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 |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
e5afd6 | diophantine_product_count_v1_1439011603_931 | Let $k = 120$. Let $u$ be the sum of all positive integers $n \leq 83$ such that $n \equiv 0 \pmod{83}$. Compute the number of positive integers $x \leq u$ such that $x$ divides $120$ and $\frac{120}{x} \leq u$. | 14 | graphs = [
Graph(
let={
"k": Const(120),
"upper": SumOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Const(83)), Eq(Mod(value=Var("n"), modulus=Const(83)), Const(0))))),
"result": CountOverSet(set=SolutionsSet(var=Var("x"), cond... | NT | null | COUNT | sympy | K14 | [
"SUM_DIVISIBLE"
] | 02dbe3 | diophantine_product_count_v1 | null | 5 | 0 | [
"K14",
"SUM_DIVISIBLE"
] | 2 | 0.083 | 2026-02-08T15:49:02.579700Z | {
"verified": true,
"answer": 14,
"timestamp": "2026-02-08T15:49:02.662840Z"
} | a240ff | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 119,
"completion_tokens": 1390
},
"timestamp": "2026-02-16T14:10:14.864Z",
"answer": 14
},
{
... | 1 | [
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "SUM_DIVISIBLE",
"status": "ok"
},
{
"lemma": "V1",
"status": "no"
},
{
"lemma": "V3",
"status": "no"
},
{
"lemma": "VAL_SUM_EQ",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
66cac5 | modular_count_residue_v1_677425708_784 | Let $r$ be the minimum value of $x + y$ over all ordered pairs $(x,y)$ of positive integers such that $xy = 9$. Let $\phi(1)$ denote Euler's totient function evaluated at $1$. Compute the number of positive integers $n \leq 57121$ such that $n \equiv r \pmod{8}$. | 7,140 | graphs = [
Graph(
let={
"upper": Const(57121),
"m": Const(8),
"r": 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(9)))), exp... | NT | null | COUNT | sympy | ONE_PHI_1 | [
"ONE_PHI_1",
"B3"
] | d3bb9b | modular_count_residue_v1 | null | 3 | 0 | [
"B3",
"ONE_PHI_1"
] | 2 | 2.049 | 2026-02-08T03:43:49.589274Z | {
"verified": true,
"answer": 7140,
"timestamp": "2026-02-08T03:43:51.638677Z"
} | 05874b | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 194,
"completion_tokens": 4994
},
"timestamp": "2026-02-09T12:12:34.704Z",
"answer": 7140
},
{
"i... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "ONE_PHI_1",
"status": "ok"
},
{
"lemma": "V5",
"status": "no"
},
{
"lemma": "... | {
"lo": -6.5,
"mid": -0.2,
"hi": 6.11
} | ||
f18c5c | comb_count_permutations_fixed_v1_601307018_8143 | Let $D_n$ denote the number of derangements of $n$ elements. Let $a$ be an integer with $0 \le a \le 60$. Define:
\[
\begin{aligned}
M &= a^{30} \bmod 61, \\
R &= 2a^3 \bmod 61, \\
S &= R^{30} \bmod 61, \\
T &= 2R^3 \bmod 61, \\
K &= T^{30} \bmod 61, \\
L &= 2T^3 \bmod 61, \\
P &= L^{30} \bmod 61, \\
Q &= M + S + K + P... | 1,855 | graphs = [
Graph(
let={
"_n": Const(61),
"n": Const(7),
"k": Binom(n=Const(16), k=CountOverSet(set=SolutionsSet(var=Var("a"), condition=And(Geq(Var("a"), Const(0)), Leq(Var("a"), Const(60)), Eq(Ref("_po_p4"), Var("a")), Neq(Ref("_po_p1"), Var("a")), Neq(Ref("_po_p2"), Var... | COMB | NT | COUNT | sympy | POLY_ORBIT_LEGENDRE | [
"POLY_ORBIT_LEGENDRE/ONE_BINOM_N"
] | 6dfc63 | comb_count_permutations_fixed_v1 | null | 7 | 0 | [
"ONE_BINOM_N",
"POLY_ORBIT_LEGENDRE"
] | 2 | 0.06 | 2026-03-10T08:37:18.175183Z | {
"verified": true,
"answer": 1855,
"timestamp": "2026-03-10T08:37:18.235421Z"
} | ddd17d | 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": 5743
},
"timestamp": "2026-04-19T08:23:10.552Z",
"answer": 1855
},
{
"... | 1 | [
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "ONE_BINOM_N",
"status": "ok_later"
},
{
"lemma": "POLY_ORBIT_LEGENDRE",
"status": "ok"
},
{
... | {
"lo": -5.34,
"mid": 1.1,
"hi": 7.53
} | ||
42485c | nt_count_divisors_in_range_v1_458359167_551 | Let $n = 332640$. Let $a$ be the minimum value of $x + y$ over all pairs of positive integers $(x, y)$ such that $xy = 9$. Let $r$ be the number of positive divisors $d$ of $n$ such that $a \leq d \leq 10083$. Find the value of $r$. | 163 | graphs = [
Graph(
let={
"n": Const(332640),
"a": MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(Mul(Var("x"), Var("y")), Const(9)))), expr=Sum(Var("x"), Var("y")))),
... | NT | null | COUNT | sympy | B3 | [
"B3"
] | 0cd20d | nt_count_divisors_in_range_v1 | null | 4 | 0 | [
"B3"
] | 1 | 0.097 | 2026-02-08T03:24:53.455630Z | {
"verified": true,
"answer": 163,
"timestamp": "2026-02-08T03:24:53.552775Z"
} | a13ffd | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 191,
"completion_tokens": 4406
},
"timestamp": "2026-02-10T13:28:39.049Z",
"answer": 163
},
{
"i... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
... | {
"lo": -3.42,
"mid": 1.86,
"hi": 7.55
} | ||
9ea46c | comb_bell_compute_v1_1915831931_2698 | Let $n$ be the number of integers $t$ such that $15 \leq t \leq 45$ and there exist positive integers $a$ and $b$, each at most 3, satisfying $t = 9a + 6b$. Let $Q$ be the remainder when $11 - B_n$ is divided by 52345, where $B_n$ denotes the $n$th Bell number. Compute $Q$. | 31,209 | graphs = [
Graph(
let={
"n": CountOverSet(set=SolutionsSet(var=Var("t"), condition=Exists(var=Var(name='a'), condition=Exists(var=Var(name='b'), condition=And(Geq(left=Var(name='a'), right=Const(value=1)), Leq(left=Var(name='a'), right=Const(value=3)), Geq(left=Var(name='b'), right=Const(value=1... | COMB | null | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | comb_bell_compute_v1 | null | 4 | 0 | [
"LIN_FORM"
] | 1 | 0.002 | 2026-02-08T17:03:56.199654Z | {
"verified": true,
"answer": 31209,
"timestamp": "2026-02-08T17:03:56.201453Z"
} | a961ad | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 140,
"completion_tokens": 760
},
"timestamp": "2026-02-17T18:24:24.661Z",
"answer": 31209
},
{... | 1 | [
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8",
"sta... | {
"lo": -4.1,
"mid": -1.76,
"hi": 1.32
} | ||
7de476 | sequence_count_fib_divisible_v1_124444284_4843 | Let $S$ be the set of all ordered pairs $(x,y)$ of positive integers such that $xy = 136161$. Define $T$ to be the set of all values $x + y$ where $(x,y) \in S$. Let $U$ be the minimum element of $T$. Let $d$ be the number of positive integers $k \leq 418$ that are divisible by $22$. Let $Q$ be the number of positive i... | 41 | graphs = [
Graph(
let={
"_n": Const(418),
"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(136161)))), expr=Sum(Var("x"), Var("y"... | NT | null | COUNT | sympy | COUNT_PRIMES | [
"B3",
"C2"
] | 83578c | sequence_count_fib_divisible_v1 | null | 7 | 0 | [
"B3",
"C2",
"COUNT_PRIMES"
] | 3 | 0.175 | 2026-02-08T06:15:16.473345Z | {
"verified": true,
"answer": 41,
"timestamp": "2026-02-08T06:15:16.648654Z"
} | 4417df | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 173,
"completion_tokens": 1501
},
"timestamp": "2026-02-12T21:38:53.584Z",
"answer": 41
},
{
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "C2",
"status": "ok"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": ... | {
"lo": -3.51,
"mid": 1.33,
"hi": 6.56
} | ||
df59ff | comb_bell_compute_v1_1918700295_684 | Let $m = 9$. Define $s$ to be the minimum value of $x + y$ over all ordered pairs $(x, y)$ of positive integers such that $xy = m$. Let $P$ be the maximum value of $xy$ over all ordered pairs $(x, y)$ of positive integers such that $x + y = s$. Compute the Bell number $B_P$. | 21,147 | graphs = [
Graph(
let={
"_m": Const(9),
"_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")))),
... | COMB | null | COMPUTE | sympy | B3 | [
"B3/B1"
] | 7f76f7 | comb_bell_compute_v1 | null | 5 | 0 | [
"B1",
"B3"
] | 2 | 0.001 | 2026-02-08T03:23:08.977791Z | {
"verified": true,
"answer": 21147,
"timestamp": "2026-02-08T03:23:08.979284Z"
} | 950198 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 192,
"completion_tokens": 853
},
"timestamp": "2026-02-10T14:11:56.484Z",
"answer": 21147
},
{
"i... | 1 | [
{
"lemma": "B1",
"status": "ok_later"
},
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"sta... | {
"lo": -5.97,
"mid": -3.96,
"hi": -1.93
} | ||
be15ed | comb_binomial_compute_v1_784195855_542 | Let $n$ be the smallest divisor of $71383$ that is at least $2$. Compute $\binom{n}{7}$. | 1,716 | graphs = [
Graph(
let={
"_n": Const(71383),
"n": MinOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Const(2)), Divides(divisor=Var("d"), dividend=Ref("_n"))))),
"k": Const(7),
"result": Binom(n=Ref("n"), k=Ref("k")),
},
goal=... | NT | null | COMPUTE | sympy | MIN_PRIME_FACTOR | [
"MIN_PRIME_FACTOR"
] | bc3776 | comb_binomial_compute_v1 | null | 3 | 0 | [
"MIN_PRIME_FACTOR"
] | 1 | 0.002 | 2026-02-08T04:27:12.783393Z | {
"verified": true,
"answer": 1716,
"timestamp": "2026-02-08T04:27:12.785424Z"
} | fee3d8 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 140,
"completion_tokens": 827
},
"timestamp": "2026-02-10T16:50:08.369Z",
"answer": 1716
},
{
"i... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "MIN_PRIME_FACTOR",
"status": "ok"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "... | {
"lo": -3.42,
"mid": 1.86,
"hi": 7.55
} | ||
544f32 | comb_sum_binomial_row_v1_151522320_1058 | Let $S$ be the set of all ordered pairs $(x_1, x_2)$ of positive odd integers such that $x_1 + x_2 = 50$. Let $P$ be the number of elements in $S$. Now consider the set of all ordered pairs $(x, y)$ of positive integers such that $xy = P$. Let $n$ be the minimum value of $x + y$ over all such pairs. Compute the remaind... | 13,790 | graphs = [
Graph(
let={
"_m": Const(50),
"_n": Const(23635),
"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")), CountOverSet(set=... | NT | null | SUM | sympy | COMB1 | [
"COMB1/B3"
] | 014cfb | comb_sum_binomial_row_v1 | null | 6 | 0 | [
"B3",
"COMB1"
] | 2 | 0.003 | 2026-02-08T03:44:10.356528Z | {
"verified": true,
"answer": 13790,
"timestamp": "2026-02-08T03:44:10.359162Z"
} | a96a43 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 225,
"completion_tokens": 1148
},
"timestamp": "2026-02-10T15:34:01.290Z",
"answer": 13790
},
{
"... | 1 | [
{
"lemma": "B3",
"status": "ok_later"
},
{
"lemma": "COMB1",
"status": "ok"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "... | {
"lo": -3.46,
"mid": 1.03,
"hi": 5.49
} | ||
c54ee3 | modular_mod_compute_v1_397696148_1220 | Let $m$ be the maximum value of $xy$ over all pairs of positive integers $(x, y)$ such that $x + y = 126$. Let $a = -13689$. Compute the remainder when $75405 \cdot (a \bmod m)$ is divided by $83774$. | 43,503 | graphs = [
Graph(
let={
"_n": Const(83774),
"a": Const(-13689),
"m": MaxOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(Sum(Var("x"), Var("y")), Const(126)))),... | NT | null | COMPUTE | sympy | B1 | [
"B1"
] | 5b950e | modular_mod_compute_v1 | null | 3 | 0 | [
"B1"
] | 1 | 0.002 | 2026-02-08T12:25:19.264029Z | {
"verified": true,
"answer": 43503,
"timestamp": "2026-02-08T12:25:19.266352Z"
} | b4126e | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 111,
"completion_tokens": 1188
},
"timestamp": "2026-02-15T01:03:58.993Z",
"answer": 43503
},
... | 1 | [
{
"lemma": "B1",
"status": "ok"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
}
] | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
9ee645 | modular_min_modexp_v1_717093673_1760 | Let $a = 13$ and $m = 761$. Let $b$ be the largest prime number satisfying $2 \leq b \leq 3$. Determine the smallest positive integer $x$ such that $1 \leq x \leq 152$ and
$$
a^x \equiv b \pmod{m}.
$$ | 113 | graphs = [
Graph(
let={
"a": Const(13),
"b": MaxOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(2)), Leq(Var("n"), Const(3)), IsPrime(Var("n"))))),
"m": Const(761),
"upper": Const(152),
"result": MinOverSet(set=SolutionsSet... | NT | null | EXTREMUM | sympy | MAX_PRIME_BELOW | [
"MAX_PRIME_BELOW"
] | dc3ad3 | modular_min_modexp_v1 | null | 5 | 0 | [
"MAX_PRIME_BELOW"
] | 1 | 0.027 | 2026-02-08T16:18:24.947013Z | {
"verified": true,
"answer": 113,
"timestamp": "2026-02-08T16:18:24.974098Z"
} | cd2331 | 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": 4623
},
"timestamp": "2026-02-17T00:49:44.176Z",
"answer": 113
},
{
... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
42a9ab | modular_modexp_compute_v1_784195855_5997 | Let $n = 26244$. Define $\mathcal{P}$ to be the set of all ordered pairs $(x, y)$ of positive integers such that $xy = n$. Let $e$ be the minimum value of $x + y$ as $(x, y)$ ranges over $\mathcal{P}$. Compute the remainder when $19^e$ is divided by $86436$. | 37,045 | graphs = [
Graph(
let={
"_n": Const(26244),
"a": Const(19),
"e": MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(Mul(Var("x"), Var("y")), Ref("_n")))), expr... | NT | null | COMPUTE | sympy | B3 | [
"B3"
] | 0cd20d | modular_modexp_compute_v1 | null | 5 | 0 | [
"B3"
] | 1 | 0.001 | 2026-02-08T08:15:07.209123Z | {
"verified": true,
"answer": 37045,
"timestamp": "2026-02-08T08:15:07.210075Z"
} | 4440ce | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 125,
"completion_tokens": 3797
},
"timestamp": "2026-02-13T15:59:22.921Z",
"answer": 37045
},
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
... | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
32a8ff | nt_count_intersection_v1_168721529_1001 | Let $b$ be the sum of all positive integers $n$ such that $1 \leq n \leq 22$ and $n \equiv \sum_{d \mid \gcd(72,108)} \mu(d) \pmod{22}$.
Let $N = 100000$. Let $a = 3$. Define $r$ to be the number of positive integers $n \leq N$ divisible by $a$ such that $\gcd(n, b) = 1$.
Let $n = 56030$. Compute the remainder when $... | 27,462 | graphs = [
Graph(
let={
"_n": Const(56030),
"N": Const(100000),
"a": Const(3),
"b": SumOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Const(22)), Eq(Mod(value=Var("n"), modulus=Const(22)), SumOverDivisors(n=GCD(a=Co... | NT | null | COUNT | sympy | MOBIUS_COPRIME | [
"MOBIUS_COPRIME",
"SUM_DIVISIBLE"
] | e34bec | nt_count_intersection_v1 | null | 6 | 0 | [
"MOBIUS_COPRIME",
"SUM_DIVISIBLE"
] | 2 | 5.699 | 2026-02-08T13:24:01.622124Z | {
"verified": true,
"answer": 27462,
"timestamp": "2026-02-08T13:24:07.320702Z"
} | f016ff | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 251,
"completion_tokens": 4703
},
"timestamp": "2026-02-09T11:53:37.877Z",
"answer": 27462
},
{
"... | 1 | [
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "MOBIUS_COPRIME",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "SUM_DIVISIBLE",
"status": "ok"
},
{
"lemma": "V8",
"... | {
"lo": -1.99,
"mid": 2.14,
"hi": 6.33
} | ||
f59974_l | diophantine_product_count_v1_1918700295_91 | Let $N = \sum_{d \mid 3149} \phi(d)$, where $\phi$ is Euler's totient function. Let $k$ be the number of positive integers $n$ such that $1 \leq n \leq N$ and $\gcd(n, 30) = 1$. Let $S$ be the set of positive integers $x$ such that $1 \leq x \leq 481$, $x$ divides $k$, and $\frac{k}{x} \leq 481$. Compute
$$
\sum_{n=1}^... | 113 | NT | null | COUNT | sympy | K3 | [
"K3/C4"
] | c1614d | diophantine_product_count_v1 | null | 7 | 0 | [
"C4",
"K3"
] | 2 | 0.019 | 2026-02-08T02:59:05.018754Z | {
"verified": false,
"answer": 111,
"timestamp": "2026-02-08T02:59:05.037969Z"
} | 4c9abf | f59974 | 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": 263,
"completion_tokens": 6424
},
"timestamp": "2026-02-23T20:50:09.020Z",
"answer": 111
},
{
"id... | 1 | [
{
"lemma": "C4",
"status": "ok_later"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K3",
"status": "ok"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "V3",
"status": "no"
},
{
"l... | {
"lo": 2.87,
"mid": 4.69,
"hi": 6.49
} | |
9ca482 | nt_sum_totient_over_divisors_v1_865884756_2342 | Let $n = 34992$. Compute the sum of $\phi(d)$ over all positive divisors $d$ of $n$, where $\phi$ is Euler's totient function. Let $r$ be the absolute value of this sum. Let $m$ be the smallest integer greater than or equal to 2 that divides 1859. Find the $r \bmod m$-th Bell number. | 1 | graphs = [
Graph(
let={
"_n": Const(1859),
"n": Const(34992),
"result": SumOverDivisors(n=Ref(name='n'), var='d', expr=EulerPhi(n=Var(name='d'))),
"Q": Bell(Mod(value=Abs(arg=Ref(name='result')), modulus=MinOverSet(set=SolutionsSet(var=Var("d1"), condition=And... | NT | COMB | COMPUTE | sympy | MIN_PRIME_FACTOR | [
"MIN_PRIME_FACTOR"
] | 58d7e9 | nt_sum_totient_over_divisors_v1 | bell_mod | 4 | 0 | [
"MIN_PRIME_FACTOR"
] | 1 | 0.005 | 2026-02-08T16:42:55.411542Z | {
"verified": true,
"answer": 1,
"timestamp": "2026-02-08T16:42:55.416596Z"
} | c9fc9c | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 130,
"completion_tokens": 975
},
"timestamp": "2026-02-17T10:57:50.410Z",
"answer": 1
},
{
... | 1 | [
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "MIN_PRIME_FACTOR",
"status": "ok"
},
{
"lemma": "VAL_SUM_EQ",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
4bb8b0 | comb_count_permutations_fixed_v1_601307018_825 | Let $D_n$ denote the number of derangements of $n$ elements. Compute $\binom{8}{k} \cdot D_{8 - k}$, where $k = \sum_{d=1}^{2} \varphi(d) \cdot \left\lfloor \frac{2}{d} \right\rfloor$. | 2,464 | graphs = [
Graph(
let={
"n": Const(8),
"k": Summation(var="k1", start=Const(1), end=Const(2), expr=Mul(EulerPhi(n=Var("k1")), Floor(Div(Const(2), Var("k1"))))),
"result": Mul(Binom(n=Ref("n"), k=Ref("k")), Subfactorial(arg=Sub(left=Ref(name='n'), right=Ref(name='k')))),
... | COMB | NT | COUNT | sympy | ONE_BINOM_N | [
"K2"
] | 6897ab | comb_count_permutations_fixed_v1 | null | 4 | 0 | [
"K2",
"ONE_BINOM_N"
] | 2 | 0.008 | 2026-03-10T01:27:53.619363Z | {
"verified": true,
"answer": 2464,
"timestamp": "2026-03-10T01:27:53.627049Z"
} | 713382 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 185,
"completion_tokens": 634
},
"timestamp": "2026-03-29T00:16:43.248Z",
"answer": 2464
},
{
"id... | 2 | [
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "K2",
"status": "ok"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
}
] | {
"lo": -10,
"mid": -6.42,
"hi": -2.84
} | ||
3c1f68 | comb_bell_compute_v1_784195855_5954 | Let $a$ and $b$ be integers with $1 \leq a \leq 3$ and $1 \leq b \leq 3$. Let $T$ be the set of all integers $t$ such that $t = 3a + 2b$ and $5 \leq t \leq 15$. Let $n$ be the number of elements in $T$. Let $B_n$ denote the $n$th Bell number, which counts the number of partitions of a set of size $n$. Find the smallest... | 10,574 | 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... | NT | COMB | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | comb_bell_compute_v1 | null | 5 | 0 | [
"LIN_FORM"
] | 1 | 0.006 | 2026-02-08T08:13:38.022057Z | {
"verified": true,
"answer": 10574,
"timestamp": "2026-02-08T08:13:38.027724Z"
} | 22d9c7 | 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": 4939
},
"timestamp": "2026-02-13T15:55:25.793Z",
"answer": 10574
},
... | 1 | [
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
}
] | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
31cb3a | nt_count_coprime_and_v1_124444284_4284 | Let $n = 385$. Let $d_{\text{min}}$ be the smallest divisor of $n$ that is at least $2$. Define $k_2 = \sum_{k=1}^{d_{\text{min}}} k$. Let $r$ be the number of positive integers $m$ such that $1 \leq m \leq 29617$, $\gcd(m, 8) = 1$, and $\gcd(m, k_2) = 1$. Compute the remainder when $78849 \cdot r$ is divided by $60830... | 32,692 | graphs = [
Graph(
let={
"_n": Const(385),
"upper": Const(29617),
"k1": Const(8),
"k2": Summation(var="k", start=Const(1), end=MinOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Const(2)), Divides(divisor=Var("d"), dividend=Ref("_n"))))), exp... | NT | null | COUNT | sympy | MIN_PRIME_FACTOR | [
"MIN_PRIME_FACTOR/SUM_ARITHMETIC"
] | 487060 | nt_count_coprime_and_v1 | null | 5 | 0 | [
"MIN_PRIME_FACTOR",
"SUM_ARITHMETIC"
] | 2 | 8.129 | 2026-02-08T05:53:31.248971Z | {
"verified": true,
"answer": 32692,
"timestamp": "2026-02-08T05:53:39.378066Z"
} | 2a6c8a | 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": 1884
},
"timestamp": "2026-02-12T16:36:28.434Z",
"answer": 32692
},
... | 1 | [
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "MIN_PRIME_FACTOR",
"status": "ok"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "SUM_ARITHMETIC",
"status": "ok_later"
},
{
"lemma": "V8_SUM",
... | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
767ecd | nt_min_phi_inverse_v1_784195855_6275 | Let $T$ be the set of all integers $t$ with $25 \leq t \leq 80$ for which there exist integers $a$ and $b$ such that $1 \leq a \leq 25$, $1 \leq b \leq 2$, and $t = 2a + 7b + 16$. Let $\text{upper}$ be the number of such integers $t$. Let $k$ be the minimum value of $x + y$ over all ordered pairs $(x, y)$ of positive i... | 23 | graphs = [
Graph(
let={
"_n": Const(121),
"upper": CountOverSet(set=SolutionsSet(var=Var("t"), condition=Exists(var=Var(name='a'), condition=Exists(var=Var(name='b'), condition=And(Geq(left=Var(name='a'), right=Const(value=1)), Leq(left=Var(name='a'), right=Const(value=25)), Geq(left... | NT | null | EXTREMUM | sympy | K2 | [
"LIN_FORM",
"B3"
] | 688dbe | nt_min_phi_inverse_v1 | null | 7 | 0 | [
"B3",
"K2",
"LIN_FORM"
] | 3 | 0.024 | 2026-02-08T08:32:13.431952Z | {
"verified": true,
"answer": 23,
"timestamp": "2026-02-08T08:32:13.455862Z"
} | f745e9 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 199,
"completion_tokens": 1309
},
"timestamp": "2026-02-13T19:32:58.401Z",
"answer": 23
},
{
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "V1",
"status": "no"
},
{
"lemma... | {
"lo": -5.55,
"mid": -3.01,
"hi": 0.32
} | ||
922c23 | alg_qf_psd_sum_v1_601307018_10535 | Let $S$ be the set of ordered pairs $(a_1, b_1)$ of positive integers with $1 \le a_1, b_1 \le 35$ satisfying
$$
17a_1^4 + 102a_1^2b_1^2 + 17b_1^4 + 68a_1^3b_1 + 68a_1b_1^3 = 6640625.
$$
Let $N = |S|$. Find the remainder when
$$
\sum_{\substack{a=1}}^{24} \sum_{b=1}^{N} \sum_{c=1}^{24} \left(38a^2 + 42ab - 2ac + 5c^2 +... | 47,712 | graphs = [
Graph(
let={
"_n": Const(24),
"result": Mod(value=SumOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("a"), Var("b"), Var("c")]), condition=And(Geq(Var("a"), Const(1)), Leq(Var("a"), Ref("_n")), Geq(Var("b"), Const(1)), Leq(Var("b"), CountOverSet(set=Solutio... | ALG | null | COMPUTE | sympy | POLY4_COUNT | [
"POLY4_COUNT"
] | 861d91 | alg_qf_psd_sum_v1 | null | 7 | 0 | [
"POLY4_COUNT"
] | 1 | 0.045 | 2026-03-10T11:00:04.325240Z | {
"verified": true,
"answer": 47712,
"timestamp": "2026-03-10T11:00:04.370662Z"
} | dc091a | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 295,
"completion_tokens": 2947
},
"timestamp": "2026-04-19T14:08:51.005Z",
"answer": 47712
},
{
... | 1 | [
{
"lemma": "POLY4_COUNT",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
}
] | {
"lo": -5.34,
"mid": 1.1,
"hi": 7.53
} | ||
f221ba | nt_count_coprime_and_v1_1742523217_779 | Let $ k_1 = 11 $ and let $ k_2 $ be the smallest integer $ d \geq 2 $ that divides 71383. Compute the number of positive integers $ n \leq 28513 $ such that $ \gcd(n, k_1) = 1 $ and $ \gcd(n, k_2) = 1 $. | 23,927 | graphs = [
Graph(
let={
"upper": Const(28513),
"k1": Const(11),
"k2": MinOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Const(2)), Divides(divisor=Var("d"), dividend=Const(71383))))),
"result": CountOverSet(set=SolutionsSet(var=Var("n"), co... | NT | null | COUNT | sympy | MIN_PRIME_FACTOR | [
"MIN_PRIME_FACTOR",
"ONE_PHI_1"
] | fb15c3 | nt_count_coprime_and_v1 | null | 4 | 0 | [
"MIN_PRIME_FACTOR",
"ONE_PHI_1"
] | 2 | 3.192 | 2026-02-08T03:14:38.061709Z | {
"verified": true,
"answer": 23927,
"timestamp": "2026-02-08T03:14:41.253663Z"
} | d82e10 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 194,
"completion_tokens": 1243
},
"timestamp": "2026-02-09T06:56:08.681Z",
"answer": 23927
},
{
... | 1 | [
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "MIN_PRIME_FACTOR",
"status": "ok"
},
{
"lemma": "ONE_PHI_1",
"status": "ok"
},
{
"lemma": "V1",
"st... | {
"lo": -6.49,
"mid": 0.51,
"hi": 7.52
} | ||
6691e8 | algebra_poly_eval_v1_48377204_1679 | Let $a = 19$. Define $\text{result} = 6a^2 + 9a + 5$. Let $n = 176$. Consider the set of all ordered pairs $(x,y)$ of positive integers such that $x + y = n$. Let $P$ be the set of all values of $xy$ as $(x,y)$ ranges over this set. Let $c$ be the maximum value in $P$. Define $Q = c - \text{result}$. Compute $Q$. | 5,402 | graphs = [
Graph(
let={
"_n": Const(176),
"a": Const(19),
"result": Sum(Mul(Const(6), Pow(Ref("a"), Const(2))), Mul(Const(9), Ref("a")), Const(5)),
"_c": MaxOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPosit... | NT | null | COMPUTE | sympy | B1 | [
"B1"
] | d2b6e1 | algebra_poly_eval_v1 | negation_mod | 3 | 0 | [
"B1"
] | 1 | 0.003 | 2026-02-08T16:18:18.629717Z | {
"verified": true,
"answer": 5402,
"timestamp": "2026-02-08T16:18:18.632590Z"
} | 97ae77 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 155,
"completion_tokens": 515
},
"timestamp": "2026-02-17T00:55:35.880Z",
"answer": 5402
},
{
... | 1 | [
{
"lemma": "B1",
"status": "ok"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "V3",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
3d888b | nt_sum_divisors_mod_v1_1915831931_2944 | Let $n$ be the minimum value of $x + y$ over all pairs of positive integers $(x, y)$ such that $xy = 14400$. Let $\sigma$ be the sum of all positive divisors of $n$. Compute the remainder when $\sigma$ is divided by $10513$. | 744 | 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(14400)))), expr=Sum(Var("x"), Var("y")))),
"M": Const(10513)... | NT | null | COMPUTE | sympy | B3 | [
"B3"
] | 0cd20d | nt_sum_divisors_mod_v1 | null | 5 | 0 | [
"B3"
] | 1 | 0.003 | 2026-02-08T17:15:11.610785Z | {
"verified": true,
"answer": 744,
"timestamp": "2026-02-08T17:15:11.613518Z"
} | 5fc4d2 | 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": 1780
},
"timestamp": "2026-02-17T22:36:57.906Z",
"answer": 744
},
{
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
}
... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
354409 | comb_count_partitions_v1_971394319_2089 | Let $S$ be the set of all integers $t$ such that there exist integers $a$ and $b$ satisfying $1 \leq a \leq 9$, $1 \leq b \leq 5$, $31 \leq t \leq 91$, and $t = 4a + 7b + 20$. Let $n$ be the number of elements in $S$. Determine the value of $p(n)$, the number of integer partitions of $n$. | 63,261 | graphs = [
Graph(
let={
"n": CountOverSet(set=SolutionsSet(var=Var("t"), condition=Exists(var=Var(name='a'), condition=Exists(var=Var(name='b'), condition=And(Geq(left=Var(name='a'), right=Const(value=1)), Leq(left=Var(name='a'), right=Const(value=9)), Geq(left=Var(name='b'), right=Const(value=1... | COMB | null | COUNT | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | comb_count_partitions_v1 | null | 4 | 0 | [
"LIN_FORM"
] | 1 | 0.003 | 2026-02-08T14:06:44.971486Z | {
"verified": true,
"answer": 63261,
"timestamp": "2026-02-08T14:06:44.974007Z"
} | 9fae17 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 218,
"completion_tokens": 21298
},
"timestamp": "2026-02-24T19:55:58.758Z",
"answer": 63261
},
{
... | 1 | [
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8",
"sta... | {
"lo": 1.15,
"mid": 4.18,
"hi": 6.61
} | ||
0daaa7 | diophantine_fbi2_min_v1_1978505735_6787 | Let $k = 14$. Let $u$ be the largest positive divisor of 744 that is at most 24. Determine the value of the smallest positive integer $d_1$ such that $2 \leq d_1 \leq u$, $d_1$ divides $k$, and $\frac{k}{d_1} \geq 6$. | 2 | graphs = [
Graph(
let={
"k": Const(14),
"upper": MaxOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Const(1)), Leq(Var("d"), Const(24)), Divides(divisor=Var("d"), dividend=Const(744))))),
"result": MinOverSet(set=SolutionsSet(var=Var("d1"), condition=An... | NT | null | EXTREMUM | sympy | MAX_DIVISOR | [
"MAX_DIVISOR"
] | 51757e | diophantine_fbi2_min_v1 | null | 3 | 0 | [
"MAX_DIVISOR"
] | 1 | 0.016 | 2026-02-08T19:47:22.622624Z | {
"verified": true,
"answer": 2,
"timestamp": "2026-02-08T19:47:22.638979Z"
} | 645601 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 122,
"completion_tokens": 772
},
"timestamp": "2026-02-18T23:32:04.874Z",
"answer": 2
},
{
... | 1 | [
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "MAX_DIVISOR",
"status": "ok"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
448868 | nt_count_digit_sum_v1_865884756_314 | Let $t$ be an integer. Define $S$ as the set of all integers $t$ such that $9 \leq t \leq 45$ and there exist positive integers $a$ and $b$, each at most 5, satisfying $t = 5a + 4b$. Let $N$ be the number of elements in $S$. Let $T$ be the set of all positive integers $n$ such that $1 \leq n \leq 10816$ and the sum of ... | 351 | graphs = [
Graph(
let={
"upper": Const(10816),
"target_sum": CountOverSet(set=SolutionsSet(var=Var("t"), condition=Exists(var=Var(name='a'), condition=Exists(var=Var(name='b'), condition=And(Geq(left=Var(name='a'), right=Const(value=1)), Leq(left=Var(name='a'), right=Const(value=5)),... | NT | null | COUNT | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | nt_count_digit_sum_v1 | null | 4 | 0 | [
"LIN_FORM"
] | 1 | 4.194 | 2026-02-08T15:18:34.890894Z | {
"verified": true,
"answer": 351,
"timestamp": "2026-02-08T15:18:39.084497Z"
} | 347e3a | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 176,
"completion_tokens": 3658
},
"timestamp": "2026-02-16T03:01:24.165Z",
"answer": 351
},
{
... | 1 | [
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
}... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
8aaf22 | alg_poly4_sum_v1_601307018_9166 | Let $S_1 = \left|\{ (a_1, b_1) : 1 \le a_1, b_1 \le 25,\, 10a_1^2 - 18a_1b_1 + 25b_1^2 \le 7489 \}\right|$ and $S_2 = \left|\{ (a_2, b_2) : 1 \le a_2, b_2 \le 40,\, 13a_2^2 - 2a_2b_2 + 2b_2^2 \le 1537 \}\right|$. Let $T$ be the sum over all positive integers $a \le S_1$, $b \le 488$ of the expression $$ S_2 \cdot a^4 +... | 54,014 | graphs = [
Graph(
let={
"_c": Const(7489),
"_m": Const(1537),
"_n": Const(2),
"result": Mod(value=SumOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("a"), Var("b")]), condition=And(Geq(Var("a"), Const(1)), Leq(Var("a"), CountOverSet(set=Solutio... | ALG | null | COMPUTE | sympy | SUM_SQUARES_IDENTITY | [
"SUM_SQUARES_IDENTITY",
"QF_PSD_COUNT_LEQ"
] | f7e397 | alg_poly4_sum_v1 | null | 8 | 0 | [
"QF_PSD_COUNT_LEQ",
"SUM_SQUARES_IDENTITY"
] | 2 | 1.475 | 2026-03-10T09:32:08.668531Z | {
"verified": true,
"answer": 54014,
"timestamp": "2026-03-10T09:32:10.143118Z"
} | 7ecd96 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 437,
"completion_tokens": 12101
},
"timestamp": "2026-04-19T10:48:24.698Z",
"answer": 54014
},
{
... | 1 | [
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "QF_PSD_COUNT_LEQ",
"status": "ok"
},
{
"lemma": "SUM_SQUARES_IDENTITY",
"status": "ok"
}
] | {
"lo": -5.34,
"mid": 1.1,
"hi": 7.53
} | ||
536ef0_n | alg_qf_psd_orbit_v1_601307018_1263 | Two hikers mark points on a trail numbered from $1$ to $453$. The hikers choose positions $a$ and $b$ with $a \leq b$, and their energy exchange is modeled by the equation $2b^2 + 2a^2 - 4ab = 97682$. How many such position pairs $(a, b)$ satisfy this condition? | 232 | ALG | null | COUNT | sympy | POLY4_COUNT | [
"MIN_PRIME_FACTOR"
] | bc3776 | alg_qf_psd_orbit_v1 | null | 5 | null | [
"MIN_PRIME_FACTOR",
"POLY4_COUNT"
] | 2 | 2.688 | 2026-03-10T01:56:02.550378Z | null | 41fb96 | 536ef0 | narrative | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 188,
"completion_tokens": 686
},
"timestamp": "2026-03-29T14:57:37.299Z",
"answer": 232
},
{
"id"... | 1 | [
{
"lemma": "MIN_PRIME_FACTOR",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
}
] | {
"lo": -5.36,
"mid": 0.27,
"hi": 5.45
} | |
752ecd | algebra_poly_eval_v1_865884756_2507 | Let $ m = 6 $. Compute the value of
$$
7m^4 - 4m^3 + \left( \text{number of integers } t \text{ with } 5 \leq t \leq 15 \text{ such that } t = 2a + 3b \text{ for some integers } a, b \in \{1,2,3\} \right) \cdot m^k - 3m - 1,
$$
where $ k $ is the number of positive integers $ p $ such that $ p < q $, $ pq = 72 $, and $... | 8,513 | graphs = [
Graph(
let={
"_m": Const(7),
"_n": Const(3),
"m": Const(6),
"result": Sum(Mul(Ref("_m"), Pow(Ref("m"), Const(4))), Mul(Const(-4), Pow(Ref("m"), Ref("_n"))), Mul(CountOverSet(set=SolutionsSet(var=Var("t"), condition=Exists(var=Var(name='a'), conditio... | NT | null | COMPUTE | sympy | COPRIME_PAIRS | [
"COPRIME_PAIRS",
"LIN_FORM"
] | 67610e | algebra_poly_eval_v1 | null | 5 | 0 | [
"COPRIME_PAIRS",
"LIN_FORM"
] | 2 | 0.006 | 2026-02-08T16:48:00.499797Z | {
"verified": true,
"answer": 8513,
"timestamp": "2026-02-08T16:48:00.505699Z"
} | 8b7a8b | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 192,
"completion_tokens": 1288
},
"timestamp": "2026-02-17T11:49:08.460Z",
"answer": 8513
},
{... | 1 | [
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma":... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
818faf | nt_count_primes_v1_238844314_489 | Let $S$ be the set of all positive integers $p$ for which there exists a positive integer $q$ such that $pq = 12$, $\gcd(p, q) = 1$, and $p < q$. Let $N$ be the number of elements in $S$. Determine the number of prime numbers $n$ such that $N \leq n \leq 29929$.
Compute the value of this number. | 3,241 | graphs = [
Graph(
let={
"upper": Const(29929),
"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'), condition=And(Eq(left=Mul(Var(name='p'),... | NT | null | COUNT | sympy | COPRIME_PAIRS | [
"COPRIME_PAIRS"
] | 2bb3aa | nt_count_primes_v1 | null | 4 | 0 | [
"COPRIME_PAIRS"
] | 1 | 1.185 | 2026-02-08T13:22:21.297682Z | {
"verified": true,
"answer": 3241,
"timestamp": "2026-02-08T13:22:22.483061Z"
} | 4fbf88 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 137,
"completion_tokens": 2731
},
"timestamp": "2026-02-15T13:45:15.922Z",
"answer": 3241
},
{... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "V8",
"status": "no"... | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
edf737 | geo_count_lattice_rect_v1_124444284_6482 | Compute the number of lattice points in the rectangle $[0, 144] \times [0, 190]$, including the boundary. | 27,695 | graphs = [
Graph(
let={
"a": Const(144),
"b": Const(190),
"result": LatticePointsRect(a=Ref(name='a'), b=Ref(name='b')),
},
goal=Ref("result"),
)
] | GEOM | null | COUNT | sympy | [] | geo_count_lattice_rect_v1 | null | 4 | 0 | null | null | 0.001 | 2026-02-08T08:28:48.966783Z | {
"verified": true,
"answer": 27695,
"timestamp": "2026-02-08T08:28:48.968109Z"
} | 20f9a9 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 139,
"completion_tokens": 275
},
"timestamp": "2026-02-24T09:34:12.327Z",
"answer": 27695
},
{
"i... | 1 | [] | {
"lo": -7.18,
"mid": -5,
"hi": -3.01
} | ||||
d2133c | modular_count_residue_v1_1353956133_133 | Let $m$ be the number of positive integers $p$ for which there exists a positive integer $q$ such that $p \cdot q = 90$, $\gcd(p, q) = 1$, and $p < q$. Let $r = 2$ and let $\text{upper} = 64516$.
Consider the set of all positive integers $n$ such that $1 \leq n \leq \text{upper}$ and $n \equiv r \pmod{m}$. Let $\text{... | 54,619 | graphs = [
Graph(
let={
"_n": Const(78109),
"upper": Const(64516),
"m": CountOverSet(set=SolutionsSet(var=Var("p"), condition=And(IsPositive(arg=Var(name='p')), Exists(var=Var(name='q'), condition=And(Eq(left=Mul(Var(name='p'), Var(name='q')), right=Const(value=90)), Eq(l... | NT | null | COUNT | sympy | COPRIME_PAIRS | [
"COPRIME_PAIRS"
] | 2bb3aa | modular_count_residue_v1 | null | 5 | 0 | [
"COPRIME_PAIRS"
] | 1 | 5.758 | 2026-02-08T11:19:20.002503Z | {
"verified": true,
"answer": 54619,
"timestamp": "2026-02-08T11:19:25.760362Z"
} | 1045cb | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 199,
"completion_tokens": 2132
},
"timestamp": "2026-02-14T11:47:12.833Z",
"answer": 54619
},
... | 1 | [
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
... | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
344618 | nt_min_phi_inverse_v1_1918700295_68 | Let $\phi(n)$ denote Euler's totient function and $\tau(n)$ denote the number of positive divisors of $n$. Let $m$ be the smallest positive integer such that $m \leq 70$ and $\phi(m) = 16$. Compute the value of $$
\tau(m + 1) + \phi(|m| + 1) + m.
$$ | 29 | graphs = [
Graph(
let={
"upper": Const(70),
"k": Const(16),
"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(Ref("result"), EulerPhi(n=Sum(Ab... | NT | null | EXTREMUM | sympy | LIOUVILLE_MINUS_ONE | [
"ONE_PHI_1"
] | f6b5a5 | nt_min_phi_inverse_v1 | null | 5 | 0 | [
"LIOUVILLE_MINUS_ONE",
"ONE_PHI_1"
] | 2 | 0.094 | 2026-02-08T02:58:18.360077Z | {
"verified": true,
"answer": 29,
"timestamp": "2026-02-08T02:58:18.453758Z"
} | e9ed67 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 196,
"completion_tokens": 808
},
"timestamp": "2026-02-08T22:30:38.549Z",
"answer": 29
},
{
"id"... | 1 | [
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "ONE_PHI_1",
"status": "ok"
}
] | {
"lo": -6.49,
"mid": 0.51,
"hi": 7.52
} | ||
3576e4 | modular_count_residue_v1_784195855_2484 | Compute the number of positive integers $n$ such that $n \leq 77777$ and $n \equiv 15 \pmod{17}$. | 4,575 | graphs = [
Graph(
let={
"upper": Const(77777),
"m": Const(17),
"r": Summation(var="k", start=Const(1), end=Const(5), expr=Var("k")),
"result": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Ref("upper")), Eq(Mo... | NT | null | COUNT | sympy | SUM_ARITHMETIC | [
"SUM_ARITHMETIC"
] | eb34f0 | modular_count_residue_v1 | null | 2 | 0 | [
"SUM_ARITHMETIC"
] | 1 | 5.446 | 2026-02-08T05:47:41.131070Z | {
"verified": true,
"answer": 4575,
"timestamp": "2026-02-08T05:47:46.577509Z"
} | 015702 | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 93,
"completion_tokens": 438
},
"timestamp": "2026-02-11T23:09:23.679Z",
"answer": 4575
},
{
"id": 11,
... | 2 | [
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "SUM_ARITHMETIC",
... | {
"lo": -9.14,
"mid": -6.05,
"hi": -3.73
} | ||
769e5a | nt_min_phi_inverse_v1_865884756_3079 | Let $S$ be the set of all ordered pairs $(x,y)$ of positive integers such that $x + y = 20$. Define $P$ to be the maximum value of $xy$ over all pairs in $S$. Let $k$ be the number of integers $t$ in the range $7 \leq t \leq 36$ for which there exist positive integers $a$ and $b$ with $1 \leq a \leq 6$, $1 \leq b \leq ... | 58,681 | graphs = [
Graph(
let={
"_n": Const(71218),
"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")), Const(20)))), expr=Mul(Var("x"), Var("y"))... | NT | null | EXTREMUM | sympy | LIN_FORM | [
"LIN_FORM",
"B1"
] | 2f9b70 | nt_min_phi_inverse_v1 | null | 7 | 0 | [
"B1",
"LIN_FORM"
] | 2 | 0.011 | 2026-02-08T17:09:47.494052Z | {
"verified": true,
"answer": 58681,
"timestamp": "2026-02-08T17:09:47.504799Z"
} | 87a03c | 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": 4203
},
"timestamp": "2026-02-17T20:52:28.698Z",
"answer": 58681
},
... | 1 | [
{
"lemma": "B1",
"status": "ok"
},
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
f06ac2 | antilemma_k3_v1_1978505735_7019 | Let $n = 60440$. Compute the remainder when $$\left| \sum_{d \mid n} \phi(d) \right|$$ is divided by $96850$, where $\phi(d)$ denotes Euler's totient function. | 60,440 | graphs = [
Graph(
let={
"_n": Const(60440),
"x": SumOverDivisors(n=Ref(name='_n'), var='d', expr=EulerPhi(n=Var(name='d'))),
"Q": Mod(value=Abs(arg=Ref(name='x')), modulus=Const(96850)),
},
goal=Ref("Q"),
)
] | NT | COMB | COMPUTE | sympy | K3 | [
"K3"
] | 54c41e | antilemma_k3_v1 | null | 3 | 0 | [
"K3"
] | 1 | 0.001 | 2026-02-08T20:00:51.004656Z | {
"verified": true,
"answer": 60440,
"timestamp": "2026-02-08T20:00:51.005415Z"
} | 5f8a7a | 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": 1840
},
"timestamp": "2026-02-18T23:47:41.343Z",
"answer": 60440
},
{... | 1 | [
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "K3",
"status": "ok"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "V1",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
bafe64 | comb_count_permutations_fixed_v1_865884756_6079 | Let $n$ be the largest prime number such that $2 \leq n \leq s$, where $s$ is the minimum value of $x + y$ over all ordered pairs $(x, y)$ of positive integers satisfying $xy = p$, and $p$ is the maximum value of $x_1 y_1$ over all ordered pairs $(x_1, y_1)$ of positive integers such that $x_1 + y_1 = 6$. Let $k = 1$. ... | 70,592 | graphs = [
Graph(
let={
"_m": Const(77689),
"_n": Const(39550),
"n": MaxOverSet(set=SolutionsSet(var=Var("n1"), condition=And(Geq(Var("n1"), Const(2)), Leq(Var("n1"), MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPosi... | NT | COMB | COUNT | sympy | B1 | [
"B1/B3/MAX_PRIME_BELOW"
] | 9c6e3c | comb_count_permutations_fixed_v1 | null | 7 | 0 | [
"B1",
"B3",
"MAX_PRIME_BELOW"
] | 3 | 0.005 | 2026-02-08T18:57:37.408636Z | {
"verified": true,
"answer": 70592,
"timestamp": "2026-02-08T18:57:37.413721Z"
} | 62fb93 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 212,
"completion_tokens": 1168
},
"timestamp": "2026-02-18T20:41:30.831Z",
"answer": 70592
},
... | 1 | [
{
"lemma": "B1",
"status": "ok"
},
{
"lemma": "B3",
"status": "ok_later"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok_later"
},... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
8538b7 | nt_max_prime_below_v1_124444284_4907 | Let $P$ be the set of all positive integers $p$ for which there exists a positive integer $q$ such that $pq = 24$, $\gcd(p, q) = 1$, and $p < q$. Let $k$ be the number of elements in $P$. Let $n$ be the largest prime number not exceeding $33333$ such that $n \geq k$. Determine the value of $n$. | 33,331 | graphs = [
Graph(
let={
"upper": Const(33333),
"result": MaxOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), CountOverSet(set=SolutionsSet(var=Var("p"), condition=And(IsPositive(arg=Var(name='p')), Exists(var=Var(name='q'), condition=And(Eq(left=Mul(Var(name='p'), V... | NT | null | EXTREMUM | sympy | COPRIME_PAIRS | [
"COPRIME_PAIRS"
] | 2bb3aa | nt_max_prime_below_v1 | null | 4 | 0 | [
"COPRIME_PAIRS"
] | 1 | 0.785 | 2026-02-08T06:17:26.983051Z | {
"verified": true,
"answer": 33331,
"timestamp": "2026-02-08T06:17:27.767704Z"
} | 430446 | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 155,
"completion_tokens": 571
},
"timestamp": "2026-02-15T17:24:09.128Z",
"answer": 31321
},
{
"id": 11... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "V3",
"status... | {
"lo": -9.14,
"mid": -6.05,
"hi": -3.73
} | ||
46a07c | antilemma_count_primes_v1_798873815_464 | Let $c = 2711$ and $m = 91932$. Let $n$ be the largest prime number less than or equal to $c$. Define $x$ to be the number of prime numbers less than or equal to $n$ that are at least the number of positive integers $p$ for which there exists a positive integer $q$ such that $p < q$, $\gcd(p, q) = 1$, and $pq = 108$. C... | 42,839 | graphs = [
Graph(
let={
"_c": Const(2711),
"_m": Const(91932),
"_n": MaxOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(2)), Leq(Var("n"), Ref("_c")), IsPrime(Var("n"))))),
"x": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And... | NT | null | COMPUTE | sympy | MAX_PRIME_BELOW | [
"MAX_PRIME_BELOW/COUNT_PRIMES",
"COPRIME_PAIRS/COUNT_PRIMES",
"COUNT_PRIMES"
] | a26032 | antilemma_count_primes_v1 | null | 5 | 0 | [
"COPRIME_PAIRS",
"COUNT_PRIMES",
"MAX_PRIME_BELOW"
] | 3 | 0.002 | 2026-02-08T02:39:10.839364Z | {
"verified": true,
"answer": 42839,
"timestamp": "2026-02-08T02:39:10.841181Z"
} | 6d5a48 | CC BY 4.0 | [
{
"id": 4,
"model": "NousResearch/Hermes-4-405B",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 170,
"completion_tokens": 510
},
"timestamp": "2026-02-09T00:26:12.554Z",
"answer": 91891
},... | 1 | [
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_PRIMES",
"status": "ok"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"stat... | {
"lo": -1.78,
"mid": 2.35,
"hi": 6.69
} | ||
1e03f8 | diophantine_fbi2_min_v1_655260480_670 | Let $k = 240$ and define $s$ to be the number of positive integers $p$ such that there exists a positive integer $q$ with $p \cdot q = 54$, $\gcd(p, q) = 1$, and $p < q$. Find the smallest positive divisor $d$ of $k$ such that $d \geq s$, $d \leq 250$, and $\frac{k}{d} \geq 5$. Compute the value of $d$. | 2 | graphs = [
Graph(
let={
"_n": Const(5),
"k": Const(240),
"upper": Const(250),
"result": MinOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), CountOverSet(set=SolutionsSet(var=Var("p"), condition=And(IsPositive(arg=Var(name='p')), Exists(var=Va... | NT | null | EXTREMUM | sympy | C3 | [
"COPRIME_PAIRS"
] | 2bb3aa | diophantine_fbi2_min_v1 | null | 5 | 0 | [
"C3",
"COPRIME_PAIRS"
] | 2 | 0.082 | 2026-02-08T15:30:57.074872Z | {
"verified": true,
"answer": 2,
"timestamp": "2026-02-08T15:30:57.156723Z"
} | e22208 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 151,
"completion_tokens": 1400
},
"timestamp": "2026-02-16T08:30:50.788Z",
"answer": 2
},
{
... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
f76f2a | algebra_quadratic_discriminant_v1_601307018_3146 | Let $M$ be the number of positive integers $p$ such that there exists an integer $q$ with $p \cdot q = 360$, $\gcd(p, q) = 1$, and $p < q$. Let $b$ be the number of positive integers $p_1$ such that there exists an integer $q$ with $p_1 \cdot q = 83853000$, $\gcd(p_1, q) = 1$, and $p_1 < q$. Compute $b^2 - M \cdot (-2)... | 144 | graphs = [
Graph(
let={
"_m": Const(2),
"_n": CountOverSet(set=SolutionsSet(var=Var("p"), condition=And(IsPositive(arg=Var(name='p')), Exists(var=Var(name='q'), condition=And(Eq(left=Mul(Var(name='p'), Var(name='q')), right=Const(value=360)), Eq(left=GCD(a=Var(name='p'), b=Var(name='... | NT | null | COMPUTE | sympy | POLY_ORBIT_COUNT | [
"COPRIME_PAIRS/COPRIME_PAIRS"
] | 3bbd71 | algebra_quadratic_discriminant_v1 | null | 5 | 0 | [
"COPRIME_PAIRS",
"POLY_ORBIT_COUNT"
] | 2 | 1.131 | 2026-03-10T03:43:48.440091Z | {
"verified": true,
"answer": 144,
"timestamp": "2026-03-10T03:43:49.571185Z"
} | 11f1a8 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 240,
"completion_tokens": 1996
},
"timestamp": "2026-03-29T07:39:24.028Z",
"answer": 144
},
{
"id... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "V1",
"status": "no"
}
] | {
"lo": -2.46,
"mid": 1.23,
"hi": 4.93
} | ||
39543a | alg_poly4_min_v1_1218484723_5306 | For each ordered pair $(a, b)$ of positive integers with $1 \le a, b \le 293$, define $$ f(a, b) = \left| \left\{ (a_1, b_1) : 1 \le a_1, b_1 \le 35,\ 25b_1^2 + 10a_1^2 - 18a_1b_1 \le 1530 \right\} \right| \cdot a^4 + 30464 \cdot b^4. $$ Find the minimum value of $f(a, b)$ over all such pairs. | 30,583 | graphs = [
Graph(
let={
"_n": Const(35),
"result": MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("a"), Var("b")]), condition=And(Geq(Var("a"), Const(1)), Leq(Var("a"), Const(293)), Geq(Var("b"), Const(1)), Leq(Var("b"), Const(293)))), expr=Sum(Mul(CountOverSet(se... | ALG | null | COMPUTE | sympy | QF_PSD_COUNT_LEQ | [
"QF_PSD_COUNT_LEQ"
] | 009d0f | alg_poly4_min_v1 | null | 5 | 0 | [
"QF_PSD_COUNT_LEQ"
] | 1 | 0.457 | 2026-02-25T06:56:14.734246Z | {
"verified": true,
"answer": 30583,
"timestamp": "2026-02-25T06:56:15.191021Z"
} | 4558d8 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 246,
"completion_tokens": 5079
},
"timestamp": "2026-03-29T20:25:35.700Z",
"answer": 30583
},
{
"... | 1 | [
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "QF_PSD_COUNT_LEQ",
"status": "ok"
}
] | {
"lo": 1.53,
"mid": 4.7,
"hi": 7.23
} | ||
77a802 | comb_count_derangements_v1_1520064083_1711 | Let $n$ be the number of positive integers $p$ such that there exists a positive integer $q$ with $p < q$, $\gcd(p, q) = 1$, and $pq = 3150$. Compute the value of the subfactorial of $n$, denoted $!n$, which is the number of derangements of $n$ elements. | 14,833 | graphs = [
Graph(
let={
"n": CountOverSet(set=SolutionsSet(var=Var("p"), condition=And(IsPositive(arg=Var(name='p')), Exists(var=Var(name='q'), condition=And(Eq(left=Mul(Var(name='p'), Var(name='q')), right=Const(value=3150)), Eq(left=GCD(a=Var(name='p'), b=Var(name='q')), right=Const(value=1)),... | NT | COMB | COUNT | sympy | COPRIME_PAIRS | [
"COPRIME_PAIRS"
] | 2bb3aa | comb_count_derangements_v1 | null | 5 | 0 | [
"COPRIME_PAIRS"
] | 1 | 0.001 | 2026-02-08T04:14:42.533170Z | {
"verified": true,
"answer": 14833,
"timestamp": "2026-02-08T04:14:42.534030Z"
} | c20360 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 189,
"completion_tokens": 1585
},
"timestamp": "2026-02-10T15:49:38.486Z",
"answer": 14833
},
{
... | 1 | [
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "VAL_SUM_EQ",
... | {
"lo": -3.49,
"mid": 1.84,
"hi": 7.55
} | ||
720e06_n | comb_count_permutations_fixed_v1_1218484723_583 | A magician has 11 unique cards, each labeled from 1 to 11. She selects a subset of $k$ cards to place face-up on a table, where $k = \sum_{j=0}^{2} 2^j$ (since $\binom{13}{13} - 1 = 0$). The remaining $11 - k$ cards are shuffled and placed into envelopes numbered 1 through $11 - k$, such that no card goes into the enve... | 2,970 | COMB | null | COUNT | sympy | SUM_GEOM | [
"SUM_GEOM",
"ZERO_BINOM_N"
] | 4e18d8 | comb_count_permutations_fixed_v1 | null | 4 | null | [
"SUM_GEOM",
"ZERO_BINOM_N"
] | 2 | 0.003 | 2026-02-25T02:15:41.298248Z | null | a28602 | 720e06 | narrative | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 240,
"completion_tokens": 3129
},
"timestamp": "2026-03-30T15:39:32.872Z",
"answer": 5441
},
{
... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "SUM_GEOM",
"status": "ok"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
},
{
"lemm... | {
"lo": 1.5,
"mid": 4.69,
"hi": 7.23
} | |
7bbcdb | nt_min_phi_inverse_v1_1520064083_7464 | Let $n$ be the smallest positive integer at most 20 such that $\phi(n) = 4$, where $\phi$ denotes Euler's totient function. Let $d$ be the smallest divisor of 126251491 that is at least 2. Compute the value of $(n \bmod 199) + 2003 \cdot (n \bmod d)$. | 10,020 | graphs = [
Graph(
let={
"upper": Const(20),
"k": Const(4),
"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 | MIN_PRIME_FACTOR | [
"MIN_PRIME_FACTOR"
] | cffc20 | nt_min_phi_inverse_v1 | two_moduli | 4 | 0 | [
"MIN_PRIME_FACTOR"
] | 1 | 0.007 | 2026-02-08T09:03:39.476869Z | {
"verified": true,
"answer": 10020,
"timestamp": "2026-02-08T09:03:39.484091Z"
} | 4f879c | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 125,
"completion_tokens": 4363
},
"timestamp": "2026-02-13T23:40:50.714Z",
"answer": 10020
},
... | 1 | [
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MIN_PRIME_FACTOR",
"status": "ok"
},
{
"lemma": "V5",
"status": "no"
}... | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
b47721 | comb_count_surjections_v1_798873815_431 | Let $n$ be the number of integers $t$ with $15 \leq t \leq 42$ for which there exist integers $a$ and $b$ such that $1 \leq a \leq 2$, $1 \leq b \leq 4$, and $t = 9a + 6b$.
Let $k$ be the number of ordered pairs $(i, j)$ with $1 \leq i \leq 3$ and $1 \leq j \leq 4$ such that $i + j = 4$.
Compute $k! \cdot S(n, k)$, w... | 5,796 | graphs = [
Graph(
let={
"_n": Const(4),
"n": CountOverSet(set=SolutionsSet(var=Var("t"), condition=Exists(var=Var(name='a'), condition=Exists(var=Var(name='b'), condition=And(Geq(left=Var(name='a'), right=Const(value=1)), Leq(left=Var(name='a'), right=Const(value=2)), Geq(left=Var(na... | COMB | null | COUNT | sympy | COUNT_CARTESIAN | [
"COUNT_SUM_EQUALS",
"LIN_FORM"
] | 7b3310 | comb_count_surjections_v1 | null | 5 | 0 | [
"COUNT_CARTESIAN",
"COUNT_SUM_EQUALS",
"LIN_FORM"
] | 3 | 0.023 | 2026-02-08T02:38:32.165953Z | {
"verified": true,
"answer": 5796,
"timestamp": "2026-02-08T02:38:32.188614Z"
} | 1d9f2d | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 284,
"completion_tokens": 1322
},
"timestamp": "2026-02-08T19:31:12.714Z",
"answer": 5796
},
{
"i... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "ok"
},
{
"lemma": "LIN_F... | {
"lo": -1.79,
"mid": 0.17,
"hi": 1.93
} | ||
9e2468 | nt_sum_totient_over_divisors_v1_655260480_546 | Let $n = 57164$. Define $r = \sum_{d \mid n} \phi(d)$, where $\phi$ denotes Euler's totient function. Let $s$ be the minimum value of $x + y$ over all ordered pairs $(x,y)$ of positive integers such that $xy = 40000$. Compute the remainder when $s - r$ is divided by $99148$. | 42,384 | graphs = [
Graph(
let={
"_n": Const(40000),
"n": Const(57164),
"result": SumOverDivisors(n=Ref(name='n'), var='d', expr=EulerPhi(n=Var(name='d'))),
"_c": MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPosit... | NT | null | COMPUTE | sympy | B3 | [
"B3"
] | fc629c | nt_sum_totient_over_divisors_v1 | negation_mod | 5 | 0 | [
"B3"
] | 1 | 0.002 | 2026-02-08T15:26:37.360296Z | {
"verified": true,
"answer": 42384,
"timestamp": "2026-02-08T15:26:37.362113Z"
} | 5563dd | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 131,
"completion_tokens": 460
},
"timestamp": "2026-02-16T07:03:08.996Z",
"answer": 42384
},
{... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
636325 | modular_modexp_compute_v1_677425708_1143 | Let $d$ be the smallest integer greater than or equal to 2 that divides 18588623. Let $a = d$. Compute $a^{961} \mod 28224$, and let $r$ be the result. Find the smallest positive integer $k$ such that the $k$-th Fibonacci number is divisible by $r + 2$. Determine the value of $k$. | 360 | graphs = [
Graph(
let={
"_n": Const(2),
"a": MinOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Ref("_n")), Divides(divisor=Var("d"), dividend=Const(18588623))))),
"e": Const(961),
"m": Const(28224),
"result": ModExp(base=Ref("a"... | NT | null | COMPUTE | sympy | MIN_PRIME_FACTOR | [
"MIN_PRIME_FACTOR"
] | bc3776 | modular_modexp_compute_v1 | null | 6 | 0 | [
"MIN_PRIME_FACTOR"
] | 1 | 0.002 | 2026-02-08T04:01:10.945484Z | {
"verified": true,
"answer": 360,
"timestamp": "2026-02-08T04:01:10.947119Z"
} | 4b5aeb | 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": 5741
},
"timestamp": "2026-02-09T16:14:26.925Z",
"answer": 360
},
{
"id... | 1 | [
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "MIN_PRIME_FACTOR",
"status": "ok"
},
{
"lemma": "V5",
"status": "no"
}
] | {
"lo": -3.53,
"mid": 1.02,
"hi": 5.49
} | ||
96eb7a | comb_factorial_compute_v1_1874849503_957 | Let $n$ be the smallest divisor of 847 that is at least 2. Compute $37636 - n!$. | 32,596 | graphs = [
Graph(
let={
"_n": Const(847),
"n": MinOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Const(2)), Divides(divisor=Var("d"), dividend=Ref("_n"))))),
"result": Factorial(Ref("n")),
"_c": Const(37636),
"Q": Sub(Ref("_c"),... | NT | null | COMPUTE | sympy | MIN_PRIME_FACTOR | [
"MIN_PRIME_FACTOR"
] | bc3776 | comb_factorial_compute_v1 | null | 2 | 0 | [
"MIN_PRIME_FACTOR"
] | 1 | 0.002 | 2026-02-08T13:27:18.648337Z | {
"verified": true,
"answer": 32596,
"timestamp": "2026-02-08T13:27:18.650068Z"
} | e095a7 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 136,
"completion_tokens": 294
},
"timestamp": "2026-02-11T07:47:51.214Z",
"answer": 32596
},
{
"... | 1 | [
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "MIN_PRIME_FACTOR",
"status": "ok"
},
{
"lemma": "V3",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
}
] | {
"lo": -5.48,
"mid": 0.74,
"hi": 7.52
} | ||
6da8db | antilemma_k2_v1_784195855_9130 | Let $n = 431$. Define
$$
x = \sum_{k=1}^{\sum_{d \mid n} \phi(d)} \phi(k) \left\lfloor \frac{n}{k} \right\rfloor.
$$
Let $c = 11717$. Compute the remainder when $c \cdot x$ is divided by $57692$. | 23,188 | graphs = [
Graph(
let={
"_n": Const(431),
"x": Summation(var="k", start=Const(1), end=SumOverDivisors(n=Const(value=431), var='d', expr=EulerPhi(n=Var(name='d'))), expr=Mul(EulerPhi(n=Var("k")), Floor(Div(Ref("_n"), Var("k"))))),
"_c": Const(11717),
"Q": Mod(v... | NT | COMB | COMPUTE | sympy | K3 | [
"K3/K2",
"K2"
] | c7f244 | antilemma_k2_v1 | null | 5 | 0 | [
"K2",
"K3"
] | 2 | 0.001 | 2026-02-08T16:33:25.106711Z | {
"verified": true,
"answer": 23188,
"timestamp": "2026-02-08T16:33:25.107581Z"
} | 75aab1 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 122,
"completion_tokens": 2346
},
"timestamp": "2026-02-17T07:27:53.168Z",
"answer": 23188
},
... | 1 | [
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K2",
"status": "ok"
},
{
"lemma": "K3",
"status": "ok"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
1214ea | sequence_fibonacci_compute_v1_151522320_229 | Let $S$ be the set of all integers $t$ such that $12 \leq t \leq 156$ and there exist positive integers $a$ and $b$ with $1 \leq a \leq 13$, $1 \leq b \leq 13$, and $t = 5a + 7b$. Let $N$ be the number of elements in $S$. Consider the set of all ordered pairs $(x, y)$ of positive integers such that $xy = N$. Let $n$ be... | 19,701 | graphs = [
Graph(
let={
"_m": Const(64874),
"_n": Const(44121),
"n": MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(Mul(Var("x"), Var("y")), CountOverSet(s... | NT | null | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM/B3"
] | 05313e | sequence_fibonacci_compute_v1 | null | 7 | 0 | [
"B3",
"LIN_FORM"
] | 2 | 0.002 | 2026-02-08T03:05:06.946553Z | {
"verified": true,
"answer": 19701,
"timestamp": "2026-02-08T03:05:06.949038Z"
} | 96c75c | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 314,
"completion_tokens": 6805
},
"timestamp": "2026-02-23T16:47:50.918Z",
"answer": 19701
},
{
... | 1 | [
{
"lemma": "B3",
"status": "ok_later"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "LTE_SUM",
"stat... | {
"lo": 1.96,
"mid": 5.23,
"hi": 8.52
} | ||
1db37e | antilemma_cartesian_v1_168721529_1198 | Compute the number of ordered pairs $(a,b)$ such that $a$ is an integer with $1 \leq a \leq 34$ and $b$ is an integer with $1 \leq b \leq 40$. | 1,360 | graphs = [
Graph(
let={
"x": CountOverSet(set=CartesianProduct(left=IntegerRange(start=Const(1), end=Const(34)), right=IntegerRange(start=Const(1), end=Const(40)))),
},
goal=Ref("x"),
)
] | COMB | GEOM | COMPUTE | sympy | COUNT_CARTESIAN | [
"COUNT_CARTESIAN"
] | 409d7d | antilemma_cartesian_v1 | null | 2 | 0 | [
"COUNT_CARTESIAN"
] | 1 | 0.001 | 2026-02-08T13:31:37.471287Z | {
"verified": true,
"answer": 1360,
"timestamp": "2026-02-08T13:31:37.471983Z"
} | 8ebab0 | 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": 145
},
"timestamp": "2026-02-09T14:32:02.986Z",
"answer": 1360
},
{
"id... | 2 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "ok"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "V8",
... | {
"lo": -10,
"mid": -7.79,
"hi": -5.57
} | ||
db7b1b | geo_count_lattice_rect_v1_48377204_176 | Compute the number of lattice points $(x, y)$ such that $0 \leq x \leq 144$ and $0 \leq y \leq 61$. | 8,990 | graphs = [
Graph(
let={
"a": Const(144),
"b": Const(61),
"result": LatticePointsRect(a=Ref(name='a'), b=Ref(name='b')),
},
goal=Ref("result"),
)
] | GEOM | null | COUNT | sympy | [] | geo_count_lattice_rect_v1 | null | 3 | 0 | null | null | 0.001 | 2026-02-08T15:16:20.816585Z | {
"verified": true,
"answer": 8990,
"timestamp": "2026-02-08T15:16:20.817632Z"
} | 133ccd | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 148,
"completion_tokens": 194
},
"timestamp": "2026-02-24T20:15:49.675Z",
"answer": 8990
},
{
"id... | 1 | [] | {
"lo": -5.65,
"mid": -3.17,
"hi": -0.81
} | ||||
6c6b57 | antilemma_cartesian_v1_1978505735_162 | Let $x$ be the number of ordered pairs $(i, j)$ such that $1 \le i \le 39$ and $1 \le j \le 46$. Compute the remainder when $74874 \cdot x$ is divided by $55969$. | 54,325 | graphs = [
Graph(
let={
"x": CountOverSet(set=CartesianProduct(left=IntegerRange(start=Const(1), end=Const(39)), right=IntegerRange(start=Const(1), end=Const(46)))),
"Q": Mod(value=Mul(Const(74874), Ref("x")), modulus=Const(55969)),
},
goal=Ref("Q"),
)
] | COMB | GEOM | COMPUTE | sympy | COUNT_CARTESIAN | [
"COUNT_CARTESIAN"
] | 409d7d | antilemma_cartesian_v1 | null | 2 | 0 | [
"COUNT_CARTESIAN"
] | 1 | 0.001 | 2026-02-08T15:12:57.812011Z | {
"verified": true,
"answer": 54325,
"timestamp": "2026-02-08T15:12:57.812768Z"
} | 475ccc | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 167,
"completion_tokens": 1285
},
"timestamp": "2026-02-24T20:06:03.030Z",
"answer": 54325
},
{
"... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "ok"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8_SUM",
"status":... | {
"lo": -2.43,
"mid": 1.2,
"hi": 4.84
} | ||
ab392c | antilemma_k3_v1_1470522791_1508 | Let $n = 30479$. Define $x = \sum_{d \mid n} \phi(d)$, where $\phi$ denotes Euler's totient function. Find the remainder when $44121 \cdot x$ is divided by $52849$. | 21,154 | graphs = [
Graph(
let={
"_n": Const(30479),
"x": SumOverDivisors(n=Ref(name='_n'), var='d', expr=EulerPhi(n=Var(name='d'))),
"Q": Mod(value=Mul(Const(44121), Ref("x")), modulus=Const(52849)),
},
goal=Ref("Q"),
)
] | NT | COMB | COMPUTE | sympy | K3 | [
"K3"
] | 54c41e | antilemma_k3_v1 | null | 3 | 0 | [
"K3"
] | 1 | 0.001 | 2026-02-08T13:42:31.769087Z | {
"verified": true,
"answer": 21154,
"timestamp": "2026-02-08T13:42:31.769725Z"
} | c9f6bc | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 99,
"completion_tokens": 1158
},
"timestamp": "2026-02-15T20:08:09.623Z",
"answer": 21154
},
{... | 1 | [
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "K3",
"status": "ok"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
}
] | {
"lo": -5.49,
"mid": 0.22,
"hi": 6.51
} | ||
59fc1b | nt_lcm_compute_v1_865884756_367 | Let $a = 1554$ and $n = 42$. Define $b = \sum_{k=1}^{42} \phi(k) \cdot \left\lfloor \frac{n}{k} \right\rfloor$, where $\phi(k)$ denotes Euler's totient function. Compute $\text{lcm}(a, b)$. | 66,822 | graphs = [
Graph(
let={
"_n": Const(42),
"a": Const(1554),
"b": Summation(var="k", start=Const(1), end=Const(42), expr=Mul(EulerPhi(n=Var("k")), Floor(Div(Ref("_n"), Var("k"))))),
"result": LCM(a=Ref("a"), b=Ref("b")),
},
goal=Ref("result"),
... | NT | null | COMPUTE | sympy | V5 | [
"K2"
] | 6897ab | nt_lcm_compute_v1 | null | 5 | 0 | [
"K2",
"V5"
] | 2 | 0.005 | 2026-02-08T15:19:43.933656Z | {
"verified": true,
"answer": 66822,
"timestamp": "2026-02-08T15:19:43.938940Z"
} | 1ad6a4 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 117,
"completion_tokens": 1236
},
"timestamp": "2026-02-16T03:58:08.686Z",
"answer": 66822
},
... | 1 | [
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "K2",
"status": "ok"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
36a1f5 | alg_qf_psd_count_leq_v1_1218484723_697 | Let $Q$ be the number of ordered triples $(a, b, c)$ of positive integers with $1 \leq a, b, c \leq 10$ such that $$-40ab + 52bc + \left|\left\{ (a_1, b_1) : 1 \leq a_1, b_1 \leq 40 \text{ and } 102a_1^2b_1^2 + 17b_1^4 + 68a_1b_1^3 + 68a_1^3b_1 + 17a_1^4 = 13770000 \right\}\right| \cdot c^2 - 50ac + 25b^2 + 26a^2 \leq ... | 520 | graphs = [
Graph(
let={
"_n": Const(40),
"result": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("a"), Var("b"), Var("c")]), condition=And(Geq(Var("a"), Const(1)), Leq(Var("a"), Const(10)), Geq(Var("b"), Const(1)), Leq(Var("b"), Const(10)), Geq(Var("c"), Const(1)), Leq(Var("c... | ALG | null | COUNT | sympy | POLY4_COUNT | [
"POLY4_COUNT"
] | 861d91 | alg_qf_psd_count_leq_v1 | null | 6 | 0 | [
"POLY4_COUNT"
] | 1 | 0.018 | 2026-02-25T02:26:43.204494Z | {
"verified": true,
"answer": 520,
"timestamp": "2026-02-25T02:26:43.222484Z"
} | 3a1f6e | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 1,
"correct": {
"strict": false,
"boxed": false,
"relaxed": true
},
"usage": {
"prompt_tokens": 290,
"completion_tokens": 26297
},
"timestamp": "2026-03-28T23:56:17.575Z",
"answer": 524
},
{
... | 1 | [
{
"lemma": "POLY4_COUNT",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
}
] | {
"lo": 4.77,
"mid": 6.8,
"hi": 9.83
} | ||
554b9e | nt_min_with_divisor_count_v1_1520064083_9409 | Find the smallest positive integer $n \leq 1764$ such that $n$ has exactly $6$ positive divisors. Compute the value of $n$. | 12 | graphs = [
Graph(
let={
"upper": Const(1764),
"div_count": Const(6),
"result": MinOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Ref("upper")), Eq(NumDivisors(n=Var("n")), Ref("div_count"))))),
},
goal=Ref("resu... | NT | null | EXTREMUM | sympy | MOBIUS_COPRIME | [
"MOBIUS_COPRIME",
"V8"
] | 0d4771 | nt_min_with_divisor_count_v1 | null | 3 | 0 | [
"MOBIUS_COPRIME",
"V8"
] | 2 | 5.334 | 2026-02-08T10:43:33.216631Z | {
"verified": true,
"answer": 12,
"timestamp": "2026-02-08T10:43:38.550227Z"
} | 1b0103 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 80,
"completion_tokens": 1241
},
"timestamp": "2026-02-14T08:13:30.699Z",
"answer": 12
},
{
... | 1 | [
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "MOBIUS_COPRIME",
"status": "ok"
},
{
... | {
"lo": -5.49,
"mid": 0.22,
"hi": 6.51
} | ||
7615eb | comb_factorial_compute_v1_601307018_6193 | Let $n$ be the minimum value of $x + y$ over all ordered pairs $(x, y)$ of positive integers such that $xy = 16$. Let $M = n!$. Find the remainder when $21521 \cdot M$ is divided by $54518$. | 18,232 | graphs = [
Graph(
let={
"n": MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(Mul(Var("x"), Var("y")), Const(16)))), expr=Sum(Var("x"), Var("y")))),
"result": Factorial(... | COMB | null | COMPUTE | sympy | SUM_GEOM | [
"B3"
] | 0cd20d | comb_factorial_compute_v1 | null | 3 | 0 | [
"B3",
"SUM_GEOM"
] | 2 | 0.033 | 2026-03-10T06:46:10.179715Z | {
"verified": true,
"answer": 18232,
"timestamp": "2026-03-10T06:46:10.213120Z"
} | 0fe03e | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 170,
"completion_tokens": 1345
},
"timestamp": "2026-04-19T03:49:09.337Z",
"answer": 18232
},
{
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
}
] | {
"lo": -5.35,
"mid": 0.52,
"hi": 5.84
} | ||
127ef6 | modular_modexp_compute_v1_677425708_3895 | Let $n = 8910$. Let $T$ be the set of all positive integers $k$ such that $1 \leq k \leq n$ and $99$ divides $k$. Let $m = |T|$. Now consider the set of all ordered pairs $(x, y)$ of positive integers such that $x + y = m$. Let $e$ be the maximum value of $x \cdot y$ over all such pairs. Compute the remainder when $37^... | 31,858 | graphs = [
Graph(
let={
"_n": Const(8910),
"a": Const(37),
"e": MaxOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(Sum(Var("x"), Var("y")), CountOverSet(set=So... | NT | null | COMPUTE | sympy | C2 | [
"C2/B1"
] | a0cd95 | modular_modexp_compute_v1 | null | 7 | 0 | [
"B1",
"C2"
] | 2 | 0.002 | 2026-02-08T06:01:18.347480Z | {
"verified": true,
"answer": 31858,
"timestamp": "2026-02-08T06:01:18.349252Z"
} | ae14c4 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 157,
"completion_tokens": 5898
},
"timestamp": "2026-02-12T18:31:20.338Z",
"answer": 31858
},
... | 1 | [
{
"lemma": "B1",
"status": "ok_later"
},
{
"lemma": "C2",
"status": "ok"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma... | {
"lo": -3.51,
"mid": 1.33,
"hi": 6.56
} | ||
e35feb | comb_count_partitions_v1_1918700295_4169 | Let $n$ be the number of integers $t$ such that $8 \leq t \leq 57$ and there exist positive integers $a$ and $b$ with $1 \leq a \leq 9$, $1 \leq b \leq 6$, and $t = 3a + 5b$. Compute the number of integer partitions of $n$. | 53,174 | graphs = [
Graph(
let={
"n": CountOverSet(set=SolutionsSet(var=Var("t"), condition=Exists(var=Var(name='a'), condition=Exists(var=Var(name='b'), condition=And(Geq(left=Var(name='a'), right=Const(value=1)), Leq(left=Var(name='a'), right=Const(value=9)), Geq(left=Var(name='b'), right=Const(value=1... | COMB | null | COUNT | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | comb_count_partitions_v1 | null | 5 | 0 | [
"LIN_FORM"
] | 1 | 0.001 | 2026-02-08T09:11:09.037875Z | {
"verified": true,
"answer": 53174,
"timestamp": "2026-02-08T09:11:09.038709Z"
} | 261cbb | 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": 32768
},
"timestamp": "2026-02-24T10:52:28.578Z",
"answer": 53174
},
{
... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "V8_SUM",
... | {
"lo": -2.35,
"mid": 1.22,
"hi": 4.84
} | ||
7a07a7 | sequence_lucas_compute_v1_151522320_1301 | Let $m = 6$. Consider the set of all ordered pairs $(x,y)$ of positive integers such that $xy = 9$. Define $n$ to be the minimum value of $x + y$ over all such pairs.
Compute the Lucas number $L_s$, where $$s = \sum_{k=1}^{n} \varphi(k) \left\lfloor \frac{m}{k} \right\rfloor.$$ | 24,476 | graphs = [
Graph(
let={
"_m": Const(6),
"_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(9)))), expr=Sum(Var("x"), Var("y")))),
... | NT | null | COMPUTE | sympy | B3 | [
"B3/K2"
] | 9f3175 | sequence_lucas_compute_v1 | null | 5 | 0 | [
"B3",
"K2"
] | 2 | 0.001 | 2026-02-08T03:52:29.305883Z | {
"verified": true,
"answer": 24476,
"timestamp": "2026-02-08T03:52:29.307153Z"
} | fc6001 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 205,
"completion_tokens": 1239
},
"timestamp": "2026-02-10T16:18:59.274Z",
"answer": 24476
},
{
"... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "K2",
"status": "ok_later"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "V1",
"status": "no"
},
{
"le... | {
"lo": -5.55,
"mid": -3.02,
"hi": 0.31
} | ||
0ed59e | comb_factorial_compute_v1_2080023795_160 | Let $m = 4$ and $n_0 = 2$. Define $n$ to be the largest prime number $p$ such that $n_0 \leq p \leq \sum_{k=1}^{m} \phi(k) \left\lfloor \frac{4}{k} \right\rfloor$, where $\phi$ is Euler's totient function. Let $Q = \sum_{k=1}^{n!} d(k)$, where $d(k)$ denotes the number of positive divisors of $k$. Compute the value of ... | 43,776 | graphs = [
Graph(
let={
"_m": Const(4),
"_n": Const(2),
"n": MaxOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Ref("_n")), Leq(Var("n"), Summation(var="k", start=Const(1), end=Ref("_m"), expr=Mul(EulerPhi(n=Var("k")), Floor(Div(Const(4), Var("k")))))),... | NT | null | COMPUTE | sympy | K2 | [
"K2/MAX_PRIME_BELOW"
] | f058da | comb_factorial_compute_v1 | null | 6 | 0 | [
"K2",
"MAX_PRIME_BELOW"
] | 2 | 0.002 | 2026-02-08T11:35:13.725227Z | {
"verified": true,
"answer": 43776,
"timestamp": "2026-02-08T11:35:13.726843Z"
} | 33958a | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 239,
"completion_tokens": 6321
},
"timestamp": "2026-02-08T20:48:00.483Z",
"answer": 43776
},
{
"... | 1 | [
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "K2",
"status": "ok"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "... | {
"lo": 3.24,
"mid": 5.68,
"hi": 8.81
} | ||
40d6d5 | diophantine_fbi2_min_v1_458359167_1881 | Let $k = 33$. Let $u$ be the largest integer such that $2^u \leq 16436755798105$. Determine the value of the smallest integer $d$ satisfying $3 \leq d \leq u$, $d$ divides $k$, and $\frac{k}{d} \geq 2$. | 3 | graphs = [
Graph(
let={
"k": Const(33),
"upper": MaxOverSet(set=SolutionsSet(var=Var("k"), condition=Leq(Pow(Const(2), Var("k")), Const(16436755798105)))),
"result": MinOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Const(3)), Leq(Var("d"), Ref("upper"... | NT | null | EXTREMUM | sympy | MAX_VAL | [
"MAX_VAL"
] | 1da621 | diophantine_fbi2_min_v1 | null | 3 | 0 | [
"MAX_VAL"
] | 1 | 0.008 | 2026-02-08T04:55:18.788533Z | {
"verified": true,
"answer": 3,
"timestamp": "2026-02-08T04:55:18.796685Z"
} | 6c7180 | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 1,
"correct": {
"strict": false,
"boxed": false,
"relaxed": true
},
"usage": {
"prompt_tokens": 136,
"completion_tokens": 756
},
"timestamp": "2026-02-11T22:04:13.112Z",
"answer": 11
},
{
"id": 11,
... | 1 | [
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K16",
"status": "same_pattern_wrong"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "ok"
},
{
"lemma": "V3",
"status": "no"
},
{
... | {
"lo": -8.32,
"mid": -5.11,
"hi": -2.37
} | ||
836189 | nt_count_coprime_and_v1_717093673_1697 | Let $k_1$ be the smallest divisor of $6125$ that is at least $2$. Let $k_2 = 9$. Let $S$ be the set of all positive integers $n$ with $1 \leq n \leq 40340$ such that $\gcd(n, k_1) = 1$ and $\gcd(n, k_2) = 1$. Compute the remainder when $96999$ times $|S|$ is divided by $92608$. | 12,205 | graphs = [
Graph(
let={
"upper": Const(40340),
"k1": MinOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Const(2)), Divides(divisor=Var("d"), dividend=Const(6125))))),
"k2": Const(9),
"result": CountOverSet(set=SolutionsSet(var=Var("n"), cond... | NT | null | COUNT | sympy | MIN_PRIME_FACTOR | [
"MIN_PRIME_FACTOR"
] | bc3776 | nt_count_coprime_and_v1 | null | 4 | 0 | [
"MIN_PRIME_FACTOR"
] | 1 | 4.89 | 2026-02-08T16:14:49.888935Z | {
"verified": true,
"answer": 12205,
"timestamp": "2026-02-08T16:14:54.778775Z"
} | b270d9 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 152,
"completion_tokens": 3143
},
"timestamp": "2026-02-17T00:44:13.839Z",
"answer": 12205
},
... | 1 | [
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "MIN_PRIME_FACTOR",
"status": "ok"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
}
... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
c773a9 | nt_sum_divisors_mod_v1_1440796553_1328 | Let $S$ be the set of all ordered pairs $(x, y)$ of positive integers such that $x \cdot y = 705600$. Let $n$ be the minimum value of $x + y$ over all pairs $(x, y) \in S$. Let $\sigma(n)$ denote the sum of the positive divisors of $n$. Compute the remainder when $\sigma(n)$ is divided by $11113$. | 5,952 | graphs = [
Graph(
let={
"n": MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(Mul(Var("x"), Var("y")), Const(705600)))), expr=Sum(Var("x"), Var("y")))),
"M": Const(11113... | NT | null | COMPUTE | sympy | B3 | [
"B3"
] | 0cd20d | nt_sum_divisors_mod_v1 | null | 6 | 0 | [
"B3"
] | 1 | 0.003 | 2026-02-08T13:38:42.835944Z | {
"verified": true,
"answer": 5952,
"timestamp": "2026-02-08T13:38:42.839242Z"
} | 7438f5 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 135,
"completion_tokens": 1805
},
"timestamp": "2026-02-15T19:29:44.976Z",
"answer": 5952
},
{... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
}
] | {
"lo": -5.49,
"mid": 0.22,
"hi": 6.51
} | ||
b92df2 | nt_gcd_compute_v1_238844314_1028 | Let $a = 680256$ and $b = 1284928$. Compute $\gcd(a, b)$. Let $s$ be the minimum value of $x + y$ over all ordered pairs $(x, y)$ of positive integers such that $xy = 1600$. Compute the remainder when $\gcd(a, b)^2 + 2 \cdot \gcd(a, b) + s$ is divided by $90884$. Determine the value of this remainder. | 33,180 | graphs = [
Graph(
let={
"_n": Const(90884),
"a": Const(680256),
"b": Const(1284928),
"result": GCD(a=Ref("a"), b=Ref("b")),
"_c": MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(... | NT | null | COMPUTE | sympy | B3 | [
"B3"
] | d720b5 | nt_gcd_compute_v1 | quadratic_mod | 3 | 0 | [
"B3"
] | 1 | 0.003 | 2026-02-08T13:51:33.084319Z | {
"verified": true,
"answer": 33180,
"timestamp": "2026-02-08T13:51:33.087351Z"
} | e98560 | 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": 1808
},
"timestamp": "2026-02-15T21:23:22.574Z",
"answer": 33180
},
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
}
] | {
"lo": -5.49,
"mid": 0.22,
"hi": 6.51
} | ||
843e1c | geo_count_lattice_triangle_v1_48377204_2221 | Let $A$ be the area of a triangle with vertices at $(0,0)$, $(109,157)$, and $(22,0)$. The area of this triangle is given by the formula $\frac{1}{2} \left| 109 \cdot 157 + 22 \cdot (-8) \right|$. Let $B$ be the number of lattice points on the boundary of this triangle, which can be computed as the sum of the greatest ... | 8,468 | graphs = [
Graph(
let={
"_n": Const(8),
"area_2x": Abs(arg=Sum(Mul(Const(value=109), Const(value=157)), Mul(Const(value=22), Sub(left=Const(value=0), right=Const(value=8))))),
"boundary": Sum(GCD(a=Abs(arg=Const(value=109)), b=Abs(arg=Ref(name='_n'))), GCD(a=Abs(arg=Sub(l... | NT | null | COUNT | sympy | COPRIME_PAIRS | [
"COPRIME_PAIRS"
] | 2bb3aa | geo_count_lattice_triangle_v1 | null | 6 | 0 | [
"COPRIME_PAIRS"
] | 1 | 0.009 | 2026-02-08T16:39:55.209338Z | {
"verified": true,
"answer": 8468,
"timestamp": "2026-02-08T16:39:55.218431Z"
} | 7a1e5f | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 272,
"completion_tokens": 3181
},
"timestamp": "2026-02-17T09:17:37.676Z",
"answer": 8468
},
{... | 1 | [
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
cc36dd | nt_count_divisible_v1_458359167_4086 | Let $n$ be a positive integer. Define $p$ to be the largest prime number less than or equal to 20. Let $S$ be the set of all positive integers $n$ such that $n \leq 38809$ and $n$ is divisible by $p$. Let $k$ be the number of elements in $S$. Compute the sum of the number of positive divisors of each integer from 1 to ... | 15,883 | graphs = [
Graph(
let={
"_n": Const(20),
"upper": Const(38809),
"divisor": MaxOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(2)), Leq(Var("n"), Ref("_n")), IsPrime(Var("n"))))),
"result": CountOverSet(set=SolutionsSet(var=Var("n"), co... | NT | null | COUNT | sympy | MAX_PRIME_BELOW | [
"MAX_PRIME_BELOW"
] | dc3ad3 | nt_count_divisible_v1 | null | 4 | 0 | [
"MAX_PRIME_BELOW"
] | 1 | 3.213 | 2026-02-08T11:30:04.902171Z | {
"verified": true,
"answer": 15883,
"timestamp": "2026-02-08T11:30:08.115324Z"
} | 16cb83 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 176,
"completion_tokens": 3170
},
"timestamp": "2026-02-14T15:25:37.886Z",
"answer": 15883
},
... | 1 | [
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok"
},
{
"lemma": "MAX_VAL",
"status": "no"
}
] | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
25598f | antilemma_sum_equals_v1_124444284_4061 | Let $m$ be the number of ordered pairs $(i, j)$ of positive integers such that $1 \leq i \leq 63$, $1 \leq j \leq 63$, and $i + j = 63$.
Let $x$ be the number of ordered pairs $(i, j)$ of positive integers such that $1 \leq i \leq 61$, $1 \leq j \leq 62$, and $i + j = m$.
Let $c = 60000$ and define $Q = c - x$.
Find... | 59,939 | graphs = [
Graph(
let={
"_n": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("i"), Var("j")]), condition=Eq(Sum(Var("i"), Var("j")), Const(63)), domain=CartesianProduct(left=IntegerRange(start=Const(1), end=Const(63)), right=IntegerRange(start=Const(1), end=Const(63))))),
"x":... | COMB | GEOM | COMPUTE | sympy | COUNT_SUM_EQUALS | [
"COUNT_SUM_EQUALS/COUNT_SUM_EQUALS",
"COUNT_SUM_EQUALS"
] | ae9919 | antilemma_sum_equals_v1 | null | 3 | 0 | [
"COUNT_SUM_EQUALS"
] | 1 | 0.009 | 2026-02-08T05:44:35.074867Z | {
"verified": true,
"answer": 59939,
"timestamp": "2026-02-08T05:44:35.084088Z"
} | a20c8e | 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": 1385
},
"timestamp": "2026-02-24T04:31:11.542Z",
"answer": 59939
},
{
"... | 2 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "ok"
},
{
"lemma": "V8",
"status": "no"
},
{
"lemma": "V8_SUM",
"status":... | {
"lo": -9.23,
"mid": -6.18,
"hi": -4.06
} | ||
c7b1c4 | modular_mod_compute_v1_1978505735_3904 | Let $a$ be the number of positive integers $p$ for which there exists a positive integer $q$ such that $p < q$, $\gcd(p, q) = 1$, and $p \cdot q = 1635133500$. Let $r = a \bmod 33124$. Compute the value of $(75841 \cdot r) \bmod 68742$. | 20,942 | graphs = [
Graph(
let={
"a": CountOverSet(set=SolutionsSet(var=Var("p"), condition=And(IsPositive(arg=Var(name='p')), Exists(var=Var(name='q'), condition=And(Eq(left=Mul(Var(name='p'), Var(name='q')), right=Const(value=1635133500)), Eq(left=GCD(a=Var(name='p'), b=Var(name='q')), right=Const(valu... | NT | null | COMPUTE | sympy | COPRIME_PAIRS | [
"COPRIME_PAIRS"
] | 2bb3aa | modular_mod_compute_v1 | null | 5 | 0 | [
"COPRIME_PAIRS"
] | 1 | 0.002 | 2026-02-08T17:55:33.918601Z | {
"verified": true,
"answer": 20942,
"timestamp": "2026-02-08T17:55:33.920128Z"
} | 1f82bf | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 130,
"completion_tokens": 2374
},
"timestamp": "2026-02-18T09:56:36.163Z",
"answer": 20942
},
... | 1 | [
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "V3",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
1d3de9 | nt_count_gcd_equals_v1_548369836_103 | Let $A$ be the number of positive integers $n$ such that $1 \leq n \leq 17424$ and $\gcd(n, 350) = 7$.
Let $B$ be the number of integers $t$ such that $23 \leq t \leq 20648$ and there exist positive integers $a \leq 3242$ and $b \leq 132$ satisfying $t = 6a + 9b + 8$.
Compute the remainder when $A \cdot B$ is divided... | 34,042 | graphs = [
Graph(
let={
"upper": Const(17424),
"k": Const(350),
"d": Const(7),
"result": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Ref("upper")), Eq(GCD(a=Var("n"), b=Ref("k")), Ref("d"))))),
"... | NT | null | COUNT | sympy | LIN_FORM | [
"LIN_FORM"
] | 3d6396 | nt_count_gcd_equals_v1 | affine_mod | 6 | 0 | [
"LIN_FORM"
] | 1 | 4.692 | 2026-02-08T02:45:35.693439Z | {
"verified": true,
"answer": 34042,
"timestamp": "2026-02-08T02:45:40.385074Z"
} | f55279 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 236,
"completion_tokens": 9389
},
"timestamp": "2026-02-23T16:07:33.236Z",
"answer": 34042
},
{
"... | 1 | [
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
... | {
"lo": 3.82,
"mid": 5.54,
"hi": 7.58
} | ||
d85816_n | comb_sum_binomial_row_v1_601307018_4620 | A puzzle designer creates a challenge based on a cubic equation: for integers $a$ and $b$ between 1 and 10, how many pairs satisfy $91a^3 - 96a^2b + 48ab^2 - 8b^3 = 40824$? Let $T$ be the count. The designer then builds a number $n = \sum_{k=0}^{T} 3^k$ and raises 2 to this power to get $R = 2^n$, forming the final puz... | 37,456 | COMB | null | SUM | sympy | POLY3_COUNT | [
"POLY3_COUNT/SUM_GEOM"
] | 631efd | comb_sum_binomial_row_v1 | null | 6 | null | [
"POLY3_COUNT",
"SUM_GEOM"
] | 2 | 0.006 | 2026-03-10T05:15:34.010695Z | null | bc7831 | d85816 | narrative | 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": 14065
},
"timestamp": "2026-03-29T19:02:05.036Z",
"answer": 37456
},
{
... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "POLY3_COUNT",
"status": "ok"
},
{
"lemma": "SUM_GEOM",
"status": "ok_later"
},
{
"lemma": "V7",
"s... | {
"lo": -5.36,
"mid": 0.27,
"hi": 5.45
} | |
313aea | nt_sum_over_divisible_v1_1918700295_1041 | Let $s$ be the minimum value of $x + y$ over all ordered pairs $(x, y)$ of positive integers such that $xy = 33856$. Let $t$ be the number of ordered pairs $(x_1, x_2)$ of positive odd integers such that $x_1 + x_2 = s$. Define $\text{result}$ to be the sum of all positive integers $n$ at most 34596 that are divisible ... | 46,539 | graphs = [
Graph(
let={
"_n": Const(58353),
"upper": Const(34596),
"divisor": 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(n... | NT | null | SUM | sympy | B3 | [
"B3/COMB1"
] | e26f7e | nt_sum_over_divisible_v1 | null | 6 | 0 | [
"B3",
"COMB1"
] | 2 | 1.52 | 2026-02-08T05:31:56.943457Z | {
"verified": true,
"answer": 46539,
"timestamp": "2026-02-08T05:31:58.463229Z"
} | 18edce | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 168,
"completion_tokens": 2179
},
"timestamp": "2026-02-12T10:06:03.877Z",
"answer": 46539
},
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "COMB1",
"status": "ok_later"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "... | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
f5f62e | comb_catalan_compute_v1_971394319_819 | Let $n$ be the number of integers $t$ such that $10 \leq t \leq 34$ and there exist integers $a$ and $b$ with $1 \leq a \leq 4$, $1 \leq b \leq 3$, and $t = 4a + 6b$. Let $Q$ be the remainder when $83873$ multiplied by the $n$-th Catalan number is divided by $81811$. Compute $Q$. | 54,641 | graphs = [
Graph(
let={
"_n": Const(83873),
"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=Va... | COMB | null | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | comb_catalan_compute_v1 | null | 4 | 0 | [
"LIN_FORM"
] | 1 | 0.003 | 2026-02-08T13:19:10.992343Z | {
"verified": true,
"answer": 54641,
"timestamp": "2026-02-08T13:19:10.995130Z"
} | 8d8bf1 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 218,
"completion_tokens": 4390
},
"timestamp": "2026-02-24T17:46:51.185Z",
"answer": 54641
},
{
"... | 1 | [
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8_SUM",
... | {
"lo": -2.35,
"mid": 1.22,
"hi": 4.84
} | ||
c9af1d | modular_inverse_v1_458359167_3550 | Let $a = 622$ and let $m$ be the largest prime number less than or equal to $725$. Let $\mathcal{S}$ be the set of positive integers $x$ such that $1 \leq x \leq 718$ and $622x \equiv 1 \pmod{m}$. Find the smallest element of $\mathcal{S}$. | 126 | graphs = [
Graph(
let={
"a": Const(622),
"m": MaxOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(2)), Leq(Var("n"), Const(725)), IsPrime(Var("n"))))),
"upper": Const(718),
"result": MinOverSet(set=SolutionsSet(var=Var("x"), condition=A... | NT | null | EXTREMUM | sympy | B3 | [
"MAX_PRIME_BELOW"
] | dc3ad3 | modular_inverse_v1 | null | 4 | 0 | [
"B3",
"MAX_PRIME_BELOW"
] | 2 | 0.413 | 2026-02-08T08:24:24.250733Z | {
"verified": true,
"answer": 126,
"timestamp": "2026-02-08T08:24:24.663771Z"
} | d222ee | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 139,
"completion_tokens": 528
},
"timestamp": "2026-02-15T20:14:13.295Z",
"answer": 542
},
{
"id": 11,
... | 1 | [
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "V1",
"status": "no"
}
] | {
"lo": -5.55,
"mid": -3.01,
"hi": 0.34
} | ||
f7c4fc | nt_count_divisible_v1_1742523217_3967 | Let $S$ be the set of all positive integers $n$ such that $1 \leq n \leq 81225$ and $n$ is divisible by $15$. Determine the value of $|S|$. | 5,415 | graphs = [
Graph(
let={
"upper": Const(81225),
"divisor": Const(15),
"result": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), EulerPhi(n=Const(1))), Leq(Var("n"), Ref("upper")), Eq(Mod(value=Var("n"), modulus=Ref("divisor")), Const(0))))),
... | NT | null | COUNT | sympy | ONE_PHI_1 | [
"ONE_PHI_1"
] | f6b5a5 | nt_count_divisible_v1 | null | 2 | 0 | [
"ONE_PHI_1"
] | 1 | 9.482 | 2026-02-08T06:09:44.336596Z | {
"verified": true,
"answer": 5415,
"timestamp": "2026-02-08T06:09:53.818418Z"
} | cbcbeb | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 143,
"completion_tokens": 278
},
"timestamp": "2026-02-19T18:14:54.917Z",
"answer": 5415
}
] | 2 | [
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "ONE_PHI_1",
"status": "ok"
},
{
"lemma": "V1",
"status": "no"
... | {
"lo": -10,
"mid": -6.47,
"hi": -2.95
} | ||
ed2346 | nt_min_crt_v1_717093673_3907 | Let $m$ be the minimum value of $x + y$ over all ordered pairs of positive integers $(x, y)$ such that $xy = 4$. Determine the smallest positive integer $n$ such that $1 \leq n \leq 20$, $n \equiv 1 \pmod{m}$, and $n \equiv 1 \pmod{5}$. Find the value of $n$. | 1 | graphs = [
Graph(
let={
"_n": Const(4),
"m": MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(Mul(Var("x"), Var("y")), Ref("_n")))), expr=Sum(Var("x"), Var("y")))),
... | NT | null | EXTREMUM | sympy | B3 | [
"B3"
] | 0cd20d | nt_min_crt_v1 | null | 6 | 0 | [
"B3"
] | 1 | 0.009 | 2026-02-08T17:57:43.985666Z | {
"verified": true,
"answer": 1,
"timestamp": "2026-02-08T17:57:43.994324Z"
} | 5fc2ae | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 143,
"completion_tokens": 361
},
"timestamp": "2026-02-16T11:46:40.709Z",
"answer": 1
},
{
"id": 11,
"... | 2 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "V3",
"status": "n... | {
"lo": -10,
"mid": -7.27,
"hi": -4.54
} | ||
1ea87d | antilemma_cartesian_v1_238844314_1101 | Let $x$ be the number of ordered pairs $(i, j)$ such that $1 \leq i \leq 17$ and $1 \leq j \leq 47$. Let $c$ be the number of ordered pairs $(x_1, x_2)$ of positive odd integers such that $x_1 + x_2 = 19602$. Compute $c - x$. | 9,002 | graphs = [
Graph(
let={
"_n": Const(19602),
"x": CountOverSet(set=CartesianProduct(left=IntegerRange(start=Const(1), end=Const(17)), right=IntegerRange(start=Const(1), end=Const(47)))),
"_c": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x1"), Var("x2")]), condit... | COMB | GEOM | COMPUTE | sympy | COMB1 | [
"COMB1",
"COUNT_CARTESIAN"
] | 20f64e | antilemma_cartesian_v1 | negation_mod | 4 | 0 | [
"COMB1",
"COUNT_CARTESIAN"
] | 2 | 0.002 | 2026-02-08T13:56:19.219385Z | {
"verified": true,
"answer": 9002,
"timestamp": "2026-02-08T13:56:19.221380Z"
} | b8a7e2 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 196,
"completion_tokens": 658
},
"timestamp": "2026-02-24T19:30:41.253Z",
"answer": 9002
},
{
"id... | 1 | [
{
"lemma": "COMB1",
"status": "ok"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "ok"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8",
"status": ... | {
"lo": -5.09,
"mid": -2.97,
"hi": -0.71
} | ||
963cdd | algebra_poly_eval_v1_1431428450_752 | Let $t = 5$. Evaluate the expression
$$
\frac{2t^5 - 46t^4 + 192t^3 + 475t^2 + pt - 144}{44},
$$
where $p$ is the largest prime number less than or equal to $603$. Let $c = 33745$. Find the remainder when $c$ times this value is divided by $55222$. | 26,955 | graphs = [
Graph(
let={
"_n": Const(603),
"t": Const(5),
"result": Div(Sum(Mul(Const(2), Pow(Ref("t"), Const(5))), Mul(Const(-46), Pow(Ref("t"), Const(4))), Mul(Const(192), Pow(Ref("t"), Const(3))), Mul(Const(475), Pow(Ref("t"), Const(2))), Mul(MaxOverSet(set=SolutionsSet... | NT | null | COMPUTE | sympy | MAX_PRIME_BELOW | [
"MAX_PRIME_BELOW"
] | dc3ad3 | algebra_poly_eval_v1 | null | 4 | 0 | [
"MAX_PRIME_BELOW"
] | 1 | 0.004 | 2026-02-08T13:39:59.204183Z | {
"verified": true,
"answer": 26955,
"timestamp": "2026-02-08T13:39:59.207877Z"
} | 710c30 | 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": 1155
},
"timestamp": "2026-02-15T19:04:39.119Z",
"answer": 26955
},
... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok"
},
{
"lemma": "V5",
"status": "no"
... | {
"lo": -5.49,
"mid": 0.22,
"hi": 6.51
} | ||
0d9d97 | nt_min_with_divisor_count_v1_1520064083_2465 | Let $\text{upper} = 28561$ and $\text{div\_count} = 8$. Let $S$ be the set of all positive integers $n$ such that $1 \leq n \leq 28561$ and $n$ has exactly $8$ positive divisors. Let $\text{result}$ be the smallest element of $S$. Compute $\sum_{n=1}^{\left|\text{result}\right|} \phi(n)$, where $\phi(n)$ denotes Euler'... | 180 | graphs = [
Graph(
let={
"upper": Const(28561),
"div_count": Const(8),
"result": MinOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Ref("upper")), Eq(NumDivisors(n=Var("n")), Ref("div_count"))))),
"Q": Summation(var="... | NT | null | EXTREMUM | sympy | B1 | [
"B1/B3/B1",
"B3/B3/B1"
] | 84ac49 | nt_min_with_divisor_count_v1 | null | 6 | 0 | [
"B1",
"B3"
] | 2 | 3.068 | 2026-02-08T04:46:25.587313Z | {
"verified": true,
"answer": 180,
"timestamp": "2026-02-08T04:46:28.655663Z"
} | 6bcbfe | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 225,
"completion_tokens": 1447
},
"timestamp": "2026-02-11T22:12:51.487Z",
"answer": 180
},
{
"i... | 1 | [
{
"lemma": "B1",
"status": "ok"
},
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "V1",
"status": "no"
},
{
"lemma": "V7",
"st... | {
"lo": -3.42,
"mid": 1.86,
"hi": 7.55
} | ||
943ffa | comb_binomial_compute_v1_1353956133_433 | Let $n$ be the number of integers $t$ with $10 \leq t \leq 36$ that can be expressed as $t = 6a + 4b$ for some integers $a$ and $b$ satisfying $1 \leq a \leq 4$ and $1 \leq b \leq 3$. Compute $51984 - \binom{n}{5}$. | 51,192 | 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... | ALG | COMB | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | comb_binomial_compute_v1 | null | 4 | 0 | [
"LIN_FORM"
] | 1 | 0.002 | 2026-02-08T11:27:01.654792Z | {
"verified": true,
"answer": 51192,
"timestamp": "2026-02-08T11:27:01.656312Z"
} | b2ee61 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 201,
"completion_tokens": 732
},
"timestamp": "2026-02-24T13:58:23.032Z",
"answer": 51192
},
{
"i... | 1 | [
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
}
] | {
"lo": -5.97,
"mid": -3.97,
"hi": -1.93
} | ||
67ab2a | nt_count_divisible_v1_1125832087_2132 | Let $d = \sum_{k=1}^{3} \phi(k) \left\lfloor \frac{3}{k} \right\rfloor$. Compute the number of positive integers $n \leq 45369$ such that
$$
n \equiv \sum_{k=0}^{3} (-1)^k \binom{3}{k} \pmod{d}.
$$ | 7,561 | graphs = [
Graph(
let={
"_n": Const(3),
"upper": Const(45369),
"divisor": Summation(var="k", start=Const(1), end=Ref("_n"), expr=Mul(EulerPhi(n=Var("k")), Floor(Div(Const(3), Var("k"))))),
"result": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq... | COMB | NT | COUNT | sympy | BINOMIAL_ALTERNATING | [
"BINOMIAL_ALTERNATING",
"K2"
] | 1ce58e | nt_count_divisible_v1 | null | 6 | 0 | [
"BINOMIAL_ALTERNATING",
"K2"
] | 2 | 4.018 | 2026-02-08T04:21:46.439496Z | {
"verified": true,
"answer": 7561,
"timestamp": "2026-02-08T04:21:50.457310Z"
} | a2afca | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 197,
"completion_tokens": 783
},
"timestamp": "2026-02-10T16:22:56.722Z",
"answer": 7561
},
{
"i... | 2 | [
{
"lemma": "BINOMIAL_ALTERNATING",
"status": "ok"
},
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "K2",
"status": "ok"
},
{
"lemma": "V7",
"status... | {
"lo": -9.14,
"mid": -6.05,
"hi": -3.73
} | ||
2bd807 | antilemma_sum_equals_v1_865884756_2757 | Let $x$ be the number of ordered pairs $(i, j)$ of positive integers with $1 \leq i \leq 92$, $1 \leq j \leq 92$, and $i + j = 94$. Compute the remainder when
$$
\left( x \bmod 199 \right) + 3001 \cdot \left( x \bmod 499 \right)
$$
is divided by 77375. | 41,057 | graphs = [
Graph(
let={
"x": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("i"), Var("j")]), condition=Eq(Sum(Var("i"), Var("j")), Const(94)), domain=CartesianProduct(left=IntegerRange(start=Const(1), end=Const(92)), right=IntegerRange(start=Const(1), end=Const(92))))),
"_c":... | COMB | GEOM | COMPUTE | sympy | COUNT_SUM_EQUALS | [
"COUNT_SUM_EQUALS"
] | 75ab0f | antilemma_sum_equals_v1 | null | 3 | 0 | [
"COUNT_SUM_EQUALS"
] | 1 | 0.005 | 2026-02-08T16:55:34.323805Z | {
"verified": true,
"answer": 41057,
"timestamp": "2026-02-08T16:55:34.329102Z"
} | 077561 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 138,
"completion_tokens": 757
},
"timestamp": "2026-02-17T16:10:48.123Z",
"answer": 41057
},
{... | 1 | [
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "ok"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8",
... | {
"lo": -2.38,
"mid": 1.74,
"hi": 6.59
} | ||
b61a60 | modular_min_linear_v1_151522320_341 | Let $a$ be the number of positive integers $t$ such that $23 \leq t \leq 15943$ and there exist positive integers $a'$ and $b'$ with $1 \leq a' \leq 603$, $1 \leq b' \leq 2476$, and $t = 10a' + 4b' + 9$. Let $b = 22945$ and $m = 63426$. Let $g$ be the sum of $\mu(d)$ over all positive divisors $d$ of $\gcd(15, k)$, whe... | 49,057 | graphs = [
Graph(
let={
"a": CountOverSet(set=SolutionsSet(var=Var("t"), condition=Exists(var=Var(name='a'), condition=Exists(var=Var(name='b'), condition=And(Geq(left=Var(name='a'), right=Const(value=1)), Leq(left=Var(name='a'), right=Const(value=603)), Geq(left=Var(name='b'), right=Const(value... | NT | null | EXTREMUM | sympy | COUNT_PRIMES | [
"COUNT_PRIMES/MOBIUS_COPRIME",
"LIN_FORM"
] | 829ac5 | modular_min_linear_v1 | null | 7 | 0 | [
"COUNT_PRIMES",
"LIN_FORM",
"MOBIUS_COPRIME"
] | 3 | 2.625 | 2026-02-08T03:09:46.959044Z | {
"verified": true,
"answer": 49057,
"timestamp": "2026-02-08T03:09:49.584111Z"
} | 5617e2 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 311,
"completion_tokens": 7545
},
"timestamp": "2026-02-09T01:43:38.517Z",
"answer": 49057
},
{
... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_PRIMES",
"status": "ok"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "MOBIUS_COPRIME",
"status": "ok_late... | {
"lo": -6.49,
"mid": 0.51,
"hi": 7.52
} | ||
746c3a | nt_count_coprime_v1_124444284_2862 | Let $k$ be the number of prime numbers $n$ such that $2 \leq n \leq 229$. Let $S$ be the set of all positive integers $n$ with $1 \leq n \leq 33489$ such that $\gcd(n, k) = 1$. Compute the number of elements in $S$. Find the value of this number. | 13,396 | graphs = [
Graph(
let={
"_n": Const(229),
"upper": Const(33489),
"k": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(2)), Leq(Var("n"), Ref("_n")), IsPrime(Var("n"))))),
"result": CountOverSet(set=SolutionsSet(var=Var("n"), condi... | NT | null | COUNT | sympy | COUNT_PRIMES | [
"COUNT_PRIMES"
] | 07c874 | nt_count_coprime_v1 | null | 4 | 0 | [
"COUNT_PRIMES"
] | 1 | 3.26 | 2026-02-08T05:03:01.426584Z | {
"verified": true,
"answer": 13396,
"timestamp": "2026-02-08T05:03:04.686612Z"
} | 4b1906 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 194,
"completion_tokens": 1924
},
"timestamp": "2026-02-11T22:47:54.756Z",
"answer": 13396
},
{
"... | 1 | [
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "COUNT_PRIMES",
"status": "ok"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "V1",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
}
] | {
"lo": -3.45,
"mid": 1.15,
"hi": 6.18
} | ||
87bd03 | antilemma_sum_equals_v1_677425708_3272 | Let $m = 88$. Let $n$ be the number of ordered pairs $(i,j)$ of positive integers with $1 \leq i \leq 88$ and $1 \leq j \leq 88$ such that $i + j = m$. Let $x$ be the number of ordered pairs $(i,j)$ of positive integers with $1 \leq i \leq 85$ and $1 \leq j \leq 86$ such that $i + j = n$. Determine the value of $x$. | 85 | graphs = [
Graph(
let={
"_m": Const(88),
"_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(88)), right=IntegerRange(start=Const(1), end=Co... | COMB | GEOM | COMPUTE | sympy | COMB1 | [
"COUNT_SUM_EQUALS/COUNT_SUM_EQUALS",
"COUNT_SUM_EQUALS"
] | ae9919 | antilemma_sum_equals_v1 | null | 4 | 0 | [
"COMB1",
"COUNT_SUM_EQUALS"
] | 2 | 0.015 | 2026-02-08T05:35:58.388660Z | {
"verified": true,
"answer": 85,
"timestamp": "2026-02-08T05:35:58.403557Z"
} | fd4494 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 228,
"completion_tokens": 2171
},
"timestamp": "2026-02-24T04:08:50.890Z",
"answer": 85
},
{
"id"... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "ok"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
}
] | {
"lo": -5.98,
"mid": -3.97,
"hi": -1.94
} | ||
5955e0 | antilemma_v8_lucas_168721529_341 | Compute the number of nonnegative integers $j$ such that $0 \leq j \leq 25911$ and $\binom{25911}{j}$ is odd. Find the value of this number. | 512 | graphs = [
Graph(
let={
"x": CountOverSet(set=SolutionsSet(var=Var("j"), condition=And(Geq(Var("j"), Const(0)), Leq(Var("j"), Const(25911)), Eq(Mod(value=Binom(n=Const(25911), k=Var("j")), modulus=Const(2)), Const(1))), domain='nonnegative_integers')),
},
goal=Ref("x"),
)
] | NT | COMB | COMPUTE | sympy | V8 | [
"V8"
] | 86348e | antilemma_v8_lucas | null | 4 | 0 | [
"V8"
] | 1 | 0.001 | 2026-02-08T13:00:01.978856Z | {
"verified": true,
"answer": 512,
"timestamp": "2026-02-08T13:00:01.979496Z"
} | 846f66 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 159,
"completion_tokens": 1897
},
"timestamp": "2026-02-09T03:57:34.593Z",
"answer": 512
},
{
"id... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "V8",
"status": "ok"
... | {
"lo": -6.69,
"mid": -2.4,
"hi": 1.77
} | ||
1710fd | nt_lcm_compute_v1_397696148_2022 | Let $S$ be the set of all ordered pairs $(x, y)$ of positive integers such that $xy = 178084$. For each such pair, compute $x + y$. Let $a$ be the minimum value of $x + y$ over all such pairs. Let $b = 1477$. Compute $\operatorname{lcm}(a, b)$. | 5,908 | graphs = [
Graph(
let={
"a": MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(Mul(Var("x"), Var("y")), Const(178084)))), expr=Sum(Var("x"), Var("y")))),
"b": Const(1477)... | NT | null | COMPUTE | sympy | B3 | [
"B3"
] | 0cd20d | nt_lcm_compute_v1 | null | 4 | 0 | [
"B3"
] | 1 | 0.001 | 2026-02-08T12:54:20.426233Z | {
"verified": true,
"answer": 5908,
"timestamp": "2026-02-08T12:54:20.427257Z"
} | 638978 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 123,
"completion_tokens": 834
},
"timestamp": "2026-02-15T07:34:18.160Z",
"answer": 5908
},
{
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
}
] | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
afd3bb | modular_count_residue_v1_1742523217_3054 | Let $m = 27$ and let $\varphi$ denote Euler's totient function. Define
$$
n_0 = \sum_{k=1}^{2} \varphi(k) \left\lfloor \frac{2}{k} \right\rfloor
$$
and
$$
r = \sum_{k=1}^{3} \varphi(k) \left\lfloor \frac{n_0}{k} \right\rfloor.
$$
Let $N$ be the number of positive integers $n \leq 30976$ such that $n \equiv r \pmod{m}$.... | 24,150 | graphs = [
Graph(
let={
"_m": Const(3),
"_n": Summation(var="k", start=Const(1), end=Const(2), expr=Mul(EulerPhi(n=Var("k")), Floor(Div(Const(2), Var("k"))))),
"upper": Const(30976),
"m": Const(27),
"r": Summation(var="k", start=Const(1), end=Ref("... | NT | null | COUNT | sympy | K2 | [
"K2/K2"
] | ddede2 | modular_count_residue_v1 | null | 6 | 0 | [
"K2"
] | 1 | 4.442 | 2026-02-08T05:30:52.295863Z | {
"verified": true,
"answer": 24150,
"timestamp": "2026-02-08T05:30:56.737821Z"
} | fa28cf | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 186,
"completion_tokens": 1260
},
"timestamp": "2026-02-12T11:46:05.010Z",
"answer": 24150
},
... | 1 | [
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "K2",
"status": "ok"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "V3",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
}
] | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
4b226a | sequence_fibonacci_compute_v1_1520064083_3017 | Let $n$ be the number of nonnegative integers $j$ such that $0 \le j \le 4865$ and $\binom{4865}{j}$ is odd, plus 5. Compute the $n$-th Fibonacci number, where $F_1 = 1$, $F_2 = 1$, and $F_k = F_{k-1} + F_{k-2}$ for $k \ge 3$. | 10,946 | graphs = [
Graph(
let={
"_n": Const(4865),
"n": Sum(CountOverSet(set=SolutionsSet(var=Var("j"), condition=And(Geq(Var("j"), Const(0)), Leq(Var("j"), Const(4865)), Eq(Mod(value=Binom(n=Ref("_n"), k=Var("j")), modulus=Const(2)), Const(1))), domain='nonnegative_integers')), Const(5)),
... | ALG | COMB | COMPUTE | sympy | V8 | [
"V8"
] | 86348e | sequence_fibonacci_compute_v1 | null | 6 | 0 | [
"V8"
] | 1 | 0.002 | 2026-02-08T05:24:29.825500Z | {
"verified": true,
"answer": 10946,
"timestamp": "2026-02-08T05:24:29.827534Z"
} | ef9140 | 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": 849
},
"timestamp": "2026-02-24T03:37:29.458Z",
"answer": 10946
},
{
"i... | 1 | [
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "V1",
"status": "no"
},
{
"lemma": "V8",
"status": "ok"
}
] | {
"lo": -2.46,
"mid": 0.47,
"hi": 3.59
} | ||
a70f43 | nt_sum_over_divisible_v1_1918700295_1334 | Let $A$ be the set of positive integers $n$ such that $n \leq 71824$ and $12$ divides $n$. Let $S_A$ be the sum of all elements of $A$. Let $C$ be the number of nonnegative integers $j \leq 132$ such that $\binom{132}{j}$ is odd. Compute the remainder when $C - S_A$ is divided by $71269$. | 61,317 | graphs = [
Graph(
let={
"_n": Const(132),
"upper": Const(71824),
"divisor": Const(12),
"result": SumOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Ref("upper")), Eq(Mod(value=Var("n"), modulus=Ref("divisor")), Const... | ALG | COMB | SUM | sympy | V8 | [
"V8"
] | 04a712 | nt_sum_over_divisible_v1 | negation_mod | 4 | 0 | [
"V8"
] | 1 | 2.379 | 2026-02-08T05:46:58.821753Z | {
"verified": true,
"answer": 61317,
"timestamp": "2026-02-08T05:47:01.201178Z"
} | 688ecc | 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": 3174
},
"timestamp": "2026-02-24T04:30:57.695Z",
"answer": 61317
},
{
"... | 1 | [
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "V1",
"status": "no"
},
{
"lemma": "V8",
"status": "ok"
... | {
"lo": -0.06,
"mid": 2.89,
"hi": 5.27
} | ||
2b5290 | alg_qf_psd_min_v1_1218484723_2093 | Let $A = \min\left\{ 50a_1^2 + 70a_1b_1 + 25b_1^2 : a_1, b_1 \in \mathbb{Z}^+,\ 1 \le a_1, b_1 \le 17 \right\}$. Find the minimum value of $111650a^2 - 107184ab + 71456b^2$ over all positive integers $a, b$ with $1 \le a \le A$ and $1 \le b \le 145$. | 75,922 | graphs = [
Graph(
let={
"_n": Const(25),
"result": MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("a"), Var("b")]), condition=And(Geq(Var("a"), Const(1)), Leq(Var("a"), MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("a1"), Var("b1")]), conditio... | ALG | null | COMPUTE | sympy | QF_PSD_MIN | [
"QF_PSD_MIN"
] | c66ce3 | alg_qf_psd_min_v1 | null | 5 | 0 | [
"QF_PSD_MIN"
] | 1 | 0.039 | 2026-02-25T03:47:54.942801Z | {
"verified": true,
"answer": 75922,
"timestamp": "2026-02-25T03:47:54.982186Z"
} | 31cda9 | 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": 6849
},
"timestamp": "2026-03-29T02:57:44.564Z",
"answer": 75922
},
{
"... | 1 | [
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "QF_PSD_MIN",
"status": "ok"
}
] | {
"lo": -2.47,
"mid": 1.2,
"hi": 4.81
} | ||
ea7d41 | lin_form_endings_v1_971394319_1915 | Let $a = 105$, $b = 75$, and $k = 85$. Let $s = \gcd(a, b)$, and let $r = \left\lfloor \frac{k}{\gcd(k, s)} \right\rfloor$. Compute the remainder when $19065 \cdot r$ is divided by $64431$. | 1,950 | graphs = [
Graph(
let={
"a_coeff": Const(105),
"b_coeff": Const(75),
"k_val": Const(85),
"step": GCD(a=Ref("a_coeff"), b=Ref("b_coeff")),
"_inner_result": Floor(Div(Ref("k_val"), GCD(a=Ref("k_val"), b=Ref("step")))),
"_scale_k": Const(1... | COMB | NT | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | lin_form_endings_v1 | null | 3 | null | [
"LIN_FORM"
] | 1 | 0.001 | 2026-02-08T14:00:19.146039Z | {
"verified": true,
"answer": 1950,
"timestamp": "2026-02-08T14:00:19.146950Z"
} | 27a984 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 118,
"completion_tokens": 453
},
"timestamp": "2026-02-15T22:39:45.292Z",
"answer": 1950
},
{
... | 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": -5.49,
"mid": 0.22,
"hi": 6.51
} | ||
ba84b7 | algebra_quadratic_discriminant_v1_1915831931_2518 | Let $a = -2$, $b = 8$, and $c = -5$. Define $D = b^2 - 4ac$. Compute $2 \cdot [D > 0] + [D = 0]$, where $[P]$ is the Iverson bracket, equal to 1 if $P$ is true and 0 otherwise. | 2 | graphs = [
Graph(
let={
"a": Const(-2),
"b": Const(8),
"c": Const(-5),
"D": Sub(Pow(Ref("b"), Const(2)), Mul(Const(4), Ref("a"), Ref("c"))),
"result": Sum(Mul(Const(2), Iverson(condition=Gt(Ref("D"), Const(0)))), Iverson(condition=Eq(Ref("D"), Cons... | NT | null | COMPUTE | sympy | COPRIME_PAIRS | [
"COPRIME_PAIRS"
] | 2bb3aa | algebra_quadratic_discriminant_v1 | null | 2 | 0 | [
"COPRIME_PAIRS"
] | 1 | 0.052 | 2026-02-08T16:54:51.706001Z | {
"verified": true,
"answer": 2,
"timestamp": "2026-02-08T16:54:51.757727Z"
} | 88a4f3 | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 133,
"completion_tokens": 340
},
"timestamp": "2026-02-16T08:37:17.868Z",
"answer": 2
},
{
"id": 11,
"... | 2 | [
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "n... | {
"lo": -10,
"mid": -7.27,
"hi": -4.54
} | ||
de9262 | nt_lcm_compute_v1_1248542787_676 | Let $a = 2086$. Let $S$ be the set of all ordered pairs $(x, y)$ of positive integers such that $xy = 129600$. Define $b$ to be the minimum value of $x + y$ as $(x, y)$ ranges over $S$. Let $\ell = \operatorname{lcm}(a, b)$. Find the remainder when $44121 \cdot \ell$ is divided by $99076$. | 11,164 | graphs = [
Graph(
let={
"a": Const(2086),
"b": MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(Mul(Var("x"), Var("y")), Const(129600)))), expr=Sum(Var("x"), Var("y"))))... | NT | null | COMPUTE | sympy | B3 | [
"B3"
] | 0cd20d | nt_lcm_compute_v1 | null | 4 | 0 | [
"B3"
] | 1 | 0.001 | 2026-02-08T03:18:23.025695Z | {
"verified": true,
"answer": 11164,
"timestamp": "2026-02-08T03:18:23.026649Z"
} | f643fc | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 212,
"completion_tokens": 5109
},
"timestamp": "2026-02-09T06:56:51.078Z",
"answer": 11164
},
{
"... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "V1",
"status": "no"
}
] | {
"lo": -3.53,
"mid": 1.02,
"hi": 5.49
} | ||
a531ac | comb_count_permutations_fixed_v1_677425708_3499 | Let $ n $ be the sum $ \sum_{k=1}^{4} k $. Compute the value of $ \binom{n}{8} \cdot !(n - 8) $, where $ !m $ denotes the number of derangements of $ m $ elements. | 45 | graphs = [
Graph(
let={
"_n": Const(4),
"n": Summation(var="k", start=Const(1), end=Ref("_n"), expr=Var("k")),
"k": Const(8),
"result": Mul(Binom(n=Ref("n"), k=Ref("k")), Subfactorial(arg=Sub(left=Ref(name='n'), right=Ref(name='k')))),
},
goal=... | COMB | null | COUNT | sympy | SUM_ARITHMETIC | [
"SUM_ARITHMETIC"
] | eb34f0 | comb_count_permutations_fixed_v1 | null | 3 | 0 | [
"SUM_ARITHMETIC"
] | 1 | 0.002 | 2026-02-08T05:46:32.042542Z | {
"verified": true,
"answer": 45,
"timestamp": "2026-02-08T05:46:32.044697Z"
} | 2cad01 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 169,
"completion_tokens": 507
},
"timestamp": "2026-02-24T04:30:35.599Z",
"answer": 45
},
{
"id":... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "SUM_ARITHMETIC",
"status": "ok"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8",
"status": "no... | {
"lo": -9.23,
"mid": -6.18,
"hi": -4.06
} | ||
7962ea | nt_min_with_divisor_count_v1_124444284_9000 | Let $D$ be the set of all positive integers $n$ such that $n \leq 87025$ and $n$ has exactly four positive divisors. Let $r$ be the smallest element of $D$. Let $d_{\min}$ be the smallest divisor of $101918191$ that is at least $2$. Let $A = 353702 \times (|r| \mod d_{\min})$. Let $B = 329703 \times \left((r^2 + 1) \mo... | 37,197 | graphs = [
Graph(
let={
"_m": Const(2),
"_n": Const(101),
"upper": Const(87025),
"div_count": Const(4),
"result": MinOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Ref("upper")), Eq(NumDivisors(n=Var("n"... | NT | null | EXTREMUM | sympy | MIN_PRIME_FACTOR | [
"MIN_PRIME_FACTOR",
"LIN_FORM"
] | e2ef0b | nt_min_with_divisor_count_v1 | crt_mix_3 | 7 | 0 | [
"LIN_FORM",
"MIN_PRIME_FACTOR"
] | 2 | 4.094 | 2026-02-08T12:07:35.293029Z | {
"verified": true,
"answer": 37197,
"timestamp": "2026-02-08T12:07:39.386688Z"
} | d5a815 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 302,
"completion_tokens": 4751
},
"timestamp": "2026-02-14T22:37:11.957Z",
"answer": 37197
},
... | 1 | [
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "MIN_PRIME_FACTOR",
"status": "ok"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"st... | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
38d0de | lin_form_endings_v1_124444284_8988 | Let $a = 20$ and $b = 28$. Let $\ell = \text{lcm}(a, b)$. Define $r = 1 \cdot \ell + a + b$. Let $s = 9309 \cdot r$ and let $M = 87068$. Compute the remainder when $s$ is divided by $M$. | 8,732 | graphs = [
Graph(
let={
"a_coeff": Const(20),
"b_coeff": Const(28),
"k_val": Const(1),
"lcm_node": LCM(a=Ref("a_coeff"), b=Ref("b_coeff")),
"_inner_result": Sum(Mul(Ref("k_val"), Ref("lcm_node")), Ref("a_coeff"), Ref("b_coeff")),
"_scal... | COMB | NT | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | lin_form_endings_v1 | null | 2 | null | [
"LIN_FORM"
] | 1 | 0.001 | 2026-02-08T12:06:50.819676Z | {
"verified": true,
"answer": 8732,
"timestamp": "2026-02-08T12:06:50.820697Z"
} | fb24e8 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 122,
"completion_tokens": 578
},
"timestamp": "2026-02-14T22:34:37.078Z",
"answer": 8732
},
{
... | 1 | [
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": ... | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
333411 | comb_count_derangements_v1_784195855_7201 | Let $T$ be the set of all positive integers $p$ for which there exists a positive integer $q$ such that $p \cdot q = 31500$, $\gcd(p, q) = 1$, and $p < q$. Let $n$ be the number of elements in $T$. Compute the subfactorial $!n$, which is the number of derangements of a set of $n$ elements. Find the value of $!n$. | 14,833 | graphs = [
Graph(
let={
"n": CountOverSet(set=SolutionsSet(var=Var("p"), condition=And(IsPositive(arg=Var(name='p')), Exists(var=Var(name='q'), condition=And(Eq(left=Mul(Var(name='p'), Var(name='q')), right=Const(value=31500)), Eq(left=GCD(a=Var(name='p'), b=Var(name='q')), right=Const(value=1))... | NT | COMB | COUNT | sympy | COPRIME_PAIRS | [
"COPRIME_PAIRS"
] | 2bb3aa | comb_count_derangements_v1 | null | 5 | 0 | [
"COPRIME_PAIRS"
] | 1 | 0.001 | 2026-02-08T09:08:42.398725Z | {
"verified": true,
"answer": 14833,
"timestamp": "2026-02-08T09:08:42.399760Z"
} | 977e3a | 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": 2535
},
"timestamp": "2026-02-14T00:54:50.158Z",
"answer": 14833
},
... | 1 | [
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"... | {
"lo": -3.51,
"mid": 1.33,
"hi": 6.56
} |
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