865884756_5993 | Let $a = 9$ and $b = 21$. Let $g$ be the greatest common divisor of $a$ and $b$. Define $a' = \left\lfloor \frac{a}{g} \right\rfloor$ and $b' = \left\lfloor \frac{b}{g} \right\rfloor$. Let $$r = a' \cdot 30 + b' \cdot 53 - a' \cdot b'.$$ Compute the remainder when $17712 \cdot r$ is divided by $84674$. | 3,272 | graphs = [
Graph(
let={
"a_coeff": Const(9),
"b_coeff": Const(21),
"A_val": Const(30),
"B_val": Const(53),
"g_step": GCD(a=Ref("a_coeff"), b=Ref("b_coeff")),
"ap_node": Floor(Div(Ref("a_coeff"), Ref("g_step"))),
"bp_node": F... | COMB | NT | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | lin_form_endings_v1 | null | 3 | null | [
"LIN_FORM"
] | 1 | 0.001 | 2026-02-08T18:54:44.452743Z | {
"verified": true,
"answer": 3272,
"timestamp": "2026-02-08T18:54:44.453695Z"
} | 3c21f8 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 161,
"completion_tokens": 1292
},
"timestamp": "2026-02-18T20:12:57.489Z",
"answer": 3272
},
{... | 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": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
ad0815 | geo_visible_lattice_v1_655260480_1166 | Let $n = 121$. Define $R$ to be the number of ordered pairs $(x, y)$ of positive integers such that $1 \leq x, y \leq n$ and $\gcd(x, y) = 1$. Compute the value of $32761 - R$. | 23,770 | graphs = [
Graph(
let={
"n": Const(121),
"result": VisibleLatticePoints(n=Ref(name='n')),
"Q": Sub(Const(32761), Ref("result")),
},
goal=Ref("Q"),
)
] | GEOM | null | COUNT | sympy | [] | geo_visible_lattice_v1 | null | 3 | 0 | null | null | 0.363 | 2026-02-08T15:56:02.182253Z | {
"verified": true,
"answer": 23770,
"timestamp": "2026-02-08T15:56:02.545395Z"
} | dac050 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 173,
"completion_tokens": 7153
},
"timestamp": "2026-02-24T19:07:50.375Z",
"answer": 23770
},
{
... | 1 | [] | {
"lo": -2.4,
"mid": 1.57,
"hi": 5.75
} | ||||
12aefd | nt_num_divisors_compute_v1_1918700295_1211 | Let $n$ be the maximum value of $xy$ over all pairs of positive integers $(x, y)$ such that $x + y = 188$. Compute the number of positive divisors of $n$. | 9 | graphs = [
Graph(
let={
"_n": Const(188),
"n": MaxOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(Sum(Var("x"), Var("y")), Ref("_n")))), expr=Mul(Var("x"), Var("y")))),
... | NT | null | COMPUTE | sympy | B1 | [
"B1"
] | 5b950e | nt_num_divisors_compute_v1 | null | 3 | 0 | [
"B1"
] | 1 | 0.02 | 2026-02-08T05:40:13.615325Z | {
"verified": true,
"answer": 9,
"timestamp": "2026-02-08T05:40:13.635256Z"
} | 1a784d | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 90,
"completion_tokens": 382
},
"timestamp": "2026-02-12T13:20:30.099Z",
"answer": 9
},
{
... | 1 | [
{
"lemma": "B1",
"status": "ok"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
}
] | {
"lo": -5.55,
"mid": -3.01,
"hi": 0.32
} | ||
2a373e | alg_sym_quad_system_v1_1218484723_5369 | Let $(a, b, c)$ range over ordered triples of positive integers satisfying
$$a^{2} + b^{2} + c^{2} = ab + bc + ca$$
and
$$6a + 7b + 4c = \min\{ x + y : x > 0,\ y > 0,\ xy = 12866569 \}.$$
Compute the remainder when
$$\sum_{(a, b, c)} \bigl(a^{3} + b^{3} + c^{3}\bigr)$$
(over all such triples $(a, b, c)$) is divided by ... | 4,284 | graphs = [
Graph(
let={
"_c": Const(7),
"_m": Const(2),
"_n": Const(3),
"result": Mod(value=SumOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("a"), Var("b"), Var("c")]), condition=And(Eq(Sum(Pow(Var("a"), Const(2)), Pow(Var("b"), Const(2)), Po... | ALG | null | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM/C3",
"B3"
] | 6eac61 | alg_sym_quad_system_v1 | null | 8 | 0 | [
"B3",
"C3",
"LIN_FORM"
] | 3 | 0.022 | 2026-02-25T06:57:15.080246Z | {
"verified": true,
"answer": 4284,
"timestamp": "2026-02-25T06:57:15.101900Z"
} | 0d740a | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 363,
"completion_tokens": 32768
},
"timestamp": "2026-03-29T20:49:49.298Z",
"answer": null
},
{
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "C3",
"status": "ok_later"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
}
] | {
"lo": 3.81,
"mid": 6.33,
"hi": 9.49
} | ||
196e37 | comb_count_derangements_v1_601307018_6024 | Let $R = (3a^4 + a^2 - 4a + 1) \bmod 4489$, $S = (3R^4 + R^2 - 4R + 1) \bmod 4489$, and let $n$ be the number of non-negative integers $a$ in $[0, 4488]$ such that $S = a$ and $R \neq a$. Let $T = D_n$, the number of derangements of $n$ elements. Compute $38809 - T$. | 23,976 | graphs = [
Graph(
let={
"_n": Const(2),
"n": CountOverSet(set=SolutionsSet(var=Var("a"), condition=And(Geq(Var("a"), Const(0)), Leq(Var("a"), Const(4488)), Eq(Ref("_po_p2"), Var("a")), Neq(Ref("_po_p1"), Var("a"))))),
"result": Subfactorial(arg=Ref(name='n')),
... | COMB | null | COUNT | sympy | LIN_FORM | [
"POLY_ORBIT_HENSEL"
] | 53b6eb | comb_count_derangements_v1 | null | 5 | 0 | [
"LIN_FORM",
"POLY_ORBIT_HENSEL"
] | 2 | 0.032 | 2026-03-10T06:37:00.827714Z | {
"verified": true,
"answer": 23976,
"timestamp": "2026-03-10T06:37:00.860118Z"
} | d0ca1c | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 229,
"completion_tokens": 15721
},
"timestamp": "2026-04-19T03:26:29.221Z",
"answer": 23976
},
{
... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "POLY_ORBIT_HENSEL",
"status": "ok"
},
{
"lemma": "V8_SUM"... | {
"lo": 2.1,
"mid": 5.36,
"hi": 8.63
} | ||
05bc4d | antilemma_sum_equals_v1_898971024_851 | Let $T$ be the set of all integers $t$ such that $10 \leq t \leq 123$ and there exist positive integers $a \leq 12$, $b \leq 13$ satisfying $t = 7a + 3b$. Let $N = |T|$. Determine the number of ordered pairs $(i, j)$ of positive integers such that $i \leq 100$, $j \leq 101$, and $i + j = N$. | 100 | graphs = [
Graph(
let={
"_n": CountOverSet(set=SolutionsSet(var=Var("t"), condition=Exists(var=Var(name='a'), condition=Exists(var=Var(name='b'), condition=And(Geq(left=Var(name='a'), right=Const(value=1)), Leq(left=Var(name='a'), right=Const(value=12)), Geq(left=Var(name='b'), right=Const(value... | COMB | GEOM | COMPUTE | sympy | COUNT_SUM_EQUALS | [
"LIN_FORM/COUNT_SUM_EQUALS",
"COUNT_SUM_EQUALS"
] | ada383 | antilemma_sum_equals_v1 | null | 5 | 0 | [
"COUNT_SUM_EQUALS",
"LIN_FORM"
] | 2 | 0.064 | 2026-02-08T15:42:00.184742Z | {
"verified": true,
"answer": 100,
"timestamp": "2026-02-08T15:42:00.248997Z"
} | 9b9aac | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 218,
"completion_tokens": 4160
},
"timestamp": "2026-02-24T18:25:57.854Z",
"answer": 100
},
{
"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": -4.1,
"mid": -1.76,
"hi": 1.3
} | ||
0f44bd | comb_count_derangements_v1_1439011603_980 | Let $n_2 = 0$. Define
$$
c = \sum_{k=0}^{n_2} (-1)^k \binom{n_2}{k}.
$$
Let $a = 2$ and $b = 4c$. Define $n_1 = a + b$. Now let
$$
u = \sum_{k_1=0}^{n_1} (-1)^{k_1} \binom{n_1}{k_1}.
$$
Let $S$ be the set of all ordered pairs $(x_1, x_2)$ of positive odd integers such that
$$
x_1 + x_2 = \left| T \right|,
$$
where $T$ ... | 3,260 | graphs = [
Graph(
let={
"_m": Const(72861),
"_n": Const(50747),
"n2": Const(0),
"c": Summation(var="k", start=Const(0), end=Ref("n2"), expr=Mul(Pow(Const(-1), Var("k")), Binom(n=Ref("n2"), k=Var("k")))),
"a": Const(2),
"b": Mul(Const(4)... | COMB | null | COUNT | sympy | COMB1 | [
"COMB1/COMB1/BINOMIAL_ALTERNATING"
] | 6a21c9 | comb_count_derangements_v1 | null | 6 | 2 | [
"BINOMIAL_ALTERNATING",
"COMB1"
] | 2 | 0.006 | 2026-02-08T15:50:51.807399Z | {
"verified": true,
"answer": 3260,
"timestamp": "2026-02-08T15:50:51.813367Z"
} | 60a72a | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 336,
"completion_tokens": 1984
},
"timestamp": "2026-02-24T18:43:58.187Z",
"answer": 3260
},
{
"... | 1 | [
{
"lemma": "BINOMIAL_ALTERNATING",
"status": "ok_later"
},
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COMB1",
"status": "ok"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INT... | {
"lo": -2.4,
"mid": 1.57,
"hi": 5.75
} | ||
9ddbd8 | antilemma_k2_v1_971394319_1562 | Let $m = 321$. Let $n$ be the sum of all real solutions $x$ to the equation $x^2 - 321x - 7182 = 0$. Define
$$
x = \sum_{k=1}^{n} \phi(k) \left\lfloor \frac{m}{k} \right\rfloor.
$$
Let $S$ be the sum of $\phi(d)$ over all positive divisors $d$ of $293$. Compute the remainder when
$$
x \bmod S + 7001 \cdot (x \bmod 337)... | 3,017 | graphs = [
Graph(
let={
"_m": Const(321),
"_n": SumOverSet(set=SolutionsSet(var=Var("x"), condition=Eq(Sum(Pow(Var("x"), Const(2)), Mul(Const(-321), Var("x")), Const(-7182)), Const(0)))),
"x": Summation(var="k", start=Const(1), end=Ref("_n"), expr=Mul(EulerPhi(n=Var("k"))... | NT | COMB | COMPUTE | sympy | K13 | [
"K3",
"VIETA_SUM/K2",
"K2"
] | a72500 | antilemma_k2_v1 | two_moduli | 6 | 0 | [
"K13",
"K2",
"K3",
"VIETA_SUM"
] | 4 | 0.005 | 2026-02-08T13:44:37.101560Z | {
"verified": true,
"answer": 3017,
"timestamp": "2026-02-08T13:44:37.106386Z"
} | 47182d | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 184,
"completion_tokens": 1311
},
"timestamp": "2026-02-15T20:22:21.938Z",
"answer": 3017
},
{... | 1 | [
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "K2",
"status": "ok"
},
{
"lemma": "K3",
"status": "ok"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma... | {
"lo": -5.49,
"mid": 0.22,
"hi": 6.51
} | ||
ab6af5 | nt_max_prime_below_v1_151522320_997 | Let $S$ be the set of all positive integers $p$ for which there exists a positive integer $q$ such that $pq = 54$, $\gcd(p,q) = 1$, and $p < q$. Let $m$ be the number of elements in $S$. Determine the value of the largest prime number $n$ such that $m \leq n \leq 63504$. Then compute the remainder when $84162$ times th... | 27,309 | graphs = [
Graph(
let={
"upper": Const(63504),
"result": MaxOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), CountOverSet(set=SolutionsSet(var=Var("p"), condition=And(IsPositive(arg=Var(name='p')), Exists(var=Var(name='q'), condition=And(Eq(left=Mul(Var(name='p'), V... | NT | null | EXTREMUM | sympy | COPRIME_PAIRS | [
"COPRIME_PAIRS"
] | 2bb3aa | nt_max_prime_below_v1 | null | 4 | 0 | [
"COPRIME_PAIRS"
] | 1 | 1.499 | 2026-02-08T03:42:18.319026Z | {
"verified": true,
"answer": 27309,
"timestamp": "2026-02-08T03:42:19.817564Z"
} | ac1b79 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 216,
"completion_tokens": 5204
},
"timestamp": "2026-02-10T15:31:39.395Z",
"answer": 27309
},
{
"... | 1 | [
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",... | {
"lo": -3.46,
"mid": 1.03,
"hi": 5.49
} | ||
f63c8e | alg_poly_orbit_hensel_v1_1218484723_3947 | For a non-negative integer $a$, define $N = (a^3 - a) \bmod 2809$ and $M = (N^3 - N) \bmod 2809$. Find the number of integers $a$ with $0 \leq a \leq 356742$ such that $M = a$ and $N \neq a$. | 6,604 | graphs = [
Graph(
let={
"p1": Mod(value=Sum(Pow(Var("a"), Const(3)), Mul(Const(-1), Var("a"))), modulus=Const(2809)),
"p2": Mod(value=Sum(Pow(Ref("p1"), Const(3)), Mul(Const(-1), Ref("p1"))), modulus=Const(2809)),
"result": CountOverSet(set=SolutionsSet(var=Var("a"), cond... | ALG | null | COUNT | sympy | POLY_ORBIT_COUNT | [
"POLY_ORBIT_COUNT"
] | 4ad965 | alg_poly_orbit_hensel_v1 | null | 5 | null | [
"POLY_ORBIT_COUNT"
] | 1 | 0.023 | 2026-02-25T05:34:01.112876Z | {
"verified": true,
"answer": 6604,
"timestamp": "2026-02-25T05:34:01.135770Z"
} | 655e6f | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 190,
"completion_tokens": 6850
},
"timestamp": "2026-03-29T13:02:25.015Z",
"answer": 52
},
{
"... | 1 | [
{
"lemma": "POLY_ORBIT_COUNT",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
}
] | {
"lo": 1.55,
"mid": 4.7,
"hi": 7.23
} | ||
632dc9_n | alg_qf_psd_orbit_v1_601307018_3625 | A game board has tiles labeled by pairs of integers $(a, b)$ where $1 \leq a, b \leq 25$. A tile is *activated* if $b^2 + 16a^2 - 8ab = 169$. Let $M$ be the number of activated tiles. In a second phase, players place tokens on new positions $(a_1, b_1)$ with $1 \leq a_1 \leq b_1 \leq 398$, satisfying $M \cdot b_1^2 + 9... | 6 | ALG | null | COUNT | sympy | POLY_ORBIT_HENSEL | [
"POLY4_COUNT/QF_PSD_COUNT_LEQ",
"B3_DIFF/QF_PSD_COUNT_LEQ",
"QF_PSD_COUNT/POLY4_COUNT"
] | 9d49c9 | alg_qf_psd_orbit_v1 | null | 7 | null | [
"B3_DIFF",
"POLY4_COUNT",
"POLY_ORBIT_HENSEL",
"QF_PSD_COUNT",
"QF_PSD_COUNT_LEQ"
] | 5 | 5.79 | 2026-03-10T04:14:52.704146Z | null | 58f27e | 632dc9 | narrative | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 249,
"completion_tokens": 14562
},
"timestamp": "2026-03-29T17:51:10.792Z",
"answer": 6
},
{
"id"... | 1 | [
{
"lemma": "B3_DIFF",
"status": "ok"
},
{
"lemma": "POLY4_COUNT",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "QF_PSD_COUNT",
"status": "ok"
},
{
"lemma": "QF_PSD_COUNT_LEQ",
"status": "ok_later"
}
] | {
"lo": -5.36,
"mid": 0.27,
"hi": 5.45
} | |
5a95ad | antilemma_k2_v1_798873815_156 | Compute $$
Q = \left( 40781 \cdot \sum_{k=1}^{442} \phi(k) \left\lfloor \frac{442}{k} \right\rfloor \right) \bmod 88380.
$$ Find the value of $Q$. | 15,743 | graphs = [
Graph(
let={
"_n": Const(442),
"x": Summation(var="k", start=Const(1), end=Ref("_n"), expr=Mul(EulerPhi(n=Var("k")), Floor(Div(Const(442), Var("k"))))),
"_c": Const(40781),
"Q": Mod(value=Mul(Ref("_c"), Ref("x")), modulus=Const(88380)),
},
... | NT | COMB | COMPUTE | sympy | K2 | [
"K2"
] | 6897ab | antilemma_k2_v1 | null | 5 | 0 | [
"K2"
] | 1 | 0 | 2026-02-08T02:29:47.037960Z | {
"verified": true,
"answer": 15743,
"timestamp": "2026-02-08T02:29:47.038421Z"
} | 7aa5e7 | 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": 17953
},
"timestamp": "2026-02-23T14:07:25.000Z",
"answer": 15743
},
{
... | 1 | [
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "K2",
"status": "ok"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "V1",
"status": "no"
}
] | {
"lo": 0.04,
"mid": 1.72,
"hi": 3.19
} | ||
860229 | algebra_quadratic_discriminant_v1_579913215_193 | Let $n = 4$, $a = -8$, and $c = 5$. Let $b$ be the number of positive integers $p$ for which there exists a positive integer $q$ such that $pq = 1470$, $\gcd(p, q) = 1$, and $p < q$.
Define $\text{result} = b^2 - n \cdot a \cdot c$.
Compute $\text{result}$. | 224 | graphs = [
Graph(
let={
"_n": Const(4),
"a": Const(-8),
"b": 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=1470)), Eq(left=GCD(a... | NT | null | COMPUTE | sympy | COPRIME_PAIRS | [
"COPRIME_PAIRS"
] | 2bb3aa | algebra_quadratic_discriminant_v1 | null | 6 | 0 | [
"COPRIME_PAIRS"
] | 1 | 0.003 | 2026-02-08T12:58:10.686305Z | {
"verified": true,
"answer": 224,
"timestamp": "2026-02-08T12:58:10.688822Z"
} | 66a9c7 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 141,
"completion_tokens": 946
},
"timestamp": "2026-02-15T08:00:48.457Z",
"answer": 224
},
{
... | 1 | [
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "VAL_SUM_EQ",
"s... | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
f5b699 | nt_count_intersection_v1_1125832087_1182 | Let $a$ be the number of positive integers $n$ from 1 to the largest prime number less than or equal to 16 that are relatively prime to 12. Let $N = 50000$ and $b = 22$. Let $r$ be the number of positive integers $n$ from 1 to $N$, inclusive, that are divisible by $a$ and relatively prime to $b$. Let $Q$ be the remaind... | 64,184 | graphs = [
Graph(
let={
"_n": Const(2),
"N": Const(50000),
"a": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), MaxOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Ref("_n")), Leq(Var("n"), Const(16)), IsP... | NT | null | COUNT | sympy | MAX_PRIME_BELOW | [
"MAX_PRIME_BELOW/C4"
] | a99ef8 | nt_count_intersection_v1 | null | 4 | 0 | [
"C4",
"MAX_PRIME_BELOW"
] | 2 | 9.019 | 2026-02-08T03:35:27.281905Z | {
"verified": true,
"answer": 64184,
"timestamp": "2026-02-08T03:35:36.300494Z"
} | dbe765 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 226,
"completion_tokens": 3131
},
"timestamp": "2026-02-10T13:56:47.013Z",
"answer": 64184
},
{
... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "C4",
"status": "ok_later"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok"
},
... | {
"lo": -3.49,
"mid": 1.84,
"hi": 7.55
} | ||
c72494 | nt_max_prime_below_v1_1080341949_190 | Let $n = 8$. Let $c$ be the number of positive integers $k \leq n$ such that $3$ divides the $k$-th Fibonacci number. Let $U = 80656$. Determine the value of the largest prime number $p$ such that $c \leq p \leq U$. | 80,651 | graphs = [
Graph(
let={
"_n": Const(8),
"upper": Const(80656),
"result": MaxOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Ref("_n")), Divides(divisor=Cons... | NT | null | EXTREMUM | sympy | COUNT_FIB_DIVISIBLE | [
"COUNT_FIB_DIVISIBLE"
] | 66de3c | nt_max_prime_below_v1 | null | 6 | 0 | [
"COUNT_FIB_DIVISIBLE"
] | 1 | 4.225 | 2026-02-08T13:16:52.092861Z | {
"verified": true,
"answer": 80651,
"timestamp": "2026-02-08T13:16:56.317906Z"
} | 6850ff | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 114,
"completion_tokens": 3629
},
"timestamp": "2026-02-15T12:17:24.672Z",
"answer": 80651
},
... | 1 | [
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "ok"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
}
] | {
"lo": -5.49,
"mid": 0.22,
"hi": 6.51
} | ||
50f97b | geo_visible_lattice_v1_153355830_2379 | Let $ n = 66 $. Define $ L $ to be the number of ordered pairs of positive integers $ (x, y) $ such that $ 1 \leq x, y \leq n $ and $ \gcd(x, y) = 1 $. Compute the remainder when $ 44121 \cdot L $ is divided by $ 62152 $. | 46,887 | graphs = [
Graph(
let={
"n": Const(66),
"result": VisibleLatticePoints(n=Ref(name='n')),
"Q": Mod(value=Mul(Const(44121), Ref("result")), modulus=Const(62152)),
},
goal=Ref("Q"),
)
] | GEOM | null | COUNT | sympy | [] | geo_visible_lattice_v1 | null | 5 | 0 | null | null | 0.728 | 2026-02-08T07:05:16.295867Z | {
"verified": true,
"answer": 46887,
"timestamp": "2026-02-08T07:05:17.024148Z"
} | c77a21 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 188,
"completion_tokens": 32768
},
"timestamp": "2026-02-24T07:37:46.427Z",
"answer": null
},
{
... | 1 | [] | {
"lo": 3.25,
"mid": 5.68,
"hi": 8.81
} | ||||
e1a219 | comb_sum_binomial_row_v1_1218484723_6553 | Let $n$ be the number of ordered pairs $(a, b)$ of positive integers with $1 \leq a \leq b \leq 35$ such that $2a^2 + 2b^2 - 4ab = 1152$. Compute $2^n$. | 2,048 | graphs = [
Graph(
let={
"_n": Const(2),
"n": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("a"), Var("b")]), condition=And(Geq(Var("a"), Const(1)), Leq(Var("a"), Const(35)), Geq(Var("b"), Const(1)), Leq(Var("b"), Const(35)), Leq(Var("a"), Var("b")), Eq(Sum(Mul(Const(2), Pow(V... | COMB | null | SUM | sympy | QF_PSD_ORBIT | [
"QF_PSD_ORBIT"
] | 1d37f3 | comb_sum_binomial_row_v1 | null | 4 | 0 | [
"QF_PSD_ORBIT"
] | 1 | 0.001 | 2026-02-25T08:06:28.286696Z | {
"verified": true,
"answer": 2048,
"timestamp": "2026-02-25T08:06:28.288032Z"
} | 02992f | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 173,
"completion_tokens": 584
},
"timestamp": "2026-03-30T02:09:18.371Z",
"answer": 2048
},
{
"id... | 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": "QF_PSD_ORBIT",
"status": "ok"
},
{
"lemm... | {
"lo": -6.2,
"mid": -2.87,
"hi": 0.44
} | ||
b1965f | antilemma_cartesian_v1_153355830_3019 | Let $x$ be the number of ordered pairs $(a, b)$ such that $1 \leq a \leq 30$ and $1 \leq b \leq 32$. Let $c = 74917$. Find the remainder when $c \cdot x$ is divided by $51561$. | 44,286 | graphs = [
Graph(
let={
"x": CountOverSet(set=CartesianProduct(left=IntegerRange(start=Const(1), end=Const(30)), right=IntegerRange(start=Const(1), end=Const(32)))),
"_c": Const(74917),
"Q": Mod(value=Mul(Ref("_c"), Ref("x")), modulus=Const(51561)),
},
goa... | COMB | GEOM | COMPUTE | sympy | COUNT_CARTESIAN | [
"COUNT_CARTESIAN"
] | 409d7d | antilemma_cartesian_v1 | null | 2 | 0 | [
"COUNT_CARTESIAN"
] | 1 | 0 | 2026-02-08T07:32:49.939364Z | {
"verified": true,
"answer": 44286,
"timestamp": "2026-02-08T07:32:49.939860Z"
} | 65f196 | 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": 6880
},
"timestamp": "2026-02-24T08:12:59.456Z",
"answer": 44286
},
{
"... | 1 | [
{
"lemma": "COUNT_CARTESIAN",
"status": "ok"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8_SU... | {
"lo": -2.35,
"mid": 1.22,
"hi": 4.84
} | ||
b25e43 | antilemma_k3_v1_784195855_6938 | Compute the sum of $\phi(d)$ over all positive divisors $d$ of $20454$, where $\phi$ denotes Euler's totient function. | 20,454 | graphs = [
Graph(
let={
"_n": Const(20454),
"x": SumOverDivisors(n=Ref(name='_n'), var='d', expr=EulerPhi(n=Var(name='d'))),
},
goal=Ref("x"),
)
] | NT | COMB | COMPUTE | sympy | K3 | [
"K3"
] | 54c41e | antilemma_k3_v1 | null | 3 | 0 | [
"K3"
] | 1 | 0 | 2026-02-08T09:00:56.118205Z | {
"verified": true,
"answer": 20454,
"timestamp": "2026-02-08T09:00:56.118622Z"
} | 812225 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 77,
"completion_tokens": 723
},
"timestamp": "2026-02-13T23:06:36.022Z",
"answer": 20454
},
{
... | 1 | [
{
"lemma": "K3",
"status": "ok"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
}
] | {
"lo": -3.51,
"mid": 1.33,
"hi": 6.56
} | ||
2a8a7a | nt_count_divisible_v1_1978505735_776 | Let $s = \sum_{k=0}^{4} (-1)^k \binom{4}{k}$. Compute the number of integers $n$ such that $0! \leq n \leq 32768$ and $n \equiv s \pmod{30}$. | 1,092 | graphs = [
Graph(
let={
"upper": Const(32768),
"divisor": Const(30),
"result": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Factorial(Const(0))), Leq(Var("n"), Ref("upper")), Eq(Mod(value=Var("n"), modulus=Ref("divisor")), Summation(var="k", sta... | COMB | null | COUNT | sympy | BINOMIAL_ALTERNATING | [
"BINOMIAL_ALTERNATING",
"ONE_FACTORIAL_0"
] | 8794cb | nt_count_divisible_v1 | null | 5 | 0 | [
"BINOMIAL_ALTERNATING",
"ONE_FACTORIAL_0"
] | 2 | 1.261 | 2026-02-08T15:35:25.768151Z | {
"verified": true,
"answer": 1092,
"timestamp": "2026-02-08T15:35:27.028980Z"
} | f88fac | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 174,
"completion_tokens": 621
},
"timestamp": "2026-02-24T18:06:42.669Z",
"answer": 1092
},
{
"i... | 1 | [
{
"lemma": "BINOMIAL_ALTERNATING",
"status": "ok"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "ONE_FACTORIAL_0",
"status": "ok"
},
{
... | {
"lo": -8,
"mid": -4.75,
"hi": -2.28
} | ||
fca2bb | antilemma_sum_equals_v1_865884756_4393 | Let $T$ be the set of all integers $t$ such that $9 \leq t \leq 74$ and there exist positive integers $a$, $b$ with $1 \leq a \leq 23$, $1 \leq b \leq 4$, and $t = 2a + 7b$. Let $m = |T|$. Determine the number of ordered pairs $(i, j)$ of positive integers such that $1 \leq i \leq 58$, $1 \leq j \leq 58$, and $i + j = ... | 56 | 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=23)), Geq(left=Var(name='b'), right=Const(value... | COMB | GEOM | COMPUTE | sympy | COUNT_CARTESIAN | [
"COUNT_SUM_EQUALS/COUNT_SUM_EQUALS",
"LIN_FORM/COUNT_SUM_EQUALS",
"COUNT_SUM_EQUALS"
] | b43a9c | antilemma_sum_equals_v1 | null | 4 | 0 | [
"COUNT_CARTESIAN",
"COUNT_SUM_EQUALS",
"LIN_FORM"
] | 3 | 0.097 | 2026-02-08T17:54:50.520214Z | {
"verified": true,
"answer": 56,
"timestamp": "2026-02-08T17:54:50.617275Z"
} | 80c8db | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 236,
"completion_tokens": 2325
},
"timestamp": "2026-02-18T09:46:45.588Z",
"answer": 56
},
{
... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "ok"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "V8",
"statu... | {
"lo": -2.38,
"mid": 1.74,
"hi": 6.59
} | ||
6d307e | antilemma_v7_kummer_151522320_239 | Let $x$ be the largest integer $k$ such that $3^k$ divides $\binom{4813}{1925}$. Compute the value of $x + 2^{x \bmod 16} \bmod 82528$. | 135 | graphs = [
Graph(
let={
"_n": Const(3),
"x": MaxKDivides(target=Binom(n=Const(4813), k=Const(1925)), base=Ref("_n")),
"Q": Sum(Ref("x"), Mod(value=Pow(Const(2), Mod(value=Ref("x"), modulus=Const(16))), modulus=Const(82528))),
},
goal=Ref("Q"),
)
] | NT | null | COMPUTE | sympy | V7 | [
"V7"
] | 0672d4 | antilemma_v7_kummer | null | 7 | 0 | [
"V7"
] | 1 | 0.003 | 2026-02-08T03:05:55.183087Z | {
"verified": true,
"answer": 135,
"timestamp": "2026-02-08T03:05:55.186578Z"
} | cf5350 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 168,
"completion_tokens": 2613
},
"timestamp": "2026-02-09T00:40:22.141Z",
"answer": 135
},
{
"i... | 1 | [
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "V7",
"status": "ok"
}
] | {
"lo": -6.49,
"mid": 0.51,
"hi": 7.52
} | ||
6098f2_l | modular_sum_quadratic_residues_v1_1520064083_4820 | Let $ p = 673 $. Define $ \text{result} = \frac{p(p-1)}{4} $. Let $ Q $ be the Bell number corresponding to $ |\text{result}| \bmod 11 $. Compute $ Q $. | 1 | COMB | null | SUM | sympy | B3 | [
"B3"
] | 0cd20d | modular_sum_quadratic_residues_v1 | null | 4 | 0 | [
"B3"
] | 1 | 0.009 | 2026-02-08T06:26:48.257521Z | {
"verified": false,
"answer": 203,
"timestamp": "2026-02-08T06:26:48.266510Z"
} | 5308c8 | 6098f2 | legacy_text | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 163,
"completion_tokens": 744
},
"timestamp": "2026-02-24T06:16:00.913Z",
"answer": 203
},
{
"id"... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
}
] | {
"lo": -2.46,
"mid": 0.47,
"hi": 3.59
} | |
937b02 | comb_factorial_compute_v1_548369836_205 | Let $n = 8$. Compute $n! + \phi(|n!| + 1) + \tau(|n!| + \phi(1))$, where $\phi$ is Euler's totient function and $\tau(m)$ denotes the number of positive divisors of $m$. | 79,924 | graphs = [
Graph(
let={
"n": Const(8),
"result": Factorial(Ref("n")),
"Q": Sum(Ref("result"), EulerPhi(n=Sum(Abs(arg=Ref(name='result')), Const(1))), NumDivisors(n=Sum(Abs(arg=Ref(name='result')), EulerPhi(n=Const(1))))),
},
goal=Ref("Q"),
)
] | NT | null | COMPUTE | sympy | ONE_PHI_1 | [
"ONE_PHI_1"
] | f6b5a5 | comb_factorial_compute_v1 | null | 3 | 0 | [
"ONE_PHI_1"
] | 1 | 0.001 | 2026-02-08T02:49:15.233038Z | {
"verified": true,
"answer": 79924,
"timestamp": "2026-02-08T02:49:15.234005Z"
} | 3a5a39 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 176,
"completion_tokens": 1252
},
"timestamp": "2026-02-08T20:11:59.371Z",
"answer": 79924
},
{
"... | 1 | [
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "ONE_PHI_1",
"status": "ok"
},
{
"lemma": "V1",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
},
{
"lemma": "VAL_SUM_EQ",
"status": "no"
}
] | {
"lo": -4.84,
"mid": -1.65,
"hi": 1.89
} | ||
7ea8e5 | comb_sum_binomial_row_v1_1125832087_607 | Let $n$ be the number of integers $j$ with $0 \leq j \leq 74304$ such that $\binom{74304}{j}$ is odd. Let $m$ be the number of positive integers $p$ such that there exists a positive integer $q$ with $\gcd(p, q) = 1$, $p < q$, and $p \cdot q = 6$. Compute $m^n$. | 65,536 | graphs = [
Graph(
let={
"_n": Const(2),
"n": CountOverSet(set=SolutionsSet(var=Var("j"), condition=And(Geq(Var("j"), Const(0)), Leq(Var("j"), Const(74304)), Eq(Mod(value=Binom(n=Const(74304), k=Var("j")), modulus=Ref("_n")), Const(1))), domain='nonnegative_integers')),
"r... | NT | null | SUM | sympy | COPRIME_PAIRS | [
"COPRIME_PAIRS",
"V8"
] | aeb4d5 | comb_sum_binomial_row_v1 | null | 6 | 0 | [
"COPRIME_PAIRS",
"V8"
] | 2 | 0.002 | 2026-02-08T03:10:04.153344Z | {
"verified": true,
"answer": 65536,
"timestamp": "2026-02-08T03:10:04.155292Z"
} | 725fe3 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 207,
"completion_tokens": 679
},
"timestamp": "2026-02-10T13:15:58.159Z",
"answer": 65536
},
{
"i... | 1 | [
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
},
... | {
"lo": -3.53,
"mid": 1.02,
"hi": 5.49
} | ||
1480ef | comb_catalan_compute_v1_601307018_6022 | Let $n$ be the number of integers $t$ such that $t = 3a + 2b + 2$ for some integers $a, b$ with $1 \leq a \leq 3$, $1 \leq b \leq 4$, and $7 \leq t \leq 19$. Let $M = C_n$, where $C_n$ denotes the $n$-th Catalan number. Find the remainder when $86729 \cdot M$ is divided by $73010$. | 16,674 | graphs = [
Graph(
let={
"n": CountOverSet(set=SolutionsSet(var=Var("t"), condition=Exists(var=Var(name='a'), condition=Exists(var=Var(name='b'), condition=And(Geq(left=Var(name='a'), right=Const(value=1)), Leq(left=Var(name='a'), right=Const(value=3)), Geq(left=Var(name='b'), right=Const(value=1... | COMB | null | COMPUTE | sympy | K13 | [
"LIN_FORM"
] | 7b2633 | comb_catalan_compute_v1 | null | 3 | 0 | [
"K13",
"LIN_FORM"
] | 2 | 0.028 | 2026-03-10T06:36:55.898165Z | {
"verified": true,
"answer": 16674,
"timestamp": "2026-03-10T06:36:55.926030Z"
} | 9bb463 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 226,
"completion_tokens": 2465
},
"timestamp": "2026-04-19T03:24:39.934Z",
"answer": 16674
},
{
... | 1 | [
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "V8",
"status": "no"
},
{
"lemma": "V8_SUM",
... | {
"lo": -5.35,
"mid": 0.52,
"hi": 5.84
} | ||
961bee | sequence_fibonacci_compute_v1_48377204_367 | Let $n = \sum_{k=1}^{6} \phi(k) \left\lfloor \frac{6}{k} \right\rfloor$, where $\phi$ denotes Euler's totient function. Compute the $n$-th Fibonacci number, where 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$. | 10,946 | graphs = [
Graph(
let={
"_n": Const(6),
"n": Summation(var="k", start=Const(1), end=Ref("_n"), expr=Mul(EulerPhi(n=Var("k")), Floor(Div(Const(6), Var("k"))))),
"result": Fibonacci(arg=Ref(name='n')),
"Q": Ref("result"),
},
goal=Ref("Q"),
)
... | NT | null | COMPUTE | sympy | K2 | [
"K2"
] | 6897ab | sequence_fibonacci_compute_v1 | null | 4 | 0 | [
"K2"
] | 1 | 0.001 | 2026-02-08T15:22:02.648646Z | {
"verified": true,
"answer": 10946,
"timestamp": "2026-02-08T15:22:02.649846Z"
} | 12fcbc | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 148,
"completion_tokens": 724
},
"timestamp": "2026-02-16T05:49:47.581Z",
"answer": 10946
},
{... | 1 | [
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K2",
"status": "ok"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
aae7d8 | sequence_lucas_compute_v1_601307018_1354 | Let $M = L_{18}$, where $L_n$ denotes the $n$-th Lucas number. Find the remainder when $M^2 + 33M + \sum_{k=1}^{8} k$ is divided by $50633$. | 6,315 | graphs = [
Graph(
let={
"_n": Const(2),
"n": Const(18),
"result": Lucas(arg=Ref(name='n')),
"Q": Mod(value=Sum(Pow(Ref("result"), Ref("_n")), Mul(Const(33), Ref("result")), Summation(var="k", start=Const(1), end=Const(8), expr=Var("k"))), modulus=Const(50633))... | ALG | null | COMPUTE | sympy | SUM_ARITHMETIC | [
"SUM_ARITHMETIC"
] | 609463 | sequence_lucas_compute_v1 | quadratic_mod | 3 | 0 | [
"SUM_ARITHMETIC"
] | 1 | 0.003 | 2026-03-10T02:01:55.871798Z | {
"verified": true,
"answer": 6315,
"timestamp": "2026-03-10T02:01:55.874725Z"
} | 9bd186 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 165,
"completion_tokens": 1059
},
"timestamp": "2026-03-29T02:01:59.320Z",
"answer": 6315
},
{
"i... | 1 | [
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "SUM_ARITHMETIC",
"status": "ok"
}
] | {
"lo": -0.92,
"mid": 2.07,
"hi": 4.68
} | ||
686ef1 | comb_catalan_compute_v1_349078426_1974 | Let $n$ be the number of elements in the Cartesian product of the sets $\{1, 2\}$ and $\{1, 2, 3, 4, 5\}$. Define $C_n$ to be the $n$th Catalan number. Compute the remainder when $85074 \cdot C_n$ is divided by $56549$. | 22,772 | graphs = [
Graph(
let={
"_n": Const(56549),
"n": CountOverSet(set=CartesianProduct(left=IntegerRange(start=Const(1), end=Const(2)), right=IntegerRange(start=Const(1), end=Const(5)))),
"result": Catalan(Ref("n")),
"_c": Const(85074),
"Q": Mod(value=... | COMB | null | COMPUTE | sympy | COUNT_CARTESIAN | [
"COUNT_CARTESIAN"
] | 409d7d | comb_catalan_compute_v1 | null | 3 | 0 | [
"COUNT_CARTESIAN"
] | 1 | 0.003 | 2026-02-08T14:02:24.359892Z | {
"verified": true,
"answer": 22772,
"timestamp": "2026-02-08T14:02:24.362456Z"
} | 61d5c9 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 189,
"completion_tokens": 2563
},
"timestamp": "2026-02-24T19:35:46.695Z",
"answer": 22772
},
{
"... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "ok"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8",
"status": ... | {
"lo": 1.15,
"mid": 4.18,
"hi": 6.61
} | ||
e43a4f | nt_count_intersection_v1_784195855_8694 | Let $N$ be the number of positive integers $k$ such that $1 \leq k \leq 555000$ and $111$ divides $k$. Let $a = 3$ and $b = 16$. Define $S$ as the set of all positive integers $n$ such that $1 \leq n \leq N$, $a$ divides $n$, and $\gcd(n, b) = 1$. Compute the number of elements in $S$. | 833 | graphs = [
Graph(
let={
"N": CountOverSet(set=SolutionsSet(var=Var("k"), condition=And(Geq(Var("k"), Const(1)), Leq(Var("k"), Const(555000)), Divides(divisor=Const(111), dividend=Var("k"))), domain='positive_integers')),
"a": Const(3),
"b": Const(16),
"result"... | NT | null | COUNT | sympy | C2 | [
"C2"
] | 9685eb | nt_count_intersection_v1 | null | 3 | 0 | [
"C2"
] | 1 | 0.237 | 2026-02-08T16:16:54.136740Z | {
"verified": true,
"answer": 833,
"timestamp": "2026-02-08T16:16:54.373535Z"
} | 157976 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 147,
"completion_tokens": 998
},
"timestamp": "2026-02-17T00:01:55.609Z",
"answer": 833
},
{
... | 1 | [
{
"lemma": "C2",
"status": "ok"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "V3",
"status": "no"
},
{
"lemma": "V7",
"status": "no... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
2adfb2 | nt_count_coprime_v1_1820931509_576 | Let $k$ be the smallest integer $d \geq 2$ that divides $7429$. Compute the number of positive integers $n \leq 10391$ such that $\gcd(n, k) = 1$. | 9,780 | graphs = [
Graph(
let={
"upper": Const(10391),
"k": MinOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Const(2)), Divides(divisor=Var("d"), dividend=Const(7429))))),
"result": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const... | NT | null | COUNT | sympy | MIN_PRIME_FACTOR | [
"MIN_PRIME_FACTOR"
] | bc3776 | nt_count_coprime_v1 | null | 4 | 0 | [
"MIN_PRIME_FACTOR"
] | 1 | 0.934 | 2026-02-08T11:46:38.104630Z | {
"verified": true,
"answer": 9780,
"timestamp": "2026-02-08T11:46:39.038419Z"
} | c48a35 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 94,
"completion_tokens": 797
},
"timestamp": "2026-02-14T18:42:43.666Z",
"answer": 9780
},
{
... | 1 | [
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "MIN_PRIME_FACTOR",
"status": "ok"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
}
] | {
"lo": -6.96,
"mid": -4.56,
"hi": -1.46
} | ||
553887 | sequence_fibonacci_compute_v1_1742523217_4691 | Let $n$ be the number of positive integers $k$ such that $1 \leq k \leq 37$ and $\gcd(k, 15) = 1$. Compute the $n$-th Fibonacci number, where the Fibonacci sequence is defined by $F_1 = 1$, $F_2 = 1$, and $F_m = F_{m-1} + F_{m-2}$ for $m \geq 3$. | 6,765 | graphs = [
Graph(
let={
"_n": Const(37),
"n": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Ref("_n")), Eq(GCD(a=Var("n"), b=Const(15)), Const(1))))),
"result": Fibonacci(arg=Ref(name='n')),
},
goal=Ref("r... | NT | null | COMPUTE | sympy | C4 | [
"C4"
] | 08d162 | sequence_fibonacci_compute_v1 | null | 4 | 0 | [
"C4"
] | 1 | 0.003 | 2026-02-08T09:05:15.398374Z | {
"verified": true,
"answer": 6765,
"timestamp": "2026-02-08T09:05:15.401042Z"
} | 905423 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 142,
"completion_tokens": 639
},
"timestamp": "2026-02-14T00:16:13.530Z",
"answer": 6765
},
{
... | 1 | [
{
"lemma": "C4",
"status": "ok"
},
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"stat... | {
"lo": -5.55,
"mid": -3.01,
"hi": 0.32
} | ||
378fc7 | alg_poly4_sum_v1_601307018_3195 | Find the remainder when $$\sum_{a=1}^{383} \sum_{b=1}^{383} \left( -172a \cdot b^{k} - 76a^3b + 97b^4 + 150a^2b^2 + 17a^4 \right)$$ is divided by $78437$, where $k = \left|\left\{ (a_1, b_1) \in \mathbb{Z}^+ \times \mathbb{Z}^+ : a_1 \leq 30,\ b_1 \leq 30,\ -2a_1b_1 + 5b_1^2 + 34a_1^2 = 10985 \right\}\right|$. | 11,091 | graphs = [
Graph(
let={
"_n": Const(17),
"result": Mod(value=SumOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("a"), Var("b")]), condition=And(Geq(Var("a"), Const(1)), Leq(Var("a"), Const(383)), Geq(Var("b"), Const(1)), Leq(Var("b"), Const(383)))), expr=Sum(Mul(Const... | ALG | null | COMPUTE | sympy | QF_PSD_COUNT | [
"QF_PSD_COUNT"
] | 09ce67 | alg_poly4_sum_v1 | null | 7 | 0 | [
"QF_PSD_COUNT"
] | 1 | 1.152 | 2026-03-10T03:45:18.400422Z | {
"verified": true,
"answer": 11091,
"timestamp": "2026-03-10T03:45:19.552462Z"
} | 3d0ba5 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 278,
"completion_tokens": 6674
},
"timestamp": "2026-03-29T07:47:04.027Z",
"answer": 66056
},
{
... | 1 | [
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "QF_PSD_COUNT",
"status": "ok"
}
] | {
"lo": 3.34,
"mid": 5.77,
"hi": 8.89
} | ||
b79467 | antilemma_v8_lucas_798873815_254 | Let $n = 47$. Let $S$ be the set of all ordered pairs $(x, y)$ of positive integers such that $xy = 529$. Let $s_{\text{min}}$ be the minimum value of $x + y$ as $(x, y)$ ranges over $S$. Let $\phi(n)$ denote Euler's totient function. Determine the number of nonnegative integers $j$ such that $\phi(n) - s_{\text{min}} ... | 512 | graphs = [
Graph(
let={
"_n": Const(47),
"x": CountOverSet(set=SolutionsSet(var=Var("j"), condition=And(Geq(Var("j"), Sub(EulerPhi(n=Ref("_n")), MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositiv... | NT | COMB | COMPUTE | sympy | B3 | [
"B3/ZERO_PHI_PRIME/V8",
"V8"
] | 4cac11 | antilemma_v8_lucas | null | 7 | 0 | [
"B3",
"V8",
"ZERO_PHI_PRIME"
] | 3 | 0.002 | 2026-02-08T02:31:57.063872Z | {
"verified": true,
"answer": 512,
"timestamp": "2026-02-08T02:31:57.065476Z"
} | 956954 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 237,
"completion_tokens": 1440
},
"timestamp": "2026-02-08T19:17:28.748Z",
"answer": 512
},
{
"id... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
... | {
"lo": -1.89,
"mid": 1.79,
"hi": 4.93
} | ||
628cdc | algebra_quadratic_discriminant_v1_1125832087_1213 | Let $n = 2$. Let $a = -2$. Define $b$ to be the number of positive integers $p$ for which there exists an integer $q$ such that $pq = 35135100$, $\gcd(p, q) = 1$, and $p < q$. Let $c = -128$. Define $D = b^n - 4ac$. Compute the value of $2 \cdot [D > 0] + [D = 0]$, where $[ \cdot ]$ denotes the Iverson bracket (1 if th... | 1 | graphs = [
Graph(
let={
"_n": Const(2),
"a": Const(-2),
"b": 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=35135100)), Eq(left=G... | NT | null | COMPUTE | sympy | MOBIUS_COPRIME | [
"COPRIME_PAIRS"
] | 2bb3aa | algebra_quadratic_discriminant_v1 | null | 6 | 0 | [
"COPRIME_PAIRS",
"MOBIUS_COPRIME"
] | 2 | 0.02 | 2026-02-08T03:36:48.687878Z | {
"verified": true,
"answer": 1,
"timestamp": "2026-02-08T03:36:48.707800Z"
} | 64d196 | 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": 1890
},
"timestamp": "2026-02-10T15:09:40.922Z",
"answer": 1
},
{
"id":... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
}
] | {
"lo": -5.55,
"mid": -3.02,
"hi": 0.31
} | ||
cd3378 | nt_min_phi_inverse_v1_548369836_251 | Let $m = 4$. Let $S$ be the set of all ordered pairs $(x, y)$ of positive integers such that $x \cdot y = m$. For each such pair, compute $x + y$, and let $n$ be the minimum of these sums. Let $P$ be the number of positive integers $p$ for which there exists a positive integer $q$ such that $p \cdot q = 180$, $\gcd(p, ... | 68,419 | graphs = [
Graph(
let={
"_m": Const(4),
"_n": MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(Mul(Var("x"), Var("y")), Ref("_m")))), expr=Sum(Var("x"), Var("y")))),
... | NT | null | EXTREMUM | sympy | COPRIME_PAIRS | [
"COPRIME_PAIRS/K2",
"B3/K2"
] | 2bf208 | nt_min_phi_inverse_v1 | null | 6 | 0 | [
"B3",
"COPRIME_PAIRS",
"K2"
] | 3 | 0.005 | 2026-02-08T02:49:42.140504Z | {
"verified": true,
"answer": 68419,
"timestamp": "2026-02-08T02:49:42.145844Z"
} | a598b6 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 315,
"completion_tokens": 1083
},
"timestamp": "2026-02-08T20:17:02.161Z",
"answer": 68419
},
{
"... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "K2",
"status": "ok_later"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lem... | {
"lo": -7.04,
"mid": -4.75,
"hi": -2.47
} | ||
f2e10c | geo_visible_lattice_v1_1742523217_5724 | Let $n = 128$. Define a lattice point $(x, y)$ to be visible from the origin if $\gcd(x, y) = 1$. Let $R$ be the number of visible lattice points $(x, y)$ with $1 \leq x, y \leq n$. Compute the remainder when $95731 \cdot R$ is divided by $86901$. | 40,670 | graphs = [
Graph(
let={
"n": Const(128),
"result": VisibleLatticePoints(n=Ref(name='n')),
"Q": Mod(value=Mul(Const(95731), Ref("result")), modulus=Const(86901)),
},
goal=Ref("Q"),
)
] | GEOM | null | COUNT | sympy | [] | geo_visible_lattice_v1 | null | 6 | 0 | null | null | 0.349 | 2026-02-08T11:11:59.501953Z | {
"verified": true,
"answer": 40670,
"timestamp": "2026-02-08T11:11:59.850495Z"
} | 9b0e99 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 193,
"completion_tokens": 5489
},
"timestamp": "2026-02-24T12:55:10.941Z",
"answer": 40670
},
{
"... | 1 | [] | {
"lo": 3.25,
"mid": 5.68,
"hi": 8.81
} | ||||
239d4c | comb_count_partitions_v1_971394319_1542 | Let $n$ be the smallest prime divisor of $5034311$. Let $p(n)$ denote the number of integer partitions of $n$. Compute the remainder when $33327 \cdot p(n)$ is divided by $81734$. | 52,551 | graphs = [
Graph(
let={
"n": MinOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Const(2)), Divides(divisor=Var("d"), dividend=Const(5034311))))),
"result": Partition(arg=Ref(name='n')),
"_c": Const(33327),
"Q": Mod(value=Mul(Ref("_c"), Ref("... | NT | COMB | COUNT | sympy | MIN_PRIME_FACTOR | [
"MIN_PRIME_FACTOR"
] | bc3776 | comb_count_partitions_v1 | null | 4 | 0 | [
"MIN_PRIME_FACTOR"
] | 1 | 0.002 | 2026-02-08T13:43:30.386725Z | {
"verified": true,
"answer": 52551,
"timestamp": "2026-02-08T13:43:30.389128Z"
} | 0c55be | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 96,
"completion_tokens": 2154
},
"timestamp": "2026-02-15T20:21:00.812Z",
"answer": 52551
},
{... | 1 | [
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "MIN_PRIME_FACTOR",
"status": "ok"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "V3",
"status": "no"
}... | {
"lo": -5.49,
"mid": 0.22,
"hi": 6.51
} | ||
211a3e | comb_catalan_compute_v1_458359167_2762 | Let $n$ be the number of integers $t$ satisfying $8 \leq t \leq 20$ for which there exist positive integers $a$ and $b$ with $1 \leq a \leq 4$, $1 \leq b \leq 3$, and $t = 2a + 3b + 3$. Compute the $n$-th Catalan number. | 58,786 | graphs = [
Graph(
let={
"n": CountOverSet(set=SolutionsSet(var=Var("t"), condition=Exists(var=Var(name='a'), condition=Exists(var=Var(name='b'), condition=And(Geq(left=Var(name='a'), right=Const(value=1)), Leq(left=Var(name='a'), right=Const(value=4)), Geq(left=Var(name='b'), right=Const(value=1... | COMB | null | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | comb_catalan_compute_v1 | null | 3 | 0 | [
"LIN_FORM"
] | 1 | 0.002 | 2026-02-08T06:45:53.777696Z | {
"verified": true,
"answer": 58786,
"timestamp": "2026-02-08T06:45:53.779729Z"
} | aa5128 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 199,
"completion_tokens": 2084
},
"timestamp": "2026-02-24T06:55:53.436Z",
"answer": 58786
},
{
"... | 1 | [
{
"lemma": "COUNT_COPRIME_GRID",
"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": -3.84,
"mid": -1.69,
"hi": 1.09
} | ||
ccb177 | nt_count_divisible_and_v1_655260480_2590 | Let $n = 792$ and let $u$ be the sum of all nonnegative integers $j$ with $0 \leq j \leq 792$ such that $\binom{792}{j}$ is odd. Determine the number of positive integers $n$ such that $1 \leq n \leq u$, $n$ is divisible by 6, and $n$ is divisible by 8. | 264 | graphs = [
Graph(
let={
"_n": Const(792),
"upper": SumOverSet(set=SolutionsSet(var=Var("j"), condition=And(Geq(Var("j"), Const(0)), Leq(Var("j"), Ref("_n")), Eq(Mod(value=Binom(n=Const(792), k=Var("j")), modulus=Const(2)), Const(1))), domain='nonnegative_integers')),
"d1"... | ALG | COMB | COUNT | sympy | V8 | [
"V8"
] | 86348e | nt_count_divisible_and_v1 | null | 5 | 0 | [
"V8"
] | 1 | 0.431 | 2026-02-08T16:50:46.101029Z | {
"verified": true,
"answer": 264,
"timestamp": "2026-02-08T16:50:46.531884Z"
} | a03c7f | 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": 1702
},
"timestamp": "2026-02-17T13:24:08.383Z",
"answer": 264
},
{
... | 1 | [
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8",
"status": "ok"
}
] | {
"lo": -2.38,
"mid": 1.74,
"hi": 6.59
} | ||
fe1bcf_n | alg_qf_psd_orbit_v1_601307018_1791 | A rectangular garden is divided into square plots of equal size. The number of plots along the width is $a$ and along the length is $b$, with $a \leq b$. The difference between the total number of plots aligned along the diagonal and those aligned along the perimeter contributes to a fixed pattern count, modeled by the... | 219 | ALG | null | COUNT | sympy | C5 | [
"C5"
] | 1d9668 | alg_qf_psd_orbit_v1 | null | 6 | null | [
"C5"
] | 1 | 0.475 | 2026-03-10T02:32:22.194820Z | null | 6cba60 | fe1bcf | narrative | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 220,
"completion_tokens": 891
},
"timestamp": "2026-03-29T15:27:12.697Z",
"answer": 219
},
{
"id"... | 1 | [
{
"lemma": "C5",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
}
] | {
"lo": -5.36,
"mid": 0.27,
"hi": 5.45
} | |
918a8a | nt_count_intersection_v1_784195855_10069 | Let $a$ be the largest prime number $n$ such that $2 \leq n \leq 12$. Let $N = 50000$ and $b = 14$. Define $\text{result}$ to be the number of positive integers $n \leq N$ such that $a$ divides $n$ and $\gcd(n, 14) = 1$. Find the remainder when $42658 \cdot \text{result}$ is divided by $76105$. | 67,229 | graphs = [
Graph(
let={
"_n": Const(2),
"N": Const(50000),
"a": MaxOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Ref("_n")), Leq(Var("n"), Const(12)), IsPrime(Var("n"))))),
"b": Const(14),
"result": CountOverSet(set=SolutionsSe... | NT | null | COUNT | sympy | MAX_PRIME_BELOW | [
"MAX_PRIME_BELOW"
] | dc3ad3 | nt_count_intersection_v1 | null | 4 | 0 | [
"MAX_PRIME_BELOW"
] | 1 | 1.619 | 2026-02-08T17:25:08.198570Z | {
"verified": true,
"answer": 67229,
"timestamp": "2026-02-08T17:25:09.817206Z"
} | 8823b8 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 147,
"completion_tokens": 1297
},
"timestamp": "2026-02-18T01:47:06.440Z",
"answer": 67229
},
... | 1 | [
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "V3",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
9de27b | comb_binomial_compute_v1_458359167_1733 | Let $k$ be the maximum value of $xy$ over all pairs of positive integers $(x, y)$ such that $x + y = 6$. Compute the remainder when $5611 \cdot \binom{16}{k}$ is divided by $93112$. | 35,672 | graphs = [
Graph(
let={
"_n": Const(93112),
"n": Const(16),
"k": MaxOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(Sum(Var("x"), Var("y")), Const(6)))), expr=... | ALG | COMB | COMPUTE | sympy | B1 | [
"B1"
] | 5b950e | comb_binomial_compute_v1 | null | 3 | 0 | [
"B1"
] | 1 | 0.003 | 2026-02-08T04:49:41.059108Z | {
"verified": true,
"answer": 35672,
"timestamp": "2026-02-08T04:49:41.062407Z"
} | c7864a | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 168,
"completion_tokens": 2524
},
"timestamp": "2026-02-24T01:56:14.948Z",
"answer": 35672
},
{
"... | 1 | [
{
"lemma": "B1",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
}
] | {
"lo": -2.46,
"mid": 0.47,
"hi": 3.59
} | ||
9ae51d | modular_sum_quadratic_residues_v1_784195855_30 | Let $p$ be the largest prime number between $2$ and $353$, inclusive. Define $N = \frac{p(p-1)}{4}$. Find the smallest positive integer $k$ such that the $k$th Fibonacci number is divisible by $N + 2$. | 8,904 | graphs = [
Graph(
let={
"_n": Const(2),
"p": MaxOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Ref("_n")), Leq(Var("n"), Const(353)), IsPrime(Var("n"))))),
"result": Div(Mul(Ref("p"), Sub(Ref("p"), Const(1))), Const(4)),
"Q": FibonacciEntry... | NT | null | SUM | sympy | MAX_PRIME_BELOW | [
"MAX_PRIME_BELOW"
] | dc3ad3 | modular_sum_quadratic_residues_v1 | null | 6 | 0 | [
"MAX_PRIME_BELOW"
] | 1 | 0.003 | 2026-02-08T02:54:53.759702Z | {
"verified": true,
"answer": 8904,
"timestamp": "2026-02-08T02:54:53.762202Z"
} | eac1d2 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 171,
"completion_tokens": 7607
},
"timestamp": "2026-02-10T12:50:04.503Z",
"answer": 8904
},
{
"i... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
}
] | {
"lo": 2.17,
"mid": 4.01,
"hi": 5.72
} | ||
94bd60 | nt_sum_over_divisible_v1_458359167_3313 | Let $d = \sum_{k=1}^{17} \phi(k) \left\lfloor \frac{17}{k} \right\rfloor$, where $\phi$ denotes Euler's totient function. Determine the value of $\sum n$, where the sum is taken over all positive integers $n \le 36100$ such that $n$ is divisible by $d$. Then compute the remainder when $12198$ times this sum is divided ... | 13,344 | graphs = [
Graph(
let={
"_n": Const(17),
"upper": Const(36100),
"divisor": Summation(var="k", start=Const(1), end=Ref("_n"), expr=Mul(EulerPhi(n=Var("k")), Floor(Div(Const(17), Var("k"))))),
"result": SumOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq... | NT | null | SUM | sympy | K2 | [
"K2"
] | 6897ab | nt_sum_over_divisible_v1 | null | 6 | 0 | [
"K2"
] | 1 | 2.401 | 2026-02-08T08:16:17.371804Z | {
"verified": true,
"answer": 13344,
"timestamp": "2026-02-08T08:16:19.773062Z"
} | d20522 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 145,
"completion_tokens": 1834
},
"timestamp": "2026-02-13T17:02:32.405Z",
"answer": 13344
},
... | 1 | [
{
"lemma": "K2",
"status": "ok"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "VAL_SUM_EQ",
"status": "no"
}
] | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
26ff64 | alg_qf_psd_orbit_v1_601307018_2631 | Find the number of ordered triples $(a, b, c)$ of positive integers with $1 \leq a \leq b \leq c \leq 41$ such that $$33c^2 - 8ac - 8bc + \left|\left\{ (a_1, b_1) : 1 \leq a_1, b_1 \leq 40,\ 68a_1^3b_1 + 17a_1^4 + \left|\left\{ (a_2, b_2) : 1 \leq a_2, b_2 \leq 40,\ 257a_2^4 + 257b_2^4 - 1028a_2^3b_2 + 1542a_2^2b_2^2 -... | 5 | graphs = [
Graph(
let={
"_m": Const(33),
"_n": Const(4),
"result": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("a"), Var("b"), Var("c")]), condition=And(Geq(Var("a"), Const(1)), Leq(Var("a"), Const(41)), Geq(Var("b"), Const(1)), Leq(Var("b"), Const(41)), Geq(Var... | ALG | null | COUNT | sympy | QF_PSD_ORBIT | [
"POLY4_COUNT/POLY4_COUNT"
] | fd26b0 | alg_qf_psd_orbit_v1 | null | 8 | 0 | [
"POLY4_COUNT",
"QF_PSD_ORBIT"
] | 2 | 0.335 | 2026-03-10T03:18:17.707890Z | {
"verified": true,
"answer": 5,
"timestamp": "2026-03-10T03:18:18.042975Z"
} | f1d480 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 377,
"completion_tokens": 9373
},
"timestamp": "2026-04-18T22:55:52.059Z",
"answer": 5
},
{
"id"... | 1 | [
{
"lemma": "POLY4_COUNT",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
}
] | {
"lo": 2.12,
"mid": 5.37,
"hi": 8.63
} | ||
e8877e | diophantine_product_count_v1_1520064083_2020 | Let $u = \sum_{k=1}^{15} \phi(k) \left\lfloor \frac{15}{k} \right\rfloor$, where $\phi$ denotes Euler's totient function. Determine the number of positive integers $x$ such that $1 \leq x \leq u$, $x$ divides $480$, and $\frac{480}{x} \leq u$. | 18 | graphs = [
Graph(
let={
"k": Const(480),
"upper": Summation(var="k", start=Const(1), end=Const(15), expr=Mul(EulerPhi(n=Var("k")), Floor(Div(Const(15), Var("k"))))),
"result": CountOverSet(set=SolutionsSet(var=Var("x"), condition=And(Geq(Var("x"), Const(1)), Leq(Var("x"),... | NT | null | COUNT | sympy | K2 | [
"K2"
] | 6897ab | diophantine_product_count_v1 | null | 6 | 0 | [
"K2"
] | 1 | 0.019 | 2026-02-08T04:27:30.040530Z | {
"verified": true,
"answer": 18,
"timestamp": "2026-02-08T04:27:30.059045Z"
} | dec06d | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 198,
"completion_tokens": 1894
},
"timestamp": "2026-02-10T16:38:10.179Z",
"answer": 18
},
{
"id... | 1 | [
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K2",
"status": "ok"
},
{
"lemma": "V3",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
}
] | {
"lo": -3.42,
"mid": 1.86,
"hi": 7.55
} | ||
d273fe | nt_min_phi_inverse_v1_124444284_9661 | Let the upper bound be $40$ and let $k = 8$. Let $n$ be a positive integer such that $1 \le n \le 40$ and $\phi(n) = 8$, where $\phi$ is Euler's totient function. Let $\text{result}$ be the smallest such $n$. Let $P$ be the largest prime number less than or equal to $1010$. Compute the value of $\text{result} \bmod{293... | 15,150 | graphs = [
Graph(
let={
"upper": Const(40),
"k": Const(8),
"result": MinOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Ref("upper")), Eq(EulerPhi(n=Var("n")), Ref("k"))))),
"Q": Sum(Mod(value=Ref("result"), modulus=... | NT | null | EXTREMUM | sympy | MAX_PRIME_BELOW | [
"MAX_PRIME_BELOW"
] | 08a653 | nt_min_phi_inverse_v1 | two_moduli | 5 | 0 | [
"MAX_PRIME_BELOW"
] | 1 | 0.006 | 2026-02-08T12:36:58.934255Z | {
"verified": true,
"answer": 15150,
"timestamp": "2026-02-08T12:36:58.940280Z"
} | 06d235 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 164,
"completion_tokens": 2732
},
"timestamp": "2026-02-15T02:43:09.608Z",
"answer": 15150
},
... | 1 | [
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "V3",
"status": "no... | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
9f6c2d | nt_sum_totient_over_divisors_v1_784195855_5319 | Let $n = 72085$. Define $r = \sum_{d \mid n} \phi(d)$, where $\phi$ denotes Euler's totient function. Let $t$ be the number of ordered pairs $(p, q)$ of positive integers such that $pq = 24$, $\gcd(p, q) = 1$, and $p < q$. Compute the remainder when $r^t + 36r + 465$ is divided by 94869. | 21,550 | graphs = [
Graph(
let={
"_n": Const(465),
"n": Const(72085),
"result": SumOverDivisors(n=Ref(name='n'), var='d', expr=EulerPhi(n=Var(name='d'))),
"Q": Mod(value=Sum(Pow(Ref("result"), CountOverSet(set=SolutionsSet(var=Var("p"), condition=And(IsPositive(arg=Var... | NT | null | COMPUTE | sympy | COPRIME_PAIRS | [
"COPRIME_PAIRS"
] | 14fbb8 | nt_sum_totient_over_divisors_v1 | quadratic_mod | 5 | 0 | [
"COPRIME_PAIRS"
] | 1 | 0.002 | 2026-02-08T07:49:38.601713Z | {
"verified": true,
"answer": 21550,
"timestamp": "2026-02-08T07:49:38.603214Z"
} | f6c670 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 146,
"completion_tokens": 2131
},
"timestamp": "2026-02-13T12:33:42.913Z",
"answer": 21550
},
... | 1 | [
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
}... | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
ebd856 | nt_num_divisors_compute_v1_1439011603_2421 | Let $n$ be the smallest divisor of $1928107$ that is at least $2$. Compute the number of positive divisors of $n$. | 2 | graphs = [
Graph(
let={
"_n": Const(2),
"n": MinOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Ref("_n")), Divides(divisor=Var("d"), dividend=Const(1928107))))),
"result": NumDivisors(n=Ref("n")),
},
goal=Ref("result"),
)
] | NT | null | COMPUTE | sympy | COMB1 | [
"MIN_PRIME_FACTOR"
] | bc3776 | nt_num_divisors_compute_v1 | null | 2 | 0 | [
"COMB1",
"MIN_PRIME_FACTOR"
] | 2 | 0.242 | 2026-02-08T16:46:33.000409Z | {
"verified": true,
"answer": 2,
"timestamp": "2026-02-08T16:46:33.242303Z"
} | 27a754 | 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": 880
},
"timestamp": "2026-02-17T11:39:12.590Z",
"answer": 2
},
{
... | 1 | [
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "MIN_PRIME_FACTOR",
"status": "ok"
},
{
"lemma": "V3",
"status": "no"
},
{
"lemma": "VAL_SUM_EQ",
"status"... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
01d1ac | geo_count_lattice_rect_v1_2051736721_1208 | Compute the number of lattice points in the rectangle $[0, 23] \times [0, 60]$, including the boundary. | 1,464 | graphs = [
Graph(
let={
"a": Const(23),
"b": Const(60),
"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 | 0.003 | 2026-02-08T15:54:12.800788Z | {
"verified": true,
"answer": 1464,
"timestamp": "2026-02-08T15:54:12.803964Z"
} | 89d1a6 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 139,
"completion_tokens": 195
},
"timestamp": "2026-02-24T18:58:31.627Z",
"answer": 1464
},
{
"i... | 1 | [] | {
"lo": -8.52,
"mid": -5.43,
"hi": -3.2
} | ||||
76c90e | lte_diff_endings_v1_1742523217_3814 | Let $a = 27$, $b = 2$, $p = 5$, $K = 5$, and $N = 14904936$. Define $d = a - b$. Let $v_p(d)$ be the largest integer $k$ such that $p^k$ divides $d$. Define $t = K - v_p(d)$, $p^t = 5^t$, and $p^{t+1} = 5^{t+1}$. Let $c_1$ be the number of positive integers less than or equal to $N$ that are divisible by $p^t$, and let... | 95,392 | graphs = [
Graph(
let={
"a_val": Const(27),
"b_val": Const(2),
"p_val": Const(5),
"K_val": Const(5),
"N_val": Const(14904936),
"ab_diff": Sub(Ref("a_val"), Ref("b_val")),
"vp_diff": MaxKDivides(target=Ref("ab_diff"), base=Re... | NT | null | COMPUTE | sympy | LTE_DIFF | [
"LTE_DIFF"
] | cf8260 | lte_diff_endings_v1 | null | 6 | null | [
"LTE_DIFF"
] | 1 | 0.001 | 2026-02-08T06:06:38.881109Z | {
"verified": true,
"answer": 95392,
"timestamp": "2026-02-08T06:06:38.881751Z"
} | ffe9bc | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 280,
"completion_tokens": 430
},
"timestamp": "2026-02-18T23:22:52.945Z",
"answer": 95392
}
] | 2 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "ok"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
... | {
"lo": -10,
"mid": -6.47,
"hi": -2.95
} | ||
188947 | algebra_quadratic_discriminant_v1_865884756_855 | Let $a = -2$, $b = 32$, and $c = -128$. Define the discriminant $D = b^2 - 4ac$. Let $r$ be the number of real solutions of the quadratic equation $ax^2 + bx + c = 0$. Define
$$
\text{result} = \begin{cases}
2 & \text{if } D > 0, \\
1 & \text{if } D = 0, \\
0 & \text{if } D < 0.
\end{cases}
$$
Let $c_1$ be the number o... | 4,849 | graphs = [
Graph(
let={
"_n": Const(2),
"a": Const(-2),
"b": Const(32),
"c": Const(-128),
"D": Sub(Pow(Ref("b"), Ref("_n")), Mul(Const(4), Ref("a"), Ref("c"))),
"result": Sum(Mul(Const(2), Iverson(condition=Gt(Ref("D"), Const(0)))), Ive... | NT | null | COMPUTE | sympy | C5 | [
"C5"
] | 833638 | algebra_quadratic_discriminant_v1 | affine_mod | 3 | 0 | [
"C5"
] | 1 | 0.004 | 2026-02-08T15:38:21.017237Z | {
"verified": true,
"answer": 4849,
"timestamp": "2026-02-08T15:38:21.021054Z"
} | fd3007 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 220,
"completion_tokens": 978
},
"timestamp": "2026-02-16T09:31:10.485Z",
"answer": 4849
},
{
... | 1 | [
{
"lemma": "C5",
"status": "ok"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
7310b3 | diophantine_fbi2_min_v1_1742523217_3545 | Let $k$ be the number of integers $t$ such that $9 \leq t \leq 41$ and there exist positive integers $a \leq 3$, $b \leq 10$ satisfying $t = 7a + 2b$. Let $S$ be the set of integers $d$ such that $5 \leq d \leq 37$, $d$ divides $k$, and $\frac{k}{d} \geq 2$. Compute the minimum value of $S$. Assume this set is nonempty... | 9 | graphs = [
Graph(
let={
"_n": Const(5),
"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=Const(value=3)), Geq(left=Var(na... | NT | null | EXTREMUM | sympy | ONE_PHI_1 | [
"COUNT_FIB_DIVISIBLE",
"LIN_FORM"
] | 0f3003 | diophantine_fbi2_min_v1 | null | 6 | 0 | [
"COUNT_FIB_DIVISIBLE",
"LIN_FORM",
"ONE_PHI_1"
] | 3 | 0.014 | 2026-02-08T05:56:09.670837Z | {
"verified": true,
"answer": 9,
"timestamp": "2026-02-08T05:56:09.684818Z"
} | ecbfde | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 160,
"completion_tokens": 1872
},
"timestamp": "2026-02-12T17:35:17.092Z",
"answer": 9
},
{
... | 1 | [
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "ok"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "V3",
"status": "no"
... | {
"lo": -5.55,
"mid": -3.01,
"hi": 0.32
} | ||
03b71e | antilemma_sum_equals_v1_717093673_492 | Let $n$ be the number of ordered pairs $(i, j)$ of positive integers such that $i \leq 2$, $j \leq 43$. Let $x$ be the number of ordered pairs $(i, j)$ of positive integers such that $i \leq 85$, $j \leq 86$, and $i + j = n$. Compute the value of $x$. | 85 | graphs = [
Graph(
let={
"_n": CountOverSet(set=CartesianProduct(left=IntegerRange(start=Const(1), end=Const(2)), right=IntegerRange(start=Const(1), end=Const(43)))),
"x": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("i"), Var("j")]), condition=Eq(Sum(Var("i"), Var("j")), Ref... | COMB | GEOM | COMPUTE | sympy | LIN_FORM | [
"COUNT_CARTESIAN/COUNT_SUM_EQUALS",
"COUNT_SUM_EQUALS"
] | 8bee9e | antilemma_sum_equals_v1 | null | 4 | 0 | [
"COUNT_CARTESIAN",
"COUNT_SUM_EQUALS",
"LIN_FORM"
] | 3 | 0.105 | 2026-02-08T15:28:38.088306Z | {
"verified": true,
"answer": 85,
"timestamp": "2026-02-08T15:28:38.193020Z"
} | a74d20 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 197,
"completion_tokens": 1380
},
"timestamp": "2026-02-24T21:00:48.963Z",
"answer": 85
},
{
"id"... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "ok"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "ok"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8",
"status": "n... | {
"lo": -8.52,
"mid": -5.43,
"hi": -3.2
} | ||
bcfd70 | comb_count_permutations_fixed_v1_601307018_2619 | Let $D_n$ denote the number of derangements of $n$ elements. For each integer $a$ with $0 \leq a \leq 9408$, define $S = (a^3 + 3a) \bmod 9409$ and $T = (S^3 + 3S) \bmod 9409$. Let $K$ be the number of such $a$ for which $T = a$ and $S \neq a$. Let $k = \sum_{k_2=0}^{2} K^{k_2}$ and $n = \sum_{k_1=1}^{4} \varphi(k_1) \... | 20,136 | graphs = [
Graph(
let={
"_d": Const(2),
"_m": Const(3),
"_n": CountOverSet(set=SolutionsSet(var=Var("a"), condition=And(Geq(Var("a"), Const(0)), Leq(Var("a"), Const(9408)), Eq(Ref("_po_p2"), Var("a")), Neq(Ref("_po_p1"), Var("a"))))),
"n": Summation(var="k1", ... | COMB | NT | COUNT | sympy | POLY_ORBIT_HENSEL | [
"POLY_ORBIT_HENSEL/SUM_GEOM",
"K2"
] | b86525 | comb_count_permutations_fixed_v1 | null | 7 | 0 | [
"K2",
"POLY_ORBIT_HENSEL",
"SUM_GEOM"
] | 3 | 0.009 | 2026-03-10T03:18:00.821256Z | {
"verified": true,
"answer": 20136,
"timestamp": "2026-03-10T03:18:00.830313Z"
} | 664085 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 312,
"completion_tokens": 4806
},
"timestamp": "2026-03-29T05:54:17.809Z",
"answer": 20136
},
{
"... | 1 | [
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "K2",
"status": "ok"
},
{
"lemma": "POLY_ORBIT_HENSEL",
"status": "ok"
},
{
"lemma": "SUM_GEO... | {
"lo": 3.34,
"mid": 5.77,
"hi": 8.89
} | ||
39b8a1 | comb_binomial_compute_v1_1218484723_5307 | Let $N = \binom{16}{8}$. Determine the remainder when $$ \left| \left\{ t \in \mathbb{Z} : 9 \le t \le 2040,\ \text{there exist integers } a, b \text{ with } 1 \le a \le 135,\ 1 \le b \le 300,\ t = 4a + 5b \right\} \right| - N $$ is divided by $68686$. | 57,836 | graphs = [
Graph(
let={
"n": Const(16),
"k": Const(8),
"result": Binom(n=Ref("n"), k=Ref("k")),
"Q": Mod(value=Sub(CountOverSet(set=SolutionsSet(var=Var("t"), condition=Exists(var=Var(name='a'), condition=Exists(var=Var(name='b'), condition=And(Geq(left=Var(na... | COMB | null | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM"
] | 324ba4 | comb_binomial_compute_v1 | negation_mod | 4 | 0 | [
"LIN_FORM"
] | 1 | 0.003 | 2026-02-25T06:56:15.241618Z | {
"verified": true,
"answer": 57836,
"timestamp": "2026-02-25T06:56:15.244318Z"
} | 627489 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 217,
"completion_tokens": 32768
},
"timestamp": "2026-03-29T20:27:36.537Z",
"answer": null
},
{
... | 1 | [
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "V8",
"status": "no"
},
{
"lemma": "V8_SUM",
"s... | {
"lo": 1.53,
"mid": 4.7,
"hi": 7.23
} | ||
a92375_l | comb_count_surjections_v1_1125832087_2356 | Let $k = 2$ and $n = 7$. Define $r = k! \cdot S(n, k)$, where $S(n, k)$ denotes the Stirling number of the second kind. Let $c$ be the number of ordered pairs $(i, j)$ of positive integers such that $i + j = 131$, $1 \leq i \leq 129$, and $1 \leq j \leq 129$. Let $d$ be the number of digits in $|r|$. Compute $$\sum_{i=... | 191 | COMB | null | COUNT | sympy | COUNT_SUM_EQUALS | [
"COUNT_SUM_EQUALS"
] | 194ba3 | comb_count_surjections_v1 | digits_weighted_mod | 5 | 0 | [
"COUNT_SUM_EQUALS"
] | 1 | 0.003 | 2026-02-08T04:34:29.929666Z | {
"verified": false,
"answer": 151,
"timestamp": "2026-02-08T04:34:29.932998Z"
} | a78659 | a92375 | legacy_text | CC BY 4.0 | [
{
"id": 1,
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"score": 1,
"correct": {
"strict": false,
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"relaxed": true
},
"usage": {
"prompt_tokens": 271,
"completion_tokens": 1866
},
"timestamp": "2026-02-11T09:28:46.305Z",
"answer": 191
},
{
"... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
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"status": "ok"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8_SUM",
"status":... | {
"lo": 3.43,
"mid": 5.73,
"hi": 8.84
} | |
cf1f62 | nt_count_divisible_and_v1_1742523217_5666 | Let $d_1 = 6$. Let $d_2$ be the number of integers $t$ such that $18 \leq t \leq 45$ and there exist integers $a$ and $b$ with $1 \leq a \leq 4$, $1 \leq b \leq 2$, and $t = 6a + 9b + 3$. Let $N$ be the number of positive integers $n$ such that $n \leq 20664$, $n \equiv \sum_{k=0}^{2} (-1)^k \binom{2}{k} \pmod{d_1}$, a... | 861 | graphs = [
Graph(
let={
"upper": Const(20664),
"d1": Const(6),
"d2": 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'), ri... | COMB | null | COUNT | sympy | BINOMIAL_ALTERNATING | [
"BINOMIAL_ALTERNATING",
"LIN_FORM"
] | 10f694 | nt_count_divisible_and_v1 | null | 5 | 0 | [
"BINOMIAL_ALTERNATING",
"LIN_FORM"
] | 2 | 0.828 | 2026-02-08T11:09:23.804093Z | {
"verified": true,
"answer": 861,
"timestamp": "2026-02-08T11:09:24.632235Z"
} | 2ec147 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 281,
"completion_tokens": 1487
},
"timestamp": "2026-02-24T12:54:19.390Z",
"answer": 861
},
{
"id... | 1 | [
{
"lemma": "BINOMIAL_ALTERNATING",
"status": "ok"
},
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "LIN_... | {
"lo": -5.97,
"mid": -3.97,
"hi": -1.93
} | ||
def050 | antilemma_k2_v1_48377204_262 | Compute $\sum_{k=1}^{296} \phi(k) \left\lfloor \frac{296}{k} \right\rfloor$, where $\phi$ denotes Euler's totient function. Find the remainder when $44121$ times this sum is divided by $93301$. | 28,090 | graphs = [
Graph(
let={
"_n": Const(296),
"x": Summation(var="k", start=Const(1), end=Const(296), expr=Mul(EulerPhi(n=Var("k")), Floor(Div(Ref("_n"), Var("k"))))),
"Q": Mod(value=Mul(Const(44121), Ref("x")), modulus=Const(93301)),
},
goal=Ref("Q"),
)
] | NT | COMB | COMPUTE | sympy | K2 | [
"K2"
] | 6897ab | antilemma_k2_v1 | null | 5 | 0 | [
"K2"
] | 1 | 0.001 | 2026-02-08T15:19:46.932878Z | {
"verified": true,
"answer": 28090,
"timestamp": "2026-02-08T15:19:46.933710Z"
} | 615e17 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 105,
"completion_tokens": 2182
},
"timestamp": "2026-02-16T03:07:08.297Z",
"answer": 28090
},
... | 1 | [
{
"lemma": "K2",
"status": "ok"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
1cf5ac | nt_count_divisible_and_v1_865884756_1224 | Let $N$ be the number of positive integers $n$ such that $1 \leq n \leq 189960$, $n$ is divisible by 10, and $n$ is divisible by 12. Let $c$ be the maximum value of $xy$ over all ordered pairs of positive integers $(x, y)$ such that $x + y = 160$. Compute $c - N$. | 3,234 | graphs = [
Graph(
let={
"upper": Const(189960),
"d1": Const(10),
"d2": Const(12),
"result": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Ref("upper")), Eq(Mod(value=Var("n"), modulus=Ref("d1")), Const(0)), Eq... | NT | null | COUNT | sympy | B1 | [
"B1"
] | d2b6e1 | nt_count_divisible_and_v1 | negation_mod | 4 | 0 | [
"B1"
] | 1 | 10.331 | 2026-02-08T15:50:29.595053Z | {
"verified": true,
"answer": 3234,
"timestamp": "2026-02-08T15:50:39.925842Z"
} | 6db7eb | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 152,
"completion_tokens": 483
},
"timestamp": "2026-02-16T06:32:49.788Z",
"answer": 3234
},
{
"id": 11,
... | 2 | [
{
"lemma": "B1",
"status": "ok"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "V1",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
}
] | {
"lo": -10,
"mid": -7.27,
"hi": -4.54
} | ||
a0dcd8 | comb_catalan_compute_v1_1080341949_180 | Let $n$ be the number of ordered pairs $(i, j)$ of positive integers such that $i + j = 12$, $1 \leq i \leq 10$, and $1 \leq j \leq 11$. Let $C_n$ denote the $n$th Catalan number. Compute the remainder when $34 - C_n$ is divided by 75887. | 59,125 | graphs = [
Graph(
let={
"_n": Const(12),
"n": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("i"), Var("j")]), condition=Eq(Sum(Var("i"), Var("j")), Ref("_n")), domain=CartesianProduct(left=IntegerRange(start=Const(1), end=Const(10)), right=IntegerRange(start=Const(1), end=Con... | COMB | null | COMPUTE | sympy | COUNT_SUM_EQUALS | [
"COUNT_SUM_EQUALS"
] | 75ab0f | comb_catalan_compute_v1 | null | 4 | 0 | [
"COUNT_SUM_EQUALS"
] | 1 | 0.029 | 2026-02-08T13:16:40.429274Z | {
"verified": true,
"answer": 59125,
"timestamp": "2026-02-08T13:16:40.458242Z"
} | fc6572 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 195,
"completion_tokens": 808
},
"timestamp": "2026-02-24T17:42:07.993Z",
"answer": 59125
},
{
"i... | 1 | [
{
"lemma": "C2",
"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_SUM",
"stat... | {
"lo": -4.92,
"mid": -2.91,
"hi": -0.68
} | ||
4e6919 | comb_count_permutations_fixed_v1_971394319_1704 | Let $n = 7$ and $m = 11$. Define $k = \sum_{k=1}^{2} \phi(k) \left\lfloor \frac{2}{k} \right\rfloor$, where $\phi$ denotes Euler's totient function. Compute $ \binom{n}{k} \cdot !(n - k) $, where $!r$ denotes the number of derangements of $r$ elements. Take the absolute value of this result, reduce it modulo $m$, and c... | 877 | graphs = [
Graph(
let={
"_n": Const(11),
"n": Const(7),
"k": Summation(var="k", start=Const(1), end=Const(2), expr=Mul(EulerPhi(n=Var("k")), Floor(Div(Const(2), Var("k"))))),
"result": Mul(Binom(n=Ref("n"), k=Ref("k")), Subfactorial(arg=Sub(left=Ref(name='n'),... | NT | COMB | COUNT | sympy | K2 | [
"K2"
] | 6897ab | comb_count_permutations_fixed_v1 | null | 6 | 0 | [
"K2"
] | 1 | 0.002 | 2026-02-08T13:52:11.952995Z | {
"verified": true,
"answer": 877,
"timestamp": "2026-02-08T13:52:11.954852Z"
} | 09664a | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 162,
"completion_tokens": 952
},
"timestamp": "2026-02-15T21:08:27.059Z",
"answer": 877
},
{
... | 1 | [
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K2",
"status": "ok"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
}
] | {
"lo": -5.49,
"mid": 0.22,
"hi": 6.51
} | ||
16b0e8 | comb_binomial_compute_v1_1440796553_638 | Let $m = 10$, and let $n$ be the number of ordered pairs $(i,j)$ of integers with $1 \le i \le 8$, $1 \le j \le 8$, and $i + j = m$. Let $f = \sum_{k=0}^{0} (-1)^k \binom{0}{k}$ and $t = \sum_{k=0}^{0} (-1)^k \binom{0}{k}$. Let $k$ be the product of $n$, $f$, and $t$. Compute $\binom{13}{k}$. | 1,716 | graphs = [
Graph(
let={
"_m": Const(10),
"_n": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("i"), Var("j")]), condition=Eq(Sum(Var("i"), Var("j")), Ref("_m")), domain=CartesianProduct(left=IntegerRange(start=Const(1), end=Const(8)), right=IntegerRange(start=Const(1), end=Con... | COMB | null | COMPUTE | sympy | COUNT_SUM_EQUALS | [
"COUNT_SUM_EQUALS/COUNT_SUM_EQUALS/BINOMIAL_ALTERNATING"
] | 8f93ab | comb_binomial_compute_v1 | null | 3 | 2 | [
"BINOMIAL_ALTERNATING",
"COUNT_SUM_EQUALS"
] | 2 | 0.023 | 2026-02-08T11:54:46.669673Z | {
"verified": true,
"answer": 1716,
"timestamp": "2026-02-08T11:54:46.692190Z"
} | bae6f6 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 242,
"completion_tokens": 730
},
"timestamp": "2026-02-24T14:58:02.050Z",
"answer": 1716
},
{
"id... | 1 | [
{
"lemma": "BINOMIAL_ALTERNATING",
"status": "ok_later"
},
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "ok"
},
{
"lemma":... | {
"lo": -5.97,
"mid": -3.97,
"hi": -1.93
} | ||
542314 | antilemma_sum_equals_v1_677425708_229 | Let $S$ be the set of all ordered pairs $(i,j)$ of integers such that $1 \leq i \leq 25$, $1 \leq j \leq 25$, and $i + j = 26$. Compute the number of elements in $S$. | 25 | graphs = [
Graph(
let={
"x": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("i"), Var("j")]), condition=Eq(Sum(Var("i"), Var("j")), Const(26)), domain=CartesianProduct(left=IntegerRange(start=Const(1), end=Const(25)), right=IntegerRange(start=Const(1), end=Const(25))))),
},
... | COMB | GEOM | COMPUTE | sympy | LIN_FORM | [
"COUNT_SUM_EQUALS"
] | 75ab0f | antilemma_sum_equals_v1 | null | 2 | 0 | [
"COUNT_SUM_EQUALS",
"LIN_FORM"
] | 2 | 0.024 | 2026-02-08T03:09:48.478936Z | {
"verified": true,
"answer": 25,
"timestamp": "2026-02-08T03:09:48.503362Z"
} | c26ba5 | 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": 192
},
"timestamp": "2026-02-08T20:25:11.496Z",
"answer": 25
},
{
"id":... | 2 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "ok"
},
{
"lemma": "V8_SU... | {
"lo": -10,
"mid": -7.78,
"hi": -5.56
} | ||
90e583 | diophantine_product_count_v1_784195855_10075 | Let $k$ be the minimum value of $x + y$ over all ordered pairs $(x,y)$ of positive integers such that $xy = 176400$. Let $S$ be the set of all positive integers $d$ such that $d$ divides $71002$ and $1 \le d \le m$, where $m$ is the minimum value of $x + y$ over all ordered pairs $(x,y)$ of positive integers such that ... | 26 | graphs = [
Graph(
let={
"_n": Const(71002),
"k": MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(Mul(Var("x"), Var("y")), Const(176400)))), expr=Sum(Var("x"), Var("y"))... | NT | null | COUNT | sympy | B3 | [
"B3/MAX_DIVISOR"
] | 33b851 | diophantine_product_count_v1 | null | 7 | 0 | [
"B3",
"MAX_DIVISOR"
] | 2 | 0.025 | 2026-02-08T17:25:14.171204Z | {
"verified": true,
"answer": 26,
"timestamp": "2026-02-08T17:25:14.196121Z"
} | 3cf56d | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 204,
"completion_tokens": 2257
},
"timestamp": "2026-02-18T01:46:33.877Z",
"answer": 26
},
{
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "MAX_DIVISOR",
"status": "ok_later"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
dab5e3 | nt_sum_divisors_mod_v1_898971024_108 | Let $n$ be the sum of $\phi(d)$ over all positive divisors $d$ of $7560$, where $\phi$ denotes Euler's totient function. Let $\sigma$ be the sum of all positive divisors of $n$. Compute the remainder when $86546 \cdot (\sigma \bmod 11491)$ is divided by $50349$. | 34,628 | graphs = [
Graph(
let={
"_n": Const(50349),
"n": SumOverDivisors(n=Const(value=7560), var='d', expr=EulerPhi(n=Var(name='d'))),
"M": Const(11491),
"sigma": SumDivisors(n=Ref("n")),
"result": Mod(value=Ref("sigma"), modulus=Ref("M")),
"_... | NT | null | COMPUTE | sympy | K3 | [
"K3"
] | 54c41e | nt_sum_divisors_mod_v1 | null | 4 | 0 | [
"K3"
] | 1 | 0.007 | 2026-02-08T15:11:28.658562Z | {
"verified": true,
"answer": 34628,
"timestamp": "2026-02-08T15:11:28.665253Z"
} | ed11be | 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": 1453
},
"timestamp": "2026-02-16T02:37:50.304Z",
"answer": 34628
},
... | 1 | [
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K3",
"status": "ok"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
8f533a | geo_count_lattice_rect_v1_865884756_345 | Let $a = 128$ and $b = 337$. Let $R$ be the number of lattice points in the rectangle $[0, a] \times [0, b]$, including the boundary. Let $c = 18091$. Compute the remainder when $c \cdot R$ is divided by $59567$. | 17,568 | graphs = [
Graph(
let={
"a": Const(128),
"b": Const(337),
"result": LatticePointsRect(a=Ref(name='a'), b=Ref(name='b')),
"_c": Const(18091),
"Q": Mod(value=Mul(Ref("_c"), Ref("result")), modulus=Const(59567)),
},
goal=Ref("Q"),
... | GEOM | null | COUNT | sympy | [] | geo_count_lattice_rect_v1 | null | 3 | 0 | null | null | 0.001 | 2026-02-08T15:19:18.373758Z | {
"verified": true,
"answer": 17568,
"timestamp": "2026-02-08T15:19:18.374546Z"
} | b498b1 | 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": 2722
},
"timestamp": "2026-02-24T20:31:36.376Z",
"answer": 17568
},
{
"... | 1 | [] | {
"lo": -2.43,
"mid": 1.2,
"hi": 4.84
} | ||||
7eae6b | comb_count_permutations_fixed_v1_784195855_10282 | Let $n$ be the largest prime number such that $2 \leq n \leq 12$. Let $k = 8$. Compute the value of $\binom{n}{k} \cdot !(n - k)$, where $!m$ denotes the number of derangements of $m$ elements. | 330 | graphs = [
Graph(
let={
"_n": Const(12),
"n": MaxOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(2)), Leq(Var("n"), Ref("_n")), IsPrime(Var("n"))))),
"k": Const(8),
"result": Mul(Binom(n=Ref("n"), k=Ref("k")), Subfactorial(arg=Sub(left... | NT | COMB | COUNT | sympy | MAX_PRIME_BELOW | [
"MAX_PRIME_BELOW"
] | dc3ad3 | comb_count_permutations_fixed_v1 | null | 4 | 0 | [
"MAX_PRIME_BELOW"
] | 1 | 0.002 | 2026-02-08T17:33:25.312951Z | {
"verified": true,
"answer": 330,
"timestamp": "2026-02-08T17:33:25.314734Z"
} | bec8d3 | 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": 527
},
"timestamp": "2026-02-18T07:35:27.817Z",
"answer": 330
},
{
... | 1 | [
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
2ac1c1 | modular_sum_quadratic_residues_v1_784195855_3603 | Let $n = 1186$. Determine the number of ordered pairs $(x_1, x_2)$ of positive odd integers such that $x_1 + x_2 = n$, and denote this number by $p$. Compute $\frac{p(p-1)}{4}$. | 87,764 | graphs = [
Graph(
let={
"_n": Const(1186),
"p": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x1"), Var("x2")]), condition=And(IsPositive(arg=Var(name='x1')), IsPositive(arg=Var(name='x2')), IsOdd(arg=Var(name='x1')), IsOdd(arg=Var(name='x2')), Eq(Sum(Var("x1"), Var("x2")), ... | NT | null | SUM | sympy | V8 | [
"COMB1"
] | 567f58 | modular_sum_quadratic_residues_v1 | null | 4 | 0 | [
"COMB1",
"V8"
] | 2 | 0.003 | 2026-02-08T06:32:35.535908Z | {
"verified": true,
"answer": 87764,
"timestamp": "2026-02-08T06:32:35.538707Z"
} | f7108a | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 105,
"completion_tokens": 904
},
"timestamp": "2026-02-13T01:49:16.543Z",
"answer": 87764
},
{... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COMB1",
"status": "ok"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
}
] | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
03d848 | nt_count_coprime_and_v1_865884756_6993 | Let $n$ be a positive integer such that $1 \leq n \leq 24772$. Let $k_1$ be the largest prime number between 2 and 9, inclusive, and let $k_2 = 11$. Compute the number of integers $n$ in this range for which $\gcd(n, k_1) = 1$ and $\gcd(n, k_2) = 1$. | 19,303 | graphs = [
Graph(
let={
"upper": Const(24772),
"k1": MaxOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(2)), Leq(Var("n"), Const(9)), IsPrime(Var("n"))))),
"k2": Const(11),
"result": CountOverSet(set=SolutionsSet(var=Var("n1"), conditi... | NT | null | COUNT | sympy | MAX_PRIME_BELOW | [
"MAX_PRIME_BELOW"
] | dc3ad3 | nt_count_coprime_and_v1 | null | 4 | 0 | [
"MAX_PRIME_BELOW"
] | 1 | 2.541 | 2026-02-08T19:31:30.869579Z | {
"verified": true,
"answer": 19303,
"timestamp": "2026-02-08T19:31:33.410262Z"
} | 50e66e | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 136,
"completion_tokens": 1599
},
"timestamp": "2026-02-18T22:45:03.375Z",
"answer": 19303
},
... | 1 | [
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok"
},
{
"lemma": "V8",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
c8da8b | antilemma_sum_factor_cartesian_v1_677425708_521 | Let $S$ be the set of all ordered pairs $(i,j)$ of positive integers with $1 \leq i \leq 9$ and $1 \leq j \leq 12$. Define $x$ to be the sum of $i \cdot j$ over all pairs $(i,j)$ in $S$. Compute the Bell number $B_n$, where $n = |x| \bmod 11$. | 1 | graphs = [
Graph(
let={
"x": SumOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("i"), Var("j")]), condition=Const(1), domain=CartesianProduct(left=IntegerRange(start=Const(1), end=Const(9)), right=IntegerRange(start=Const(1), end=Const(12)))), expr=Mul(Var("i"), Var("j")))),
... | NT | COMB | COMPUTE | sympy | LIN_FORM | [
"SUM_FACTOR_CARTESIAN"
] | d9e436 | antilemma_sum_factor_cartesian_v1 | null | 3 | 0 | [
"LIN_FORM",
"SUM_FACTOR_CARTESIAN"
] | 2 | 0.014 | 2026-02-08T03:35:24.494626Z | {
"verified": true,
"answer": 1,
"timestamp": "2026-02-08T03:35:24.508735Z"
} | bcb928 | 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": 637
},
"timestamp": "2026-02-08T20:41:49.499Z",
"answer": 1
},
{
"id": ... | 1 | [
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "SUM_FACTOR_CARTESIAN",
"status": "ok"
},
{
"lemma": "V3",
"status": "no"
}
] | {
"lo": -6.51,
"mid": -0.32,
"hi": 5.36
} | ||
64df73 | alg_poly3_count_v1_1218484723_228 | Let $T = \left| \left\{ t = 4a_1 + 10b_1 + 3 : 1 \le a_1 \le 320,\ 1 \le b_1 \le 1055,\ 17 \le t \le 11833 \right\} \right|$, and let $B = \left| \left\{ (a_1,b_1) : 1 \le a_1,b_1 \le 40,\ 10a_1^2 - 18a_1b_1 + 25b_1^2 \le T \right\} \right|$. Find the number of ordered pairs $(a,b)$ of positive integers with $1 \le a \... | 474 | graphs = [
Graph(
let={
"_m": Const(3),
"_n": Const(25),
"result": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("a"), Var("b")]), condition=And(Geq(Var("a"), Const(1)), Leq(Var("a"), Const(474)), Geq(Var("b"), Const(1)), Leq(Var("b"), CountOverSet(set=SolutionsSe... | ALG | null | COUNT | sympy | ABS_INEQ | [
"LIN_FORM/QF_PSD_COUNT_LEQ"
] | 77251b | alg_poly3_count_v1 | null | 6 | 0 | [
"ABS_INEQ",
"LIN_FORM",
"QF_PSD_COUNT_LEQ"
] | 3 | 9.228 | 2026-02-25T01:55:00.302480Z | {
"verified": true,
"answer": 474,
"timestamp": "2026-02-25T01:55:09.530756Z"
} | 859fa2 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 1,
"correct": {
"strict": false,
"boxed": false,
"relaxed": true
},
"usage": {
"prompt_tokens": 299,
"completion_tokens": 32768
},
"timestamp": "2026-03-10T09:04:01.215Z",
"answer": null
},
{
... | 1 | [
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "QF_PSD_COUNT_LEQ",
"status": "ok_later"
}
] | {
"lo": 4.78,
"mid": 6.81,
"hi": 9.84
} | ||
15cc3a | alg_poly4_count_v1_1218484723_3654 | Let $Q$ be the number of ordered pairs $(a, b)$ of positive integers with $1 \le a, b \le 320$ such that $$A \cdot b^4 + B \cdot a^2b^2 + 162a^4 - 432a^3b - 192ab^3 = 15985077602,$$ where $$A = \left|\left\{ (a_1, b_1) : 1 \le a_1 \le b_1 \le 35,\ 50b_1^2 + 50a_1^2 - 100a_1b_1 = 450 \right\}\right|,$$ $$B = \left|\left... | 164 | graphs = [
Graph(
let={
"_d": Const(2),
"_c": Const(320),
"_m": Const(2),
"_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(320)), Geq(Var("b... | ALG | null | COUNT | sympy | POLY3_COUNT | [
"QF_PSD_ORBIT/QF_PSD_COUNT_LEQ",
"LIN_FORM/QF_PSD_COUNT_LEQ"
] | 7a1f47 | alg_poly4_count_v1 | null | 5 | 0 | [
"LIN_FORM",
"POLY3_COUNT",
"QF_PSD_COUNT_LEQ",
"QF_PSD_ORBIT"
] | 4 | 2.257 | 2026-02-25T05:17:57.164769Z | {
"verified": true,
"answer": 164,
"timestamp": "2026-02-25T05:17:59.422257Z"
} | 73777c | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 530,
"completion_tokens": 32768
},
"timestamp": "2026-03-29T11:31:42.689Z",
"answer": null
},
{
... | 1 | [
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "QF_PSD_COUNT_LEQ",
"status": "ok_later"
},
{
"lemma": "QF_PSD_ORBIT",
"status": "ok"
}
] | {
"lo": 1.55,
"mid": 4.7,
"hi": 7.23
} | ||
64a4fa | sequence_count_fib_divisible_v1_1439011603_387 | Let $S$ be the set of all ordered pairs $(x, y)$ of positive integers such that $xy = 242064$. Let $u$ be the minimum value of $x + y$ as $(x, y)$ ranges over $S$. Let $d = \sum_{k=1}^{3} \phi(k) \left\lfloor \frac{3}{k} \right\rfloor$, where $\phi$ is Euler's totient function. Determine the number of positive integers... | 82 | graphs = [
Graph(
let={
"_n": Const(3),
"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(242064)))), expr=Sum(Var("x"), Var("y"))... | NT | null | COUNT | sympy | B3 | [
"B3",
"K2"
] | f1ea07 | sequence_count_fib_divisible_v1 | null | 6 | 0 | [
"B3",
"K2"
] | 2 | 0.05 | 2026-02-08T15:26:11.355778Z | {
"verified": true,
"answer": 82,
"timestamp": "2026-02-08T15:26:11.405436Z"
} | 1163a0 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 180,
"completion_tokens": 2850
},
"timestamp": "2026-02-16T06:30:30.365Z",
"answer": 82
},
{
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "K2",
"status": "ok"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "V3",
"status": "no"
},
{
"lemma": "V7",
"statu... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
3c90b6 | comb_sum_binomial_row_v1_1915831931_137 | Let $n$ be the minimum value of $x + y$ over all ordered pairs of positive integers $(x, y)$ such that $xy = 36$. Let $Q$ be the remainder when $32753 \cdot 2^n$ is divided by 74028. Compute $Q$. | 17,552 | graphs = [
Graph(
let={
"_n": Const(74028),
"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(36)))), expr=Sum(Var("x"), Var("y")))),
... | NT | null | SUM | sympy | B3 | [
"B3"
] | 0cd20d | comb_sum_binomial_row_v1 | null | 3 | 0 | [
"B3"
] | 1 | 0.001 | 2026-02-08T15:12:09.396589Z | {
"verified": true,
"answer": 17552,
"timestamp": "2026-02-08T15:12:09.398009Z"
} | 64a720 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 109,
"completion_tokens": 3648
},
"timestamp": "2026-02-16T01:54:01.412Z",
"answer": 17552
},
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "V3",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
dbadf5 | comb_catalan_compute_v1_1439011603_1242 | Let $n = 10$. Define $h = \sum_{k=0}^{0} (-1)^k \binom{0}{k}$ and $v = \sum_{k_1=0}^{10} (-1)^{k_1} \binom{10}{k_1}$. Let $c = 21809$ and $C_n$ denote the $n$th Catalan number. Compute the remainder when $c \cdot C_n$ is divided by $68270 \cdot h + v$. | 35,414 | graphs = [
Graph(
let={
"n2": Const(0),
"h": Summation(var="k", start=Const(0), end=Ref("n2"), expr=Mul(Pow(Const(-1), Var("k")), Binom(n=Ref("n2"), k=Var("k")))),
"u": Const(9),
"n1": Sum(Ref("u"), Const(1)),
"v": Summation(var="k1", start=Const(0... | COMB | null | COMPUTE | sympy | BINOMIAL_ALTERNATING | [
"BINOMIAL_ALTERNATING"
] | c21569 | comb_catalan_compute_v1 | null | 4 | 2 | [
"BINOMIAL_ALTERNATING"
] | 1 | 0.003 | 2026-02-08T15:59:35.140233Z | {
"verified": true,
"answer": 35414,
"timestamp": "2026-02-08T15:59:35.142762Z"
} | 33e80d | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 224,
"completion_tokens": 1531
},
"timestamp": "2026-02-24T19:26:50.952Z",
"answer": 35414
},
{
... | 1 | [
{
"lemma": "BINOMIAL_ALTERNATING",
"status": "ok"
},
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "... | {
"lo": -2.4,
"mid": 1.57,
"hi": 5.75
} | ||
dfd123 | nt_count_primes_v1_1353956133_520 | Let $P$ be the set of all positive integers $p$ for which there exists a positive integer $q$ such that $pq = 54$, $\gcd(p, q) = 1$, and $p < q$. Let $c$ be the number of elements in $P$. Let $S$ be the set of all prime numbers $n$ such that $c \leq n \leq 80000$. Let $r$ be the number of elements in $S$. Compute the r... | 13,477 | graphs = [
Graph(
let={
"_n": Const(63006),
"upper": Const(80000),
"result": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), CountOverSet(set=SolutionsSet(var=Var("p"), condition=And(IsPositive(arg=Var(name='p')), Exists(var=Var(name='q'), conditio... | NT | null | COUNT | sympy | COPRIME_PAIRS | [
"COPRIME_PAIRS"
] | 2bb3aa | nt_count_primes_v1 | null | 4 | 0 | [
"COPRIME_PAIRS"
] | 1 | 2.095 | 2026-02-08T11:29:33.971644Z | {
"verified": true,
"answer": 13477,
"timestamp": "2026-02-08T11:29:36.066533Z"
} | bbc1bb | 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": 2459
},
"timestamp": "2026-02-14T14:53:06.882Z",
"answer": 13477
},
... | 1 | [
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "V1",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
}
] | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
535726 | alg_sym_quad_system_v1_601307018_1984 | Find the remainder when $\sum_{\substack{a^2 + b^2 + c^2 = ab + bc + ca \\ 4a + 9b + 2c = 585 \\ a,b,c \geq 1}} (a^4 + b^4 + c^4)$ is divided by $\left|\left\{ n : 1 \leq n \leq 53334,\, 9 \mid n,\, \gcd\left(n,\, \max\{ d : d \mid 1295,\, d^2 \leq 1295 \}\right) = 1 \right\}\right|.$ | 3,075 | graphs = [
Graph(
let={
"_m": Const(2),
"_n": Const(4),
"result": Mod(value=SumOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("a"), Var("b"), Var("c")]), condition=And(Eq(Sum(Pow(Var("a"), Const(2)), Pow(Var("b"), Ref("_m")), Pow(Var("c"), Const(2))), Sum... | NT | null | COMPUTE | sympy | B3_CLOSEST | [
"B3_CLOSEST/C5"
] | e79f08 | alg_sym_quad_system_v1 | null | 8 | 0 | [
"B3_CLOSEST",
"C5"
] | 2 | 0.04 | 2026-03-10T02:43:48.522312Z | {
"verified": true,
"answer": 3075,
"timestamp": "2026-03-10T02:43:48.562339Z"
} | 7fa520 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 252,
"completion_tokens": 1776
},
"timestamp": "2026-04-18T15:58:26.905Z",
"answer": 3075
},
{
"... | 1 | [
{
"lemma": "B3_CLOSEST",
"status": "ok"
},
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "C5",
"status": "ok_later"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
},
{
"... | {
"lo": -3.33,
"mid": 1,
"hi": 5.06
} | ||
9bef84 | nt_sum_divisors_range_v1_1742523217_1843 | Let $ S $ be the set of all ordered pairs $ (x,y) $ of positive integers such that $ x + y = 150 $. Let $ m $ be the maximum value of $ xy $ over all such pairs. Determine the value of $ \sum_{n=1}^{m} \tau(n) $, where $ \tau(n) $ denotes the number of positive divisors of $ n $. | 49,451 | graphs = [
Graph(
let={
"_n": Const(150),
"upper": MaxOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(Sum(Var("x"), Var("y")), Ref("_n")))), expr=Mul(Var("x"), Var("y"))))... | NT | null | SUM | sympy | ONE_PHI_2 | [
"B1"
] | 5b950e | nt_sum_divisors_range_v1 | null | 4 | 0 | [
"B1",
"ONE_PHI_2"
] | 2 | 0.667 | 2026-02-08T04:18:32.530062Z | {
"verified": true,
"answer": 49451,
"timestamp": "2026-02-08T04:18:33.197510Z"
} | d39f3e | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 194,
"completion_tokens": 2741
},
"timestamp": "2026-02-10T16:09:48.221Z",
"answer": 49449
},
{
... | 1 | [
{
"lemma": "B1",
"status": "ok"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
}
] | {
"lo": 1.96,
"mid": 5.23,
"hi": 8.52
} | ||
07ccf2 | nt_sum_divisors_mod_v1_1874849503_1226 | Let $S$ be the set of all ordered pairs of positive integers $(x, y)$ such that $x y = 176400$. Define $n$ as the minimum value of $x + y$ over all such pairs. Let $\sigma(n)$ denote the sum of all positive divisors of $n$. Compute the remainder when $\sigma(n)$ is divided by $10259$. | 2,880 | 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(176400)))), expr=Sum(Var("x"), Var("y")))),
"M": Const(10259... | NT | null | COMPUTE | sympy | B3 | [
"B3"
] | 0cd20d | nt_sum_divisors_mod_v1 | null | 4 | 0 | [
"B3"
] | 1 | 0.004 | 2026-02-08T13:43:13.658994Z | {
"verified": true,
"answer": 2880,
"timestamp": "2026-02-08T13:43:13.663020Z"
} | c55be5 | 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": 1204
},
"timestamp": "2026-02-10T02:28:21.970Z",
"answer": 2880
},
{
"i... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
}
] | {
"lo": -5.49,
"mid": 0.03,
"hi": 6.12
} | ||
cc3f74 | comb_binomial_compute_v1_1978505735_2014 | Let $k$ be the largest prime number between $2$ and $10$, inclusive. Compute $\binom{16}{k}$. | 11,440 | graphs = [
Graph(
let={
"_n": Const(2),
"n": Const(16),
"k": MaxOverSet(set=SolutionsSet(var=Var("n1"), condition=And(Geq(Var("n1"), Ref("_n")), Leq(Var("n1"), Const(10)), IsPrime(Var("n1"))))),
"result": Binom(n=Ref("n"), k=Ref("k")),
},
goal=... | NT | null | COMPUTE | sympy | MAX_PRIME_BELOW | [
"MAX_PRIME_BELOW"
] | dc3ad3 | comb_binomial_compute_v1 | null | 3 | 0 | [
"MAX_PRIME_BELOW"
] | 1 | 0.004 | 2026-02-08T16:36:51.324036Z | {
"verified": true,
"answer": 11440,
"timestamp": "2026-02-08T16:36:51.327656Z"
} | e3ae90 | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 85,
"completion_tokens": 522
},
"timestamp": "2026-02-16T07:31:27.752Z",
"answer": 10368
},
{
"id": 11,... | 1 | [
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "VAL_SUM_EQ",
"status": "no"
... | {
"lo": -8.26,
"mid": -5.01,
"hi": -1.76
} | ||
65a58c | nt_count_gcd_equals_v1_655260480_3149 | Let $S$ be the set of all integers $t$ such that $8 \leq t \leq 3772$ and there exist positive integers $a \leq 398$ and $b \leq 594$ satisfying $t = 5a + 3b$. Let $n$ be the number of elements in $S$. Let $d$ be the smallest divisor of $n$ that is at least 2. Determine the value of $$\#\left\{ n \in \mathbb{Z}^+ \mid ... | 1,433 | 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=398)), Geq(left=Var(name='b'), right=Const(valu... | NT | null | COUNT | sympy | LIN_FORM | [
"LIN_FORM/MIN_PRIME_FACTOR"
] | bb1a13 | nt_count_gcd_equals_v1 | null | 6 | 0 | [
"LIN_FORM",
"MIN_PRIME_FACTOR"
] | 2 | 4.469 | 2026-02-08T17:12:13.521632Z | {
"verified": true,
"answer": 1433,
"timestamp": "2026-02-08T17:12:17.990546Z"
} | a4e015 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 185,
"completion_tokens": 5281
},
"timestamp": "2026-02-17T21:09:57.804Z",
"answer": 1433
},
{... | 1 | [
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "MIN_PRIME_FACTOR",
"status": "ok_later"
},
{
"lemma": "V1",
"status"... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
59aab9 | comb_count_surjections_v1_151522320_241 | Let $k$ be the number of ordered pairs $(i, j)$ of integers such that $1 \leq i \leq 5$, $1 \leq j \leq 5$, and $i + j = 5$. Define $n = 8$. Let $R = k! \cdot S(n, k)$, where $S(n, k)$ denotes the Stirling number of the second kind. Compute the remainder when $34373 \cdot R$ is divided by $75928$. | 17,984 | graphs = [
Graph(
let={
"_n": Const(5),
"n": Const(8),
"k": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("i"), Var("j")]), condition=Eq(Sum(Var("i"), Var("j")), Ref("_n")), domain=CartesianProduct(left=IntegerRange(start=Const(1), end=Const(5)), right=IntegerRang... | COMB | null | COUNT | sympy | COUNT_SUM_EQUALS | [
"COUNT_SUM_EQUALS"
] | 75ab0f | comb_count_surjections_v1 | null | 5 | 0 | [
"COUNT_SUM_EQUALS"
] | 1 | 0.013 | 2026-02-08T03:06:05.472522Z | {
"verified": true,
"answer": 17984,
"timestamp": "2026-02-08T03:06:05.485912Z"
} | 524256 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 220,
"completion_tokens": 2291
},
"timestamp": "2026-02-10T13:05:40.989Z",
"answer": 17984
},
{
"... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "ok"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8_SUM",
"status":... | {
"lo": -2.46,
"mid": 0.47,
"hi": 3.59
} | ||
afdc40 | diophantine_product_count_v1_1820931509_657 | Let $k = 840$. Let $U$ be the number of ordered pairs $(i,j)$ of integers such that $1 \leq i \leq 23$, $1 \leq j \leq 23$, and $\gcd(i,j) = 1$. Define $S$ as the set of all positive integers $x$ such that $1 \leq x \leq U$, $x$ divides $k$, and $\frac{k}{x} \leq U$. Compute the value of
$$
\sum_{n=1}^{|S|} \tau(n),
$$... | 101 | graphs = [
Graph(
let={
"k": Const(840),
"upper": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("i"), Var("j")]), condition=Eq(GCD(a=Var("i"), b=Var("j")), Const(1)), domain=CartesianProduct(left=IntegerRange(start=Const(1), end=Const(23)), right=IntegerRange(start=Const(1), ... | NT | null | COUNT | sympy | COUNT_COPRIME_GRID | [
"COUNT_COPRIME_GRID"
] | 20ec03 | diophantine_product_count_v1 | null | 6 | 0 | [
"COUNT_COPRIME_GRID"
] | 1 | 0.042 | 2026-02-08T11:49:15.552872Z | {
"verified": true,
"answer": 101,
"timestamp": "2026-02-08T11:49:15.594663Z"
} | 8fb4d4 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 180,
"completion_tokens": 3353
},
"timestamp": "2026-02-14T19:26:34.085Z",
"answer": 101
},
{
... | 1 | [
{
"lemma": "COUNT_COPRIME_GRID",
"status": "ok"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "VAL_SUM_EQ",
"status": "... | {
"lo": -5.49,
"mid": 0.22,
"hi": 6.51
} |
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