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 |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
4323ab | comb_sum_binomial_row_v1_124444284_9952 | Let $n = 1 + 2 + 3 + 4 + 5$. Define $R = 2^n$. Compute the remainder when $12547 \cdot R$ is divided by $51425$. | 48,646 | graphs = [
Graph(
let={
"_n": Const(5),
"n": Summation(var="k", start=Const(1), end=Ref("_n"), expr=Var("k")),
"result": Pow(Const(2), Ref("n")),
"_c": Const(12547),
"Q": Mod(value=Mul(Ref("_c"), Ref("result")), modulus=Const(51425)),
},
... | NT | null | SUM | sympy | SUM_ARITHMETIC | [
"SUM_ARITHMETIC"
] | eb34f0 | comb_sum_binomial_row_v1 | null | 3 | 0 | [
"SUM_ARITHMETIC"
] | 1 | 0.001 | 2026-02-08T12:44:33.547573Z | {
"verified": true,
"answer": 48646,
"timestamp": "2026-02-08T12:44:33.548503Z"
} | e799c9 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 92,
"completion_tokens": 896
},
"timestamp": "2026-02-15T04:36:58.459Z",
"answer": 48646
},
{
... | 1 | [
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "SUM_ARITHMETIC",
"status":... | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
1882aa | comb_count_permutations_fixed_v1_168721529_1815 | Let $n$ be the smallest integer greater than or equal to $2$ that divides $143$. Compute the value of $\binom{n}{8} \cdot !(n - 8)$, where $!m$ denotes the number of derangements of $m$ elements. | 330 | graphs = [
Graph(
let={
"_n": Const(2),
"n": MinOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Ref("_n")), Divides(divisor=Var("d"), dividend=Const(143))))),
"k": Const(8),
"result": Mul(Binom(n=Ref("n"), k=Ref("k")), Subfactorial(arg=Sub(l... | NT | COMB | COUNT | sympy | MIN_PRIME_FACTOR | [
"MIN_PRIME_FACTOR"
] | bc3776 | comb_count_permutations_fixed_v1 | null | 3 | 0 | [
"MIN_PRIME_FACTOR"
] | 1 | 0.003 | 2026-02-08T13:56:45.696834Z | {
"verified": true,
"answer": 330,
"timestamp": "2026-02-08T13:56:45.699775Z"
} | 8a25e3 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 170,
"completion_tokens": 640
},
"timestamp": "2026-02-09T21:56:37.410Z",
"answer": 330
},
{
"id"... | 1 | [
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "MIN_PRIME_FACTOR",
"status": "ok"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
},
{
"lemma": "VAL_SUM_EQ",
"status": "no"
}
] | {
"lo": -8.26,
"mid": -5.01,
"hi": -1.76
} | ||
8613c7 | modular_sum_quadratic_residues_v1_1116507919_422 | Let $c = 1386$ and $m = 4$. Let $p$ be the largest prime number $n$ such that $2 \leq n \leq k$, where $k$ is the largest integer for which $7^k$ divides $1386!$. Let $s$ be the minimum value of $x + y$ over all ordered pairs $(x,y)$ of positive integers such that $xy = 4$. Compute $\frac{p(p-1)}{s}$. | 13,053 | graphs = [
Graph(
let={
"_c": Const(1386),
"_m": Const(4),
"_n": Const(2),
"p": MaxOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Ref("_n")), Leq(Var("n"), MaxKDivides(target=Factorial(Ref("_c")), base=Const(7))), IsPrime(Var("n"))))),
... | NT | null | SUM | sympy | V1 | [
"V1/MAX_PRIME_BELOW",
"B3"
] | 029b5c | modular_sum_quadratic_residues_v1 | null | 5 | 0 | [
"B3",
"MAX_PRIME_BELOW",
"V1"
] | 3 | 0.003 | 2026-02-08T02:34:11.367096Z | {
"verified": true,
"answer": 13053,
"timestamp": "2026-02-08T02:34:11.370441Z"
} | e6cd3b | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 221,
"completion_tokens": 1095
},
"timestamp": "2026-02-08T19:32:39.039Z",
"answer": 13053
},
{
"... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "K5",
"status": "same_pattern_wrong"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok_later"
},
{
"lemma": "MOD_MUL... | {
"lo": -4.6,
"mid": 0.15,
"hi": 4.61
} | ||
a1e258 | nt_count_coprime_and_v1_151522320_1531 | Let $A$ be the set of all positive integers $p$ for which there exists a positive integer $q$ such that $p \cdot q = 24$, $\gcd(p, q) = 1$, and $p < q$. Let $m$ be the number of elements in $A$. Let $d$ be the smallest divisor of $71383$ that is at least $m$. Compute the number of positive integers $n$ such that $n \le... | 23,215 | graphs = [
Graph(
let={
"_n": Const(71383),
"upper": Const(27663),
"k1": Const(11),
"k2": 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=... | NT | null | COUNT | sympy | COPRIME_PAIRS | [
"COPRIME_PAIRS/MIN_PRIME_FACTOR"
] | 52cee2 | nt_count_coprime_and_v1 | null | 5 | 0 | [
"COPRIME_PAIRS",
"MIN_PRIME_FACTOR"
] | 2 | 6.072 | 2026-02-08T04:04:55.039251Z | {
"verified": true,
"answer": 23215,
"timestamp": "2026-02-08T04:05:01.111248Z"
} | 8caf00 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 240,
"completion_tokens": 2044
},
"timestamp": "2026-02-10T15:19:39.750Z",
"answer": 23222
},
{
... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "MIN_PRIME_FACTOR",
"status"... | {
"lo": 1.96,
"mid": 5.23,
"hi": 8.52
} | ||
7323e5 | geo_count_lattice_rect_v1_1742523217_5183 | Let $a = 100$ and $b = 48$. Define $R$ to be the number of lattice points $(x, y)$ such that $0 \leq x \leq a$ and $0 \leq y \leq b$. Compute the remainder when $44121 \cdot R$ is divided by $56612$. | 2,345 | graphs = [
Graph(
let={
"a": Const(100),
"b": Const(48),
"result": LatticePointsRect(a=Ref(name='a'), b=Ref(name='b')),
"Q": Mod(value=Mul(Const(44121), Ref("result")), modulus=Const(56612)),
},
goal=Ref("Q"),
)
] | GEOM | null | COUNT | sympy | [] | geo_count_lattice_rect_v1 | null | 3 | 0 | null | null | 0.001 | 2026-02-08T10:51:05.631462Z | {
"verified": true,
"answer": 2345,
"timestamp": "2026-02-08T10:51:05.632621Z"
} | e2fa62 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 184,
"completion_tokens": 4413
},
"timestamp": "2026-02-24T12:23:01.360Z",
"answer": 2345
},
{
"i... | 1 | [] | {
"lo": -2.35,
"mid": 1.22,
"hi": 4.84
} | ||||
05b5a2 | geo_count_lattice_rect_v1_1440796553_1026 | Compute the number of lattice points in the rectangle $[0, 90] \times [0, 139]$. | 12,740 | graphs = [
Graph(
let={
"a": Const(90),
"b": Const(139),
"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 | 0.004 | 2026-02-08T12:07:05.039757Z | {
"verified": true,
"answer": 12740,
"timestamp": "2026-02-08T12:07:05.043524Z"
} | 8d468f | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 135,
"completion_tokens": 273
},
"timestamp": "2026-02-24T15:17:11.394Z",
"answer": 12740
},
{
"i... | 2 | [] | {
"lo": -10,
"mid": -7.79,
"hi": -5.57
} | ||||
a1899f | nt_count_divisors_in_range_v1_1918700295_1750 | Let $m = 5041$. Consider the set of all ordered pairs $(x, y)$ of positive integers such that $x \cdot y = m$. Let $s$ be the minimum value of $x + y$ over all such pairs. Now consider the set of all ordered pairs $(x, y)$ of positive integers such that $x + y = s$. Let $b$ be the maximum value of $x \cdot y$ over all ... | 16,389 | graphs = [
Graph(
let={
"_m": Const(5041),
"_n": Const(4),
"n": Const(110880),
"a": Const(1),
"b": MaxOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(... | NT | null | COUNT | sympy | B3 | [
"B3/B1"
] | 7f76f7 | nt_count_divisors_in_range_v1 | null | 6 | 0 | [
"B1",
"B3"
] | 2 | 0.048 | 2026-02-08T05:59:22.964688Z | {
"verified": true,
"answer": 16389,
"timestamp": "2026-02-08T05:59:23.013149Z"
} | fb6c08 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 196,
"completion_tokens": 2463
},
"timestamp": "2026-02-12T17:51:26.177Z",
"answer": 16389
},
... | 1 | [
{
"lemma": "B1",
"status": "ok_later"
},
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"le... | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
2892a0 | comb_count_permutations_fixed_v1_809748730_1302 | Let $n = 9$. Let $k$ be the largest prime number such that $2 \leq k \leq 6$. Compute $\binom{n}{k} \cdot !(n - k)$, where $!m$ denotes the number of derangements of $m$ elements. | 1,134 | graphs = [
Graph(
let={
"n": Const(9),
"k": MaxOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(2)), Leq(Var("n"), Const(6)), IsPrime(Var("n"))))),
"result": Mul(Binom(n=Ref("n"), k=Ref("k")), Subfactorial(arg=Sub(left=Ref(name='n'), right=Ref(name... | NT | COMB | COUNT | sympy | MAX_PRIME_BELOW | [
"MAX_PRIME_BELOW"
] | dc3ad3 | comb_count_permutations_fixed_v1 | null | 4 | 0 | [
"MAX_PRIME_BELOW"
] | 1 | 0.002 | 2026-02-08T12:20:07.220509Z | {
"verified": true,
"answer": 1134,
"timestamp": "2026-02-08T12:20:07.222479Z"
} | dd0ee2 | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 117,
"completion_tokens": 836
},
"timestamp": "2026-02-16T03:35:02.769Z",
"answer": 1134
},
{
"id": 11,
... | 2 | [
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "V3",
"status": "no"
},
{
"lemma": "V5",
"status": "... | {
"lo": -10,
"mid": -7.71,
"hi": -5.43
} | ||
db5b62 | nt_sum_divisors_mod_v1_458359167_424 | Let $n$ be the number of prime numbers between $2$ and $5443$, inclusive. Let $\sigma$ be the sum of all positive divisors of $n$. Find the remainder when $\sigma$ is divided by $11503$. | 2,418 | graphs = [
Graph(
let={
"_n": Const(2),
"n": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Ref("_n")), Leq(Var("n"), Const(5443)), IsPrime(Var("n"))))),
"M": Const(11503),
"sigma": SumDivisors(n=Ref("n")),
"result": Mod(va... | NT | null | COMPUTE | sympy | COUNT_PRIMES | [
"COUNT_PRIMES"
] | 07c874 | nt_sum_divisors_mod_v1 | null | 4 | 0 | [
"COUNT_PRIMES"
] | 1 | 0.003 | 2026-02-08T03:17:18.045495Z | {
"verified": true,
"answer": 2418,
"timestamp": "2026-02-08T03:17:18.048437Z"
} | 59feec | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 161,
"completion_tokens": 14951
},
"timestamp": "2026-02-23T18:33:09.952Z",
"answer": 960
},
{
... | 1 | [
{
"lemma": "COUNT_PRIMES",
"status": "ok"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "V3",
"status": "no"
},
{
"lemma": "VAL_SUM_EQ",
"status": "no"
}
] | {
"lo": 1.96,
"mid": 5.23,
"hi": 8.52
} | ||
f95a11 | modular_count_residue_v1_865884756_515 | Let $S$ be the set of all ordered pairs $(x_1, y_1)$ of positive integers such that $x_1 + y_1 = 14$. Define $P$ to be the maximum value of $x_1 y_1$ over all such pairs in $S$. Now, let $T$ be the set of all ordered pairs $(x, y)$ of positive integers such that $xy = P$. Define $m$ to be the minimum value of $x + y$ o... | 21,147 | graphs = [
Graph(
let={
"upper": Const(40000),
"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")), MaxOverSet(set=MapOverSet(set=SolutionsSet(... | COMB | null | COUNT | sympy | B1 | [
"B1/B3"
] | 80b49d | modular_count_residue_v1 | null | 6 | 0 | [
"B1",
"B3"
] | 2 | 3.582 | 2026-02-08T15:29:04.892331Z | {
"verified": true,
"answer": 21147,
"timestamp": "2026-02-08T15:29:08.473947Z"
} | 522aa3 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 302,
"completion_tokens": 1029
},
"timestamp": "2026-02-24T20:56:44.667Z",
"answer": 21147
},
{
"... | 1 | [
{
"lemma": "B1",
"status": "ok"
},
{
"lemma": "B3",
"status": "ok_later"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "V8",
"status... | {
"lo": -4.1,
"mid": -1.76,
"hi": 1.26
} | ||
0fc5bd | diophantine_fbi2_min_v1_865884756_1355 | Let $k = 14$ and let $u = 24$. Let $d$ be the smallest integer such that $2 \le d \le u$, $d$ divides $k$, and $k/d \ge 2$. Let $m$ be the smallest divisor of $294151$ that is at least $2$. Compute the $d$-th Bell number modulo $m$. Determine the value of this remainder. | 2 | graphs = [
Graph(
let={
"k": Const(14),
"upper": Const(24),
"result": MinOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Const(2)), Leq(Var("d"), Ref("upper")), Divides(divisor=Var("d"), dividend=Ref("k")), Geq(Div(Ref("k"), Var("d")), Const(2))))),
... | NT | COMB | EXTREMUM | sympy | MIN_PRIME_FACTOR | [
"MIN_PRIME_FACTOR"
] | 58d7e9 | diophantine_fbi2_min_v1 | bell_mod | 6 | 0 | [
"MIN_PRIME_FACTOR"
] | 1 | 0.007 | 2026-02-08T15:58:32.768527Z | {
"verified": true,
"answer": 2,
"timestamp": "2026-02-08T15:58:32.775956Z"
} | bd8e29 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 136,
"completion_tokens": 709
},
"timestamp": "2026-02-16T17:56:54.513Z",
"answer": 2
},
{
... | 1 | [
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MIN_PRIME_FACTOR",
"status": "ok"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"st... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
b36e43 | nt_sum_totient_over_divisors_v1_865884756_5413 | Let $n = 46414$. Let $\mathcal{D}$ be the set of all positive divisors of $n$, and define $R = \sum_{d \mid n} \varphi(d)$, where $\varphi$ is Euler's totient function. Let $m$ be the largest prime number less than or equal to $5$. Compute the value of
$$
R + \left( 2^{R \bmod (1 + 2 + \cdots + m)} \bmod 74114 \right).... | 46,430 | graphs = [
Graph(
let={
"_n": MaxOverSet(set=SolutionsSet(var=Var("n1"), condition=And(Geq(Var("n1"), Const(2)), Leq(Var("n1"), Const(5)), IsPrime(Var("n1"))))),
"n": Const(46414),
"result": SumOverDivisors(n=Ref(name='n'), var='d', expr=EulerPhi(n=Var(name='d'))),
... | NT | null | COMPUTE | sympy | MAX_PRIME_BELOW | [
"MAX_PRIME_BELOW/SUM_ARITHMETIC"
] | 442c69 | nt_sum_totient_over_divisors_v1 | mod_exp | 4 | 0 | [
"MAX_PRIME_BELOW",
"SUM_ARITHMETIC"
] | 2 | 0.003 | 2026-02-08T18:35:43.155223Z | {
"verified": true,
"answer": 46430,
"timestamp": "2026-02-08T18:35:43.158141Z"
} | 9acf2c | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 176,
"completion_tokens": 1226
},
"timestamp": "2026-02-16T12:57:05.165Z",
"answer": 93084
},
{
"id": 1... | 1 | [
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "SUM_ARITHMET... | {
"lo": -8.26,
"mid": -5.01,
"hi": -1.76
} | ||
3aa7b9 | antilemma_k2_v1_2051736721_3008 | Let $n = 321$. Let $s$ be the sum of all real solutions $x_1$ to the equation $x_1^2 - 321x_1 + 18104 = 0$. Compute $\sum_{k=1}^{s} \phi(k) \left\lfloor \frac{n}{k} \right\rfloor$, where $\phi$ denotes Euler's totient function. | 51,681 | graphs = [
Graph(
let={
"_n": Const(321),
"x": Summation(var="k", start=Const(1), end=SumOverSet(set=SolutionsSet(var=Var("x1"), condition=Eq(Sum(Pow(Var("x1"), Const(2)), Mul(Const(-321), Var("x1")), Const(18104)), Const(0)))), expr=Mul(EulerPhi(n=Var("k")), Floor(Div(Ref("_n"), Var... | NT | COMB | COMPUTE | sympy | K13 | [
"VIETA_SUM/K2",
"K2"
] | 6be084 | antilemma_k2_v1 | null | 5 | 0 | [
"K13",
"K2",
"VIETA_SUM"
] | 3 | 0.003 | 2026-02-08T17:03:49.736457Z | {
"verified": true,
"answer": 51681,
"timestamp": "2026-02-08T17:03:49.739303Z"
} | ef9244 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 132,
"completion_tokens": 677
},
"timestamp": "2026-02-17T18:08:28.801Z",
"answer": 51681
},
{... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "K2",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma"... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
3b2955 | nt_num_divisors_compute_v1_784195855_6025 | Let $n = 4096$. Let $\text{result}$ be the number of positive divisors of $n$. Let $Q = \text{result} + \phi(|\text{result}| + 1) + \tau(|\text{result}| + 1)$, where $\phi$ denotes Euler's totient function and $\tau(m)$ denotes the number of positive divisors of $m$. Compute $Q$. | 23 | graphs = [
Graph(
let={
"n": Const(4096),
"result": NumDivisors(n=Ref("n")),
"Q": Sum(Ref("result"), EulerPhi(n=Sum(Abs(arg=Ref(name='result')), Const(1))), NumDivisors(n=Sum(Abs(arg=Ref(name='result')), Const(1)))),
},
goal=Ref("Q"),
)
] | NT | null | COMPUTE | sympy | COMB1 | [
"COMB1"
] | 567f58 | nt_num_divisors_compute_v1 | null | 4 | 0 | [
"COMB1"
] | 1 | 0.016 | 2026-02-08T08:15:34.024008Z | {
"verified": true,
"answer": 23,
"timestamp": "2026-02-08T08:15:34.039719Z"
} | d0281b | 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": 465
},
"timestamp": "2026-02-13T16:57:17.584Z",
"answer": 23
},
{
... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COMB1",
"status": "ok"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
}
] | {
"lo": -9.14,
"mid": -6.05,
"hi": -3.73
} | ||
e7b991 | antilemma_v1_legendre_1520064083_3038 | Let $x$ be the largest integer $k$ such that $13^k$ divides $80301!$. Compute $x$. | 6,690 | graphs = [
Graph(
let={
"x": MaxKDivides(target=Factorial(Const(80301)), base=Const(13)),
},
goal=Ref("x"),
)
] | NT | null | COMPUTE | sympy | V1 | [
"V1"
] | dae96f | antilemma_v1_legendre | null | 5 | 0 | [
"V1"
] | 1 | 0 | 2026-02-08T05:25:43.540827Z | {
"verified": true,
"answer": 6690,
"timestamp": "2026-02-08T05:25:43.541033Z"
} | 2044e9 | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 125,
"completion_tokens": 682
},
"timestamp": "2026-02-18T16:21:10.977Z",
"answer": 6690
}
] | 2 | [
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "K5",
"status": "same_pattern_wrong"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "V1",
"status": "ok"
},
{
... | {
"lo": -10,
"mid": -6.47,
"hi": -2.95
} | ||
026a3f | alg_qf_psd_orbit_v1_1218484723_3663 | Find the number of ordered triples $(a, b, c)$ of positive integers such that $1 \leq a \leq b \leq c \leq 20$ and $$45a^2 + 45b^2 + 45c^2 - 40ab - 40ac - 40bc = 5770.$$ | 5 | graphs = [
Graph(
let={
"result": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("a"), Var("b"), Var("c")]), condition=And(Geq(Var("a"), Const(1)), Leq(Var("a"), Const(20)), Geq(Var("b"), Const(1)), Leq(Var("b"), Const(20)), Geq(Var("c"), Const(1)), Leq(Var("c"), Const(20)), Leq(Var("a"),... | ALG | null | COUNT | sympy | B3 | [
"B3"
] | 0cd20d | alg_qf_psd_orbit_v1 | null | 3 | null | [
"B3"
] | 1 | 0.423 | 2026-02-25T05:18:30.798786Z | {
"verified": true,
"answer": 5,
"timestamp": "2026-02-25T05:18:31.222264Z"
} | a7d7a9 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 1,
"correct": {
"strict": false,
"boxed": false,
"relaxed": true
},
"usage": {
"prompt_tokens": 183,
"completion_tokens": 7832
},
"timestamp": "2026-03-29T11:31:48.542Z",
"answer": 4
},
{
"id... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
}
] | {
"lo": 3.81,
"mid": 6.33,
"hi": 9.49
} | ||
752bb2 | comb_binomial_compute_v1_1520064083_9592 | Let $n = 14$. Let $k$ be the largest prime number $p$ such that $2 \leq p \leq 10$. Compute $\binom{n}{k}$. | 3,432 | graphs = [
Graph(
let={
"_n": Const(2),
"n": Const(14),
"k": MaxOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Ref("_n")), Leq(Var("n"), Const(10)), IsPrime(Var("n"))))),
"result": Binom(n=Ref("n"), k=Ref("k")),
},
goal=Ref(... | NT | null | COMPUTE | sympy | MAX_PRIME_BELOW | [
"MAX_PRIME_BELOW"
] | dc3ad3 | comb_binomial_compute_v1 | null | 3 | 0 | [
"MAX_PRIME_BELOW"
] | 1 | 0.001 | 2026-02-08T10:53:11.399625Z | {
"verified": true,
"answer": 3432,
"timestamp": "2026-02-08T10:53:11.400385Z"
} | 5f59d5 | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 97,
"completion_tokens": 786
},
"timestamp": "2026-02-15T21:05:50.518Z",
"answer": 3432
},
{
"id": 11,
... | 2 | [
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
}
] | {
"lo": -10,
"mid": -7.71,
"hi": -5.43
} | ||
8bc3bc | nt_count_intersection_v1_1918700295_1938 | Let $N = 50000$. Let $a$ be the smallest divisor of 11011 that is at least 2. Let $b = 15$. Determine the value of the number of positive integers $n$ such that $1 \leq n \leq N$, $a$ divides $n$, and $\gcd(n, b) = 1$. | 3,810 | graphs = [
Graph(
let={
"N": Const(50000),
"a": MinOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Const(2)), Divides(divisor=Var("d"), dividend=Const(11011))))),
"b": Const(15),
"result": CountOverSet(set=SolutionsSet(var=Var("n"), conditio... | NT | null | COUNT | sympy | MIN_PRIME_FACTOR | [
"MIN_PRIME_FACTOR"
] | bc3776 | nt_count_intersection_v1 | null | 4 | 0 | [
"MIN_PRIME_FACTOR"
] | 1 | 1.946 | 2026-02-08T06:11:22.316215Z | {
"verified": true,
"answer": 3810,
"timestamp": "2026-02-08T06:11:24.262376Z"
} | f45dbd | 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": 1292
},
"timestamp": "2026-02-13T11:22:23.309Z",
"answer": 3810
},
{... | 1 | [
{
"lemma": "MIN_PRIME_FACTOR",
"status": "ok"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
},
{
"lemma": "VAL_SUM_EQ",
"status": "... | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
45b92e | nt_min_crt_v1_1742523217_3390 | Let $n = 7$. Define $$
\text{upper} = \sum_{k=1}^{n} \phi(k) \left\lfloor \frac{7}{k} \right\rfloor,
$$ where $\phi$ denotes Euler's totient function. Let $\text{result}$ be the smallest positive integer $n$ such that $1 \leq n \leq \text{upper}$, $n \equiv 1 \pmod{4}$, and $n \equiv 3 \pmod{7}$. Compute the remainder ... | 11,516 | graphs = [
Graph(
let={
"_n": Const(7),
"m": Const(4),
"k": Const(7),
"a": Const(1),
"b": Const(3),
"upper": Summation(var="k", start=Const(1), end=Ref("_n"), expr=Mul(EulerPhi(n=Var("k")), Floor(Div(Const(7), Var("k"))))),
... | NT | null | EXTREMUM | sympy | K2 | [
"K2"
] | 6897ab | nt_min_crt_v1 | null | 6 | 0 | [
"K2"
] | 1 | 0.01 | 2026-02-08T05:49:38.635373Z | {
"verified": true,
"answer": 11516,
"timestamp": "2026-02-08T05:49:38.644941Z"
} | a2e741 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 175,
"completion_tokens": 1190
},
"timestamp": "2026-02-12T14:57:40.509Z",
"answer": 11516
},
... | 1 | [
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K2",
"status": "ok"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "V1",
"status": "no"
}
] | {
"lo": -5.92,
"mid": -3.14,
"hi": 0.26
} | ||
9df417 | nt_count_primes_v1_1978505735_1893 | Let $A$ be the number of positive integers $p$ for which there exists a positive integer $q$ such that $pq = 6$, $\gcd(p, q) = 1$, and $p < q$. Let $S$ be the set of all prime numbers $n$ such that $A \leq n \leq 28224$. Compute the number of elements in $S$. | 3,076 | graphs = [
Graph(
let={
"upper": Const(28224),
"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 | 3 | 0 | [
"COPRIME_PAIRS"
] | 1 | 0.652 | 2026-02-08T16:31:07.662322Z | {
"verified": true,
"answer": 3076,
"timestamp": "2026-02-08T16:31:08.314227Z"
} | c7a1ac | 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": 1946
},
"timestamp": "2026-02-17T05:01:20.663Z",
"answer": 3076
},
{... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "V1",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
0294f7 | nt_count_intersection_v1_124444284_8046 | Let $N = 100000$. Let $T$ be the set of all integers $t$ such that $21 \leq t \leq 60$ and there exist positive integers $a$ and $b$ with $1 \leq a \leq 2$, $1 \leq b \leq 5$, and $t = 15a + 6b$. Let $b$ be the number of elements in $T$. Let $a = 7$. Define $S$ as the set of all positive integers $n$ such that $1 \leq ... | 5,714 | graphs = [
Graph(
let={
"N": Const(100000),
"a": Const(7),
"b": CountOverSet(set=SolutionsSet(var=Var("t"), condition=Exists(var=Var(name='a'), condition=Exists(var=Var(name='b'), condition=And(Geq(left=Var(name='a'), right=Const(value=1)), Leq(left=Var(name='a'), right=C... | NT | null | COUNT | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | nt_count_intersection_v1 | null | 5 | 0 | [
"LIN_FORM"
] | 1 | 3.591 | 2026-02-08T09:30:59.529156Z | {
"verified": true,
"answer": 5714,
"timestamp": "2026-02-08T09:31:03.120362Z"
} | 5d1523 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 197,
"completion_tokens": 1291
},
"timestamp": "2026-02-14T04:42:15.581Z",
"answer": 5714
},
{... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "VAL_SUM_EQ",
"status": "no"
}... | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
e53458 | antilemma_sum_equals_v1_548369836_129 | Let $m = 7$. Let $n$ be the number of ordered pairs $(i,j)$ of positive integers such that $1 \leq i \leq 80$, $1 \leq j \leq 80$, and $i + j = 81$. Let $x$ be the number of ordered pairs $(i,j)$ of positive integers such that $1 \leq i \leq 79$, $1 \leq j \leq 80$, and $i + j = n$. Compute the sum of the number of pos... | 358 | graphs = [
Graph(
let={
"_m": Const(7),
"_n": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("i"), Var("j")]), condition=Eq(Sum(Var("i"), Var("j")), Const(81)), domain=CartesianProduct(left=IntegerRange(start=Const(1), end=Const(80)), right=IntegerRange(start=Const(1), end=Con... | COMB | GEOM | COMPUTE | sympy | COUNT_SUM_EQUALS | [
"COUNT_SUM_EQUALS/COUNT_SUM_EQUALS",
"COUNT_SUM_EQUALS",
"ONE_BINOM_0"
] | 4ed70a | antilemma_sum_equals_v1 | null | 4 | 0 | [
"COUNT_SUM_EQUALS",
"ONE_BINOM_0"
] | 2 | 0.064 | 2026-02-08T02:46:45.521474Z | {
"verified": true,
"answer": 358,
"timestamp": "2026-02-08T02:46:45.585043Z"
} | 359723 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 264,
"completion_tokens": 2927
},
"timestamp": "2026-02-08T19:54:07.566Z",
"answer": 358
},
{
"id... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "ok"
},
{
"lemma": "ONE_BINOM_0",
"status": "ok"
},
{
"lemma": "V7",
"sta... | {
"lo": 0.04,
"mid": 1.71,
"hi": 3.18
} | ||
5f4d40 | nt_gcd_compute_v1_1742523217_3912 | Let $A$ be the number of ordered pairs $(p, q)$ of positive integers such that $p < q$, $pq = 36$, and $\gcd(p, q) = 1$.
Let $r$ be the greatest common divisor of $612008$ and $1147515$.
Let $T$ be the set of all real numbers $x$ such that $x^A - 9025x + 671250 = 0$. Let $s$ be the sum of all elements in $T$.
Comput... | 35,016 | graphs = [
Graph(
let={
"_m": Const(51246),
"_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=36)), Eq(left=GCD(a=Var(name='p'), b=Var(nam... | NT | null | COMPUTE | sympy | COPRIME_PAIRS | [
"COPRIME_PAIRS/VIETA_SUM"
] | ea2fe2 | nt_gcd_compute_v1 | negation_mod | 6 | 0 | [
"COPRIME_PAIRS",
"VIETA_SUM"
] | 2 | 0.004 | 2026-02-08T06:08:04.798712Z | {
"verified": true,
"answer": 35016,
"timestamp": "2026-02-08T06:08:04.802421Z"
} | d2607e | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 172,
"completion_tokens": 2344
},
"timestamp": "2026-02-12T20:02:18.782Z",
"answer": 35016
},
... | 1 | [
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
... | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
b56e51 | algebra_poly_eval_v1_784195855_6692 | Let $b = 25$. Define $S$ as the set of all integers $t$ such that there exist integers $a$ and $b'$ with $1 \leq a \leq 2$, $1 \leq b' \leq 3$, $5 \leq t \leq 12$, and $t = 3a + 2b'$. Let $c$ be the number of ordered pairs $(x_1, x_2)$ of positive odd integers such that $x_1 + x_2 = 94$. Compute the remainder when $c -... | 75,756 | graphs = [
Graph(
let={
"_n": Const(94),
"b": Const(25),
"result": Sum(Pow(Ref("b"), Const(2)), Mul(Const(-2), Ref("b")), CountOverSet(set=SolutionsSet(var=Var("t"), condition=Exists(var=Var(name='a'), condition=Exists(var=Var(name='b'), condition=And(Geq(left=Var(name='a... | NT | null | COMPUTE | sympy | COMB1 | [
"COMB1",
"LIN_FORM"
] | 2bb5bf | algebra_poly_eval_v1 | negation_mod | 4 | 0 | [
"COMB1",
"LIN_FORM"
] | 2 | 0.004 | 2026-02-08T08:47:54.321898Z | {
"verified": true,
"answer": 75756,
"timestamp": "2026-02-08T08:47:54.325489Z"
} | 596a92 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 189,
"completion_tokens": 987
},
"timestamp": "2026-02-13T21:51:57.854Z",
"answer": 75756
},
{... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COMB1",
"status": "ok"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "V3",
... | {
"lo": -5.55,
"mid": -3.01,
"hi": 0.32
} | ||
5d4404 | geo_visible_lattice_v1_1125832087_389 | Let $n = 80$. Define $\text{result}$ as the number of visible lattice points $(x, y)$ with $1 \leq x, y \leq n$, meaning the number of ordered pairs of positive integers $(x, y)$ in that range such that $\gcd(x, y) = 1$. Let $Q = 24025 - \text{result}$. Compute $Q$. | 20,094 | graphs = [
Graph(
let={
"n": Const(80),
"result": VisibleLatticePoints(n=Ref(name='n')),
"_c": Const(24025),
"Q": Sub(Ref("_c"), Ref("result")),
},
goal=Ref("Q"),
)
] | GEOM | null | COUNT | sympy | [] | geo_visible_lattice_v1 | null | 6 | 0 | null | null | 0.131 | 2026-02-08T03:02:44.037677Z | {
"verified": true,
"answer": 20094,
"timestamp": "2026-02-08T03:02:44.168960Z"
} | b0b72a | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 197,
"completion_tokens": 32768
},
"timestamp": "2026-02-23T21:28:11.476Z",
"answer": null
},
{
... | 1 | [] | {
"lo": 1.97,
"mid": 4.36,
"hi": 6.69
} | ||||
26467a | comb_count_partitions_v1_151522320_687 | Let $n$ be the largest prime number less than or equal to $41$. Compute the number of unordered partitions of $n$ into positive integers, where the order of parts does not matter. | 44,583 | graphs = [
Graph(
let={
"_n": Const(41),
"n": MaxOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(2)), Leq(Var("n"), Ref("_n")), IsPrime(Var("n"))))),
"result": Partition(arg=Ref(name='n')),
},
goal=Ref("result"),
)
] | NT | COMB | COUNT | sympy | MAX_PRIME_BELOW | [
"MAX_PRIME_BELOW"
] | dc3ad3 | comb_count_partitions_v1 | null | 4 | 0 | [
"MAX_PRIME_BELOW"
] | 1 | 0.002 | 2026-02-08T03:27:32.895547Z | {
"verified": true,
"answer": 44583,
"timestamp": "2026-02-08T03:27:32.897210Z"
} | 734ebc | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 150,
"completion_tokens": 1240
},
"timestamp": "2026-02-10T14:32:30.719Z",
"answer": 44583
},
{
"... | 1 | [
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
},
{
"lemma": "V8",
"status": ... | {
"lo": -3.46,
"mid": 1.03,
"hi": 5.49
} | ||
9cf6bd | geo_count_lattice_triangle_v1_1915831931_1592 | Let $A$ be the area of the triangle with vertices at $(128, 100)$, $(153, 222)$, and $(0, 0)$, multiplied by $2$. Let $B$ be the number of lattice points on the boundary of this triangle. Compute $\frac{A - B + 2}{2}$. | 6,555 | graphs = [
Graph(
let={
"_n": Const(2),
"area_2x": Abs(arg=Sum(Mul(Const(value=128), Const(value=222)), Mul(Const(value=153), Sub(left=Const(value=0), right=Const(value=100))))),
"boundary": Sum(GCD(a=Abs(arg=Const(value=128)), b=Abs(arg=Const(value=100))), GCD(a=Abs(arg=... | ALG | NT | COUNT | sympy | VIETA_SUM | [
"VIETA_SUM"
] | b33a7a | geo_count_lattice_triangle_v1 | null | 6 | 0 | [
"VIETA_SUM"
] | 1 | 0.009 | 2026-02-08T16:17:52.509666Z | {
"verified": true,
"answer": 6555,
"timestamp": "2026-02-08T16:17:52.518257Z"
} | a66b7a | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 113,
"completion_tokens": 1637
},
"timestamp": "2026-02-17T00:33:46.655Z",
"answer": 6555
},
{... | 1 | [
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "VIETA_SUM",
"status": "ok"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
24e8a0 | algebra_poly_eval_v1_168721529_15 | Let $ d_0 $ be the smallest integer greater than or equal to 2 that divides 385. Let $ k_0 $ be the largest integer $ k $ such that $ d_0^k \le 1171938523 $. Compute the value of $ 7k_0^3 - 8k_0^2 + 9k_0 + 3 $. | 11,055 | graphs = [
Graph(
let={
"_m": Const(3),
"_n": Const(3),
"b": MaxOverSet(set=SolutionsSet(var=Var("k"), condition=Leq(Pow(MinOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Const(2)), Divides(divisor=Var("d"), dividend=Const(385))))), Var("k")), Const(11... | NT | null | COMPUTE | sympy | MIN_PRIME_FACTOR | [
"MIN_PRIME_FACTOR/MAX_VAL"
] | 266d37 | algebra_poly_eval_v1 | null | 5 | 0 | [
"MAX_VAL",
"MIN_PRIME_FACTOR"
] | 2 | 0.003 | 2026-02-08T12:46:03.684022Z | {
"verified": true,
"answer": 11055,
"timestamp": "2026-02-08T12:46:03.686954Z"
} | daedf5 | 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": 633
},
"timestamp": "2026-02-08T20:53:24.901Z",
"answer": 11055
},
{
"i... | 1 | [
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "ok_later"
},
{
"lemma": "MIN_PRIME_FACTOR",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "V1",
... | {
"lo": -5.3,
"mid": -2.04,
"hi": 1.84
} | ||
cefd57 | modular_sum_quadratic_residues_v1_1520064083_7902 | Let $m = 2$ and $n = 2$. Let $P$ be the set of all prime numbers $p$ such that $2 \leq p \leq T$, where $T$ is the number of prime numbers in the interval $[2, 1129]$. Let $p$ be the largest element of $P$. Compute $\frac{p(p-1)}{4}$. | 8,145 | graphs = [
Graph(
let={
"_m": Const(2),
"_n": Const(2),
"p": MaxOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Ref("_n")), Leq(Var("n"), CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Ref("_m")), Leq(Var("n"), Const(1129)), IsP... | NT | null | SUM | sympy | COUNT_PRIMES | [
"COUNT_PRIMES/MAX_PRIME_BELOW"
] | d51604 | modular_sum_quadratic_residues_v1 | null | 5 | 0 | [
"COUNT_PRIMES",
"MAX_PRIME_BELOW"
] | 2 | 0.002 | 2026-02-08T09:21:54.684438Z | {
"verified": true,
"answer": 8145,
"timestamp": "2026-02-08T09:21:54.686799Z"
} | 56d5a8 | 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": 1019
},
"timestamp": "2026-02-14T03:54:29.969Z",
"answer": 8145
},
{... | 1 | [
{
"lemma": "COUNT_PRIMES",
"status": "ok"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok_later"
},
{
"lemma": "MOD_ADD",
"status": "... | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
b96cfc | comb_binomial_compute_v1_458359167_1871 | Let $n = 12$. Define $k$ to be the number of integers $t$ with $17 \leq t \leq 24$ such that there exist positive integers $a$ and $b$ satisfying $1 \leq a \leq 3$, $1 \leq b \leq 2$, and $t = 2a + 3b + 12$. Let $R = \binom{n}{k}$. Compute the remainder when $76567 \cdot R$ is divided by $54661$. | 16,574 | graphs = [
Graph(
let={
"n": Const(12),
"k": CountOverSet(set=SolutionsSet(var=Var("t"), condition=Exists(var=Var(name='a'), condition=Exists(var=Var(name='b'), condition=And(Geq(left=Var(name='a'), right=Const(value=1)), Leq(left=Var(name='a'), right=Const(value=3)), Geq(left=Var(na... | ALG | COMB | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | comb_binomial_compute_v1 | null | 5 | 0 | [
"LIN_FORM"
] | 1 | 0.003 | 2026-02-08T04:55:00.324246Z | {
"verified": true,
"answer": 16574,
"timestamp": "2026-02-08T04:55:00.326785Z"
} | 6be73b | 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": 1741
},
"timestamp": "2026-02-24T02:18:01.519Z",
"answer": 16574
},
{
"... | 1 | [
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
}
] | {
"lo": -2.46,
"mid": 0.47,
"hi": 3.59
} | ||
f4e04f | comb_count_permutations_fixed_v1_1520064083_7096 | Let $n$ be the sum $\sum_{k=1}^{4} k$. Let $k$ be the largest prime number satisfying $2 \leq k \leq 5$. Define $\text{result} = \binom{n}{k} \cdot !(n - k)$, where $!m$ denotes the number of derangements of $m$ elements. Let $Q$ be the remainder when $58643 \times \text{result}$ is divided by $50814$. Compute $Q$. | 17,640 | graphs = [
Graph(
let={
"_m": Const(58643),
"_n": Const(50814),
"n": Summation(var="k", start=Const(1), end=Const(4), expr=Var("k")),
"k": MaxOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(2)), Leq(Var("n"), Const(5)), IsPrime(Var("n"... | NT | COMB | COUNT | sympy | MAX_PRIME_BELOW | [
"MAX_PRIME_BELOW",
"SUM_ARITHMETIC"
] | 15f63b | comb_count_permutations_fixed_v1 | null | 3 | 0 | [
"MAX_PRIME_BELOW",
"SUM_ARITHMETIC"
] | 2 | 0.002 | 2026-02-08T08:45:34.295544Z | {
"verified": true,
"answer": 17640,
"timestamp": "2026-02-08T08:45:34.297513Z"
} | fdcef9 | 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": 1354
},
"timestamp": "2026-02-13T21:29:40.964Z",
"answer": 17640
},
... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "SUM_ARITHMETIC",
"status": "ok"
},
{
"lemma": "V1",
"status": "no"
},
{
... | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
c640a5 | diophantine_fbi2_count_v1_1440796553_289 | Let $S$ be the set of all ordered pairs $(x, y)$ of positive integers such that $xy = 32400$. For each such pair, compute $x + y$, and let $k$ be the minimum value of $x + y$ over all such pairs. Determine the number of positive integers $d$ such that $6 \leq d \leq 71$, $d$ divides $k$, and $4 \leq \frac{k}{d} \leq 69... | 14 | graphs = [
Graph(
let={
"_n": Const(6),
"k": MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(Mul(Var("x"), Var("y")), Const(32400)))), expr=Sum(Var("x"), Var("y")))),
... | NT | null | COUNT | sympy | MAX_PRIME_BELOW | [
"B3"
] | 0cd20d | diophantine_fbi2_count_v1 | null | 5 | 0 | [
"B3",
"MAX_PRIME_BELOW"
] | 2 | 0.114 | 2026-02-08T11:43:21.838027Z | {
"verified": true,
"answer": 14,
"timestamp": "2026-02-08T11:43:21.952326Z"
} | fb41f3 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 150,
"completion_tokens": 1419
},
"timestamp": "2026-02-14T17:43:31.972Z",
"answer": 14
},
{
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
},
{
"lemma": "VAL_SUM_EQ",
"status": "no"
}
] | {
"lo": -6.96,
"mid": -4.56,
"hi": -1.46
} | ||
b5ae4d | nt_sum_over_divisible_v1_784195855_10010 | Let $k$ be a positive integer such that $1 \leq k \leq 1249924$ and $169$ divides $k$. Let $N$ be the number of such integers $k$. Let $S$ be the set of all positive integers $n$ such that $1 \leq n \leq N$ and $n$ is divisible by $63$. Compute the remainder when
$$
\left( \sum_{n \in S} n \right) + \left( 2^{\left( \... | 11,233 | graphs = [
Graph(
let={
"upper": CountOverSet(set=SolutionsSet(var=Var("k"), condition=And(Geq(Var("k"), Const(1)), Leq(Var("k"), Const(1249924)), Divides(divisor=Const(169), dividend=Var("k"))), domain='positive_integers')),
"divisor": Const(63),
"result": SumOverSet(set... | ALG | NT | SUM | sympy | C2 | [
"C2"
] | 9685eb | nt_sum_over_divisible_v1 | null | 4 | 0 | [
"C2"
] | 1 | 0.899 | 2026-02-08T17:22:26.651888Z | {
"verified": true,
"answer": 11233,
"timestamp": "2026-02-08T17:22:27.550768Z"
} | dc1ff6 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 189,
"completion_tokens": 1331
},
"timestamp": "2026-02-18T00:43:45.302Z",
"answer": 11233
},
... | 1 | [
{
"lemma": "C2",
"status": "ok"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
6c58f0 | nt_count_divisors_in_range_v1_798873815_228 | Let $n = 15120$. Let $A$ be the set of all positive integers $k \leq 270$ such that $10$ divides $F_k$, the $k$-th Fibonacci number. Define $a = |A|$.
Let $B$ be the set of all integers $t$ such that $22 \leq t \leq 4376$ and there exist positive integers $a \leq 477$, $b \leq 40$ satisfying $t = 8a + 14b$. Define $b ... | 122 | graphs = [
Graph(
let={
"n": Const(15120),
"a": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Const(270)), Divides(divisor=Const(10), dividend=Fibonacci(arg=Var(name='n')))))),
"b": CountOverSet(set=SolutionsSet(var=Var("... | NT | null | COUNT | sympy | COUNT_FIB_DIVISIBLE | [
"COUNT_FIB_DIVISIBLE",
"LIN_FORM"
] | 0f3003 | nt_count_divisors_in_range_v1 | null | 6 | 0 | [
"COUNT_FIB_DIVISIBLE",
"LIN_FORM"
] | 2 | 0.032 | 2026-02-08T02:31:30.505374Z | {
"verified": true,
"answer": 122,
"timestamp": "2026-02-08T02:31:30.537529Z"
} | e5542e | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 319,
"completion_tokens": 32768
},
"timestamp": "2026-02-23T14:23:53.556Z",
"answer": null
},
{
... | 1 | [
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "ok"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",... | {
"lo": 1.31,
"mid": 2.95,
"hi": 4.47
} | ||
2bc5f8 | antilemma_sum_equals_v1_1520064083_7885 | Compute the number of ordered pairs $(i, j)$ of integers such that $1 \leq i \leq 7$, $1 \leq j \leq 7$, and $i + j = 7$. | 6 | graphs = [
Graph(
let={
"x": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("i"), Var("j")]), condition=Eq(Sum(Var("i"), Var("j")), Const(7)), domain=CartesianProduct(left=IntegerRange(start=Const(1), end=Const(7)), right=IntegerRange(start=Const(1), end=Const(7))))),
},
g... | COMB | GEOM | COMPUTE | sympy | COUNT_SUM_EQUALS | [
"COUNT_SUM_EQUALS"
] | 75ab0f | antilemma_sum_equals_v1 | null | 2 | 0 | [
"COUNT_SUM_EQUALS"
] | 1 | 0.066 | 2026-02-08T09:21:33.273920Z | {
"verified": true,
"answer": 6,
"timestamp": "2026-02-08T09:21:33.340383Z"
} | cc7f8a | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 158,
"completion_tokens": 181
},
"timestamp": "2026-02-24T11:16:08.101Z",
"answer": 6
},
{
"id": ... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "ok"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
}
] | {
"lo": -9.23,
"mid": -6.18,
"hi": -4.06
} | ||
80f808 | algebra_poly_eval_v1_124444284_5301 | Let $t$ be the number of integers $t$ in the range $5 \leq t \leq 15$ for which there exist integers $a$ and $b$, each between 1 and 3 inclusive, such that $t = 3a + 2b$. Let $r$ be the number of positive integers $p$ for which there exists an integer $q$ such that $pq = 120$, $\gcd(p, q) = 1$, and $p < q$. Compute the... | 45,530 | graphs = [
Graph(
let={
"_m": Const(4),
"_n": Const(58621),
"t": 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=... | NT | null | COMPUTE | sympy | COPRIME_PAIRS | [
"COPRIME_PAIRS",
"LIN_FORM"
] | 67610e | algebra_poly_eval_v1 | null | 6 | 0 | [
"COPRIME_PAIRS",
"LIN_FORM"
] | 2 | 0.006 | 2026-02-08T06:32:13.601423Z | {
"verified": true,
"answer": 45530,
"timestamp": "2026-02-08T06:32:13.606938Z"
} | 69364d | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 196,
"completion_tokens": 1910
},
"timestamp": "2026-02-13T01:17:33.094Z",
"answer": 45530
},
... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
... | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
e454ae | nt_sum_divisors_mod_v1_1978505735_328 | Let $n$ be the number of prime numbers between $2$ and $14323$, inclusive. Let $\sigma(n)$ denote the sum of all positive divisors of $n$. Compute the remainder when $\sigma(n)$ is divided by $10243$. | 5,952 | graphs = [
Graph(
let={
"_n": Const(2),
"n": CountOverSet(set=SolutionsSet(var=Var("n1"), condition=And(Geq(Var("n1"), Ref("_n")), Leq(Var("n1"), Const(14323)), IsPrime(Var("n1"))))),
"M": Const(10243),
"sigma": SumDivisors(n=Ref("n")),
"result": M... | NT | null | COMPUTE | sympy | COUNT_PRIMES | [
"COUNT_PRIMES"
] | 07c874 | nt_sum_divisors_mod_v1 | null | 3 | 0 | [
"COUNT_PRIMES"
] | 1 | 0.006 | 2026-02-08T15:18:35.670145Z | {
"verified": true,
"answer": 5952,
"timestamp": "2026-02-08T15:18:35.676360Z"
} | 0f4b48 | 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": 3840
},
"timestamp": "2026-02-16T04:29:01.989Z",
"answer": 5952
},
{
... | 1 | [
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "COUNT_PRIMES",
"status": "ok"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "VAL_SUM_EQ",
"status": "no"... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
1879c0 | comb_binomial_compute_v1_124444284_6194 | Let $c = 5$. Define $m$ to be the sum
$$
\sum_{k=1}^{n} \phi(k) \left\lfloor \frac{5}{k} \right\rfloor,
$$
where $n$ is the largest prime at most $5$. Let $p$ be the largest prime number that is at most $m$. Compute the remainder when $44121 \cdot \binom{p}{5}$ is divided by $82399$. | 10,816 | graphs = [
Graph(
let={
"_c": Const(5),
"_m": Const(82399),
"_n": Summation(var="k", start=Const(1), end=MaxOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(2)), Leq(Var("n"), Const(5)), IsPrime(Var("n"))))), expr=Mul(EulerPhi(n=Var("k")), Floor(Di... | NT | null | COMPUTE | sympy | MAX_PRIME_BELOW | [
"MAX_PRIME_BELOW/K2/MAX_PRIME_BELOW"
] | 1000f8 | comb_binomial_compute_v1 | null | 4 | 0 | [
"K2",
"MAX_PRIME_BELOW"
] | 2 | 0.003 | 2026-02-08T08:11:21.198508Z | {
"verified": true,
"answer": 10816,
"timestamp": "2026-02-08T08:11:21.201358Z"
} | c6d87e | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 144,
"completion_tokens": 1491
},
"timestamp": "2026-02-13T15:35:35.604Z",
"answer": 10816
},
... | 1 | [
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "K2",
"status": "ok_later"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
... | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
c19fbc | nt_sum_over_divisible_v1_458359167_1011 | Let $\text{upper}$ be the number of ordered pairs $(i, j)$ such that $1 \le i \le 70$ and $1 \le j \le 100$. Let $\text{result}$ be the sum of all positive integers $n \le \text{upper}$ such that $n$ is divisible by 99. Find the remainder when $72977 \cdot \text{result}$ is divided by 63160. | 17,175 | graphs = [
Graph(
let={
"upper": CountOverSet(set=CartesianProduct(left=IntegerRange(start=Const(1), end=Const(70)), right=IntegerRange(start=Const(1), end=Const(100)))),
"divisor": Const(99),
"result": SumOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"),... | NT | null | SUM | sympy | COUNT_CARTESIAN | [
"COUNT_CARTESIAN"
] | 409d7d | nt_sum_over_divisible_v1 | null | 3 | 0 | [
"COUNT_CARTESIAN"
] | 1 | 0.223 | 2026-02-08T04:13:27.624700Z | {
"verified": true,
"answer": 17175,
"timestamp": "2026-02-08T04:13:27.847208Z"
} | 53a10e | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 205,
"completion_tokens": 2022
},
"timestamp": "2026-02-10T15:53:14.496Z",
"answer": 17175
},
{
... | 1 | [
{
"lemma": "COUNT_CARTESIAN",
"status": "ok"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "V1",
"status": "no"
}
] | {
"lo": -3.42,
"mid": 1.86,
"hi": 7.55
} | ||
dc3cb7 | comb_count_permutations_fixed_v1_458359167_2643 | Let $n = 7$. Let $k$ be the sum of all integers $x$ such that $x^2 - 2x - 4899 = 0$. Compute $\binom{n}{k} \cdot !(n - k)$, where $!m$ denotes the number of derangements of $m$ elements. | 924 | graphs = [
Graph(
let={
"_n": Const(2),
"n": Const(7),
"k": SumOverSet(set=SolutionsSet(var=Var("x"), condition=Eq(Sum(Pow(Var("x"), Ref("_n")), Mul(Const(-2), Var("x")), Const(-4899)), Const(0)))),
"result": Mul(Binom(n=Ref("n"), k=Ref("k")), Subfactorial(arg... | COMB | null | COUNT | sympy | V8 | [
"VIETA_SUM"
] | b33a7a | comb_count_permutations_fixed_v1 | null | 4 | 0 | [
"V8",
"VIETA_SUM"
] | 2 | 0.008 | 2026-02-08T06:24:36.907579Z | {
"verified": true,
"answer": 924,
"timestamp": "2026-02-08T06:24:36.915775Z"
} | 972835 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 183,
"completion_tokens": 1047
},
"timestamp": "2026-02-24T06:48:39.035Z",
"answer": 924
},
{
"id... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
},
{
"lemma": "VIETA_SUM",
"status": "ok"
}... | {
"lo": -7.18,
"mid": -5,
"hi": -3.01
} | ||
396f44 | sequence_lucas_compute_v1_1915831931_2516 | Let $m = 4235$ and $N = 18$. Let $n$ be the number of positive integers $j$ such that $1 \le j \le N$ and $j^d \le 1889568$, where $d$ is the smallest divisor of $m$ that is at least $2$. Let $L_n$ denote the $n$-th Lucas number, defined by $L_1 = 1$, $L_2 = 3$, and $L_k = L_{k-1} + L_{k-2}$ for $k \ge 3$. Determine th... | 5,778 | graphs = [
Graph(
let={
"_m": Const(4235),
"_n": Const(18),
"n": CountOverSet(set=SolutionsSet(var=Var("j"), condition=And(Geq(Var("j"), Const(1)), Leq(Var("j"), Ref("_n")), Leq(Pow(Var("j"), MinOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Const(2)),... | NT | null | COMPUTE | sympy | MIN_PRIME_FACTOR | [
"MIN_PRIME_FACTOR/C3"
] | 92256e | sequence_lucas_compute_v1 | null | 5 | 0 | [
"C3",
"MIN_PRIME_FACTOR"
] | 2 | 0.004 | 2026-02-08T16:54:51.637437Z | {
"verified": true,
"answer": 5778,
"timestamp": "2026-02-08T16:54:51.641615Z"
} | eadfe5 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 183,
"completion_tokens": 754
},
"timestamp": "2026-02-17T15:20:44.794Z",
"answer": 5778
},
{
... | 1 | [
{
"lemma": "C3",
"status": "ok_later"
},
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "MIN_PRIME_FACTOR",
"status": "ok"
},
{
"lemma": "MOD_FACTORIAL",
"statu... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
223efb | nt_euler_phi_compute_v1_48377204_3062 | Let $c$ be the minimum value of $x + y$ over all pairs of positive integers $(x, y)$ such that $xy = 14288400$. Compute $\phi(80656)$, and let this value be $\varphi$. Find the remainder when $c - \varphi$ is divided by 93406. | 61,206 | graphs = [
Graph(
let={
"n": Const(80656),
"result": EulerPhi(n=Ref("n")),
"_c": 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")), Co... | NT | null | COMPUTE | sympy | B3 | [
"B3"
] | fc629c | nt_euler_phi_compute_v1 | negation_mod | 4 | 0 | [
"B3"
] | 1 | 0.006 | 2026-02-08T17:09:20.408187Z | {
"verified": true,
"answer": 61206,
"timestamp": "2026-02-08T17:09:20.414508Z"
} | d76643 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 114,
"completion_tokens": 1465
},
"timestamp": "2026-02-17T20:37:37.501Z",
"answer": 61206
},
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
18ac3b | comb_bell_compute_v1_168721529_1411 | Let $m$ be the number of positive integers $p$ for which there exists a positive integer $q$ such that $pq=54$, $\gcd(p,q)=1$, and $p<q$.
Let $d$ be the smallest positive integer such that $d\ge m$ and $d$ divides $48841$.
Consider all ordered pairs $(i,j)$ of integers with $1\le i\le 10$, $1\le j\le 10$, and $i+j=10... | 65,226 | graphs = [
Graph(
let={
"_m": Const(48841),
"_n": CountOverSet(set=SolutionsSet(var=Var("p"), condition=And(IsPositive(arg=Var(name='p')), Exists(var=Var(name='q'), condition=And(Eq(left=Mul(Var(name='p'), Var(name='q')), right=Const(value=54)), Eq(left=GCD(a=Var(name='p'), b=Var(nam... | NT | COMB | COMPUTE | sympy | COPRIME_PAIRS | [
"COPRIME_PAIRS/MIN_PRIME_FACTOR",
"COUNT_SUM_EQUALS"
] | b5673b | comb_bell_compute_v1 | negation_mod | 6 | 0 | [
"COPRIME_PAIRS",
"COUNT_SUM_EQUALS",
"MIN_PRIME_FACTOR"
] | 3 | 0.016 | 2026-02-08T13:41:28.444482Z | {
"verified": true,
"answer": 65226,
"timestamp": "2026-02-08T13:41:28.460417Z"
} | 7ed318 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 271,
"completion_tokens": 2233
},
"timestamp": "2026-02-09T16:36:50.738Z",
"answer": 65226
},
{
"... | 1 | [
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "ok"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": ... | {
"lo": -1.95,
"mid": 2.14,
"hi": 6.33
} | ||
f2c3b1 | nt_num_divisors_compute_v1_2051736721_5297 | Let $n$ be the number of nonnegative integers $j$ such that $0 \leq j \leq 79860$ and $\binom{79860}{j}$ is odd. Let $d$ be the number of positive divisors of $n$. Compute the remainder when $|d|$ is divided by 60856. | 12 | graphs = [
Graph(
let={
"_n": Const(60856),
"n": CountOverSet(set=SolutionsSet(var=Var("j"), condition=And(Geq(Var("j"), Const(0)), Leq(Var("j"), Const(79860)), Eq(Mod(value=Binom(n=Const(79860), k=Var("j")), modulus=Const(2)), Const(1))), domain='nonnegative_integers')),
... | NT | null | COMPUTE | sympy | VIETA_SUM | [
"V8"
] | 86348e | nt_num_divisors_compute_v1 | null | 7 | 0 | [
"V8",
"VIETA_SUM"
] | 2 | 0.019 | 2026-02-08T18:28:39.954913Z | {
"verified": true,
"answer": 12,
"timestamp": "2026-02-08T18:28:39.973670Z"
} | f8f940 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 116,
"completion_tokens": 3206
},
"timestamp": "2026-02-18T17:21:39.854Z",
"answer": 12
},
{
... | 1 | [
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "V1",
"status": "no"
},
{
"lemma": "V3",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
},
{
"lemma": "V8",
"status": "ok"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
5349ea | nt_count_divisible_v1_784195855_8319 | Let $d$ be the smallest divisor of $143$ that is greater than or equal to $2$. Compute the number of positive integers $n$ such that $n \leq 37249$ and $n$ is divisible by $d$. | 3,386 | graphs = [
Graph(
let={
"_n": Const(143),
"upper": Const(37249),
"divisor": MinOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Const(2)), Divides(divisor=Var("d"), dividend=Ref("_n"))))),
"result": CountOverSet(set=SolutionsSet(var=Var("n"),... | NT | null | COUNT | sympy | MIN_PRIME_FACTOR | [
"MIN_PRIME_FACTOR"
] | bc3776 | nt_count_divisible_v1 | null | 2 | 0 | [
"MIN_PRIME_FACTOR"
] | 1 | 1.316 | 2026-02-08T16:00:42.508254Z | {
"verified": true,
"answer": 3386,
"timestamp": "2026-02-08T16:00:43.824746Z"
} | cd032b | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 114,
"completion_tokens": 276
},
"timestamp": "2026-02-16T06:51:03.754Z",
"answer": 3386
},
{
"id": 11,
... | 2 | [
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "MIN_PRIME_FACTOR",
"status": "ok"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "V5",
"sta... | {
"lo": -10,
"mid": -7.27,
"hi": -4.54
} | ||
c47f3e | nt_gcd_compute_v1_1978505735_2631 | Let $d = \gcd(458416, 859530)$. Let $p$ be the largest prime number at most $5006$. Compute the value of $d \bmod 293 + p \cdot (d \bmod 337)$. | 60,203 | graphs = [
Graph(
let={
"_n": Const(293),
"a": Const(458416),
"b": Const(859530),
"result": GCD(a=Ref("a"), b=Ref("b")),
"_c": MaxOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(2)), Leq(Var("n"), Const(5006)), IsPrime(Var(... | NT | null | COMPUTE | sympy | MAX_PRIME_BELOW | [
"MAX_PRIME_BELOW"
] | 08a653 | nt_gcd_compute_v1 | two_moduli | 3 | 0 | [
"MAX_PRIME_BELOW"
] | 1 | 0.003 | 2026-02-08T17:02:14.556112Z | {
"verified": true,
"answer": 60203,
"timestamp": "2026-02-08T17:02:14.558746Z"
} | b93623 | 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": 1559
},
"timestamp": "2026-02-17T18:34:22.484Z",
"answer": 60203
},
{... | 1 | [
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "V1",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
707519 | diophantine_product_count_v1_458359167_888 | Let $n = 3$. Define $S = \sum_{k=1}^{n} \varphi(k) \left\lfloor \frac{3}{k} \right\rfloor$, and let $T = \sum_{k=1}^{S} k$. Determine the number of positive integers $x$ such that $1 \leq x \leq T$, $x$ divides $240$, and $\frac{240}{x} \leq T$. Compute this number. | 4 | graphs = [
Graph(
let={
"_n": Const(3),
"k": Const(240),
"upper": Summation(var="k", start=Const(1), end=Summation(var="k", start=Const(1), end=Ref("_n"), expr=Mul(EulerPhi(n=Var("k")), Floor(Div(Const(3), Var("k"))))), expr=Var("k")),
"result": CountOverSet(s... | NT | null | COUNT | sympy | B3 | [
"K2/SUM_ARITHMETIC"
] | 5a4674 | diophantine_product_count_v1 | null | 4 | 0 | [
"B3",
"K2",
"SUM_ARITHMETIC"
] | 3 | 0.285 | 2026-02-08T04:09:01.113136Z | {
"verified": true,
"answer": 4,
"timestamp": "2026-02-08T04:09:01.398156Z"
} | 4da09b | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 215,
"completion_tokens": 1295
},
"timestamp": "2026-02-10T15:34:56.432Z",
"answer": 4
},
{
"id"... | 1 | [
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "K2",
"status": "ok"
},
{
"lemma": "SUM_ARITHMETIC",
"status": "ok_later"
},
{
"lemma... | {
"lo": -3.42,
"mid": 1.86,
"hi": 7.55
} | ||
73e596 | comb_count_permutations_fixed_v1_458359167_2959 | Let $k$ be the number of integers $t$ in the range $5 \leq t \leq 15$ for which there exist integers $a$ and $b$, each at least 1 and at most 3, such that $t = 3a + 2b$. Let $n = 11$. Compute $\binom{n}{k} \cdot !(n - k)$, where $!m$ denotes the number of derangements of $m$ elements. Then find the remainder when $8978... | 50,205 | graphs = [
Graph(
let={
"_n": Const(65170),
"n": Const(11),
"k": CountOverSet(set=SolutionsSet(var=Var("t"), condition=Exists(var=Var(name='a'), condition=Exists(var=Var(name='b'), condition=And(Geq(left=Var(name='a'), right=Const(value=1)), Leq(left=Var(name='a'), right=... | COMB | null | COUNT | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | comb_count_permutations_fixed_v1 | null | 5 | 0 | [
"LIN_FORM"
] | 1 | 0.002 | 2026-02-08T06:52:03.487843Z | {
"verified": true,
"answer": 50205,
"timestamp": "2026-02-08T06:52:03.489679Z"
} | 018c7b | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 241,
"completion_tokens": 2454
},
"timestamp": "2026-02-24T07:10:59.351Z",
"answer": 50205
},
{
"... | 1 | [
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8_SUM",
"st... | {
"lo": -2.46,
"mid": 0.47,
"hi": 3.59
} | ||
f8e0f2 | antilemma_sum_equals_v1_458359167_2257 | Let $d = 68$. Let $m$ be the number of ordered pairs $(i, j)$ of positive integers such that $1 \leq i \leq 66$, $1 \leq j \leq 67$, and $i + j = d$. Let $n$ be the number of ordered pairs $(i, j)$ of positive integers such that $1 \leq i \leq 64$, $1 \leq j \leq 65$, and $i + j = m$. Let $x$ be the number of ordered p... | 18,323 | graphs = [
Graph(
let={
"_d": Const(68),
"_m": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("i"), Var("j")]), condition=Eq(Sum(Var("i"), Var("j")), Ref("_d")), domain=CartesianProduct(left=IntegerRange(start=Const(1), end=Const(66)), right=IntegerRange(start=Const(1), end=Co... | COMB | GEOM | COMPUTE | sympy | LIN_FORM | [
"COUNT_SUM_EQUALS/COUNT_SUM_EQUALS",
"COUNT_SUM_EQUALS"
] | ae9919 | antilemma_sum_equals_v1 | null | 4 | 0 | [
"COUNT_SUM_EQUALS",
"LIN_FORM"
] | 2 | 0.032 | 2026-02-08T05:14:07.303567Z | {
"verified": true,
"answer": 18323,
"timestamp": "2026-02-08T05:14:07.335774Z"
} | 19b32d | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 295,
"completion_tokens": 830
},
"timestamp": "2026-02-24T03:02:16.303Z",
"answer": 18323
},
{
"i... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "ok"
},
{
"lemma": "V8",
"status": "no"
},
{
"lemma": "V8_SUM",
"status":... | {
"lo": -4.93,
"mid": -2.91,
"hi": -0.71
} | ||
a6bf6f | sequence_fibonacci_compute_v1_1978505735_1818 | Let $n = 20$. Define $S$ to be the set of all ordered pairs $(x, y)$ of positive integers such that $x + y$ equals the number of positive integers $n_1 \leq 696$ for which $9$ divides the $n_1$-th Fibonacci number. Let $P$ be the set of all values of $xy$ as $(x, y)$ ranges over $S$. Compute the remainder when
$$
\max... | 74,982 | graphs = [
Graph(
let={
"_m": Const(9),
"_n": Const(80906),
"n": Const(20),
"result": Fibonacci(arg=Ref(name='n')),
"Q": Mod(value=Sub(MaxOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg... | NT | null | COMPUTE | sympy | COUNT_FIB_DIVISIBLE | [
"COUNT_FIB_DIVISIBLE/B1"
] | e038e4 | sequence_fibonacci_compute_v1 | negation_mod | 6 | 0 | [
"B1",
"COUNT_FIB_DIVISIBLE"
] | 2 | 0.003 | 2026-02-08T16:24:29.159860Z | {
"verified": true,
"answer": 74982,
"timestamp": "2026-02-08T16:24:29.163271Z"
} | 603d39 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 174,
"completion_tokens": 1379
},
"timestamp": "2026-02-17T04:54:43.413Z",
"answer": 74982
},
... | 1 | [
{
"lemma": "B1",
"status": "ok_later"
},
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "ok"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
518c16 | comb_bell_compute_v1_1742523217_1215 | Let $ n = 9 $. Compute the Bell number $ B_n $, and let $ r $ be the remainder when $ B_n $ is divided by 11. Determine the value of $ B_r $. | 52 | graphs = [
Graph(
let={
"n": Const(9),
"result": Bell(Ref("n")),
"Q": Bell(Mod(value=Abs(arg=Ref(name='result')), modulus=Const(11))),
},
goal=Ref("Q"),
)
] | COMB | null | COMPUTE | sympy | K3 | [
"MIN_PRIME_FACTOR",
"COPRIME_PAIRS"
] | e00f22 | comb_bell_compute_v1 | bell_mod | 4 | 0 | [
"COPRIME_PAIRS",
"K3",
"MIN_PRIME_FACTOR"
] | 3 | 0.043 | 2026-02-08T03:32:07.097158Z | {
"verified": true,
"answer": 52,
"timestamp": "2026-02-08T03:32:07.139867Z"
} | ad3766 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 152,
"completion_tokens": 454
},
"timestamp": "2026-02-10T05:09:31.734Z",
"answer": 52
},
{
"id":... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "MIN_PRIME_FACTOR",
"status": "ok"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
}... | {
"lo": -3.83,
"mid": -1.68,
"hi": 1.09
} | ||
9b7490 | antilemma_sum_equals_v1_1742523217_2360 | Let $m = 2$. Define $n$ to be the number of integers $t$ such that $5 \leq t \leq 21$ and there exist positive integers $a$ and $b$ with $1 \leq a \leq 6$, $1 \leq b \leq 3$, and $t = 2a + 3b$. Let $x$ be the number of ordered pairs $(i, j)$ of positive integers such that $1 \leq i \leq 15$, $1 \leq j \leq 15$, and $i ... | 20 | graphs = [
Graph(
let={
"_m": Const(2),
"_n": CountOverSet(set=SolutionsSet(var=Var("t"), condition=Exists(var=Var(name='a'), condition=Exists(var=Var(name='b'), condition=And(Geq(left=Var(name='a'), right=Const(value=1)), Leq(left=Var(name='a'), right=Const(value=6)), Geq(left=Var(n... | COMB | GEOM | COMPUTE | sympy | COMB1 | [
"COMB1",
"LIN_FORM/COUNT_SUM_EQUALS",
"COUNT_SUM_EQUALS",
"ONE_FACTORIAL_0"
] | 2acf76 | antilemma_sum_equals_v1 | digits_weighted_mod | 6 | 0 | [
"COMB1",
"COUNT_SUM_EQUALS",
"LIN_FORM",
"ONE_FACTORIAL_0"
] | 4 | 0.019 | 2026-02-08T04:43:04.206309Z | {
"verified": true,
"answer": 20,
"timestamp": "2026-02-08T04:43:04.225290Z"
} | 296bd0 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 335,
"completion_tokens": 2292
},
"timestamp": "2026-02-11T21:54:15.490Z",
"answer": 20
},
{
"id"... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COMB1",
"status": "ok"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "ok"
},
{
"lemma": "LIN_FORM",
"sta... | {
"lo": -2.46,
"mid": 0.47,
"hi": 3.59
} | ||
5eebbc | nt_count_divisible_and_v1_655260480_2428 | Let $ m = 2 $ and let $ n $ be the number of prime numbers between $ m $ and $ 97 $, inclusive. Let $ S $ be the set of all ordered pairs $ (x, y) $ of positive integers such that $ xy = n $. Let $ d_1 $ be the minimum value of $ x + y $ as $ (x, y) $ ranges over $ S $, and let $ d_2 = 15 $. Determine the number of pos... | 3,352 | graphs = [
Graph(
let={
"_m": Const(2),
"_n": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Ref("_m")), Leq(Var("n"), Const(97)), IsPrime(Var("n"))))),
"upper": Const(100560),
"d1": MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple... | NT | null | COUNT | sympy | COUNT_PRIMES | [
"COUNT_PRIMES/B3"
] | 3caaca | nt_count_divisible_and_v1 | null | 6 | 0 | [
"B3",
"COUNT_PRIMES"
] | 2 | 5.078 | 2026-02-08T16:43:34.956091Z | {
"verified": true,
"answer": 3352,
"timestamp": "2026-02-08T16:43:40.034164Z"
} | ce6a13 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 188,
"completion_tokens": 731
},
"timestamp": "2026-02-17T11:18:34.658Z",
"answer": 3352
},
{
... | 1 | [
{
"lemma": "B3",
"status": "ok_later"
},
{
"lemma": "COUNT_PRIMES",
"status": "ok"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
8919b7_n | algebra_poly_eval_v1_1218484723_7430 | A cryptography lab studies a three-stage encryption process on integers $a$ between $0$ and $78$ inclusive. First, $a$ is cubed and reduced modulo $79$. Second, the result is cubed again and reduced modulo $79$. Third, that result is cubed once more and reduced modulo $M$, where $M$ is the smallest positive integer tha... | 3,854 | ALG | null | COMPUTE | sympy | MIN_PRIME_FACTOR | [
"MIN_PRIME_FACTOR/POLY_ORBIT_COUNT"
] | 0f1936 | algebra_poly_eval_v1 | null | 7 | null | [
"MIN_PRIME_FACTOR",
"POLY_ORBIT_COUNT"
] | 2 | 0.005 | 2026-02-25T08:52:26.664275Z | null | 2b9c88 | 8919b7 | narrative | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 307,
"completion_tokens": 32768
},
"timestamp": "2026-03-31T02:25:50.761Z",
"answer": null
},
{
... | 1 | [
{
"lemma": "MIN_PRIME_FACTOR",
"status": "ok"
},
{
"lemma": "POLY_ORBIT_COUNT",
"status": "ok_later"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
}
] | {
"lo": 3.8,
"mid": 6.33,
"hi": 9.49
} | |
b0e6be | modular_sum_quadratic_residues_v1_1125832087_189 | Let $n = 661$. Define $p = \sum_{d \mid n} \phi(d)$, where $\phi$ denotes Euler's totient function. Let $r = \frac{p(p-1)}{4}$. Compute the remainder when $44121 \cdot r$ is divided by $53920$. | 20,385 | graphs = [
Graph(
let={
"_n": Const(661),
"p": SumOverDivisors(n=Ref(name='_n'), var='d', expr=EulerPhi(n=Var(name='d'))),
"result": Div(Mul(Ref("p"), Sub(Ref("p"), Const(1))), Const(4)),
"Q": Mod(value=Mul(Const(44121), Ref("result")), modulus=Const(53920)),
... | NT | null | SUM | sympy | K3 | [
"K3"
] | 54c41e | modular_sum_quadratic_residues_v1 | null | 5 | 0 | [
"K3"
] | 1 | 0.002 | 2026-02-08T02:55:40.099782Z | {
"verified": true,
"answer": 20385,
"timestamp": "2026-02-08T02:55:40.101689Z"
} | 46e959 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 180,
"completion_tokens": 1457
},
"timestamp": "2026-02-10T12:49:24.867Z",
"answer": 20385
},
{
"... | 1 | [
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "K3",
"status": "ok"
},
{
"lemma": "V7",
"status": "no"
}
] | {
"lo": -0.04,
"mid": 1.69,
"hi": 3.25
} | ||
163bef | diophantine_product_count_v1_1470522791_1894 | Let $k = 420$. Let $S$ be the set of all ordered pairs $(x, y)$ of positive integers such that $xy = 13456$. Let $u$ be the minimum value of $x + y$ as $(x, y)$ ranges over $S$. Define $T$ to be the set of all positive integers $x$ such that $1 \leq x \leq u$, $x$ divides $k$, and $\frac{k}{x} \leq u$. Let $r$ be the n... | 44,088 | graphs = [
Graph(
let={
"k": Const(420),
"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(13456)))), expr=Sum(Var("x"), Var("y"))... | NT | null | COUNT | sympy | B3 | [
"B3"
] | 0cd20d | diophantine_product_count_v1 | null | 5 | 0 | [
"B3"
] | 1 | 0.013 | 2026-02-08T14:04:54.262060Z | {
"verified": true,
"answer": 44088,
"timestamp": "2026-02-08T14:04:54.274716Z"
} | aea2f9 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 191,
"completion_tokens": 1835
},
"timestamp": "2026-02-15T23:49:19.542Z",
"answer": 44088
},
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "V1",
"status": "no"
},
{
"lemma": "VAL_SUM_EQ",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
eef587 | antilemma_k2_v1_655260480_81 | Let $n = 50$. Compute the remainder when $44121$ times the sum $\sum_{k=1}^{50} \phi(k) \left\lfloor \frac{n}{k} \right\rfloor$ is divided by 87151, where $\phi(k)$ denotes Euler's totient function. | 41,880 | graphs = [
Graph(
let={
"_n": Const(50),
"x": Summation(var="k", start=Const(1), end=Const(50), expr=Mul(EulerPhi(n=Var("k")), Floor(Div(Ref("_n"), Var("k"))))),
"Q": Mod(value=Mul(Const(44121), Ref("x")), modulus=Const(87151)),
},
goal=Ref("Q"),
)
] | NT | COMB | COMPUTE | sympy | K2 | [
"K2"
] | 6897ab | antilemma_k2_v1 | null | 4 | 0 | [
"K2"
] | 1 | 0.001 | 2026-02-08T15:10:17.757265Z | {
"verified": true,
"answer": 41880,
"timestamp": "2026-02-08T15:10:17.758156Z"
} | 8051b4 | 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": 939
},
"timestamp": "2026-02-16T00:27:58.208Z",
"answer": 41880
},
{... | 1 | [
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "K2",
"status": "ok"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
bdd92c | antilemma_k3_v1_151522320_2554 | Let $x$ be the sum of $\phi(d)$ over all positive divisors $d$ of $47385$, where $\phi$ denotes Euler's totient function. Compute $75625 - x$. | 28,240 | graphs = [
Graph(
let={
"x": SumOverDivisors(n=Const(value=47385), var='d', expr=EulerPhi(n=Var(name='d'))),
"Q": Sub(Const(75625), Ref("x")),
},
goal=Ref("Q"),
)
] | NT | COMB | COMPUTE | sympy | K3 | [
"K3"
] | 54c41e | antilemma_k3_v1 | null | 3 | 0 | [
"K3"
] | 1 | 0.001 | 2026-02-08T04:52:43.734898Z | {
"verified": true,
"answer": 28240,
"timestamp": "2026-02-08T04:52:43.735439Z"
} | b29d68 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 153,
"completion_tokens": 283
},
"timestamp": "2026-02-11T22:21:38.425Z",
"answer": 28240
},
{
"... | 1 | [
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "K3",
"status": "ok"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "V3",
"status": "no"
}
] | {
"lo": -3.42,
"mid": 1.86,
"hi": 7.55
} | ||
3654bc | alg_linear_system_2x2_v1_1218484723_7703 | Let $\det = 14$, $N = 1051491 - 217 \cdot (-3)$, $M = 14 \cdot 217$, and $R = \frac{N}{\det} + \frac{M}{\det}$. Compute $|R|$. | 75,370 | graphs = [
Graph(
let={
"num_x": Sub(Const(1051491), Mul(Const(217), Const(-3))),
"num_y": Mul(Const(14), Const(217)),
"det": Const(14),
"result": Sum(Div(Ref("num_x"), Ref("det")), Div(Ref("num_y"), Ref("det"))),
"Q": Abs(arg=Ref(name='result')),
... | ALG | null | COMPUTE | sympy | POLY_ORBIT_COUNT | [
"POLY_ORBIT_COUNT/QF_PSD_MIN"
] | e0f30b | alg_linear_system_2x2_v1 | null | 2 | 0 | [
"POLY_ORBIT_COUNT",
"QF_PSD_MIN"
] | 2 | 0.1 | 2026-02-25T09:10:44.170946Z | {
"verified": true,
"answer": 75370,
"timestamp": "2026-02-25T09:10:44.270731Z"
} | 719ea5 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 173,
"completion_tokens": 737
},
"timestamp": "2026-03-30T06:00:54.266Z",
"answer": 75370
},
{
"i... | 1 | [
{
"lemma": "POLY_ORBIT_COUNT",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "QF_PSD_MIN",
"status": "ok_later"
}
] | {
"lo": -6.2,
"mid": -2.87,
"hi": 0.44
} | ||
81e6dc | alg_poly_preperiod_count_v1_601307018_9000 | Let $N \equiv a^2 - 6 \pmod{89}$, $M \equiv N^2 - 6 \pmod{89}$, $R \equiv M^2 - 6 \pmod{89}$, $S \equiv R^2 - 6 \pmod{89}$, and $T \equiv S^2 - 6 \pmod{89}$. Find the number of non-negative integers $a$ with $0 \le a \le 165361$ such that $T = M$, $R \ne M$, and $S \ne M$. | 14,864 | graphs = [
Graph(
let={
"p1": Mod(value=Sum(Pow(Var("a"), Const(2)), Const(-6)), modulus=Const(89)),
"p2": Mod(value=Sum(Pow(Ref("p1"), Const(2)), Const(-6)), modulus=Const(89)),
"p3": Mod(value=Sum(Pow(Ref("p2"), Const(2)), Const(-6)), modulus=Const(89)),
"p4... | ALG | null | COUNT | sympy | POLY_ORBIT_COUNT | [
"POLY_ORBIT_COUNT"
] | 4ad965 | alg_poly_preperiod_count_v1 | null | 6 | null | [
"POLY_ORBIT_COUNT"
] | 1 | 0.031 | 2026-03-10T09:25:51.010354Z | {
"verified": true,
"answer": 14864,
"timestamp": "2026-03-10T09:25:51.041065Z"
} | 20cf4c | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 244,
"completion_tokens": 20163
},
"timestamp": "2026-04-19T10:24:20.031Z",
"answer": 14864
},
{
... | 1 | [
{
"lemma": "POLY_ORBIT_COUNT",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
}
] | {
"lo": -5.34,
"mid": 1.1,
"hi": 7.53
} | ||
51e7e6 | lin_form_endings_v1_1918700295_4415 | Let $a = 21$ and $b = 6$. Let $A = 41$ and $B = 42$. Let $g = \gcd(a, b)$. Define $N = (aA + bB) - (a + b)$. Let $k = 11103$ and $M = 52207$. Compute the remainder when $k \left( \left\lfloor \frac{N}{g} \right\rfloor + 1 \right)$ is divided by $M$. | 10,450 | graphs = [
Graph(
let={
"a_coeff": Const(21),
"b_coeff": Const(6),
"A_val": Const(41),
"B_val": Const(42),
"g_step": GCD(a=Ref("a_coeff"), b=Ref("b_coeff")),
"numerator": Sub(Sum(Mul(Ref("a_coeff"), Ref("A_val")), Mul(Ref("b_coeff"), Re... | COMB | NT | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | lin_form_endings_v1 | null | 3 | null | [
"LIN_FORM"
] | 1 | 0.001 | 2026-02-08T09:21:50.102642Z | {
"verified": true,
"answer": 10450,
"timestamp": "2026-02-08T09:21:50.103262Z"
} | e72880 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 153,
"completion_tokens": 915
},
"timestamp": "2026-02-14T03:19:04.236Z",
"answer": 10450
},
{... | 1 | [
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
... | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
866b59 | algebra_poly_eval_v1_349078426_210 | Let $m = 3$ and $n = 4$. Let $k = 6$. Define
$$
\ell = 8k^n - 10k^3 + \left( \sum_{k=1}^{\sum_{k=1}^{2} \phi(k) \left\lfloor \frac{2}{k} \right\rfloor} \phi(k) \left\lfloor \frac{m}{k} \right\rfloor \right) k^2 - k - 10.
$$
Compute the sum of the number of positive divisors of all positive integers from $1$ to $|\ell|$... | 77,289 | graphs = [
Graph(
let={
"_m": Const(3),
"_n": Const(4),
"k": Const(6),
"result": Sum(Mul(Const(8), Pow(Ref("k"), Ref("_n"))), Mul(Const(-10), Pow(Ref("k"), Const(3))), Mul(Summation(var="k", start=Const(1), end=Summation(var="k", start=Const(1), end=Const(2), ... | NT | null | COMPUTE | sympy | K2 | [
"K2/K2"
] | ddede2 | algebra_poly_eval_v1 | null | 6 | 0 | [
"K2"
] | 1 | 0.004 | 2026-02-08T12:52:39.909703Z | {
"verified": true,
"answer": 77289,
"timestamp": "2026-02-08T12:52:39.913493Z"
} | b262b2 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 177,
"completion_tokens": 6028
},
"timestamp": "2026-02-15T07:14:32.663Z",
"answer": 77289
},
... | 1 | [
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "K2",
"status": "ok"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
... | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
f9895a | alg_poly_preperiod_count_v1_601307018_5573 | For a non-negative integer $a$, define a sequence by $N = (a^2 - 22) \bmod 97$, $M = (N^2 - 22) \bmod 97$, $R = (M^2 - 22) \bmod 97$, and $S = (R^2 - 22) \bmod 97$. Find the number of integers $a$ with $0 \le a \le 88657$ such that $S = M$ and $R \ne M$. | 4,570 | graphs = [
Graph(
let={
"p1": Mod(value=Sum(Pow(Var("a"), Const(2)), Const(-22)), modulus=Const(97)),
"p2": Mod(value=Sum(Pow(Ref("p1"), Const(2)), Const(-22)), modulus=Const(97)),
"p3": Mod(value=Sum(Pow(Ref("p2"), Const(2)), Const(-22)), modulus=Const(97)),
... | ALG | null | COUNT | sympy | POLY_ORBIT_COUNT | [
"POLY_ORBIT_COUNT"
] | 4ad965 | alg_poly_preperiod_count_v1 | null | 6 | null | [
"POLY_ORBIT_COUNT"
] | 1 | 0.027 | 2026-03-10T06:08:56.747101Z | {
"verified": true,
"answer": 4570,
"timestamp": "2026-03-10T06:08:56.774531Z"
} | c35db6 | 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": 6508
},
"timestamp": "2026-04-19T02:24:50.675Z",
"answer": 4570
},
{
"... | 1 | [
{
"lemma": "POLY_ORBIT_COUNT",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
}
] | {
"lo": -3.31,
"mid": 1.32,
"hi": 5.87
} | ||
e1b275 | alg_qf_psd_sum_v1_1218484723_7600 | Let $M$ be the number of ordered pairs $(a, b)$ of positive integers with $1 \le a \le b \le 30$ such that
\[
32b^{2} + 32a^{2} - 64ab = 9248.
\]
Compute the remainder when
\[
\sum_{\substack{1 \le a_1 \le 187\\1 \le b_1 \le 187}} \Bigl(M b_1^{2} + 10a_1 b_1 + \left|\{(a_2,b_2) : 1 \le a_2 \le 35,\ 1 \le b_2 \le 35,\\ ... | 7,684 | graphs = [
Graph(
let={
"_c": Const(32),
"_m": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("a"), Var("b")]), condition=And(Geq(Var("a"), Const(1)), Leq(Var("a"), Const(30)), Geq(Var("b"), Const(1)), Leq(Var("b"), Const(30)), Leq(Var("a"), Var("b")), Eq(Sum(Mul(Const(32), Po... | ALG | null | COMPUTE | sympy | B3 | [
"B3/QF_PSD_COUNT",
"QF_PSD_ORBIT/B3"
] | 410b59 | alg_qf_psd_sum_v1 | null | 8 | 0 | [
"B3",
"QF_PSD_COUNT",
"QF_PSD_ORBIT"
] | 3 | 0.078 | 2026-02-25T09:02:00.149569Z | {
"verified": true,
"answer": 7684,
"timestamp": "2026-02-25T09:02:00.227402Z"
} | 696048 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 337,
"completion_tokens": 5448
},
"timestamp": "2026-03-30T05:27:11.323Z",
"answer": 7684
},
{
"i... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "QF_PSD_COUNT",
"status": "ok_later"
},
{
"lemma": "QF_PSD_ORBIT",
"status": "ok"
}
] | {
"lo": -3.33,
"mid": 1.03,
"hi": 5.26
} | ||
23fff7 | nt_max_prime_below_v1_717093673_632 | Let $m = 2$. Let $d_0$ be the smallest integer $d$ such that $d \geq m$ and $d$ divides 143. Let $N$ be the largest prime number less than or equal to 57600. Let $p_{\text{max}}$ be the largest prime number less than or equal to $d_0$. Compute the Bell number $B_r$, where $r$ is the remainder when $N$ is divided by $p_... | 4,140 | graphs = [
Graph(
let={
"_m": Const(2),
"_n": MinOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Ref("_m")), Divides(divisor=Var("d"), dividend=Const(143))))),
"upper": Const(57600),
"result": MaxOverSet(set=SolutionsSet(var=Var("n"), condit... | NT | COMB | EXTREMUM | sympy | MIN_PRIME_FACTOR | [
"MIN_PRIME_FACTOR/MAX_PRIME_BELOW"
] | 8ad15a | nt_max_prime_below_v1 | bell_mod | 6 | 0 | [
"MAX_PRIME_BELOW",
"MIN_PRIME_FACTOR"
] | 2 | 3.404 | 2026-02-08T15:34:43.462480Z | {
"verified": true,
"answer": 4140,
"timestamp": "2026-02-08T15:34:46.866015Z"
} | da94c4 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 154,
"completion_tokens": 2258
},
"timestamp": "2026-02-16T08:29:27.638Z",
"answer": 4140
},
{... | 1 | [
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok_later"
},
{
"lemma": "MIN_PRIME_FACTOR",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "V5",... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
999037 | nt_sum_gcd_range_mod_v1_1874849503_1229 | Let $S$ be the set of all ordered pairs $(x, y)$ of positive integers such that $x + y = 178$. Let $N$ be the maximum value of $xy$ over all pairs $(x, y) \in S$. Let $k = 360$ and $M = 11329$. Compute the remainder when $\sum_{n=1}^{N} \gcd(n, k)$ is divided by $M$. | 3,858 | graphs = [
Graph(
let={
"N": MaxOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(Sum(Var("x"), Var("y")), Const(178)))), expr=Mul(Var("x"), Var("y")))),
"k": Const(360),
... | NT | null | COMPUTE | sympy | C3 | [
"B1"
] | 5b950e | nt_sum_gcd_range_mod_v1 | null | 5 | 0 | [
"B1",
"C3"
] | 2 | 0.842 | 2026-02-08T13:43:13.984805Z | {
"verified": true,
"answer": 3858,
"timestamp": "2026-02-08T13:43:14.827146Z"
} | 588d67 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 204,
"completion_tokens": 4309
},
"timestamp": "2026-02-11T07:57:16.404Z",
"answer": 3858
},
{
"... | 1 | [
{
"lemma": "B1",
"status": "ok"
},
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
}
] | {
"lo": -5.48,
"mid": 0.74,
"hi": 7.52
} | ||
79ccc7 | modular_inverse_v1_971394319_1362 | Let $n = 5849$. Define $a$ to be the number of prime numbers $p$ such that $2 \leq p \leq n$. Let $m = 823$. Find the smallest positive integer $x$ such that $1 \leq x \leq 822$ and $$a \cdot x \equiv 1 \pmod{m}.$$ Determine the value of $x$. | 404 | graphs = [
Graph(
let={
"_n": Const(5849),
"a": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(2)), Leq(Var("n"), Ref("_n")), IsPrime(Var("n"))))),
"m": Const(823),
"upper": Const(822),
"result": MinOverSet(set=Soluti... | NT | null | EXTREMUM | sympy | COUNT_PRIMES | [
"COUNT_PRIMES"
] | 07c874 | modular_inverse_v1 | null | 4 | 0 | [
"COUNT_PRIMES"
] | 1 | 0.096 | 2026-02-08T13:39:29.947066Z | {
"verified": true,
"answer": 404,
"timestamp": "2026-02-08T13:39:30.042649Z"
} | df8fda | 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": 3404
},
"timestamp": "2026-02-15T18:55:13.915Z",
"answer": 404
},
{
... | 1 | [
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_PRIMES",
"status": "ok"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
}... | {
"lo": -5.49,
"mid": 0.22,
"hi": 6.51
} | ||
181993 | sequence_count_fib_divisible_v1_1978505735_979 | Let $n$ be a positive integer such that $1 \leq n \leq 2573$ and $\gcd(n, 30) = 1$. Let $N$ be the number of such integers $n$. Determine the number of positive integers $n_1$ with $1 \leq n_1 \leq N$ for which the Fibonacci number $F_{n_1}$ is divisible by 20. Compute this number. | 22 | graphs = [
Graph(
let={
"_n": Const(30),
"upper": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Const(2573)), Eq(GCD(a=Var("n"), b=Ref("_n")), Const(1))))),
"d": Const(20),
"result": CountOverSet(set=Solutions... | NT | null | COUNT | sympy | C4 | [
"C4"
] | 08d162 | sequence_count_fib_divisible_v1 | null | 6 | 0 | [
"C4"
] | 1 | 0.031 | 2026-02-08T15:43:30.336089Z | {
"verified": true,
"answer": 22,
"timestamp": "2026-02-08T15:43:30.367067Z"
} | 38c86b | 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": 2054
},
"timestamp": "2026-02-16T12:58:28.686Z",
"answer": 22
},
{
... | 1 | [
{
"lemma": "C4",
"status": "ok"
},
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
bcdaaf | modular_min_linear_v1_124444284_8729 | Let $n = 13$ and $a = 265$. Let $b$ be the number of positive integers $n$ with $1 \leq n \leq 28266$ such that the $n$-th Fibonacci number is divisible by $13$. Let $m = 34013$. Determine the value of the smallest positive integer $x$ such that $1 \leq x \leq m$ and $265x \equiv b \pmod{34013}$. | 15,289 | graphs = [
Graph(
let={
"_n": Const(13),
"a": Const(265),
"b": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Const(28266)), Divides(divisor=Ref("_n"), dividend=Fibonacci(arg=Var(name='n')))))),
"m": Const(3401... | NT | null | EXTREMUM | sympy | COPRIME_PAIRS | [
"COUNT_FIB_DIVISIBLE"
] | 66de3c | modular_min_linear_v1 | null | 7 | 0 | [
"COPRIME_PAIRS",
"COUNT_FIB_DIVISIBLE"
] | 2 | 2.882 | 2026-02-08T11:52:54.248669Z | {
"verified": true,
"answer": 15289,
"timestamp": "2026-02-08T11:52:57.130638Z"
} | 503370 | 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": 2827
},
"timestamp": "2026-02-14T20:15:02.727Z",
"answer": 15289
},
... | 1 | [
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "ok"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "VAL_SUM_EQ",
"status": "no"
}
] | {
"lo": -5.49,
"mid": 0.22,
"hi": 6.51
} | ||
353cef_l | nt_count_phi_equals_v1_1125832087_265 | Let $m = 77284$ and $n = 75051$. Let $u$ be the sum of all real solutions $x$ to the equation $x^2 - 2000x + 160944 = 0$. Let $k$ be the minimum value of $x + y$ over all pairs of positive integers $(x, y)$ such that $xy = m$. Let $r$ be the number of positive integers $\nu$ such that $1 \leq \nu \leq u$ and $\phi(\nu)... | 0 | NT | null | COUNT | sympy | K14 | [
"VIETA_SUM",
"B3"
] | 018050 | nt_count_phi_equals_v1 | null | 7 | 0 | [
"B3",
"K14",
"VIETA_SUM"
] | 3 | 1.536 | 2026-02-08T02:59:33.621176Z | {
"verified": false,
"answer": 72440,
"timestamp": "2026-02-08T02:59:35.156870Z"
} | 050807 | 353cef | legacy_text | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 257,
"completion_tokens": 7767
},
"timestamp": "2026-02-10T12:23:52.839Z",
"answer": 72340
},
{
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
},
{
"lemma": "VIETA_SUM",
... | {
"lo": 1.14,
"mid": 3.16,
"hi": 4.94
} | |
a773e6_n | alg_sym_quad_system_v1_1218484723_4510 | An architect is designing triangular roof trusses. Each truss is described by three positive integer lengths $(a, b, c)$ that must satisfy the structural balance condition
$$a^{2} + b^{2} + c^{2} = ab + bc + ca.$$
Additionally, the weighted sum of the lengths must equal the minimal possible perimeter of a rectangular s... | 5,466 | ALG | null | COMPUTE | sympy | B3 | [
"B3",
"C4"
] | 8d18b3 | alg_sym_quad_system_v1 | null | 7 | null | [
"B3",
"C4"
] | 2 | 0.019 | 2026-02-25T06:11:07.074829Z | null | e752e4 | a773e6 | narrative | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 324,
"completion_tokens": 5185
},
"timestamp": "2026-03-30T21:46:31.401Z",
"answer": 2865
},
{
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "C4",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
}
] | {
"lo": 1.5,
"mid": 4.69,
"hi": 7.23
} | |
9117b6 | lin_form_endings_v1_458359167_2525 | Let $S$ be the set of all integers $t$ such that $60 \leq t \leq 2100$ and there exist positive integers $a \leq 14$ and $b \leq 44$ for which $t = 18a + 42b$. Let $k = 17809$ and let $M = 77073$. Compute the remainder when $k$ times the number of elements in $S$ is divided by $M$. | 1,613 | graphs = [
Graph(
let={
"_inner_result": CountOverSet(set=SolutionsSet(var=Var("t"), condition=Exists(var=Var(name='a'), condition=Exists(var=Var(name='b'), condition=And(Geq(left=Var(name='a'), right=Const(value=1)), Leq(left=Var(name='a'), right=Const(value=14)), Geq(left=Var(name='b'), right=... | COMB | null | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | lin_form_endings_v1 | null | 3 | null | [
"LIN_FORM"
] | 1 | 0.002 | 2026-02-08T06:18:42.685955Z | {
"verified": true,
"answer": 1613,
"timestamp": "2026-02-08T06:18:42.688390Z"
} | 8972a1 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 212,
"completion_tokens": 32768
},
"timestamp": "2026-02-24T05:59:56.521Z",
"answer": null
},
{
... | 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": "no"
},
{
"lemma": "LIN_F... | {
"lo": 3.43,
"mid": 5.73,
"hi": 8.84
} | ||
e8a0c6 | sequence_fibonacci_compute_v1_349078426_468 | Let $n$ be the number of integers $t$ with $24 \leq t \leq 114$ for which there exist positive integers $a \leq 4$ and $b \leq 6$ such that
$$
t = 15a + 9b.
$$
Compute the $n$-th Fibonacci number, where the Fibonacci sequence is defined by $F_1 = 1$, $F_2 = 1$, and $F_k = F_{k-1} + F_{k-2}$ for $k \geq 3$. | 28,657 | 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... | NT | null | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | sequence_fibonacci_compute_v1 | null | 3 | 0 | [
"LIN_FORM"
] | 1 | 0.002 | 2026-02-08T13:05:40.258553Z | {
"verified": true,
"answer": 28657,
"timestamp": "2026-02-08T13:05:40.260420Z"
} | 37bf75 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 164,
"completion_tokens": 2183
},
"timestamp": "2026-02-15T09:24:10.852Z",
"answer": 28657
},
... | 1 | [
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "V3",
"status": "no"
},
{
"lemma": "VAL_SUM_EQ"... | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
bf7e94 | nt_min_phi_inverse_v1_153355830_1985 | Let $n = 14$. Let $T$ be the set of all integers $t$ such that $8 \leq t \leq 240$ and $t = 3a + 5b$ for some positive integers $a \leq 20$ and $b \leq 36$. Let $U$ be the number of positive integers $n'$ not exceeding $|T|$ such that $5$ divides $n'$ and $\gcd(n', n) = 1$. Let $k = 6$. Determine the value of the small... | 7 | graphs = [
Graph(
let={
"_n": Const(14),
"upper": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), CountOverSet(set=SolutionsSet(var=Var("t"), condition=Exists(var=Var(name='a'), condition=Exists(var=Var(name='b'), condition=And(Geq(lef... | NT | null | EXTREMUM | sympy | LIN_FORM | [
"LIN_FORM/C5"
] | 683493 | nt_min_phi_inverse_v1 | null | 6 | 0 | [
"C5",
"LIN_FORM"
] | 2 | 0.006 | 2026-02-08T06:50:42.068341Z | {
"verified": true,
"answer": 7,
"timestamp": "2026-02-08T06:50:42.074149Z"
} | a5c251 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 189,
"completion_tokens": 3877
},
"timestamp": "2026-02-13T05:18:25.560Z",
"answer": 7
},
{
... | 1 | [
{
"lemma": "C5",
"status": "ok_later"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
... | {
"lo": -5.55,
"mid": -3.01,
"hi": 0.32
} | ||
e9a267 | nt_lcm_compute_v1_48377204_901 | Let $a$ be the minimum value of $x + y$ over all pairs of positive integers $(x, y)$ such that $xy = 1256641$. Let $b = 619$. Let $\text{result}$ be the least common multiple of $a$ and $b$. Let $Q$ be the remainder when $\text{result} + 2^{\text{result} \bmod 14} \bmod 68786$ is divided by $68786$. Find the value of $... | 12,142 | graphs = [
Graph(
let={
"_n": Const(68786),
"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(1256641)))), expr=Sum(Var("x"), Var("y")... | NT | null | COMPUTE | sympy | B3 | [
"B3"
] | 0cd20d | nt_lcm_compute_v1 | null | 5 | 0 | [
"B3"
] | 1 | 0.003 | 2026-02-08T15:45:17.391791Z | {
"verified": true,
"answer": 12142,
"timestamp": "2026-02-08T15:45:17.394742Z"
} | 4712af | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 156,
"completion_tokens": 2102
},
"timestamp": "2026-02-16T13:23:25.378Z",
"answer": 12142
},
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "V5",
"status": "n... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
40a2b6 | nt_sum_gcd_range_mod_v1_151522320_1 | Let $p_1 = 53$ and $q_1 = 3$. Define $n_1 = p_1^2 (q_1 + 1)$. Let $f = \mu(n_1)^2$, where $\mu$ is the M\"obius function. Similarly, let $p = 43$ and $q = 53$, define $n = p^2 (q + 1)$, and let $u = \mu(n)^2$. Let $k = 336 + f + u$ and $N = 9801$. Define
$$
\text{sum} = \sum_{n=1}^{N} \gcd(n, k).
$$
Let $M = 11087$. Co... | 2,209 | graphs = [
Graph(
let={
"p1": Const(53),
"q1": Const(3),
"n1": Mul(Pow(Ref("p1"), Const(2)), Sum(Ref("q1"), Const(1))),
"f": Pow(MoebiusMu(n=Ref(name='n1')), Const(2)),
"p": Const(43),
"q": Const(53),
"n": Mul(Pow(Ref("p"), ... | NT | null | COMPUTE | sympy | MOBIUS_SQUAREFREE | [
"MOBIUS_SQUAREFREE"
] | 6fcd31 | nt_sum_gcd_range_mod_v1 | null | 5 | 2 | [
"MOBIUS_SQUAREFREE"
] | 1 | 0.857 | 2026-02-08T02:55:04.378826Z | {
"verified": true,
"answer": 2209,
"timestamp": "2026-02-08T02:55:05.235609Z"
} | 93cccb | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 1,
"correct": {
"strict": false,
"boxed": false,
"relaxed": true
},
"usage": {
"prompt_tokens": 287,
"completion_tokens": 5045
},
"timestamp": "2026-02-08T19:57:37.559Z",
"answer": 209
},
{
"... | 1 | [
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "MOBIUS_SQUAREFREE",
"status": "ok"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "V1",
"status": "no... | {
"lo": 1.69,
"mid": 5.03,
"hi": 8.38
} | ||
74dbb8 | comb_count_permutations_fixed_v1_1470522791_1641 | Let $n$ be the largest prime number satisfying $2 \leq n \leq 11$, and let $k = 6$. Compute the value of $\binom{n}{k} \cdot !(n - k)$, where $!m$ denotes the number of derangements of $m$ elements. | 20,328 | graphs = [
Graph(
let={
"n": MaxOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(2)), Leq(Var("n"), Const(11)), IsPrime(Var("n"))))),
"k": Const(6),
"result": Mul(Binom(n=Ref("n"), k=Ref("k")), Subfactorial(arg=Sub(left=Ref(name='n'), right=Ref(nam... | NT | COMB | COUNT | sympy | MAX_PRIME_BELOW | [
"MAX_PRIME_BELOW"
] | dc3ad3 | comb_count_permutations_fixed_v1 | null | 3 | 0 | [
"MAX_PRIME_BELOW"
] | 1 | 0.002 | 2026-02-08T13:47:34.846488Z | {
"verified": true,
"answer": 20328,
"timestamp": "2026-02-08T13:47:34.848565Z"
} | 2ea1c4 | 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": 857
},
"timestamp": "2026-02-15T21:10:19.873Z",
"answer": 20328
},
{... | 1 | [
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok"
},
{
"lemma": "MOD_ADD",
"status": "no"
}
] | {
"lo": -5.49,
"mid": 0.22,
"hi": 6.51
} | ||
a62af9 | geo_count_lattice_triangle_v1_1218484723_6801 | Let $T = \left|100 \cdot 121 + 15 \cdot (0 - 2)\right|$ and define $$K = \gcd(100, 2) + \gcd(|15 - 100|, \left|\sum_{k=0}^{4} 3^k - 2\right|) + \gcd\left(\left|0 - \sum_{k=0}^{3} 2^k\right|, \left|0 - \left|\left\{ v \geq 73 : v \leq \pi(91367),\ \exists\, 1 \leq a,b \leq 11\ \text{s.t.}\ 17a^2 + 36ab + 20b^2 = v \righ... | 6,026 | graphs = [
Graph(
let={
"_d": Const(2),
"_c": Const(15),
"_m": Const(15),
"_n": Const(100),
"area_2x": Abs(arg=Sum(Mul(Const(value=100), Const(value=121)), Mul(Ref(name='_m'), Sub(left=Const(value=0), right=Const(value=2))))),
"boundary... | GEOM | NT | COUNT | sympy | COUNT_PRIMES | [
"COUNT_PRIMES/QF_PSD_DISTINCT",
"SUM_GEOM"
] | 9f3ae3 | geo_count_lattice_triangle_v1 | null | 6 | 0 | [
"COUNT_PRIMES",
"QF_PSD_DISTINCT",
"SUM_GEOM"
] | 3 | 0.034 | 2026-02-25T08:16:48.134881Z | {
"verified": true,
"answer": 6026,
"timestamp": "2026-02-25T08:16:48.168411Z"
} | d10586 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 321,
"completion_tokens": 32768
},
"timestamp": "2026-03-30T02:43:24.502Z",
"answer": null
},
{
... | 1 | [
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "COUNT_PRIMES",
"status": "ok"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "QF_P... | {
"lo": -3.33,
"mid": 1.03,
"hi": 5.26
} | ||
8a143d | comb_count_derangements_v1_784195855_4021 | Let $n$ be the number of ordered pairs $(i, j)$ of integers such that $1 \leq i \leq 8$, $1 \leq j \leq 8$, and $i + j = 10$. Compute the subfactorial of $n$, defined as the number of derangements of an $n$-element set. | 1,854 | graphs = [
Graph(
let={
"_n": Const(10),
"n": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("i"), Var("j")]), condition=Eq(Sum(Var("i"), Var("j")), Ref("_n")), domain=CartesianProduct(left=IntegerRange(start=Const(1), end=Const(8)), right=IntegerRange(start=Const(1), end=Cons... | COMB | null | COUNT | sympy | COUNT_SUM_EQUALS | [
"COUNT_SUM_EQUALS"
] | 75ab0f | comb_count_derangements_v1 | null | 5 | 0 | [
"COUNT_SUM_EQUALS"
] | 1 | 0.014 | 2026-02-08T06:45:29.140390Z | {
"verified": true,
"answer": 1854,
"timestamp": "2026-02-08T06:45:29.154869Z"
} | 93d54c | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 187,
"completion_tokens": 837
},
"timestamp": "2026-02-24T07:05:06.806Z",
"answer": 1854
},
{
"id... | 1 | [
{
"lemma": "COUNT_CARTESIAN",
"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":... | {
"lo": -5.98,
"mid": -3.97,
"hi": -1.94
} | ||
3541b4 | nt_sum_divisors_range_v1_798873815_318 | Let $T$ be the set of all integers $t$ such that $28 \leq t \leq 10692$ and there exist positive integers $a \leq 39$ and $b \leq 2572$ satisfying $t = 10a + 4b + 14$. Let $u = |T|$. Define $S$ to be the set of all positive integers $n$ such that $n \leq u$. Compute $\sum_{n \in S} \tau(n)$, where $\tau(n)$ denotes the... | 46,558 | graphs = [
Graph(
let={
"upper": CountOverSet(set=SolutionsSet(var=Var("t"), condition=Exists(var=Var(name='a'), condition=Exists(var=Var(name='b'), condition=And(Geq(left=Var(name='a'), right=Const(value=1)), Leq(left=Var(name='a'), right=Const(value=39)), Geq(left=Var(name='b'), right=Const(va... | NT | null | SUM | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | nt_sum_divisors_range_v1 | null | 7 | 0 | [
"LIN_FORM"
] | 1 | 0.174 | 2026-02-08T02:33:14.196722Z | {
"verified": true,
"answer": 46558,
"timestamp": "2026-02-08T02:33:14.370640Z"
} | 4b16b2 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 290,
"completion_tokens": 14083
},
"timestamp": "2026-02-23T14:33:02.915Z",
"answer": 2952
},
{
... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "V3",
"status": "no"
}
] | {
"lo": 4.32,
"mid": 5.91,
"hi": 7.89
} | ||
e64652 | nt_sum_gcd_range_mod_v1_124444284_4093 | Let $N$ be the number of positive integers $k$ such that $k \leq 94864$ and $49$ divides $k$. Compute the sum $\sum_{n=1}^{N} \gcd(n, 108)$. Then find the remainder when this sum is divided by $11867$. | 11,538 | graphs = [
Graph(
let={
"_n": Const(49),
"N": CountOverSet(set=SolutionsSet(var=Var("k"), condition=And(Geq(Var("k"), Const(1)), Leq(Var("k"), Const(94864)), Divides(divisor=Ref("_n"), dividend=Var("k"))), domain='positive_integers')),
"k": Const(108),
"M": Co... | NT | null | COMPUTE | sympy | C2 | [
"C2"
] | 9685eb | nt_sum_gcd_range_mod_v1 | null | 4 | 0 | [
"C2"
] | 1 | 0.965 | 2026-02-08T05:46:06.123712Z | {
"verified": true,
"answer": 11538,
"timestamp": "2026-02-08T05:46:07.089104Z"
} | 0b5057 | 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": 4591
},
"timestamp": "2026-02-12T14:25:53.061Z",
"answer": 11538
},
... | 1 | [
{
"lemma": "C2",
"status": "ok"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
}
] | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
643728 | nt_max_prime_below_v1_1918700295_3825 | Let $S$ be the set of all positive integers $p$ for which there exists a positive integer $q$ such that $pq = 36$, $\gcd(p, q) = 1$, and $p < q$. Let $m$ be the number of elements in $S$. Let $T$ be the set of all prime numbers $n$ such that $n \geq m$ and $n \leq 37636$. Determine the value of the largest element in $... | 37,633 | graphs = [
Graph(
let={
"upper": Const(37636),
"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 | 3 | 0 | [
"COPRIME_PAIRS"
] | 1 | 1.595 | 2026-02-08T08:58:49.704704Z | {
"verified": true,
"answer": 37633,
"timestamp": "2026-02-08T08:58:51.299404Z"
} | 8e6aa6 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 150,
"completion_tokens": 2101
},
"timestamp": "2026-02-13T22:47:53.354Z",
"answer": 37633
},
... | 1 | [
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"
}
] | {
"lo": -5.55,
"mid": -3.01,
"hi": 0.32
} | ||
ddb9b5 | nt_min_coprime_above_v1_784195855_2146 | Let $S$ be the set of all ordered pairs $(i,j)$ of positive integers such that $i + j = 89$, $1 \le i \le 87$, and $1 \le j \le 87$. Let $m$ be the number of elements in $S$. Find the smallest integer $n$ such that $68121 < n \le 68217$ and $\gcd(n, m) = 1$. | 68,123 | graphs = [
Graph(
let={
"start": Const(68121),
"upper": Const(68217),
"modulus": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("i"), Var("j")]), condition=Eq(Sum(Var("i"), Var("j")), Const(89)), domain=CartesianProduct(left=IntegerRange(start=Const(1), end=Const(8... | NT | null | EXTREMUM | sympy | COUNT_SUM_EQUALS | [
"COUNT_SUM_EQUALS"
] | 75ab0f | nt_min_coprime_above_v1 | null | 4 | 0 | [
"COUNT_SUM_EQUALS"
] | 1 | 0.014 | 2026-02-08T05:30:53.978265Z | {
"verified": true,
"answer": 68123,
"timestamp": "2026-02-08T05:30:53.991922Z"
} | f38acc | 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": 1019
},
"timestamp": "2026-02-12T10:41:53.798Z",
"answer": 68123
},
... | 1 | [
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "ok"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "V8",
... | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
d89ca4 | geo_visible_lattice_v1_1520064083_7280 | Let $n = 91$. Define a visible lattice point $(x, y)$ as a point with integer coordinates such that $1 \le x, y \le n$ and $\gcd(x, y) = 1$. Let $r$ be the number of visible lattice points in the $n \times n$ grid. Find the smallest positive integer $k$ such that the $k$-th Fibonacci number is divisible by $r + 2$. | 510 | graphs = [
Graph(
let={
"n": Const(91),
"result": VisibleLatticePoints(n=Ref(name='n')),
"Q": FibonacciEntryPoint(modulus=Sum(Abs(arg=Ref(name='result')), Const(value=2))),
},
goal=Ref("Q"),
)
] | GEOM | NT | COUNT | sympy | [] | geo_visible_lattice_v1 | null | 3 | 0 | null | null | 0.176 | 2026-02-08T08:52:55.499043Z | {
"verified": true,
"answer": 510,
"timestamp": "2026-02-08T08:52:55.674700Z"
} | cec826 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 206,
"completion_tokens": 32768
},
"timestamp": "2026-02-24T10:16:33.819Z",
"answer": null
},
{
... | 1 | [] | {
"lo": 3.25,
"mid": 5.68,
"hi": 8.81
} | ||||
86097b | alg_telescope_v1_1218484723_148 | Let $F_n$ denote the $n$-th Fibonacci number. Let
$$
A = \left|\{ (a, b) : 1 \leq a, b \leq 40,\ -2ab + 2b^2 + \left|\{ n : 1 \leq n \leq 312,\ 14 \mid F_n \}\right| \cdot a^2 \leq 6250 \}\right|,
$$
and let
$$
B = \left|\{ t : 12 \leq t \leq 6527,\ \exists\text{ integers } a \in [1,222], b \in [1,1464] \text{ such th... | 22,904 | graphs = [
Graph(
let={
"_m": Const(2),
"_n": Const(62537),
"result": Mod(value=Summation(var="k", start=Const(0), end=CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("a"), Var("b")]), condition=And(Geq(Var("a"), Const(1)), Leq(Var("a"), Const(40)), Geq(Var("b"), Co... | ALG | NT | COMPUTE | sympy | COUNT_FIB_DIVISIBLE | [
"COUNT_FIB_DIVISIBLE/QF_PSD_COUNT_LEQ",
"LIN_FORM"
] | 0f4f39 | alg_telescope_v1 | null | 7 | 0 | [
"COUNT_FIB_DIVISIBLE",
"LIN_FORM",
"QF_PSD_COUNT_LEQ"
] | 3 | 0.022 | 2026-02-25T01:51:06.883580Z | {
"verified": true,
"answer": 22904,
"timestamp": "2026-02-25T01:51:06.905379Z"
} | 36a860 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 338,
"completion_tokens": 32768
},
"timestamp": "2026-03-28T21:52:27.444Z",
"answer": null
},
{
... | 0 | [
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "ok"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "QF_PSD_COUNT_LEQ",
"sta... | {
"lo": 5.81,
"mid": 8.21,
"hi": 10
} | ||
07fa5e | antilemma_coprime_grid_v1_1742523217_227 | Let $n = 85892$. Let $x$ be the number of ordered pairs $(i,j)$ of positive integers with $1 \leq i \leq 8$ and $1 \leq j \leq 60$ such that $\gcd(i,j) = 1$. Let $c$ be the smallest divisor of $324856255817$ that is at least $2$. Compute the remainder when $c \cdot x$ is divided by $n$.\n\nFind the value of this remain... | 67,982 | graphs = [
Graph(
let={
"_n": Const(85892),
"x": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("i"), Var("j")]), condition=Eq(GCD(a=Var("i"), b=Var("j")), Const(1)), domain=CartesianProduct(left=IntegerRange(start=Const(1), end=Const(8)), right=IntegerRange(start=Const(1), en... | NT | COMB | COMPUTE | sympy | MIN_PRIME_FACTOR | [
"MIN_PRIME_FACTOR",
"COUNT_COPRIME_GRID"
] | de9abd | antilemma_coprime_grid_v1 | affine_mod | 4 | 0 | [
"COUNT_COPRIME_GRID",
"MIN_PRIME_FACTOR"
] | 2 | 0.001 | 2026-02-08T02:56:18.756708Z | {
"verified": true,
"answer": 67982,
"timestamp": "2026-02-08T02:56:18.757873Z"
} | b2e00c | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 217,
"completion_tokens": 510
},
"timestamp": "2026-02-17T16:06:56.382Z",
"answer": 96
}
] | 0 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "ok"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "MIN_PRIME_FACTOR",
"status": "ok"
},
{
... | {
"lo": -6.48,
"mid": 1.54,
"hi": 9.56
} | ||
3abc85 | antilemma_k2_v1_2051736721_2632 | Let $x = \sum_{k=1}^{370} \phi(k) \left\lfloor \frac{370}{k} \right\rfloor$, where $\phi(k)$ denotes Euler's totient function. Compute the remainder when $65536 - x$ is divided by 69498. | 66,399 | graphs = [
Graph(
let={
"_n": Const(370),
"x": Summation(var="k", start=Const(1), end=Const(370), expr=Mul(EulerPhi(n=Var("k")), Floor(Div(Ref("_n"), Var("k"))))),
"_c": Const(65536),
"Q": Mod(value=Sub(Ref("_c"), Ref("x")), modulus=Const(69498)),
},
... | NT | COMB | COMPUTE | sympy | K2 | [
"K2"
] | 6897ab | antilemma_k2_v1 | null | 4 | 0 | [
"K2"
] | 1 | 0.001 | 2026-02-08T16:49:32.145946Z | {
"verified": true,
"answer": 66399,
"timestamp": "2026-02-08T16:49:32.146894Z"
} | 387f4f | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 108,
"completion_tokens": 724
},
"timestamp": "2026-02-17T13:07:32.469Z",
"answer": 66399
},
{... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K2",
"status": "ok"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "V1",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
7cfd78 | sequence_lucas_compute_v1_601307018_4225 | Let $m = \min\{ |x - y| : x > 0, y > 0,\, xy = 1566 \}$. Let $V = \left|\{ v : 17 \le v \le 11348,\, \text{there exist integers } a, b \text{ with } 1 \le a, b \le 17 \text{ such that } 9b^2 - 30ab + 41a^2 = v \}\right|$. Let $n$ be the number of ordered pairs $(a, b)$ of positive integers with $1 \le a \le m$ and $1 \... | 21,275 | graphs = [
Graph(
let={
"_m": Const(44121),
"_n": Const(2),
"n": CountOverSet(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("x"), Var("y")]... | ALG | null | COMPUTE | sympy | QF_PSD_DISTINCT | [
"QF_PSD_DISTINCT/POLY3_COUNT",
"B3_DIFF/POLY3_COUNT"
] | 129d13 | sequence_lucas_compute_v1 | null | 7 | 0 | [
"B3_DIFF",
"POLY3_COUNT",
"QF_PSD_DISTINCT"
] | 3 | 0.019 | 2026-03-10T04:51:31.671507Z | {
"verified": true,
"answer": 21275,
"timestamp": "2026-03-10T04:51:31.690844Z"
} | 4d5b21 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 329,
"completion_tokens": 32768
},
"timestamp": "2026-03-29T11:29:00.107Z",
"answer": null
},
{
... | 1 | [
{
"lemma": "B3_DIFF",
"status": "ok"
},
{
"lemma": "POLY3_COUNT",
"status": "ok_later"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "QF_PSD_DISTINCT",
"status": "ok"
}
] | {
"lo": 3.34,
"mid": 5.77,
"hi": 8.89
} | ||
9db578_n | geo_count_lattice_triangle_v1_1419126231_1824 | A city planner designs a park with three rectangular sections. The first has area $196 \times 121$, the second is subtracted as a lake of area $100 \times 48$, so the net land area is $N = |196 \cdot 121 - 100 \cdot 48|$. To install fencing, the planner computes $M$, the sum of the greatest common divisors of the side ... | 9,456 | GEOM | null | COUNT | sympy | [] | geo_count_lattice_triangle_v1 | null | 3 | null | null | null | 0.002 | 2026-02-25T11:22:29.775458Z | null | cdf981 | 9db578 | narrative | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 253,
"completion_tokens": 841
},
"timestamp": "2026-03-31T05:07:31.850Z",
"answer": 9456
},
{
"id... | 2 | [] | {
"lo": -10,
"mid": -5.89,
"hi": -1.79
} | |||
671f07 | nt_count_divisible_v1_2051736721_1868 | Let $m = 20$ and $n = 6$. Define
$$
S = \left\{ (k, j) \mid 1 \leq k \leq 6,\ 1 \leq j \leq 5 \right\}.
$$
Let
$$
T = \left\{ \phi(k) \left\lfloor \frac{n}{k} \right\rfloor \ \middle|\ (k, j) \in S \right\},
$$
where $\phi$ denotes Euler's totient function. Define
$$
d = \frac{4 \sum_{x \in T} x}{m}.
$$
Let $U$ be the ... | 2,928 | graphs = [
Graph(
let={
"_m": Const(20),
"_n": Const(6),
"upper": Const(61504),
"divisor": Div(Mul(Const(4), SumOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("k"), Var("_j")]), condition=Const(1), domain=CartesianProduct(left=IntegerRange(sta... | NT | null | COUNT | sympy | SUM_INDEPENDENT | [
"SUM_INDEPENDENT",
"K2"
] | d64c9f | nt_count_divisible_v1 | null | 5 | 0 | [
"K2",
"SUM_INDEPENDENT"
] | 2 | 2.523 | 2026-02-08T16:16:53.568593Z | {
"verified": true,
"answer": 2928,
"timestamp": "2026-02-08T16:16:56.092005Z"
} | 26a63a | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 221,
"completion_tokens": 1329
},
"timestamp": "2026-02-17T00:15:21.878Z",
"answer": 2928
},
{... | 1 | [
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "K2",
"status": "ok"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "SUM_INDEPENDENT",
"status": "ok"
},
{
"lemma": "V1",
"status": "no"
}... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
0b395e | comb_count_surjections_v1_601307018_2524 | Let $c = \sum_{k_1=0}^{0} (-1)^{k_1} \binom{0}{k_1}$, $S = 38051c$, $s = \sum_{k_2=0}^{0} (-1)^{k_2} \binom{0}{k_2}$, $w = \sum_{k_3=0}^{0} (-1)^{k_3} \binom{0}{k_3}$, and $n = 5w$. Let $T = 2! \cdot S(n, 2)$, where $S(n, k)$ denotes the Stirling numbers of the second kind. Find the remainder when $S \cdot T$ is divide... | 6,345 | graphs = [
Graph(
let={
"n3": Const(0),
"c": Summation(var="k1", start=Const(0), end=Ref("n3"), expr=Mul(Pow(Const(-1), Var("k1")), Binom(n=Ref("n3"), k=Var("k1")))),
"n2": Const(0),
"s": Summation(var="k2", start=Const(0), end=Ref("n2"), expr=Mul(Pow(Const(-1... | COMB | null | COUNT | sympy | POLY_ORBIT_LEGENDRE | [
"BINOMIAL_ALTERNATING"
] | c21569 | comb_count_surjections_v1 | null | 3 | 3 | [
"BINOMIAL_ALTERNATING",
"POLY_ORBIT_LEGENDRE"
] | 2 | 0.047 | 2026-03-10T03:13:34.736509Z | {
"verified": true,
"answer": 6345,
"timestamp": "2026-03-10T03:13:34.783412Z"
} | 988142 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 278,
"completion_tokens": 792
},
"timestamp": "2026-03-29T05:38:23.894Z",
"answer": 6345
},
{
"id... | 1 | [
{
"lemma": "BINOMIAL_ALTERNATING",
"status": "ok"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
},
{
"lemma": "V8_SUM",
"st... | {
"lo": -4.26,
"mid": -1.81,
"hi": 1.24
} | ||
ab32ec | alg_qf_psd_count_v1_1218484723_3222 | Find the number of ordered pairs $(a, b)$ of positive integers with $1 \leq a \leq 181$ and $1 \leq b \leq 181$ such that $5a^2 + 5b^2 = 90625$, where $181$ is the largest prime not exceeding $184$. | 10 | graphs = [
Graph(
let={
"_n": Const(2),
"result": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("a"), Var("b")]), condition=And(Geq(Var("a"), Const(1)), Leq(Var("a"), MaxOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(2)), Leq(Var("n"), Const(184)), I... | NT | null | COUNT | sympy | QF_PSD_DISTINCT | [
"MAX_PRIME_BELOW"
] | dc3ad3 | alg_qf_psd_count_v1 | null | 3 | 0 | [
"MAX_PRIME_BELOW",
"QF_PSD_DISTINCT"
] | 2 | 4.937 | 2026-02-25T04:54:50.667676Z | {
"verified": true,
"answer": 10,
"timestamp": "2026-02-25T04:54:55.604690Z"
} | 47e685 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 181,
"completion_tokens": 9984
},
"timestamp": "2026-03-29T09:02:35.862Z",
"answer": 10
},
{
"id"... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok"
}
] | {
"lo": -2.45,
"mid": 1.37,
"hi": 5.29
} | ||
13ae59 | comb_catalan_compute_v1_601307018_3549 | Let $n$ be the number of ordered pairs $(x_1, x_2)$ of positive integers such that $x_1 + x_2 = 22$ and both $x_1$ and $x_2$ are odd. Let $M = C_n$, where $C_n$ denotes the $n$-th Catalan number. Find the remainder when $54217 \cdot M$ is divided by $81696$. | 76,210 | graphs = [
Graph(
let={
"_n": Const(54217),
"n": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x1"), Var("x2")]), condition=And(IsPositive(arg=Var(name='x1')), IsPositive(arg=Var(name='x2')), IsOdd(arg=Var(name='x1')), IsOdd(arg=Var(name='x2')), Eq(Sum(Var("x1"), Var("x2")),... | COMB | null | COMPUTE | sympy | POLY_ORBIT_LEGENDRE | [
"COMB1"
] | 567f58 | comb_catalan_compute_v1 | null | 3 | 0 | [
"COMB1",
"POLY_ORBIT_LEGENDRE"
] | 2 | 0.069 | 2026-03-10T04:09:26.588064Z | {
"verified": true,
"answer": 76210,
"timestamp": "2026-03-10T04:09:26.657108Z"
} | 45d95e | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 204,
"completion_tokens": 5460
},
"timestamp": "2026-03-29T09:03:22.341Z",
"answer": 76210
},
{
"... | 1 | [
{
"lemma": "COMB1",
"status": "ok"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
... | {
"lo": -2.46,
"mid": 1.23,
"hi": 4.93
} | ||
470cc1 | diophantine_fbi2_min_v1_1439011603_1215 | Let $k$ be the sum of all positive integers that can be expressed as the product $xy$, where $x$ and $y$ are positive integers such that $x + y = 4$. Let $d$ be the smallest integer at least $3$ and at most $20$ such that $d$ divides $k$ and $\frac{k}{d} \geq 2$. Compute the remainder when $7^{|d|} + 31329$ is divided ... | 48,136 | graphs = [
Graph(
let={
"_n": Const(31329),
"k": Summation(var="k1", start=Const(1), end=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(... | NT | null | EXTREMUM | sympy | B1 | [
"B1/SUM_ARITHMETIC"
] | 8e3bd4 | diophantine_fbi2_min_v1 | null | 5 | 0 | [
"B1",
"SUM_ARITHMETIC"
] | 2 | 0.008 | 2026-02-08T15:58:46.133110Z | {
"verified": true,
"answer": 48136,
"timestamp": "2026-02-08T15:58:46.140873Z"
} | 40737d | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 171,
"completion_tokens": 569
},
"timestamp": "2026-02-16T06:50:20.647Z",
"answer": 48136
},
{
"id": 11,
... | 2 | [
{
"lemma": "B1",
"status": "ok"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "SUM_ARITHMETIC",
"status": "ok_later"
},
{
"lemma": "V5",
"status": "no"
},
... | {
"lo": -10,
"mid": -7.27,
"hi": -4.54
} | ||
cd0bd1_l | comb_count_partitions_v1_677425708_3837 | Let $T$ be the set of all ordered pairs $(k,j)$ where $k$ is an integer from 1 to 9 and $j$ is an integer from 1 to 8. Define $S$ to be the set of values $k$ over all pairs $(k,j) \in T$. Let $n = \frac{5}{40}$ times the sum of all elements in $S$. Compute the number of integer partitions of $n$. | 0 | COMB | null | COUNT | sympy | SUM_INDEPENDENT | [
"SUM_INDEPENDENT",
"SUM_ARITHMETIC"
] | 9f7183 | comb_count_partitions_v1 | null | 5 | 0 | [
"SUM_ARITHMETIC",
"SUM_INDEPENDENT"
] | 2 | 0.002 | 2026-02-08T05:57:20.268402Z | {
"verified": false,
"answer": 89134,
"timestamp": "2026-02-08T05:57:20.270049Z"
} | 76d824 | cd0bd1 | legacy_text | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 1,
"correct": {
"strict": false,
"boxed": false,
"relaxed": true
},
"usage": {
"prompt_tokens": 207,
"completion_tokens": 2567
},
"timestamp": "2026-02-24T05:08:10.270Z",
"answer": 0
},
{
"id... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "SUM_ARITHMETIC",
"status": "ok"
},
{
"lemma": "SUM_INDEPENDENT",
"status": "ok"
},
{
"lemma": "V8",
... | {
"lo": 1.97,
"mid": 4.36,
"hi": 6.69
} | |
ea0c29 | geo_visible_lattice_v1_1439011603_2399 | Let $n = 196$. Define $\mathcal{P}$ as the set of all ordered pairs $(x, y)$ of positive integers such that $1 \le x, y \le n$ and $\gcd(x, y) = 1$. Let $R$ denote the number of elements in $\mathcal{P}$. Compute the remainder when $59196 \cdot R$ is divided by $52433$. | 30,024 | graphs = [
Graph(
let={
"n": Const(196),
"result": VisibleLatticePoints(n=Ref(name='n')),
"Q": Mod(value=Mul(Const(59196), Ref("result")), modulus=Const(52433)),
},
goal=Ref("Q"),
)
] | GEOM | null | COUNT | sympy | [] | geo_visible_lattice_v1 | null | 4 | 0 | null | null | 2.816 | 2026-02-08T16:45:31.098859Z | {
"verified": true,
"answer": 30024,
"timestamp": "2026-02-08T16:45:33.914692Z"
} | 8acf56 | 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": 5630
},
"timestamp": "2026-02-17T11:38:56.205Z",
"answer": 30024
},
... | 1 | [] | {
"lo": -2.38,
"mid": 1.74,
"hi": 6.59
} | ||||
3f8f14 | comb_sum_binomial_row_v1_238844314_49 | Let $N$ be the number of integers $j$ with $0\le j\le 2049$ such that
$$
\binom{2049}{j}\equiv 1 \pmod{2}.
$$
For each positive integer $k$, let $f(k)$ be the number of positive integers $p$ for which there exists a positive integer $q$ such that
$$
pq=2700,\quad \gcd(p,q)=1,\quad p<q.
$$
Let
$$
n = \sum_{k=1}^{N} \var... | 69,448 | graphs = [
Graph(
let={
"_c": Const(95573),
"_m": Const(44121),
"_n": CountOverSet(set=SolutionsSet(var=Var("j"), condition=And(Geq(Var("j"), Const(0)), Leq(Var("j"), Const(2049)), Eq(Mod(value=Binom(n=Const(2049), k=Var("j")), modulus=Const(2)), Const(1))), domain='nonne... | NT | null | SUM | sympy | COPRIME_PAIRS | [
"COPRIME_PAIRS/K2",
"V8/K2"
] | 1c64f9 | comb_sum_binomial_row_v1 | null | 8 | 0 | [
"COPRIME_PAIRS",
"K2",
"V8"
] | 3 | 0.005 | 2026-02-08T13:06:06.059192Z | {
"verified": true,
"answer": 69448,
"timestamp": "2026-02-08T13:06:06.064082Z"
} | 5c4db1 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 236,
"completion_tokens": 2597
},
"timestamp": "2026-02-15T09:32:28.260Z",
"answer": 69448
},
... | 1 | [
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "K2",
"status": "ok_later"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "V5",
"status": "... | {
"lo": -5.49,
"mid": 0.22,
"hi": 6.51
} | ||
142f7e | nt_count_primes_v1_349078426_1583 | Let $k$ be the number of positive integers $p$ for which there exists a positive integer $q$ such that $pq = 24$, $\gcd(p, q) = 1$, and $p < q$. Determine the number of prime numbers $n$ such that $k \leq n \leq 48841$. | 5,022 | graphs = [
Graph(
let={
"upper": Const(48841),
"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 | 3 | 0 | [
"COPRIME_PAIRS"
] | 1 | 1.684 | 2026-02-08T13:43:53.802643Z | {
"verified": true,
"answer": 5022,
"timestamp": "2026-02-08T13:43:55.486337Z"
} | 2ab679 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 116,
"completion_tokens": 2190
},
"timestamp": "2026-02-15T20:06:41.369Z",
"answer": 5022
},
{... | 1 | [
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "V3",
"status": "no"
... | {
"lo": -5.49,
"mid": 0.22,
"hi": 6.51
} | ||
6093c7 | sequence_count_fib_divisible_v1_717093673_1578 | Let $ S $ be the sum of the integers from 1 to 34. Compute the number of positive integers $ n $ such that $ 1 \leq n \leq S $ and $ 5 $ divides the $ n $-th Fibonacci number $ F_n $. Determine the value of this count. | 119 | graphs = [
Graph(
let={
"upper": Summation(var="k", start=Const(1), end=Const(34), expr=Var("k")),
"d": Const(5),
"result": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Ref("upper")), Divides(divisor=Ref("d"), dividend=F... | NT | null | COUNT | sympy | SUM_ARITHMETIC | [
"SUM_ARITHMETIC"
] | eb34f0 | sequence_count_fib_divisible_v1 | null | 5 | 0 | [
"SUM_ARITHMETIC"
] | 1 | 0.054 | 2026-02-08T16:10:51.554572Z | {
"verified": true,
"answer": 119,
"timestamp": "2026-02-08T16:10:51.608671Z"
} | 4b0199 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 109,
"completion_tokens": 1292
},
"timestamp": "2026-02-16T22:01:12.965Z",
"answer": 119
},
{
... | 1 | [
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "SUM_ARITHMETIC",
"status": "ok"
},
{
"lemma": "VAL_SUM_EQ",
"status": "no"
}
... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
5c7fa4 | alg_qf_psd_sum_v1_1218484723_559 | Find the remainder when $$\sum_{a=1}^7 \sum_{b=1}^7 \sum_{c=1}^7 \left(3a^2 - 8ab - 22ac + 16b^2 + 24bc + K c^2\right)$$ is divided by $71043$, where $$K = \left|\left\{ v \in [72, 4608] : \exists\, a,b \in \mathbb{Z},\, 1 \le a,b \le 8,\, 50a^2 + 20ab + 2b^2 = v \right\}\right|.$$ | 37,177 | graphs = [
Graph(
let={
"_n": Const(7),
"result": Mod(value=SumOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("a"), Var("b"), Var("c")]), condition=And(Geq(Var("a"), Const(1)), Leq(Var("a"), Const(7)), Geq(Var("b"), Const(1)), Leq(Var("b"), Const(7)), Geq(Var("c"), C... | ALG | null | COMPUTE | sympy | QF_PSD_DISTINCT | [
"QF_PSD_DISTINCT"
] | a8f9cb | alg_qf_psd_sum_v1 | null | 7 | 0 | [
"QF_PSD_DISTINCT"
] | 1 | 0.015 | 2026-02-25T02:13:05.919910Z | {
"verified": true,
"answer": 37177,
"timestamp": "2026-02-25T02:13:05.935008Z"
} | 4f5c12 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 254,
"completion_tokens": 14935
},
"timestamp": "2026-03-28T23:10:35.643Z",
"answer": 37277
},
{
... | 1 | [
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "QF_PSD_DISTINCT",
"status": "ok"
}
] | {
"lo": 1.22,
"mid": 3.76,
"hi": 5.73
} |
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