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 |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
75dfd9 | nt_sum_divisors_mod_v1_458359167_1123 | Let $n$ be the largest positive divisor of $2850960$ that is less than or equal to the number of positive integers $k \leq 11760$ for which $13$ divides the $k$-th Fibonacci number. Compute the remainder when the sum of all positive divisors of $n$ is divided by $10193$. | 5,952 | graphs = [
Graph(
let={
"_n": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Const(11760)), Divides(divisor=Const(13), dividend=Fibonacci(arg=Var(name='n')))))),
"n": MaxOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"... | NT | null | COMPUTE | sympy | COUNT_FIB_DIVISIBLE | [
"COUNT_FIB_DIVISIBLE/MAX_DIVISOR"
] | 9d7062 | nt_sum_divisors_mod_v1 | null | 7 | 0 | [
"COUNT_FIB_DIVISIBLE",
"MAX_DIVISOR"
] | 2 | 0.003 | 2026-02-08T04:23:28.736510Z | {
"verified": true,
"answer": 5952,
"timestamp": "2026-02-08T04:23:28.739281Z"
} | 233df4 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 183,
"completion_tokens": 2609
},
"timestamp": "2026-02-10T16:27:37.247Z",
"answer": 5952
},
{
"... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "ok"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "MAX_DIVISOR",
"status": "ok_later"
... | {
"lo": -3.42,
"mid": 1.86,
"hi": 7.55
} | ||
e6e49c | alg_poly4_count_v1_601307018_8200 | Let $M$ be the largest prime $n$ with $2 \leq n \leq 18$. Let $d_{\min} = \min\{ |x - y| : x > 0, y > 0,\, x \cdot y = 114003 \}$. Find the number of ordered pairs $(a, b)$ of positive integers with $1 \leq a \leq d_{\min}$ and $1 \leq b \leq 238$ such that $M \cdot b^4 = 4019163392$. | 238 | graphs = [
Graph(
let={
"_m": Const(2),
"_n": MaxOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Ref("_m")), Leq(Var("n"), Const(18)), IsPrime(Var("n"))))),
"result": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("a"), Var("b")]), condition=And(... | NT | null | COUNT | sympy | B3_DIFF | [
"MAX_PRIME_BELOW/B3_DIFF"
] | 55b648 | alg_poly4_count_v1 | null | 5 | 0 | [
"B3_DIFF",
"MAX_PRIME_BELOW"
] | 2 | 1.814 | 2026-03-10T08:43:19.830531Z | {
"verified": true,
"answer": 238,
"timestamp": "2026-03-10T08:43:21.644164Z"
} | 8302e0 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 232,
"completion_tokens": 2934
},
"timestamp": "2026-04-19T08:28:17.008Z",
"answer": 238
},
{
"i... | 1 | [
{
"lemma": "B3_DIFF",
"status": "ok_later"
},
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},... | {
"lo": -5.34,
"mid": 1.1,
"hi": 7.53
} | ||
a30a3a | nt_max_prime_below_v1_1918700295_3612 | Let $S$ be the set of all positive integers $p$ for which there exists a positive integer $q$ such that $pq = 54$, $\gcd(p, q) = 1$, and $p < q$. Let $T$ be the set of all prime numbers $n$ such that $n \geq |S|$ and $n \leq 10427$. Compute the largest element of $T$. | 10,427 | graphs = [
Graph(
let={
"upper": Const(10427),
"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 | 5 | 0 | [
"COPRIME_PAIRS"
] | 1 | 2.624 | 2026-02-08T08:46:26.112745Z | {
"verified": true,
"answer": 10427,
"timestamp": "2026-02-08T08:46:28.736983Z"
} | a9469f | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 1,
"correct": {
"strict": false,
"boxed": false,
"relaxed": true
},
"usage": {
"prompt_tokens": 152,
"completion_tokens": 581
},
"timestamp": "2026-02-15T20:20:48.228Z",
"answer": 10423
},
{
"id": 11,... | 1 | [
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
},
{
"lemma": "VAL_SUM_EQ",
"status": "no"
... | {
"lo": -5.55,
"mid": -3.01,
"hi": 0.34
} | ||
67e4a1 | comb_factorial_compute_v1_1248542787_240 | Let $n$ be the number of integers $t$ such that $22 \leq t \leq 49$ and there exist positive integers $a$ and $b$ with $1 \leq a \leq 4$, $1 \leq b \leq 2$, and
$$
t = 6a + 9b + 7.
$$
Compute $n!$. | 40,320 | graphs = [
Graph(
let={
"n": CountOverSet(set=SolutionsSet(var=Var("t"), condition=Exists(var=Var(name='a'), condition=Exists(var=Var(name='b'), condition=And(Geq(left=Var(name='a'), right=Const(value=1)), Leq(left=Var(name='a'), right=Const(value=4)), Geq(left=Var(name='b'), right=Const(value=1... | ALG | COMB | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | comb_factorial_compute_v1 | null | 4 | 0 | [
"LIN_FORM"
] | 1 | 0.001 | 2026-02-08T03:02:01.529412Z | {
"verified": true,
"answer": 40320,
"timestamp": "2026-02-08T03:02:01.530195Z"
} | 8a3e7f | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 201,
"completion_tokens": 607
},
"timestamp": "2026-02-09T01:47:59.912Z",
"answer": 40320
},
{
"i... | 1 | [
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
}
] | {
"lo": -2.87,
"mid": -0.89,
"hi": 0.97
} | ||
f39565 | sequence_count_fib_divisible_v1_601307018_7131 | Let $F_n$ denote the $n$-th Fibonacci number. Let $d$ be the largest positive integer such that $d^2 \le 77$ and $d \mid 77$. Let $M$ be the minimum value of $|x - y|$ over all ordered pairs $(x, y)$ of positive integers with $xy = 750312$. Let $R$ be the number of positive integers $n$ with $1 \le n \le M$ such that $... | 26,338 | graphs = [
Graph(
let={
"_n": Const(44121),
"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(750312)))), expr=Abs(arg=Sub(left=Va... | NT | null | COUNT | sympy | B3_CLOSEST | [
"B3_CLOSEST",
"B3_DIFF"
] | e18306 | sequence_count_fib_divisible_v1 | null | 6 | 0 | [
"B3_CLOSEST",
"B3_DIFF"
] | 2 | 0.011 | 2026-03-10T07:45:19.205791Z | {
"verified": true,
"answer": 26338,
"timestamp": "2026-03-10T07:45:19.216699Z"
} | 0b9b3b | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 237,
"completion_tokens": 4945
},
"timestamp": "2026-04-19T06:02:43.172Z",
"answer": 26338
},
{
... | 1 | [
{
"lemma": "B3_CLOSEST",
"status": "ok"
},
{
"lemma": "B3_DIFF",
"status": "ok"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma":... | {
"lo": -5.34,
"mid": 1.1,
"hi": 7.53
} | ||
af7bb2 | nt_count_coprime_v1_784195855_7812 | Let $m = 2$ and $n = 5$. Define $k$ to be the sum
$$
\sum_{k=1}^{N} \varphi(k) \left\lfloor \frac{n}{k} \right\rfloor,
$$
where $N$ is the largest prime number between $m$ and $6$, inclusive. Let $S$ be the set of all positive integers $n$ such that $1 \leq n \leq 41209$ and $\gcd(n, k) = 1$. Compute the remainder when... | 21,979 | graphs = [
Graph(
let={
"_m": Const(2),
"_n": Const(5),
"upper": Const(41209),
"k": Summation(var="k", start=Const(1), end=MaxOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Ref("_m")), Leq(Var("n"), Const(6)), IsPrime(Var("n"))))), expr=Mul... | NT | null | COUNT | sympy | MAX_PRIME_BELOW | [
"MAX_PRIME_BELOW/K2"
] | 7eb1ee | nt_count_coprime_v1 | null | 5 | 0 | [
"K2",
"MAX_PRIME_BELOW"
] | 2 | 9.538 | 2026-02-08T09:32:27.067310Z | {
"verified": true,
"answer": 21979,
"timestamp": "2026-02-08T09:32:36.605406Z"
} | 813a1c | 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": 1031
},
"timestamp": "2026-02-14T05:00:48.480Z",
"answer": 21979
},
... | 1 | [
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "K2",
"status": "ok_later"
},
{
"lemma": "MAX_PRIME_BELOW... | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
e68f50 | comb_count_surjections_v1_1520064083_4062 | Let $m = 8$ and $n = 5$. Let $n$ be the number of ordered pairs $(i, j)$ of integers such that $1 \le i \le 7$, $1 \le j \le 7$, and $i + j = m$. Let $k$ be the number of ordered pairs $(i, j)$ of integers such that $1 \le i \le 5$, $1 \le j \le 5$, and $i + j = n$. Compute the value of $k! \cdot S(n, k)$, where $S(n, ... | 8,400 | graphs = [
Graph(
let={
"_m": Const(8),
"_n": Const(5),
"n": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("i"), Var("j")]), condition=Eq(Sum(Var("i"), Var("j")), Ref("_m")), domain=CartesianProduct(left=IntegerRange(start=Const(1), end=Const(7)), right=IntegerRan... | COMB | null | COUNT | sympy | COUNT_SUM_EQUALS | [
"COUNT_SUM_EQUALS"
] | 75ab0f | comb_count_surjections_v1 | null | 5 | 0 | [
"COUNT_SUM_EQUALS"
] | 1 | 0.028 | 2026-02-08T06:03:18.805844Z | {
"verified": true,
"answer": 8400,
"timestamp": "2026-02-08T06:03:18.833682Z"
} | 44413e | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 288,
"completion_tokens": 3136
},
"timestamp": "2026-02-24T05:18:45.365Z",
"answer": 8400
},
{
"i... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "ok"
},
{
"lemma": "V8",
"status": "no"
},
{
"lemma": "V8_SUM",
"stat... | {
"lo": -3.84,
"mid": -1.69,
"hi": 1.09
} | ||
89e671 | modular_mod_compute_v1_1248542787_162 | Let $d=2$ and $m_0=2$. Let $N$ be the number of integers $n$ with $1\le n\le 489$ such that
\[n\equiv \left\lfloor \frac{n}{2} \right\rfloor \pmod{5}.
\]
Let $a=-66$ and $M=52441$. Define $r$ by
\[r\equiv a\pmod{M},\quad 0\le r<M.
\]
Let $c=1$. Let $P$ be the largest prime number $n$ such that $2\le n\le 102$. Let $D... | 43,805 | graphs = [
Graph(
let={
"_d": Const(2),
"_m": Const(2),
"_n": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Const(489)), Congruent(a=Var(name='n'), b=Floor(arg=Div(left=Var(name='n'), right=Const(value=2))), modulus=Const... | NT | null | COMPUTE | sympy | L3C | [
"L3C/MIN_PRIME_FACTOR",
"MAX_PRIME_BELOW"
] | ffac99 | modular_mod_compute_v1 | crt_mix_3 | 6 | 0 | [
"L3C",
"MAX_PRIME_BELOW",
"MIN_PRIME_FACTOR"
] | 3 | 0.005 | 2026-02-08T02:58:39.082291Z | {
"verified": true,
"answer": 43805,
"timestamp": "2026-02-08T02:58:39.087295Z"
} | 7f63b1 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 417,
"completion_tokens": 6057
},
"timestamp": "2026-02-09T13:41:28.134Z",
"answer": 43805
},
{
... | 1 | [
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "L3C",
"status": "ok"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok"
},
{
"lemma": "MIN_PRIME_FACTOR",
"status": "ok_later"
},
{
"lemma": "MOD_SUB",
"status": "... | {
"lo": 2.9,
"mid": 4.6,
"hi": 6.41
} | ||
2dea9e | nt_count_coprime_v1_458359167_2277 | Let $k$ be the minimum value of $x + y$ over all pairs of positive integers $(x, y)$ such that $xy = 400$. Determine the number of positive integers $n$ with $1 \le n \le 12769$ such that $\gcd(n, k) = 1$. | 5,108 | graphs = [
Graph(
let={
"upper": Const(12769),
"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(400)))), expr=Sum(Var("x"), Var("y"))... | NT | null | COUNT | sympy | B3 | [
"B3"
] | 0cd20d | nt_count_coprime_v1 | null | 4 | 0 | [
"B3"
] | 1 | 4.669 | 2026-02-08T05:17:15.058020Z | {
"verified": true,
"answer": 5108,
"timestamp": "2026-02-08T05:17:19.727068Z"
} | 0b48b8 | 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": 1004
},
"timestamp": "2026-02-12T06:01:19.600Z",
"answer": 5108
},
{... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
}
] | {
"lo": -5.55,
"mid": -3.01,
"hi": 0.32
} | ||
7f6ee1 | nt_num_divisors_compute_v1_784195855_7686 | Let $n = 55$. Compute the number of positive divisors of $n$. | 4 | graphs = [
Graph(
let={
"n": Const(55),
"result": NumDivisors(n=Ref("n")),
},
goal=Ref("result"),
)
] | NT | null | COMPUTE | sympy | B3 | [
"B3/EULER_TOTIENT_SUM/MOBIUS_SUM"
] | e6a587 | nt_num_divisors_compute_v1 | null | 2 | 0 | [
"B3",
"EULER_TOTIENT_SUM",
"MOBIUS_SUM"
] | 3 | 0.015 | 2026-02-08T09:26:42.844199Z | {
"verified": true,
"answer": 4,
"timestamp": "2026-02-08T09:26:42.858914Z"
} | 858b75 | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 74,
"completion_tokens": 321
},
"timestamp": "2026-02-15T20:42:29.732Z",
"answer": 4
},
{
"id": 11,
"m... | 2 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "EULER_TOTIENT_SUM",
"status": "ok_later"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
... | {
"lo": -10,
"mid": -7.71,
"hi": -5.43
} | ||
73115d | antilemma_sum_equals_v1_124444284_9020 | Let $m = 90374$. Let $n$ be the number of ordered pairs $(i, j)$ of positive integers such that $1 \leq i \leq 31$, $1 \leq j \leq 31$, and $i + j = 32$. Let $x$ be the number of ordered pairs $(i, j)$ of positive integers such that $1 \leq i \leq 30$, $1 \leq j \leq 31$, and $i + j = n$. Compute the remainder when $44... | 58,394 | graphs = [
Graph(
let={
"_m": Const(90374),
"_n": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("i"), Var("j")]), condition=Eq(Sum(Var("i"), Var("j")), Const(32)), domain=CartesianProduct(left=IntegerRange(start=Const(1), end=Const(31)), right=IntegerRange(start=Const(1), end... | COMB | GEOM | COMPUTE | sympy | COMB1 | [
"COUNT_SUM_EQUALS/COUNT_SUM_EQUALS",
"COUNT_SUM_EQUALS"
] | ae9919 | antilemma_sum_equals_v1 | null | 4 | 0 | [
"COMB1",
"COUNT_SUM_EQUALS"
] | 2 | 0.03 | 2026-02-08T12:08:08.621768Z | {
"verified": true,
"answer": 58394,
"timestamp": "2026-02-08T12:08:08.651568Z"
} | 96a7d7 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 238,
"completion_tokens": 1108
},
"timestamp": "2026-02-24T15:17:50.848Z",
"answer": 58394
},
{
"... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "ok"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8_SUM",
"status":... | {
"lo": -3.84,
"mid": -1.67,
"hi": 1.32
} | ||
cf89aa | nt_num_divisors_compute_v1_458359167_5369 | Let $n = 19881$. Compute the number of positive divisors of $n$. | 9 | graphs = [
Graph(
let={
"n": Const(19881),
"result": NumDivisors(n=Ref("n")),
},
goal=Ref("result"),
)
] | NT | null | COMPUTE | sympy | B3 | [
"B3"
] | 0cd20d | nt_num_divisors_compute_v1 | null | 2 | 0 | [
"B3"
] | 1 | 0.009 | 2026-02-08T12:26:43.051579Z | {
"verified": true,
"answer": 9,
"timestamp": "2026-02-08T12:26:43.060152Z"
} | 043eaa | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 65,
"completion_tokens": 491
},
"timestamp": "2026-02-15T01:00:02.515Z",
"answer": 9
},
{
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
... | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
34d850 | modular_mod_compute_v1_1742523217_39 | Let $n = 29$. Define $m$ to be the number of positive integers $k$ such that $1 \leq k \leq 214484$ and $n$ divides $k$. Compute the remainder when $-67600$ is divided by $m$. | 6,360 | graphs = [
Graph(
let={
"_n": Const(29),
"a": Const(-67600),
"m": CountOverSet(set=SolutionsSet(var=Var("k"), condition=And(Geq(Var("k"), Const(1)), Leq(Var("k"), Const(214484)), Divides(divisor=Ref("_n"), dividend=Var("k"))), domain='positive_integers')),
"re... | NT | null | COMPUTE | sympy | C2 | [
"C2"
] | 9685eb | modular_mod_compute_v1 | null | 3 | 0 | [
"C2"
] | 1 | 0.001 | 2026-02-08T02:50:44.520645Z | {
"verified": true,
"answer": 6360,
"timestamp": "2026-02-08T02:50:44.521901Z"
} | 7e0fdf | 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": 793
},
"timestamp": "2026-02-09T12:47:05.021Z",
"answer": 6360
},
{
"id... | 1 | [
{
"lemma": "C2",
"status": "ok"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "VAL_SUM_EQ",
"status": ... | {
"lo": -3.06,
"mid": -0.92,
"hi": 1.04
} | ||
8f42bc | comb_sum_binomial_row_v1_784195855_5271 | Let $n$ be the number of nonnegative integers $j$ such that $0 \leq j \leq 16532$ and $\binom{16532}{j}$ is odd. Compute $2^n$. | 65,536 | graphs = [
Graph(
let={
"_n": Const(16532),
"n": CountOverSet(set=SolutionsSet(var=Var("j"), condition=And(Geq(Var("j"), Const(0)), Leq(Var("j"), Const(16532)), Eq(Mod(value=Binom(n=Ref("_n"), k=Var("j")), modulus=Const(2)), Const(1))), domain='nonnegative_integers')),
"r... | ALG | COMB | SUM | sympy | V8 | [
"V8"
] | 86348e | comb_sum_binomial_row_v1 | null | 6 | 0 | [
"V8"
] | 1 | 0.001 | 2026-02-08T07:48:43.335341Z | {
"verified": true,
"answer": 65536,
"timestamp": "2026-02-08T07:48:43.336571Z"
} | 47f52d | 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": 964
},
"timestamp": "2026-02-24T08:28:36.939Z",
"answer": 65536
},
{
"i... | 1 | [
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "V8",
"status": "ok"
},
{
"lemma": "VAL_SUM_EQ",
"status": "no"
... | {
"lo": -2.35,
"mid": 1.22,
"hi": 4.84
} | ||
da4e96 | nt_count_divisors_in_range_v1_1080341949_236 | Let $m = 2592$. Define $S$ to be the set of all ordered pairs $(x,y)$ of positive integers such that $xy = k$, where $k$ is the number of positive integers at most $m$ that are divisible by 32. Let $a$ be the minimum value of $x + y$ over all pairs $(x,y) \in S$. Let $n = 221760$ and $b = 24647$. Determine the number o... | 20,105 | graphs = [
Graph(
let={
"_m": Const(2592),
"_n": Const(44121),
"n": Const(221760),
"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(... | NT | null | COUNT | sympy | C2 | [
"C2/B3"
] | 7c8509 | nt_count_divisors_in_range_v1 | null | 7 | 0 | [
"B3",
"C2"
] | 2 | 0.214 | 2026-02-08T13:20:59.900038Z | {
"verified": true,
"answer": 20105,
"timestamp": "2026-02-08T13:21:00.113827Z"
} | 63751f | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 194,
"completion_tokens": 2663
},
"timestamp": "2026-02-15T14:45:26.779Z",
"answer": 20105
},
... | 1 | [
{
"lemma": "B3",
"status": "ok_later"
},
{
"lemma": "C2",
"status": "ok"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "V1",
"status": "no"
},
{
"lemma": ... | {
"lo": -5.49,
"mid": 0.22,
"hi": 6.51
} | ||
b0fb31 | diophantine_sum_product_min_v1_1742523217_37 | Let $n = 115$ and $S = 116$. Let $P$ be the number of integers $t$ such that $8 \leq t \leq 3298$ and there exist positive integers $a \leq 386$ and $b \leq 456$ satisfying $t = 5a + 3b$. Determine the value of $x$, where $x$ is the smallest positive integer satisfying $1 \leq x \leq n$ and $x(S - x) = P$. | 49 | graphs = [
Graph(
let={
"_n": Const(115),
"S": Const(116),
"P": 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 | EXTREMUM | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | diophantine_sum_product_min_v1 | null | 6 | 0 | [
"LIN_FORM"
] | 1 | 0.153 | 2026-02-08T02:50:44.298321Z | {
"verified": true,
"answer": 49,
"timestamp": "2026-02-08T02:50:44.451034Z"
} | 9c7be7 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 1,
"correct": {
"strict": false,
"boxed": false,
"relaxed": true
},
"usage": {
"prompt_tokens": 223,
"completion_tokens": 32768
},
"timestamp": "2026-02-23T17:09:16.176Z",
"answer": null
},
{
... | 1 | [
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "MAX_PRIM... | {
"lo": -1.46,
"mid": 1.07,
"hi": 3.53
} | ||
9e339d | nt_count_divisors_in_range_v1_784195855_2138 | Let $n = 1680$, $a = 13$, and $b = 115$. Let $d$ be the number of positive divisors of $n$ that are between $a$ and $b$, inclusive. Let $Q$ be the remainder when $11081 \cdot d$ is divided by $95637$. Compute $Q$. | 19,265 | graphs = [
Graph(
let={
"n": Const(1680),
"a": Const(13),
"b": Const(115),
"result": CountOverSet(set=SolutionsSet(var=Var("d"), condition=And(Divides(divisor=Var("d"), dividend=Ref("n")), Geq(Var("d"), Ref("a")), Leq(Var("d"), Ref("b"))))),
"_c": ... | NT | null | COUNT | sympy | LIN_FORM | [
"LIN_FORM",
"LTE_DIFF"
] | 02f7ca | nt_count_divisors_in_range_v1 | null | 3 | 0 | [
"LIN_FORM",
"LTE_DIFF"
] | 2 | 0.041 | 2026-02-08T05:30:33.744744Z | {
"verified": true,
"answer": 19265,
"timestamp": "2026-02-08T05:30:33.785962Z"
} | 52e7e4 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 120,
"completion_tokens": 1557
},
"timestamp": "2026-02-12T10:40:20.148Z",
"answer": 19265
},
... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "LTE_DIFF",
"status": "ok"
},
{
... | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
796bc9 | nt_count_coprime_v1_1978505735_4058 | Let $k$ be the value of $$\frac{\min\{d \in \mathbb{Z} \mid d \geq 2 \text{ and } d \mid 245\} \times \sum_{k_1=1}^9 \sum_{j=1}^9 k_1}{45}.$$ Compute the number of positive integers $n$ such that $1 \leq n \leq 35344$ and $\gcd(n, k) = 1$. Find the value of this count. | 18,851 | graphs = [
Graph(
let={
"upper": Const(35344),
"k": Div(Mul(MinOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Const(2)), Divides(divisor=Var("d"), dividend=Const(245))))), SumOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("k1"), Var("_j")]), condi... | NT | null | COUNT | sympy | MIN_PRIME_FACTOR | [
"MIN_PRIME_FACTOR/SUM_INDEPENDENT/SUM_ARITHMETIC"
] | 879a99 | nt_count_coprime_v1 | null | 6 | 0 | [
"MIN_PRIME_FACTOR",
"SUM_ARITHMETIC",
"SUM_INDEPENDENT"
] | 3 | 2.711 | 2026-02-08T17:59:37.773253Z | {
"verified": true,
"answer": 18851,
"timestamp": "2026-02-08T17:59:40.484211Z"
} | c9eadd | 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": 1591
},
"timestamp": "2026-02-18T10:48:16.772Z",
"answer": 18851
},
... | 1 | [
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "MIN_PRIME_FACTOR",
"status": "ok"
},
{
"lemma": "SUM_ARITHMETIC",
"status": "ok_later"
},
{
"lemma": "SUM_INDEPENDENT",
"status":... | {
"lo": -7.08,
"mid": -0.32,
"hi": 6.26
} | ||
34ebea | diophantine_fbi2_count_v1_1248542787_928 | Let $k = 420$. Let $S$ be the set of all integers $d$ such that $2 \leq d \leq 101$, $d$ divides $k$, $\frac{k}{d} \geq 6$, and $\frac{k}{d} \leq T$, where $T$ is the number of positive integers $t$ with $35 \leq t \leq 371$ for which there exist positive integers $a \leq 25$ and $b \leq 9$ such that $t = 9a + 15b + 11... | 16 | graphs = [
Graph(
let={
"_n": Const(2),
"k": Const(420),
"result": CountOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Ref("_n")), Leq(Var("d"), Const(101)), Divides(divisor=Var("d"), dividend=Ref("k")), Geq(Div(Ref("k"), Var("d")), Const(6)), Leq(Div(... | NT | null | COUNT | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | diophantine_fbi2_count_v1 | null | 6 | 0 | [
"LIN_FORM"
] | 1 | 0.008 | 2026-02-08T03:29:37.339603Z | {
"verified": true,
"answer": 16,
"timestamp": "2026-02-08T03:29:37.347626Z"
} | 610041 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 249,
"completion_tokens": 3516
},
"timestamp": "2026-02-09T23:01:57.638Z",
"answer": 16
},
{
"id... | 1 | [
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "n... | {
"lo": -3.49,
"mid": 1.84,
"hi": 7.55
} | ||
bdeeba | comb_count_surjections_v1_53965629_32 | Let $n$ be the number of ordered pairs $(i, j)$ of integers such that $1 \leq i \leq 7$, $1 \leq j \leq 7$, and $i + j = 9$. Let $k = 4$. Define $\text{result} = k! \cdot S(n, k)$, where $S(n, k)$ denotes the Stirling number of the second kind. Find the smallest positive integer $m$ such that the $m$-th Fibonacci numbe... | 210 | graphs = [
Graph(
let={
"_n": Const(9),
"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(7)), right=IntegerRange(start=Const(1), end=Const... | COMB | NT | COUNT | sympy | COUNT_SUM_EQUALS | [
"COUNT_SUM_EQUALS"
] | 75ab0f | comb_count_surjections_v1 | null | 5 | 0 | [
"COUNT_SUM_EQUALS"
] | 1 | 0.042 | 2026-02-08T11:13:53.940088Z | {
"verified": true,
"answer": 210,
"timestamp": "2026-02-08T11:13:53.981933Z"
} | a9a0a3 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 239,
"completion_tokens": 2595
},
"timestamp": "2026-02-09T11:05:23.580Z",
"answer": 210
},
{
"id... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "ok"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8",
"status":... | {
"lo": -2.35,
"mid": 1.22,
"hi": 4.84
} | ||
6594f2 | nt_min_coprime_above_v1_168721529_152 | Let $S$ be the set of all real numbers $x$ such that $x^2 - 320x + 9975 = 0$. Define $m$ to be the sum of all elements of $S$. Let $T$ be the set of all integers $n$ such that $74529 < n \leq 74859$ and $\gcd(n, m) = 1$. Compute the smallest element of $T$. | 74,531 | graphs = [
Graph(
let={
"_n": Const(2),
"start": Const(74529),
"upper": Const(74859),
"modulus": SumOverSet(set=SolutionsSet(var=Var("x"), condition=Eq(Sum(Pow(Var("x"), Ref("_n")), Mul(Const(-320), Var("x")), Const(9975)), Const(0)))),
"result": M... | NT | null | EXTREMUM | sympy | VIETA_SUM | [
"VIETA_SUM"
] | b33a7a | nt_min_coprime_above_v1 | null | 6 | 0 | [
"VIETA_SUM"
] | 1 | 0.032 | 2026-02-08T12:50:59.049839Z | {
"verified": true,
"answer": 74531,
"timestamp": "2026-02-08T12:50:59.081485Z"
} | 65fb51 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 208,
"completion_tokens": 669
},
"timestamp": "2026-02-08T21:06:41.773Z",
"answer": 74531
},
{
"i... | 1 | [
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "V3",
"status": "no"
},
{
"lemma": "VIETA_SUM",
"sta... | {
"lo": -9.12,
"mid": -6.02,
"hi": -3.64
} | ||
e7d438 | diophantine_product_count_v1_1520064083_9397 | Let $k$ be the number of ordered pairs $(a,b)$ such that $1 \leq a \leq 6$ and $1 \leq b \leq 10$. Let $u$ be the number of nonnegative integers $j$ such that $0 \leq j \leq 32779$ and $\binom{32779}{j}$ is odd. Define $S$ as the set of all positive integers $x$ such that $1 \leq x \leq u$, $x$ divides $k$, and $\frac{... | 22,887 | graphs = [
Graph(
let={
"_n": Const(77821),
"k": CountOverSet(set=CartesianProduct(left=IntegerRange(start=Const(1), end=Const(6)), right=IntegerRange(start=Const(1), end=Const(10)))),
"upper": CountOverSet(set=SolutionsSet(var=Var("j"), condition=And(Geq(Var("j"), Const(... | NT | null | COUNT | sympy | COUNT_CARTESIAN | [
"COUNT_CARTESIAN",
"V8"
] | 2b9d9f | diophantine_product_count_v1 | null | 6 | 0 | [
"COUNT_CARTESIAN",
"V8"
] | 2 | 0.008 | 2026-02-08T10:42:56.993074Z | {
"verified": true,
"answer": 22887,
"timestamp": "2026-02-08T10:42:57.000835Z"
} | d3575b | 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": 1409
},
"timestamp": "2026-02-14T08:12:27.891Z",
"answer": 22887
},
... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "ok"
},
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K5",
"status"... | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
d72368 | nt_count_divisible_and_v1_458359167_3196 | Let $d_2$ be the number of integers $t$ with $7 \leq t \leq 22$ for which there exist integers $a$ and $b$ such that $1 \leq a \leq 6$, $1 \leq b \leq 2$, and $t = 2a + 5b$. Let $N$ be the number of positive integers $n$ not exceeding 231060 such that $n$ is divisible by both 10 and $d_2$. Compute the remainder when $4... | 48,997 | graphs = [
Graph(
let={
"_n": Const(40703),
"upper": Const(231060),
"d1": Const(10),
"d2": CountOverSet(set=SolutionsSet(var=Var("t"), condition=Exists(var=Var(name='a'), condition=Exists(var=Var(name='b'), condition=And(Geq(left=Var(name='a'), right=Const(val... | NT | null | COUNT | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | nt_count_divisible_and_v1 | null | 4 | 0 | [
"LIN_FORM"
] | 1 | 8.708 | 2026-02-08T07:02:34.189972Z | {
"verified": true,
"answer": 48997,
"timestamp": "2026-02-08T07:02:42.898223Z"
} | f2afdc | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 171,
"completion_tokens": 1407
},
"timestamp": "2026-02-13T16:12:20.803Z",
"answer": 48997
},
... | 1 | [
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "V3",
"status": "no"
}
] | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
712ff6 | sequence_fibonacci_compute_v1_784195855_1205 | Let $c = 2500$. Let $s$ be the minimum value of $x + y$ over all pairs of positive integers $(x, y)$ such that $xy = c$. Let $m$ be the largest positive divisor $d$ of 10700 such that $d \leq s$. Let $t$ be the minimum value of $x + y$ over all pairs of positive integers $(x, y)$ such that $xy = m$. Determine the value... | 6,765 | graphs = [
Graph(
let={
"_c": Const(2500),
"_m": MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(Mul(Var("x"), Var("y")), Ref("_c")))), expr=Sum(Var("x"), Var("y")))),
... | NT | null | COMPUTE | sympy | B3 | [
"B3/MAX_DIVISOR/B3"
] | 69a416 | sequence_fibonacci_compute_v1 | null | 6 | 0 | [
"B3",
"MAX_DIVISOR"
] | 2 | 0.004 | 2026-02-08T04:54:11.926602Z | {
"verified": true,
"answer": 6765,
"timestamp": "2026-02-08T04:54:11.930754Z"
} | bc7926 | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 218,
"completion_tokens": 380
},
"timestamp": "2026-02-11T22:04:58.678Z",
"answer": 377
},
{
"id": 11,
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "MAX_DIVISOR",
"status": "ok_later"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
},... | {
"lo": -5.55,
"mid": -3.01,
"hi": 0.34
} | ||
2681ac | comb_count_surjections_v1_601307018_8781 | Let $n = \sum_{k_1=0}^{2} 2^{k_1}$ and let $R = 7! \cdot S(n, 7)$, where $S(n, k)$ denotes the Stirling number of the second kind. Compute $53361 - R$. | 48,321 | graphs = [
Graph(
let={
"_n": Const(2),
"n": Summation(var="k1", start=Const(0), end=Const(2), expr=Pow(Ref("_n"), Var("k1"))),
"k": Const(7),
"result": Mul(Factorial(Ref("k")), Stirling2(n=Ref(name='n'), k=Ref(name='k'))),
"_c": Const(53361),
... | COMB | null | COUNT | sympy | POLY_ORBIT_LEGENDRE | [
"SUM_GEOM"
] | 04214c | comb_count_surjections_v1 | null | 3 | 0 | [
"POLY_ORBIT_LEGENDRE",
"SUM_GEOM"
] | 2 | 0.281 | 2026-03-10T09:14:22.529244Z | {
"verified": true,
"answer": 48321,
"timestamp": "2026-03-10T09:14:22.810277Z"
} | 7085aa | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 174,
"completion_tokens": 357
},
"timestamp": "2026-04-19T09:46:36.066Z",
"answer": 48321
},
{
"... | 2 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "SUM_GEOM",
"status": "ok"
},
{
"lemma": "V8",
"st... | {
"lo": -10,
"mid": -5.89,
"hi": -1.79
} | ||
affb8e | comb_binomial_compute_v1_1116507919_183 | Let $\phi(n)$ denote Euler's totient function, the number of positive integers less than or equal to $n$ that are relatively prime to $n$. Define
$$
k = \sum_{i=1}^{3} \phi(i) \left\lfloor \frac{3}{i} \right\rfloor.
$$
Compute $\binom{13}{k}$. | 1,716 | graphs = [
Graph(
let={
"_n": Const(3),
"n": Const(13),
"k": Summation(var="k", start=Const(1), end=Const(3), expr=Mul(EulerPhi(n=Var("k")), Floor(Div(Ref("_n"), Var("k"))))),
"result": Binom(n=Ref("n"), k=Ref("k")),
},
goal=Ref("result"),
... | NT | null | COMPUTE | sympy | K2 | [
"K2"
] | 6897ab | comb_binomial_compute_v1 | null | 4 | 0 | [
"K2"
] | 1 | 0.001 | 2026-02-08T02:27:18.810298Z | {
"verified": true,
"answer": 1716,
"timestamp": "2026-02-08T02:27:18.811228Z"
} | 805054 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 196,
"completion_tokens": 548
},
"timestamp": "2026-02-08T19:10:37.389Z",
"answer": 1716
},
{
"id... | 2 | [
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K2",
"status": "ok"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
}
] | {
"lo": -10,
"mid": -8.21,
"hi": -6.42
} | ||
a1d639 | algebra_poly_eval_v1_1874849503_551 | Let $n = 29$. Let $d$ be the smallest divisor of $735$ that is at least $2$. Compute the absolute value of the expression $n^d - 6n^2 + 4n - 1$. | 19,458 | graphs = [
Graph(
let={
"_n": Const(2),
"n": Const(29),
"result": Sum(Pow(Ref("n"), MinOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Const(2)), Divides(divisor=Var("d"), dividend=Const(735)))))), Mul(Const(-6), Pow(Ref("n"), Ref("_n"))), Mul(Const(4),... | NT | null | COMPUTE | sympy | MIN_PRIME_FACTOR | [
"MIN_PRIME_FACTOR"
] | bc3776 | algebra_poly_eval_v1 | null | 4 | 0 | [
"MIN_PRIME_FACTOR"
] | 1 | 0.002 | 2026-02-08T13:09:48.809864Z | {
"verified": true,
"answer": 19458,
"timestamp": "2026-02-08T13:09:48.812114Z"
} | 72b556 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 161,
"completion_tokens": 662
},
"timestamp": "2026-02-09T18:22:17.006Z",
"answer": 19458
},
{
"i... | 1 | [
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "MIN_PRIME_FACTOR",
"status": "ok"
... | {
"lo": -5.15,
"mid": 0.12,
"hi": 6.12
} | ||
7ce084 | modular_count_residue_v1_677425708_511 | Let $a = \gcd(3,5)$. Define
$$
A = \sum_{d \mid a} \mu(d),
$$
where $\mu$ denotes the Möbius function. Let $S$ be the set of all even integers $n$ such that $A \leq n \leq 6$. Define $m = \sum_{n \in S} n$.
Let $U = 38025$. Determine the number of positive integers $n$ such that $1 \leq n \leq U$ and $n \equiv 0 \pmod... | 3,168 | graphs = [
Graph(
let={
"upper": Const(38025),
"m": SumOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), SumOverDivisors(n=GCD(a=Const(value=3), b=Const(value=5)), var='d', expr=MoebiusMu(n=Var(name='d')))), Leq(Var("n"), Const(6)), Eq(Mod(value=Var("n"), modulus=Con... | NT | null | COUNT | sympy | MOBIUS_COPRIME | [
"MOBIUS_COPRIME",
"SUM_DIVISIBLE"
] | e34bec | modular_count_residue_v1 | null | 3 | 0 | [
"MOBIUS_COPRIME",
"SUM_DIVISIBLE"
] | 2 | 1.31 | 2026-02-08T03:35:09.181733Z | {
"verified": true,
"answer": 3168,
"timestamp": "2026-02-08T03:35:10.491570Z"
} | 05d5ba | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 246,
"completion_tokens": 726
},
"timestamp": "2026-02-08T20:41:09.684Z",
"answer": 3168
},
{
"id... | 2 | [
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "MOBIUS_COPRIME",
"status": "ok"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "SUM_DIVISIBLE",
"status": "ok"
},
{
"lemma": "V1",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
... | {
"lo": -10,
"mid": -6.47,
"hi": -2.95
} | ||
cd4bea | diophantine_fbi2_min_v1_1918700295_1063 | Let $A$ be the set of all integers $t$ such that $14 \leq t \leq 290$ and there exist positive integers $a \leq 25$, $b \leq 19$ satisfying $t = 4a + 10b$. Let $u$ be the number of elements in $A$. Let $P$ be the set of all positive integers $p$ such that there exists a positive integer $q > p$ with $pq = 12$ and $\gcd... | 5 | graphs = [
Graph(
let={
"_n": Const(4),
"k": Const(125),
"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... | NT | null | EXTREMUM | sympy | B1 | [
"COPRIME_PAIRS",
"LIN_FORM"
] | 67610e | diophantine_fbi2_min_v1 | null | 6 | 0 | [
"B1",
"COPRIME_PAIRS",
"LIN_FORM"
] | 3 | 0.051 | 2026-02-08T05:32:31.342358Z | {
"verified": true,
"answer": 5,
"timestamp": "2026-02-08T05:32:31.393405Z"
} | e200ce | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 224,
"completion_tokens": 3932
},
"timestamp": "2026-02-12T10:13:06.856Z",
"answer": 5
},
{
... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"le... | {
"lo": -7.01,
"mid": -4.68,
"hi": -2.15
} | ||
94cdec | antilemma_k3_v1_1978505735_2283 | Let $n = 49060$. Define $x$ to be the sum of $\phi(d)$ over all positive divisors $d$ of $n$, where $\phi$ denotes Euler's totient function. Let $c = 45818$. Compute the remainder when $c \cdot x$ is divided by $72369$. Determine the value of this remainder. | 49,940 | graphs = [
Graph(
let={
"x": SumOverDivisors(n=Const(value=49060), var='d', expr=EulerPhi(n=Var(name='d'))),
"_c": Const(45818),
"Q": Mod(value=Mul(Ref("_c"), Ref("x")), modulus=Const(72369)),
},
goal=Ref("Q"),
)
] | NT | COMB | COMPUTE | sympy | K3 | [
"K3"
] | 54c41e | antilemma_k3_v1 | null | 3 | 0 | [
"K3"
] | 1 | 0.001 | 2026-02-08T16:48:44.894452Z | {
"verified": true,
"answer": 49940,
"timestamp": "2026-02-08T16:48:44.895395Z"
} | afa2bf | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 121,
"completion_tokens": 1905
},
"timestamp": "2026-02-17T12:34:50.153Z",
"answer": 49940
},
... | 1 | [
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "K3",
"status": "ok"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status"... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
f0ff1c | nt_count_divisible_v1_1520064083_9982 | Let $A$ be the number of positive multiples of 27 that are less than or equal to 30803. Let $B$ be the maximum value of $xy$ where $x$ and $y$ are positive integers such that $x + y = 124$. Define $Q$ to be the sum of the digits of $A$, where the digit in the $10^i$ place is multiplied by $(i+1)^2$, plus $B$. Find the ... | 3,885 | graphs = [
Graph(
let={
"_n": Const(2),
"upper": Const(30803),
"divisor": Const(27),
"result": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Ref("upper")), Eq(Mod(value=Var("n"), modulus=Ref("divisor")), Const... | NT | null | COUNT | sympy | B1 | [
"B1"
] | 51a773 | nt_count_divisible_v1 | digits_weighted_mod | 5 | 0 | [
"B1"
] | 1 | 0.986 | 2026-02-08T11:05:54.302947Z | {
"verified": true,
"answer": 3885,
"timestamp": "2026-02-08T11:05:55.289183Z"
} | abc866 | 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": 785
},
"timestamp": "2026-02-14T10:37:12.624Z",
"answer": 3885
},
{
... | 1 | [
{
"lemma": "B1",
"status": "ok"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
}
] | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
6692a5 | nt_count_divisible_v1_2051736721_4688 | Let $N$ be the number of positive integers $n$ such that $n \leq 65536$ and $n$ is divisible by 27. Let $c$ be the number of ordered pairs $(p, q)$ of positive integers such that $p \cdot q = 72$, $\gcd(p, q) = 1$, and $p < q$. Compute the remainder when $c - N$ is divided by 86777. | 84,352 | graphs = [
Graph(
let={
"upper": Const(65536),
"divisor": Const(27),
"result": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Ref("upper")), Eq(Mod(value=Var("n"), modulus=Ref("divisor")), Const(0))))),
"_c": C... | NT | null | COUNT | sympy | COPRIME_PAIRS | [
"COPRIME_PAIRS"
] | c90628 | nt_count_divisible_v1 | negation_mod | 3 | 0 | [
"COPRIME_PAIRS"
] | 1 | 2.231 | 2026-02-08T18:06:46.742581Z | {
"verified": true,
"answer": 84352,
"timestamp": "2026-02-08T18:06:48.973935Z"
} | f61cc3 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 141,
"completion_tokens": 1754
},
"timestamp": "2026-02-18T13:28:14.709Z",
"answer": 84352
},
... | 1 | [
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "V1",
"status": "no"
},
{
"lemma": "V3",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
2c0195 | lin_form_endings_v1_151522320_523 | Let $a = 9$, $b = 21$, $A = 24$, and $B = 14$. Let $g = \gcd(a, b)$, and define $a' = \left\lfloor \frac{a}{g} \right\rfloor$ and $b' = \left\lfloor \frac{b}{g} \right\rfloor$. Let $T$ be a set whose size is given by $|T| = a' \cdot A + b' \cdot B - a' \cdot b'$. Define the total quantity
$$
\text{total} = (a \cdot A +... | 62,224 | graphs = [
Graph(
let={
"a_coeff": Const(9),
"b_coeff": Const(21),
"A_val": Const(24),
"B_val": Const(14),
"g_step": GCD(a=Ref("a_coeff"), b=Ref("b_coeff")),
"ap_node": Floor(Div(Ref("a_coeff"), Ref("g_step"))),
"bp_node": F... | COMB | NT | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | lin_form_endings_v1 | null | 6 | null | [
"LIN_FORM"
] | 1 | 0.003 | 2026-02-08T03:22:04.139005Z | {
"verified": true,
"answer": 62224,
"timestamp": "2026-02-08T03:22:04.141650Z"
} | 94fdfc | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 313,
"completion_tokens": 907
},
"timestamp": "2026-02-10T14:00:07.189Z",
"answer": 62224
},
{
"i... | 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": -3.46,
"mid": 1.03,
"hi": 5.49
} | ||
6b0e1d | sequence_fibonacci_compute_v1_1470522791_1004 | Let $S$ be the set of all integers $t$ such that $20 \leq t \leq 76$ and $t = 6a + 8b + 6$ for some integers $a$ and $b$ with $1 \leq a \leq 5$ and $1 \leq b \leq 5$. Let $n$ be the number of elements in $S$. Compute the $n$-th Fibonacci number. | 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=5)), Geq(left=Var(name='b'), right=Const(value=1... | NT | null | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | sequence_fibonacci_compute_v1 | null | 4 | 0 | [
"LIN_FORM"
] | 1 | 0.002 | 2026-02-08T13:22:36.120079Z | {
"verified": true,
"answer": 28657,
"timestamp": "2026-02-08T13:22:36.121722Z"
} | 67598c | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 141,
"completion_tokens": 2981
},
"timestamp": "2026-02-15T14:04:35.064Z",
"answer": 28657
},
... | 1 | [
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
... | {
"lo": -5.49,
"mid": 0.22,
"hi": 6.51
} | ||
508f3f | nt_sum_over_divisible_v1_1353956133_632 | Let $A$ be the number of positive integers $n$ such that $1 \leq n \leq 18631$ and the sum of the decimal digits of $n$ is odd. Let $B$ be the sum of all positive integers $n$ such that $1 \leq n \leq A$ and $n$ is divisible by $151$. Compute the remainder when $44121 \cdot B$ is divided by $99059$. | 30,841 | graphs = [
Graph(
let={
"_n": Const(99059),
"upper": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Const(18631)), Eq(Mod(value=DigitSum(Var("n")), modulus=Const(2)), Const(1))))),
"divisor": Const(151),
"resul... | NT | null | SUM | sympy | L3B | [
"L3B"
] | cc148f | nt_sum_over_divisible_v1 | null | 5 | 0 | [
"L3B"
] | 1 | 0.317 | 2026-02-08T11:45:18.065832Z | {
"verified": true,
"answer": 30841,
"timestamp": "2026-02-08T11:45:18.382741Z"
} | 449f0d | 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": 3609
},
"timestamp": "2026-02-14T17:54:38.532Z",
"answer": 30841
},
... | 1 | [
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "L3B",
"status": "ok"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "V3",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
}
] | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
87e6fc | alg_poly_orbit_count_v1_1218484723_6694 | For a non-negative integer $a$, define a sequence modulo $37$ by $N = a^2 \bmod 37$, $M = N^2 \bmod 37$, $R = M^2 \bmod 37$, $S = R^2 \bmod 37$, $T = S^2 \bmod 37$, and $K = T^2 \bmod 37$. Find the number of integers $a$ with $0 \le a \le 70928$ such that $K = a$ but $a$ does not appear earlier in the sequence (i.e., $... | 11,502 | graphs = [
Graph(
let={
"p1": Mod(value=Pow(Var("a"), Const(2)), modulus=Const(37)),
"p2": Mod(value=Pow(Ref("p1"), Const(2)), modulus=Const(37)),
"p3": Mod(value=Pow(Ref("p2"), Const(2)), modulus=Const(37)),
"p4": Mod(value=Pow(Ref("p3"), Const(2)), modulus=C... | ALG | null | COUNT | sympy | POLY_ORBIT_COUNT | [
"POLY_ORBIT_COUNT"
] | 4ad965 | alg_poly_orbit_count_v1 | null | 6 | null | [
"POLY_ORBIT_COUNT"
] | 1 | 0.014 | 2026-02-25T08:12:33.122881Z | {
"verified": true,
"answer": 11502,
"timestamp": "2026-02-25T08:12:33.136722Z"
} | 221090 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 260,
"completion_tokens": 4677
},
"timestamp": "2026-03-30T02:36:41.581Z",
"answer": 11502
},
{
"... | 1 | [
{
"lemma": "POLY_ORBIT_COUNT",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
}
] | {
"lo": 1.53,
"mid": 4.7,
"hi": 7.23
} | ||
9be0c5 | modular_min_linear_v1_48377204_2935 | Let $b$ be the number of ordered pairs $(x_1, x_2)$ of positive odd integers such that $x_1 + x_2 = 4968$. Let $m = 2748$ and $a = 329$. Let $x$ be the smallest positive integer such that $1 \leq x \leq m$ and $329x \equiv b \pmod{2748}$. Let $Q$ be the Bell number $B_k$, where $k$ is the remainder when $|x|$ is divide... | 4,140 | graphs = [
Graph(
let={
"_n": Const(4968),
"a": Const(329),
"b": 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')), E... | COMB | null | EXTREMUM | sympy | LIN_FORM | [
"COMB1"
] | 567f58 | modular_min_linear_v1 | null | 6 | 0 | [
"COMB1",
"LIN_FORM"
] | 2 | 2.919 | 2026-02-08T17:04:53.636185Z | {
"verified": true,
"answer": 4140,
"timestamp": "2026-02-08T17:04:56.554822Z"
} | 6958fa | 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": 1810
},
"timestamp": "2026-02-17T18:50:37.203Z",
"answer": 4140
},
{... | 1 | [
{
"lemma": "COMB1",
"status": "ok"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
}
] | {
"lo": -2.38,
"mid": 1.74,
"hi": 6.59
} | ||
0c7cf2 | comb_factorial_compute_v1_1742523217_3547 | Let $n$ be the smallest positive divisor of $77077$ that is at least as large as the number of ordered pairs $(p,q)$ of positive integers such that $p < q$, $\gcd(p,q) = 1$, and $p \cdot q = 216$. Compute $n!$. | 5,040 | graphs = [
Graph(
let={
"_n": Const(77077),
"n": 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=Var(name='q'), condition=And(Eq(left=Mul(Var(name='p'), Var(name=... | NT | null | COMPUTE | sympy | COPRIME_PAIRS | [
"COPRIME_PAIRS/MIN_PRIME_FACTOR"
] | 52cee2 | comb_factorial_compute_v1 | null | 6 | 0 | [
"COPRIME_PAIRS",
"MIN_PRIME_FACTOR"
] | 2 | 0.001 | 2026-02-08T05:56:09.712231Z | {
"verified": true,
"answer": 5040,
"timestamp": "2026-02-08T05:56:09.713416Z"
} | d2c228 | 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": 1196
},
"timestamp": "2026-02-12T17:35:45.137Z",
"answer": 5040
},
{... | 1 | [
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "MIN_PRIME_FACTOR",
"st... | {
"lo": -5.55,
"mid": -3.01,
"hi": 0.32
} | ||
2d0bb4 | sequence_lucas_compute_v1_168721529_1620 | Let $r$ be the sum of the solutions to the equation $x^2 - 121x - 15246 = 0$. Let $T$ be the set of all ordered pairs $(x,y)$ of positive integers such that $xy = r$. Define $s$ to be the minimum value of $x + y$ over all pairs $(x,y) \in T$. Let $L_s$ denote the $s$-th Lucas number. Find the smallest positive integer ... | 4,895 | graphs = [
Graph(
let={
"_m": Const(2),
"_n": SumOverSet(set=SolutionsSet(var=Var("x"), condition=Eq(Sum(Pow(Var("x"), Ref("_m")), Mul(Const(-121), Var("x")), Const(-15246)), Const(0)))),
"n": MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y... | NT | null | COMPUTE | sympy | VIETA_SUM | [
"VIETA_SUM/B3"
] | d036a4 | sequence_lucas_compute_v1 | null | 6 | 0 | [
"B3",
"VIETA_SUM"
] | 2 | 0.002 | 2026-02-08T13:48:51.741775Z | {
"verified": true,
"answer": 4895,
"timestamp": "2026-02-08T13:48:51.743910Z"
} | 77dac3 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 235,
"completion_tokens": 5775
},
"timestamp": "2026-02-09T19:29:21.153Z",
"answer": 4895
},
{
"i... | 1 | [
{
"lemma": "B3",
"status": "ok_later"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "VAL_SUM_EQ",
"status": "no"
},
... | {
"lo": -5.49,
"mid": 0.03,
"hi": 6.12
} | ||
430696 | modular_inverse_v1_2051736721_4431 | Consider all ordered pairs $(i,j)$ of integers with $1\le i\le 52$ and $1\le j\le 52$ such that $i+j=54$. Let $u$ be the number of such ordered pairs.
Let $T$ be the set of all integers $t$ such that $14\le t\le 122$ and there exist integers $a$ and $b$ with $1\le a\le 3$, $1\le b\le 23$, and
$$t=10a+4b.$$
Let $v$ be ... | 24,296 | graphs = [
Graph(
let={
"_d": Const(44121),
"_c": Const(1243),
"_m": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("i"), Var("j")]), condition=Eq(Sum(Var("i"), Var("j")), Const(54)), domain=CartesianProduct(left=IntegerRange(start=Const(1), end=Const(52)), right=I... | NT | null | EXTREMUM | sympy | COUNT_SUM_EQUALS | [
"COUNT_SUM_EQUALS/MAX_PRIME_BELOW/K2",
"LIN_FORM/K2"
] | 556a8c | modular_inverse_v1 | null | 6 | 0 | [
"COUNT_SUM_EQUALS",
"K2",
"LIN_FORM",
"MAX_PRIME_BELOW"
] | 4 | 0.068 | 2026-02-08T17:59:02.437385Z | {
"verified": true,
"answer": 24296,
"timestamp": "2026-02-08T17:59:02.504976Z"
} | 1e279a | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 307,
"completion_tokens": 4577
},
"timestamp": "2026-02-18T11:31:39.782Z",
"answer": 24296
},
... | 1 | [
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "ok"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K2",
"status": "ok_later"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "MAX_PRIME_BELOW",
... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
f46f96 | sequence_count_fib_divisible_v1_1248542787_196 | Let $d$ be the smallest divisor of 6125 that is greater than or equal to 2. Let $U$ be the number of ordered pairs $(i, j)$ such that $1 \leq i \leq 25$ and $1 \leq j \leq 30$. Let $\text{result}$ be the number of positive integers $n$ such that $1 \leq n \leq U$ and $d$ divides the $n$th Fibonacci number. Compute $\te... | 150 | graphs = [
Graph(
let={
"_n": Const(6125),
"upper": CountOverSet(set=CartesianProduct(left=IntegerRange(start=Const(1), end=Const(25)), right=IntegerRange(start=Const(1), end=Const(30)))),
"d": MinOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Const(2)... | NT | null | COUNT | sympy | LIN_FORM | [
"MIN_PRIME_FACTOR",
"COUNT_CARTESIAN"
] | fea473 | sequence_count_fib_divisible_v1 | null | 5 | 0 | [
"COUNT_CARTESIAN",
"LIN_FORM",
"MIN_PRIME_FACTOR"
] | 3 | 0.437 | 2026-02-08T03:00:53.397723Z | {
"verified": true,
"answer": 150,
"timestamp": "2026-02-08T03:00:53.834672Z"
} | 64db0a | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 226,
"completion_tokens": 855
},
"timestamp": "2026-02-09T01:13:21.648Z",
"answer": 150
},
{
"id"... | 1 | [
{
"lemma": "COUNT_CARTESIAN",
"status": "ok"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MIN_PRIME_FACTOR",
"status": "ok"
},
{
"lemma": "V1",
"status... | {
"lo": -3.97,
"mid": -1.31,
"hi": 0.91
} | ||
d154bf | nt_sum_gcd_range_mod_v1_124444284_628 | Let $S$ be the set of all ordered pairs $(x, y)$ of positive integers such that $xy = 11108889$. Let $N$ be the minimum value of $x + y$ over all such pairs. Let $k$ be the number of integers $t$ with $7 \leq t \leq 190$ such that there exist positive integers $a \leq 50$ and $b \leq 18$ satisfying $t = 2a + 5b$. Let $... | 9,161 | graphs = [
Graph(
let={
"N": MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(Mul(Var("x"), Var("y")), Const(11108889)))), expr=Sum(Var("x"), Var("y")))),
"k": CountOver... | NT | null | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM",
"ONE_PHI_1",
"B3"
] | cf33d8 | nt_sum_gcd_range_mod_v1 | null | 6 | 0 | [
"B3",
"LIN_FORM",
"ONE_PHI_1"
] | 3 | 0.316 | 2026-02-08T03:24:44.400133Z | {
"verified": true,
"answer": 9161,
"timestamp": "2026-02-08T03:24:44.716315Z"
} | ced46f | 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": 5220
},
"timestamp": "2026-02-09T20:02:06.522Z",
"answer": 9123
},
{
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "ONE_PHI_1",
"status": "ok"
},
... | {
"lo": 1.69,
"mid": 5.03,
"hi": 8.38
} | ||
03ee79 | modular_sum_quadratic_residues_v1_151522320_653 | Let $p$ be the largest prime number less than or equal to $405$.
Define
$$
\text{result} = \frac{p(p - 1)}{4}.
$$
Let $Q$ be the remainder when $12161 \cdot \text{result}$ is divided by $77087$.
Compute $Q$. | 3,738 | graphs = [
Graph(
let={
"_n": Const(405),
"p": MaxOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(2)), Leq(Var("n"), Ref("_n")), IsPrime(Var("n"))))),
"result": Div(Mul(Ref("p"), Sub(Ref("p"), Const(1))), Const(4)),
"Q": Mod(value=Mul(... | NT | null | SUM | sympy | MAX_PRIME_BELOW | [
"MAX_PRIME_BELOW"
] | dc3ad3 | modular_sum_quadratic_residues_v1 | null | 4 | 0 | [
"MAX_PRIME_BELOW"
] | 1 | 0.002 | 2026-02-08T03:26:50.806400Z | {
"verified": true,
"answer": 3738,
"timestamp": "2026-02-08T03:26:50.807926Z"
} | 64ed04 | 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": 1491
},
"timestamp": "2026-02-10T14:31:09.018Z",
"answer": 3738
},
{
"i... | 1 | [
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok"
},
{
"lemma": "V1",
"status": "no"
... | {
"lo": -3.46,
"mid": 1.03,
"hi": 5.49
} | ||
c193ff | alg_poly_orbit_count_v1_1419126231_149 | For each integer $a$ with $0 \le a \le 35371$, define $N = (2a^3 + 5a) \bmod 37$, $M = (2N^3 + 5N) \bmod 37$, and $R = (2M^3 + 5M) \bmod 37$. Let $Q$ be the number of such $a$ for which $R = a$, $N \neq a$, and $M \neq a$. Find $Q$. | 5,736 | graphs = [
Graph(
let={
"p1": Mod(value=Sum(Mul(Const(2), Pow(Var("a"), Const(3))), Mul(Const(5), Var("a"))), modulus=Const(37)),
"p2": Mod(value=Sum(Mul(Const(2), Pow(Ref("p1"), Const(3))), Mul(Const(5), Ref("p1"))), modulus=Const(37)),
"p3": Mod(value=Sum(Mul(Const(2), ... | ALG | null | COUNT | sympy | POLY_ORBIT_COUNT | [
"POLY_ORBIT_COUNT"
] | 4ad965 | alg_poly_orbit_count_v1 | null | 6 | null | [
"POLY_ORBIT_COUNT"
] | 1 | 0.018 | 2026-02-25T09:42:45.580208Z | {
"verified": true,
"answer": 5736,
"timestamp": "2026-02-25T09:42:45.597835Z"
} | 88ee3f | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 223,
"completion_tokens": 7844
},
"timestamp": "2026-03-30T07:18:35.713Z",
"answer": 5736
},
{
"i... | 1 | [
{
"lemma": "POLY_ORBIT_COUNT",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
}
] | {
"lo": 3.8,
"mid": 6.33,
"hi": 9.49
} | ||
80b549 | comb_sum_binomial_row_v1_677425708_1388 | Let $n$ be the number of positive integers $p$ for which there exists a positive integer $q$ such that $p < q$, $\gcd(p, q) = 1$, and $pq = 83853000$. Compute the value of $2^n$. | 65,536 | graphs = [
Graph(
let={
"_n": Const(2),
"n": CountOverSet(set=SolutionsSet(var=Var("p"), condition=And(IsPositive(arg=Var(name='p')), Exists(var=Var(name='q'), condition=And(Eq(left=Mul(Var(name='p'), Var(name='q')), right=Const(value=83853000)), Eq(left=GCD(a=Var(name='p'), b=Var(na... | NT | null | SUM | sympy | COPRIME_PAIRS | [
"COPRIME_PAIRS"
] | 2bb3aa | comb_sum_binomial_row_v1 | null | 6 | 0 | [
"COPRIME_PAIRS"
] | 1 | 0.002 | 2026-02-08T04:10:06.803289Z | {
"verified": true,
"answer": 65536,
"timestamp": "2026-02-08T04:10:06.805048Z"
} | 267dbc | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 169,
"completion_tokens": 2050
},
"timestamp": "2026-02-09T19:19:17.363Z",
"answer": 65536
},
{
"... | 1 | [
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"s... | {
"lo": -3.46,
"mid": 1.03,
"hi": 5.49
} | ||
5af953 | nt_count_divisible_and_v1_784195855_3540 | Let $d_1$ be the number of elements in the Cartesian product of the sets $\{1, 2\}$ and $\{1, 2, 3, 4, 5\}$. Let $d_2 = 15$. Determine the number of positive integers $n$ such that $1 \le n \le 124470$, $n \equiv \sum_{k=0}^{2} (-1)^k \binom{2}{k} \pmod{d_1}$, and $n \equiv 0 \pmod{d_2}$. | 4,149 | graphs = [
Graph(
let={
"upper": Const(124470),
"d1": CountOverSet(set=CartesianProduct(left=IntegerRange(start=Const(1), end=Const(2)), right=IntegerRange(start=Const(1), end=Const(5)))),
"d2": Const(15),
"result": CountOverSet(set=SolutionsSet(var=Var("n"), ... | COMB | null | COUNT | sympy | BINOMIAL_ALTERNATING | [
"BINOMIAL_ALTERNATING",
"COUNT_CARTESIAN"
] | ceaf09 | nt_count_divisible_and_v1 | null | 5 | 0 | [
"BINOMIAL_ALTERNATING",
"COUNT_CARTESIAN"
] | 2 | 7.272 | 2026-02-08T06:29:25.104701Z | {
"verified": true,
"answer": 4149,
"timestamp": "2026-02-08T06:29:32.376679Z"
} | 344ddb | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 238,
"completion_tokens": 832
},
"timestamp": "2026-02-24T06:19:10.220Z",
"answer": 4149
},
{
"id... | 1 | [
{
"lemma": "BINOMIAL_ALTERNATING",
"status": "ok"
},
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "ok"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "V8"... | {
"lo": -5.98,
"mid": -3.97,
"hi": -1.94
} | ||
67973c | antilemma_product_of_sums_v1_1742523217_4231 | Let $m = 2$. Let $n$ be the largest prime number such that $m \leq n \leq 9$. Define $S_1 = \sum_{k=1}^{n} k$. Let $S_2$ be the sum of the first components of all ordered pairs $(k, j)$ of positive integers with $1 \leq k \leq 9$ and $1 \leq j \leq 8$. Compute the value of $S_1 \cdot S_2$. | 10,080 | graphs = [
Graph(
let={
"_m": Const(2),
"_n": MaxOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Ref("_m")), Leq(Var("n"), Const(9)), IsPrime(Var("n"))))),
"S1": Summation(var="k", start=Const(1), end=Ref("_n"), expr=Var("k")),
"S2": SumOver... | NT | null | COMPUTE | sympy | MAX_PRIME_BELOW | [
"MAX_PRIME_BELOW/PRODUCT_OF_SUMS/SUM_ARITHMETIC"
] | 8df830 | antilemma_product_of_sums_v1 | null | 3 | 0 | [
"MAX_PRIME_BELOW",
"PRODUCT_OF_SUMS",
"SUM_ARITHMETIC"
] | 3 | 0.002 | 2026-02-08T07:08:20.220099Z | {
"verified": true,
"answer": 10080,
"timestamp": "2026-02-08T07:08:20.221861Z"
} | d5a420 | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 199,
"completion_tokens": 302
},
"timestamp": "2026-02-19T23:52:19.768Z",
"answer": 9072
}
] | 0 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok"
},
{
"lemma": "PRODUCT_OF_SUMS",
"status": "ok_later"
},
{
"lemma": "SUM_ARITHMETIC",
"status": ... | {
"lo": -6.48,
"mid": 1.54,
"hi": 9.56
} | ||
5964a4 | geo_visible_lattice_v1_1978505735_3381 | Let $n = 81$. A visible lattice point $(x, y)$ is a point in the plane with integer coordinates such that $1 \leq x, y \leq n$ and $\gcd(x, y) = 1$.
Let $V$ denote the number of visible lattice points $(x, y)$ with $1 \leq x, y \leq 81$.
Compute $57600 - V$. | 53,561 | graphs = [
Graph(
let={
"n": Const(81),
"result": VisibleLatticePoints(n=Ref(name='n')),
"_c": Const(57600),
"Q": Sub(Ref("_c"), Ref("result")),
},
goal=Ref("Q"),
)
] | GEOM | null | COUNT | sympy | [] | geo_visible_lattice_v1 | null | 3 | 0 | null | null | 2.328 | 2026-02-08T17:35:57.473644Z | {
"verified": true,
"answer": 53561,
"timestamp": "2026-02-08T17:35:59.801471Z"
} | 178c5e | 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": 4004
},
"timestamp": "2026-02-18T04:53:55.541Z",
"answer": 53561
},
... | 1 | [] | {
"lo": -2.38,
"mid": 1.74,
"hi": 6.59
} | ||||
5ea086 | nt_min_coprime_above_v1_865884756_985 | Let $n = 182$. Define $s$ to be the maximum value of $xy$ over all ordered pairs $(x, y)$ of positive integers such that $x + y = n$. Find the smallest integer $m$ such that $s < m \leq 8719$ and $\gcd(m, 428) = 1$. | 8,283 | graphs = [
Graph(
let={
"_n": Const(182),
"start": MaxOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(Sum(Var("x"), Var("y")), Ref("_n")))), expr=Mul(Var("x"), Var("y"))))... | NT | null | EXTREMUM | sympy | B1 | [
"B1"
] | 5b950e | nt_min_coprime_above_v1 | null | 4 | 0 | [
"B1"
] | 1 | 0.203 | 2026-02-08T15:42:24.026417Z | {
"verified": true,
"answer": 8283,
"timestamp": "2026-02-08T15:42:24.228989Z"
} | 457237 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 119,
"completion_tokens": 755
},
"timestamp": "2026-02-16T12:00:13.545Z",
"answer": 8283
},
{
... | 1 | [
{
"lemma": "B1",
"status": "ok"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "VAL_SUM_EQ",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
913e3f | sequence_lucas_compute_v1_898971024_2267 | Let $c = 121$. Consider the set of all ordered pairs $(x, y)$ of positive integers such that $xy = c$. For each such pair, compute $x + y$, and let $m$ be the minimum value of $x + y$ over all such pairs.
Now consider the set of all ordered pairs $(x_1, y_1)$ of positive integers such that $x_1 + y_1 = m$. For each su... | 39,603 | graphs = [
Graph(
let={
"_c": Const(121),
"_m": MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(Mul(Var("x"), Var("y")), Ref("_c")))), expr=Sum(Var("x"), Var("y")))),
... | NT | null | COMPUTE | sympy | B3 | [
"B3/B1/B3"
] | 7fe69e | sequence_lucas_compute_v1 | null | 6 | 0 | [
"B1",
"B3"
] | 2 | 0.003 | 2026-02-08T16:38:20.242079Z | {
"verified": true,
"answer": 39603,
"timestamp": "2026-02-08T16:38:20.245154Z"
} | 8a5d6e | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 259,
"completion_tokens": 984
},
"timestamp": "2026-02-17T09:37:00.446Z",
"answer": 39603
},
{... | 1 | [
{
"lemma": "B1",
"status": "ok_later"
},
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
},
{
"lemma": "V8_SUM",
... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
a2b3be | comb_count_derangements_v1_784195855_7857 | Let $n$ be the number of positive integers $p$ for which there exists a positive integer $q$ such that $p < q$, $\gcd(p, q) = 1$, and $pq = 630$. Compute the subfactorial of $n$. | 14,833 | graphs = [
Graph(
let={
"n": CountOverSet(set=SolutionsSet(var=Var("p"), condition=And(IsPositive(arg=Var(name='p')), Exists(var=Var(name='q'), condition=And(Eq(left=Mul(Var(name='p'), Var(name='q')), right=Const(value=630)), Eq(left=GCD(a=Var(name='p'), b=Var(name='q')), right=Const(value=1)), ... | NT | COMB | COUNT | sympy | COPRIME_PAIRS | [
"COPRIME_PAIRS"
] | 2bb3aa | comb_count_derangements_v1 | null | 5 | 0 | [
"COPRIME_PAIRS"
] | 1 | 0.003 | 2026-02-08T09:33:54.231279Z | {
"verified": true,
"answer": 14833,
"timestamp": "2026-02-08T09:33:54.233805Z"
} | 7ffe26 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 103,
"completion_tokens": 1981
},
"timestamp": "2026-02-14T05:04:24.309Z",
"answer": 14833
},
... | 1 | [
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "V3",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
}
] | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
45f400 | alg_poly_preperiod_count_v1_601307018_8237 | Let $N \equiv a^2 + 2 \pmod{17}$, $M \equiv N^2 + 2 \pmod{17}$, $R \equiv M^2 + 2 \pmod{17}$, $S \equiv R^2 + 2 \pmod{17}$, and $T \equiv S^2 + 2 \pmod{17}$. Find the number of non-negative integers $a$ with $0 \le a \le 26502$ such that $T = N$, $M \ne N$, $R \ne N$, and $S \ne N$. | 12,472 | graphs = [
Graph(
let={
"p1": Mod(value=Sum(Pow(Var("a"), Const(2)), Const(2)), modulus=Const(17)),
"p2": Mod(value=Sum(Pow(Ref("p1"), Const(2)), Const(2)), modulus=Const(17)),
"p3": Mod(value=Sum(Pow(Ref("p2"), Const(2)), Const(2)), modulus=Const(17)),
"p4": ... | ALG | null | COUNT | sympy | POLY_ORBIT_COUNT | [
"POLY_ORBIT_COUNT"
] | 4ad965 | alg_poly_preperiod_count_v1 | null | 7 | null | [
"POLY_ORBIT_COUNT"
] | 1 | 0.017 | 2026-03-10T08:45:19.470100Z | {
"verified": true,
"answer": 12472,
"timestamp": "2026-03-10T08:45:19.486773Z"
} | a5218e | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 250,
"completion_tokens": 3281
},
"timestamp": "2026-04-19T08:33:58.735Z",
"answer": 12472
},
{
... | 1 | [
{
"lemma": "POLY_ORBIT_COUNT",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
}
] | {
"lo": -5.34,
"mid": 1.1,
"hi": 7.53
} | ||
366bb7 | antilemma_k2_v1_655260480_2987 | Let $s = \sum_{k=1}^{21} \phi(k) \left\lfloor \frac{21}{k} \right\rfloor$, where $\phi$ denotes Euler's totient function. Compute the value of $\sum_{k=1}^{s} \phi(k) \left\lfloor \frac{231}{k} \right\rfloor$. | 26,796 | graphs = [
Graph(
let={
"_n": Const(21),
"x": Summation(var="k", start=Const(1), end=Summation(var="k1", start=Const(1), end=Ref("_n"), expr=Mul(EulerPhi(n=Var("k1")), Floor(Div(Const(21), Var("k1"))))), expr=Mul(EulerPhi(n=Var("k")), Floor(Div(Const(231), Var("k"))))),
},
... | NT | COMB | COMPUTE | sympy | K13 | [
"K2/K2",
"K2"
] | 76610f | antilemma_k2_v1 | null | 6 | 0 | [
"K13",
"K2"
] | 2 | 0.005 | 2026-02-08T17:06:18.749573Z | {
"verified": true,
"answer": 26796,
"timestamp": "2026-02-08T17:06:18.754893Z"
} | 80ceb5 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 123,
"completion_tokens": 735
},
"timestamp": "2026-02-17T19:39:28.272Z",
"answer": 26796
},
{... | 1 | [
{
"lemma": "K2",
"status": "ok"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "VAL_SUM_EQ",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
fb78ee | antilemma_product_of_sums_v1_784195855_3076 | Let $S_1$ be the sum of all values of $k$ as $(k, j)$ ranges over all ordered pairs of positive integers with $1 \leq k \leq 11$ and $1 \leq j \leq 2$. Let $S_2$ be the sum of $i \cdot j$ as $(i, j)$ ranges over all ordered pairs of positive integers with $1 \leq i \leq 5$ and $1 \leq j \leq 6$. Let $x = S_1 \cdot S_2$... | 29,140 | graphs = [
Graph(
let={
"S1": SumOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("k"), Var("_j")]), condition=Const(1), domain=CartesianProduct(left=IntegerRange(start=Const(1), end=Const(11)), right=IntegerRange(start=Const(1), end=Const(2)))), expr=Var("k"))),
"S2":... | NT | null | COMPUTE | sympy | LTE_SUM | [
"PRODUCT_OF_SUMS",
"ONE_PHI_1"
] | 10ba65 | antilemma_product_of_sums_v1 | null | 3 | 0 | [
"LTE_SUM",
"ONE_PHI_1",
"PRODUCT_OF_SUMS"
] | 3 | 0.019 | 2026-02-08T06:12:58.527362Z | {
"verified": true,
"answer": 29140,
"timestamp": "2026-02-08T06:12:58.546209Z"
} | a5a634 | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 235,
"completion_tokens": 579
},
"timestamp": "2026-02-19T02:55:41.534Z",
"answer": 33010
}
] | 0 | [
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "ONE_PHI_1",
"status": "ok"
},
{
"lemma": "PRODUCT_OF_SUMS",
"status": "ok"
},
{
"lemma": "V8",
"status": "no... | {
"lo": -6.48,
"mid": 1.54,
"hi": 9.56
} | ||
d275c2 | antilemma_k2_v1_1978505735_6050 | Let $n = 102$. Consider the quadratic equation $x^2 - 102x + 2501 = 0$. Let $k_{\text{max}}$ be the sum of all real solutions to this equation. Compute the sum
$$
\sum_{k=1}^{k_{\text{max}}} \phi(k) \left\lfloor \frac{n}{k} \right\rfloor,
$$
where $\phi(k)$ denotes Euler's totient function. | 5,253 | graphs = [
Graph(
let={
"_n": Const(102),
"x": Summation(var="k", start=Const(1), end=SumOverSet(set=SolutionsSet(var=Var("x1"), condition=Eq(Sum(Pow(Var("x1"), Const(2)), Mul(Const(-102), Var("x1")), Const(2501)), 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 | 6 | 0 | [
"K13",
"K2",
"VIETA_SUM"
] | 3 | 0.002 | 2026-02-08T19:23:45.388366Z | {
"verified": true,
"answer": 5253,
"timestamp": "2026-02-08T19:23:45.389989Z"
} | fa7f0a | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 141,
"completion_tokens": 1564
},
"timestamp": "2026-02-18T22:07:01.290Z",
"answer": 5253
},
{... | 1 | [
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "K2",
"status": "ok"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
},
{
"lemma": ... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
a98d81 | geo_count_lattice_triangle_v1_1419126231_1107 | Let $R = \left|120 \cdot 100 + 60 \cdot (-256)\right|$, $S = \gcd(120, 256) + \gcd(|60 - 120|, |100 - 256|) + \gcd(60, 100)$, and $T = \frac{R + 2 - S}{2}$. Find the remainder when $76859 \cdot T$ is divided by $82194$. | 15,517 | graphs = [
Graph(
let={
"_n": Const(2225),
"area_2x": Abs(arg=Sum(Mul(Const(value=120), Const(value=100)), Mul(Const(value=60), Sub(left=Const(value=0), right=Const(value=256))))),
"boundary": Sum(GCD(a=Abs(arg=Const(value=120)), b=Abs(arg=Const(value=256))), GCD(a=Abs(ar... | GEOM | NT | COUNT | sympy | QF_PSD_DISTINCT | [
"QF_PSD_DISTINCT"
] | a8f9cb | geo_count_lattice_triangle_v1 | null | 4 | 0 | [
"QF_PSD_DISTINCT"
] | 1 | 0.005 | 2026-02-25T10:38:04.551595Z | {
"verified": true,
"answer": 15517,
"timestamp": "2026-02-25T10:38:04.556545Z"
} | 59bfef | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 212,
"completion_tokens": 1611
},
"timestamp": "2026-03-30T11:26:23.272Z",
"answer": 15517
},
{
"... | 1 | [
{
"lemma": "QF_PSD_DISTINCT",
"status": "ok"
}
] | {
"lo": -5.37,
"mid": 0.23,
"hi": 5.22
} | ||
9bf26f | sequence_lucas_compute_v1_601307018_10485 | Let $n$ be the number of ordered pairs $(a, b)$ of positive integers with $1 \le a, b \le 30$ such that
$$
128b^3 + 128a^3 + 384a^2b + 384ab^2 = 8192000.
$$
Let $M = L_n$, where $L_n$ denotes the $n$-th Lucas number. Find the remainder when $20536M$ is divided by $89737$. | 22,199 | graphs = [
Graph(
let={
"_n": Const(128),
"n": 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)), Eq(Sum(Mul(Const(128), Pow(Var("b"), Const(3))), ... | ALG | null | COMPUTE | sympy | POLY3_COUNT | [
"POLY3_COUNT"
] | 355dbe | sequence_lucas_compute_v1 | null | 6 | 0 | [
"POLY3_COUNT"
] | 1 | 0.002 | 2026-03-10T10:57:49.113038Z | {
"verified": true,
"answer": 22199,
"timestamp": "2026-03-10T10:57:49.115485Z"
} | 7275ee | 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": 1442
},
"timestamp": "2026-04-19T13:55:04.377Z",
"answer": 22199
},
{
... | 1 | [
{
"lemma": "POLY3_COUNT",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
}
] | {
"lo": -5.34,
"mid": 1.1,
"hi": 7.53
} | ||
c880ef | antilemma_k2_v1_1874849503_1676 | Compute
\[
\sum_{k=1}^{378} \varphi(k) \left\lfloor \frac{1}{k} \sum_{i=1}^{27} \varphi(i) \left\lfloor \frac{27}{i} \right\rfloor \right\rfloor.
\] | 71,631 | graphs = [
Graph(
let={
"_n": Const(378),
"x": Summation(var="k", start=Const(1), end=Ref("_n"), expr=Mul(EulerPhi(n=Var("k")), Floor(Div(Summation(var="k", start=Const(1), end=Const(27), expr=Mul(EulerPhi(n=Var("k")), Floor(Div(Const(27), Var("k"))))), Var("k"))))),
},
... | NT | COMB | COMPUTE | sympy | K2 | [
"K2/K2",
"K2"
] | 76610f | antilemma_k2_v1 | null | 7 | 0 | [
"K2"
] | 1 | 0.001 | 2026-02-08T14:01:54.274041Z | {
"verified": true,
"answer": 71631,
"timestamp": "2026-02-08T14:01:54.275335Z"
} | 10c3e7 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 179,
"completion_tokens": 1469
},
"timestamp": "2026-02-10T06:18:24.678Z",
"answer": 71631
},
{
"... | 1 | [
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "K2",
"status": "ok"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
}
] | {
"lo": -5.49,
"mid": 0.03,
"hi": 6.12
} | ||
929918_l | antilemma_sum_equals_v1_349078426_1538 | Let $c$ be the number of ordered pairs $(x, y)$ with $1 \leq x \leq 12$ and $1 \leq y \leq 17$. Let $m$ be the number of ordered pairs $(x_1, x_2)$ of positive odd integers such that $x_1 + x_2 = c$. Let $n$ be the number of ordered pairs $(x_1, x_2)$ of positive odd integers such that $x_1 + x_2 = m$. Compute the numb... | 0 | COMB | GEOM | COMPUTE | sympy | COUNT_SUM_EQUALS | [
"COUNT_CARTESIAN/COMB1/COUNT_SUM_EQUALS",
"COMB1/COMB1/COUNT_SUM_EQUALS",
"COUNT_SUM_EQUALS"
] | 48574a | antilemma_sum_equals_v1 | null | 4 | 0 | [
"COMB1",
"COUNT_CARTESIAN",
"COUNT_SUM_EQUALS"
] | 3 | 0.091 | 2026-02-08T13:42:01.960350Z | {
"verified": false,
"answer": 48,
"timestamp": "2026-02-08T13:42:02.051803Z"
} | 4e932d | 929918 | legacy_text | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 258,
"completion_tokens": 1346
},
"timestamp": "2026-02-24T18:57:30.385Z",
"answer": 48
},
{
"id"... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COMB1",
"status": "ok"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "ok"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS... | {
"lo": -3.84,
"mid": -1.67,
"hi": 1.32
} | |
b58b7f | nt_num_divisors_compute_v1_1978505735_7838 | Let $n = 180$ and $c = 37$. Let $r$ be the number of positive divisors of $n$. Define
$$
Q = \left( 353702 \cdot (r \bmod d_0) + 329703 \cdot (r^2 + 1 \bmod 101) + 215534 \cdot (r + c \bmod 103) \right) \bmod 1009091,
$$
where $d_0$ is the smallest integer greater than or equal to 2 that divides 103936373. Find the rem... | 66,715 | graphs = [
Graph(
let={
"_n": Const(101),
"n": Const(180),
"result": NumDivisors(n=Ref("n")),
"_c": Const(37),
"Q": Mod(value=Mod(value=Sum(Mul(Const(353702), Mod(value=Abs(arg=Ref(name='result')), modulus=MinOverSet(set=SolutionsSet(var=Var("d"), ... | NT | null | COMPUTE | sympy | MIN_PRIME_FACTOR | [
"MIN_PRIME_FACTOR"
] | b5b91a | nt_num_divisors_compute_v1 | crt_mix_3 | 3 | 0 | [
"MIN_PRIME_FACTOR"
] | 1 | 0.003 | 2026-02-08T20:31:08.190685Z | {
"verified": true,
"answer": 66715,
"timestamp": "2026-02-08T20:31:08.194012Z"
} | e2124f | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 182,
"completion_tokens": 2669
},
"timestamp": "2026-02-19T00:37:47.688Z",
"answer": 66715
},
... | 1 | [
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "MIN_PRIME_FACTOR",
"status": "ok"
},
{
"lemma": "V3",
"status": "no"
},
{
"lemma": "V8",
"status": "n... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
717e4e | nt_count_gcd_equals_v1_1439011603_266 | Let $k$ be the minimum value of $x + y$ where $x$ and $y$ are positive integers such that $xy = 58081$. Determine the number of positive integers $n$ with $1 \le n \le 30976$ such that $\gcd(n, k) = 2$. Compute this number. | 15,424 | graphs = [
Graph(
let={
"_n": Const(58081),
"upper": Const(30976),
"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")), Ref("_n")))... | NT | null | COUNT | sympy | B3 | [
"B3"
] | 0cd20d | nt_count_gcd_equals_v1 | null | 5 | 0 | [
"B3"
] | 1 | 4.112 | 2026-02-08T15:22:46.192495Z | {
"verified": true,
"answer": 15424,
"timestamp": "2026-02-08T15:22:50.304532Z"
} | 3ce2e9 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 118,
"completion_tokens": 880
},
"timestamp": "2026-02-16T05:18:19.811Z",
"answer": 15424
},
{... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
e8dcf3 | nt_min_coprime_above_v1_1742523217_3103 | Let $S$ be the set of all ordered pairs $(x,y)$ of positive integers such that $xy = 28900$. Define $m$ to be the minimum value of $x + y$ over all pairs in $S$. Let $n$ be the smallest integer greater than $28561$ and at most $28911$ such that $\gcd(n, m) = 1$. Find the remainder when $44121 \times n$ is divided by $8... | 80,682 | graphs = [
Graph(
let={
"_n": Const(44121),
"start": Const(28561),
"upper": Const(28911),
"modulus": MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y'))... | NT | null | EXTREMUM | sympy | B3 | [
"B3"
] | 0cd20d | nt_min_coprime_above_v1 | null | 6 | 0 | [
"B3"
] | 1 | 0.091 | 2026-02-08T05:39:24.729490Z | {
"verified": true,
"answer": 80682,
"timestamp": "2026-02-08T05:39:24.820105Z"
} | 043940 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 147,
"completion_tokens": 4166
},
"timestamp": "2026-02-12T12:28:07.267Z",
"answer": 80682
},
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "VAL_SUM_EQ",
"status": "no"
}
] | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
19cffd | antilemma_sum_factor_cartesian_v1_1125832087_1452 | Let $x$ be the sum of $i \cdot j$ over all ordered pairs $(i,j)$ where $i$ is an integer from 1 to 6 and $j$ is an integer from 1 to 8. Let $a = x \bmod 293$. Let $k$ range over the positive integers from 1 to 301043 that are divisible by 43, and let $c$ be the number of such integers. Let $b = x \bmod 337$. Compute th... | 11,627 | graphs = [
Graph(
let={
"_n": Const(293),
"x": SumOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("i"), Var("j")]), condition=Const(1), domain=CartesianProduct(left=IntegerRange(start=Const(1), end=Const(6)), right=IntegerRange(start=Const(1), end=Const(8)))), expr=Mu... | NT | null | COMPUTE | sympy | C2 | [
"C2",
"SUM_FACTOR_CARTESIAN"
] | 035125 | antilemma_sum_factor_cartesian_v1 | two_moduli | 3 | 0 | [
"C2",
"SUM_FACTOR_CARTESIAN"
] | 2 | 0.002 | 2026-02-08T03:44:49.450061Z | {
"verified": true,
"answer": 11627,
"timestamp": "2026-02-08T03:44:49.451799Z"
} | 67b241 | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 233,
"completion_tokens": 475
},
"timestamp": "2026-02-18T05:26:36.895Z",
"answer": 23617
}
] | 0 | [
{
"lemma": "C2",
"status": "ok"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "SUM_FACTOR_CARTESIAN",
"statu... | {
"lo": -6.48,
"mid": 1.54,
"hi": 9.56
} | ||
3ffd54 | v7_endings_v1_677425708_1131 | Compute the sum of all integers $k$ with $0 \leq k \leq 2942$ such that $2$ does not divide $\binom{2942}{k}$. Find the remainder when this sum is divided by $100000$. Determine the value of this remainder. | 53,152 | graphs = [
Graph(
let={
"_n": Const(2),
"_inner_result": SumOverSet(set=SolutionsSet(var=Var("k"), condition=And(Geq(Var("k"), Const(0)), Leq(Var("k"), Const(2942)), Not(Divides(divisor=Ref("_n"), dividend=Binom(n=Const(2942), k=Var("k"))))))),
"_mod_M": Const(100000),
... | NT | COMB | COMPUTE | sympy | V7 | [
"V7"
] | 0672d4 | v7_endings_v1 | null | 7 | null | [
"V7"
] | 1 | 0.001 | 2026-02-08T04:00:33.083007Z | {
"verified": true,
"answer": 53152,
"timestamp": "2026-02-08T04:00:33.084461Z"
} | 9f159d | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 171,
"completion_tokens": 1721
},
"timestamp": "2026-02-09T16:04:14.554Z",
"answer": 53152
},
{
"... | 1 | [
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "V3",
"status": "no"
},
{
"lemma": "V7",
"status": "ok"
},
{
"lemma": "V8",
"status": "no"
}
] | {
"lo": -6.5,
"mid": -0.2,
"hi": 6.11
} | ||
e99f8a | geo_count_lattice_rect_v1_1742523217_1495 | Compute the number of lattice points $(x, y)$ such that $0 \le x \le 289$ and $0 \le y \le 285$. | 82,940 | graphs = [
Graph(
let={
"a": Const(289),
"b": Const(285),
"result": LatticePointsRect(a=Ref(name='a'), b=Ref(name='b')),
},
goal=Ref("result"),
)
] | GEOM | null | COUNT | sympy | [] | geo_count_lattice_rect_v1 | null | 3 | 0 | null | null | 0.001 | 2026-02-08T04:01:58.573329Z | {
"verified": true,
"answer": 82940,
"timestamp": "2026-02-08T04:01:58.573862Z"
} | f7c843 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 144,
"completion_tokens": 329
},
"timestamp": "2026-02-10T16:33:53.445Z",
"answer": 82940
},
{
"i... | 1 | [] | {
"lo": -5.97,
"mid": -3.96,
"hi": -1.93
} | ||||
08f2ab | sequence_lucas_compute_v1_2051736721_5370 | Let $L_n$ denote the $n$th Lucas number, defined by $L_0=2$, $L_1=1$, and $L_{n+1}=L_n+L_{n-1}$ for all integers $n\ge1$. Let $n=20$, and let $R=L_n$.
Let $c$ be the maximum value of $xy$ over all ordered pairs $(x,y)$ of positive integers such that $x+y=50$.
Let $m$ be the number of positive integers $k$ with $1\le ... | 51,258 | graphs = [
Graph(
let={
"_m": Const(256),
"_n": Const(2),
"n": Const(20),
"result": Lucas(arg=Ref(name='n')),
"_c": MaxOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), Is... | NT | null | COMPUTE | sympy | C2 | [
"C2/B3",
"B1"
] | 732982 | sequence_lucas_compute_v1 | quadratic_mod | 7 | 0 | [
"B1",
"B3",
"C2"
] | 3 | 0.004 | 2026-02-08T18:31:28.215810Z | {
"verified": true,
"answer": 51258,
"timestamp": "2026-02-08T18:31:28.219844Z"
} | c7bdec | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 259,
"completion_tokens": 1986
},
"timestamp": "2026-02-18T17:35:21.954Z",
"answer": 51258
},
... | 1 | [
{
"lemma": "B1",
"status": "ok"
},
{
"lemma": "B3",
"status": "ok_later"
},
{
"lemma": "C2",
"status": "ok"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "V1",... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
1d032d | nt_count_coprime_and_v1_1520064083_4167 | Let $A$ be the number of positive integers $n \leq 10951$ such that the sum of the digits of $n$ is even. Let $B$ be the number of positive integers $n \leq A$ such that $\gcd(n, 8) = 1$ and $\gcd(n, 9) = 1$. Compute the remainder when $44121 \cdot B$ is divided by $74923$. | 53,523 | graphs = [
Graph(
let={
"upper": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Const(10951)), Eq(Mod(value=DigitSum(Var("n")), modulus=Const(2)), Const(0))))),
"k1": Const(8),
"k2": Const(9),
"result": CountOv... | NT | null | COUNT | sympy | L3B | [
"L3B"
] | cc148f | nt_count_coprime_and_v1 | null | 4 | 0 | [
"L3B"
] | 1 | 0.529 | 2026-02-08T06:07:32.005495Z | {
"verified": true,
"answer": 53523,
"timestamp": "2026-02-08T06:07:32.534364Z"
} | 1d5934 | 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": 2726
},
"timestamp": "2026-02-12T20:12:45.235Z",
"answer": 53523
},
... | 1 | [
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "L3B",
"status": "ok"
},
{
"lemma": "V1",
"status": "no"
}
] | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
92df33 | alg_poly_orbit_count_v1_1218484723_4004 | Let $f(x) = (3x^5 - x^4 + 3x^3 - 5x^2 - 3) \bmod 73$. Define a sequence by $N = f(a)$, $M = f(N)$, $R = f(M)$, $S = f(R)$, $T = f(S)$. Find the number of non-negative integers $a$ with $0 \leq a \leq 73948$ such that $T = a$ but $N, M, R, S \neq a$. | 5,065 | graphs = [
Graph(
let={
"p1": Mod(value=Sum(Mul(Const(3), Pow(Var("a"), Const(5))), Mul(Const(-1), Pow(Var("a"), Const(4))), Mul(Const(3), Pow(Var("a"), Const(3))), Mul(Const(-5), Pow(Var("a"), Const(2))), Const(-3)), modulus=Const(73)),
"p2": Mod(value=Sum(Mul(Const(3), Pow(Ref("p1"... | ALG | null | COUNT | sympy | POLY_ORBIT_COUNT | [
"POLY_ORBIT_COUNT"
] | 4ad965 | alg_poly_orbit_count_v1 | null | 4 | null | [
"POLY_ORBIT_COUNT"
] | 1 | 0.331 | 2026-02-25T05:37:29.134206Z | {
"verified": true,
"answer": 5065,
"timestamp": "2026-02-25T05:37:29.465273Z"
} | 39eeb9 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 230,
"completion_tokens": 25368
},
"timestamp": "2026-03-29T13:20:33.877Z",
"answer": 5065
},
{
"... | 1 | [
{
"lemma": "POLY_ORBIT_COUNT",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
}
] | {
"lo": 3.81,
"mid": 6.33,
"hi": 9.49
} | ||
f255cf | sequence_lucas_compute_v1_48377204_2360 | Let $n$ be the number of prime numbers $p$ such that $2 \leq p \leq 61$. Compute the $n$-th Lucas number. | 5,778 | graphs = [
Graph(
let={
"_n": Const(61),
"n": CountOverSet(set=SolutionsSet(var=Var("n1"), condition=And(Geq(Var("n1"), Const(2)), Leq(Var("n1"), Ref("_n")), IsPrime(Var("n1"))))),
"result": Lucas(arg=Ref(name='n')),
},
goal=Ref("result"),
)
] | NT | null | COMPUTE | sympy | COUNT_PRIMES | [
"COUNT_PRIMES"
] | 07c874 | sequence_lucas_compute_v1 | null | 3 | 0 | [
"COUNT_PRIMES"
] | 1 | 0.001 | 2026-02-08T16:44:54.422754Z | {
"verified": true,
"answer": 5778,
"timestamp": "2026-02-08T16:44:54.424244Z"
} | e5ff56 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 81,
"completion_tokens": 686
},
"timestamp": "2026-02-17T10:36:11.217Z",
"answer": 5778
},
{
... | 1 | [
{
"lemma": "COUNT_PRIMES",
"status": "ok"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "V3",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
643ba1 | sequence_count_fib_divisible_v1_1080341949_53 | Let $S$ be the set of all integers $t$ such that $5 \leq t \leq 592$ and there exist positive integers $a$ and $b$ with $1 \leq a \leq 140$, $1 \leq b \leq 86$, and $t = 3a + 2b$. Let $U$ be the number of elements in $S$. Determine the number of positive integers $n$ such that $1 \leq n \leq U$ and the Fibonacci number... | 195 | 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=140)), Geq(left=Var(name='b'), right=Const(v... | NT | null | COUNT | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | sequence_count_fib_divisible_v1 | null | 6 | 0 | [
"LIN_FORM"
] | 1 | 0.064 | 2026-02-08T13:10:07.503419Z | {
"verified": true,
"answer": 195,
"timestamp": "2026-02-08T13:10:07.567451Z"
} | ccd1df | 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": 2776
},
"timestamp": "2026-02-15T10:43:22.884Z",
"answer": 195
},
{
... | 1 | [
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "MOD_ADD",
"status": "no"
}
] | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
95f68a | alg_poly3_sum_v1_601307018_9871 | Let $B = \max \{ d \geq 1 : d \mid 15240 \text{ and } d^2 \leq 15240 \}$. Compute the remainder when
$$
\sum_{a=1}^{120} \sum_{b=1}^{B} \left( -48a b^2 - 91a^3 - 96a^2 b - 8b^3 \right)
$$
is divided by $88349$. | 28,198 | graphs = [
Graph(
let={
"_n": Const(2),
"result": Mod(value=SumOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("a"), Var("b")]), condition=And(Geq(Var("a"), Const(1)), Leq(Var("a"), Const(120)), Geq(Var("b"), Const(1)), Leq(Var("b"), MaxOverSet(set=SolutionsSet(var=Va... | NT | null | COMPUTE | sympy | B3_CLOSEST | [
"B3_CLOSEST"
] | 25e610 | alg_poly3_sum_v1 | null | 5 | 0 | [
"B3_CLOSEST"
] | 1 | 0.041 | 2026-03-10T10:16:15.894509Z | {
"verified": true,
"answer": 28198,
"timestamp": "2026-03-10T10:16:15.935871Z"
} | b24963 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 213,
"completion_tokens": 5848
},
"timestamp": "2026-04-19T12:20:50.633Z",
"answer": 28198
},
{
... | 1 | [
{
"lemma": "B3_CLOSEST",
"status": "ok"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "VAL_SUM_EQ",
"status": "... | {
"lo": -5.34,
"mid": 1.1,
"hi": 7.53
} | ||
8d22a8 | nt_min_coprime_above_v1_124444284_9589 | Let $m$ be the number of positive integers $n$ such that $1 \leq n \leq 57$ and $n \equiv 0 \pmod{57}$. Find the smallest integer $n$ such that $70000 < n \leq 70067$ and $\gcd(n, m) = 1$. Compute the remainder when $46473$ times this value is divided by $76063$. | 18,026 | graphs = [
Graph(
let={
"_n": Const(57),
"start": Const(70000),
"upper": Const(70067),
"modulus": SumOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Ref("_n")), Eq(Mod(value=Var("n"), modulus=Const(57)), Const(0)))))... | NT | null | EXTREMUM | sympy | SUM_DIVISIBLE | [
"SUM_DIVISIBLE"
] | 02dbe3 | nt_min_coprime_above_v1 | null | 3 | 0 | [
"SUM_DIVISIBLE"
] | 1 | 0.055 | 2026-02-08T12:34:28.099058Z | {
"verified": true,
"answer": 18026,
"timestamp": "2026-02-08T12:34:28.153855Z"
} | 16f094 | 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": 1750
},
"timestamp": "2026-02-15T02:26:04.069Z",
"answer": 18026
},
... | 1 | [
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "SUM_DIVISIBLE",
"status": "ok"
},
{
"lemma": "V8_SUM",
"status": "no"
},
{
"lemma": "VAL_SUM_EQ",
"status": "no"
}
] | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
aecb51 | geo_count_lattice_rect_v1_655260480_3082 | Let $a = 64$ and $b = 132$. Compute the number of lattice points $(x, y)$ such that $0 \leq x \leq 64$ and $0 \leq y \leq 132$. | 8,645 | graphs = [
Graph(
let={
"a": Const(64),
"b": Const(132),
"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 | 0.002 | 2026-02-08T17:10:36.117263Z | {
"verified": true,
"answer": 8645,
"timestamp": "2026-02-08T17:10:36.119142Z"
} | c6427b | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 95,
"completion_tokens": 488
},
"timestamp": "2026-02-24T22:20:09.581Z",
"answer": 8645
},
{
... | 1 | [] | {
"lo": -8.52,
"mid": -5.43,
"hi": -3.2
} | ||||
1087f9 | comb_count_surjections_v1_1742523217_2032 | Let $\mathcal{P}$ be the set of all ordered pairs $(i, j)$ of integers such that $i + j = 10$, $1 \leq i \leq 8$, and $1 \leq j \leq 8$. Let $n$ be the number of elements in $\mathcal{P}$. Let $k = 4$. Define $\text{result} = k! \cdot S(n, k)$, where $S(n, k)$ is the Stirling number of the second kind. Let $c = 25281$ ... | 16,881 | graphs = [
Graph(
let={
"n": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("i"), Var("j")]), condition=Eq(Sum(Var("i"), Var("j")), Const(10)), domain=CartesianProduct(left=IntegerRange(start=Const(1), end=Const(8)), right=IntegerRange(start=Const(1), end=Const(8))))),
"k": Co... | COMB | null | COUNT | sympy | BINOMIAL_ALTERNATING | [
"COUNT_SUM_EQUALS"
] | 75ab0f | comb_count_surjections_v1 | null | 5 | 0 | [
"BINOMIAL_ALTERNATING",
"COUNT_SUM_EQUALS"
] | 2 | 0.023 | 2026-02-08T04:25:42.616715Z | {
"verified": true,
"answer": 16881,
"timestamp": "2026-02-08T04:25:42.639570Z"
} | b1eb2a | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 252,
"completion_tokens": 932
},
"timestamp": "2026-02-24T00:40:58.901Z",
"answer": 16881
},
{
"i... | 1 | [
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "ok"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
},
{
"lemma": "V8_SUM",
"stat... | {
"lo": -3.83,
"mid": -1.68,
"hi": 1.09
} | ||
a61722 | comb_count_surjections_v1_865884756_4811 | Let $k$ be the number of ordered pairs $(x_1, x_2)$ of positive odd integers such that $x_1 + x_2 = 4$. Let $n = 7$. Define $c = 81233$ and let $r = k! \cdot S(n, k)$, where $S(n, k)$ denotes the Stirling number of the second kind. Find the remainder when $c \cdot r$ is divided by 75106. | 20,942 | graphs = [
Graph(
let={
"_n": Const(75106),
"n": Const(7),
"k": 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... | COMB | null | COUNT | sympy | COMB1 | [
"COMB1"
] | 567f58 | comb_count_surjections_v1 | null | 4 | 0 | [
"COMB1"
] | 1 | 0.003 | 2026-02-08T18:09:36.894731Z | {
"verified": true,
"answer": 20942,
"timestamp": "2026-02-08T18:09:36.897306Z"
} | fdb6b1 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 146,
"completion_tokens": 1658
},
"timestamp": "2026-02-18T14:51:43.032Z",
"answer": 20942
},
... | 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": "no"
},
{
"lemma": "V8_SUM",
"statu... | {
"lo": -3.12,
"mid": 1.47,
"hi": 6.57
} | ||
f5eec8 | comb_binomial_compute_v1_151522320_2589 | Let $d$ be the smallest prime divisor of $79781$. Let $k$ be the number of ordered pairs $(x_1, x_2)$ of positive odd integers such that $x_1 + x_2 = 14$. Let $r = \binom{d}{k}$. Compute the remainder when $93633 \cdot r$ is divided by $67297$. | 36,289 | graphs = [
Graph(
let={
"_n": Const(14),
"n": MinOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Const(2)), Divides(divisor=Var("d"), dividend=Const(79781))))),
"k": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x1"), Var("x2")]), condition=And... | NT | null | COMPUTE | sympy | MIN_PRIME_FACTOR | [
"MIN_PRIME_FACTOR",
"COMB1"
] | e219fc | comb_binomial_compute_v1 | null | 6 | 0 | [
"COMB1",
"MIN_PRIME_FACTOR"
] | 2 | 0.002 | 2026-02-08T04:53:17.335111Z | {
"verified": true,
"answer": 36289,
"timestamp": "2026-02-08T04:53:17.336882Z"
} | e1162c | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 193,
"completion_tokens": 1957
},
"timestamp": "2026-02-11T22:23:40.760Z",
"answer": 36289
},
{
"... | 1 | [
{
"lemma": "COMB1",
"status": "ok"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "MIN_PRIME_FACTOR",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"statu... | {
"lo": 1.71,
"mid": 5.04,
"hi": 8.38
} | ||
367e9c | comb_count_permutations_fixed_v1_865884756_1100 | Let $n$ be the minimum value of $x + y$ over all ordered pairs $(x, y)$ of positive integers such that $xy = 25$. Let $k = 8$. 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 $46034 \cdot \text{result}$ is divided by $686... | 12,840 | graphs = [
Graph(
let={
"_n": Const(68623),
"n": MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(Mul(Var("x"), Var("y")), Const(25)))), expr=Sum(Var("x"), Var("y")))),
... | COMB | null | COUNT | sympy | B3 | [
"B3"
] | 0cd20d | comb_count_permutations_fixed_v1 | null | 4 | 0 | [
"B3"
] | 1 | 0.003 | 2026-02-08T15:47:34.469767Z | {
"verified": true,
"answer": 12840,
"timestamp": "2026-02-08T15:47:34.472651Z"
} | 8cd6c1 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 222,
"completion_tokens": 914
},
"timestamp": "2026-02-24T18:36:02.753Z",
"answer": 12840
},
{
"... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
}
] | {
"lo": -5.65,
"mid": -3.17,
"hi": -0.81
} | ||
2551c7 | comb_sum_binomial_row_v1_784195855_8148 | Let $t = \sum_{k=0}^{0} (-1)^k \binom{0}{k}$ and $e = \sum_{k=0}^{0} (-1)^k \binom{0}{k}$. Let $n = 13e$ and let $r = (2t)^n$. Compute $r$. | 8,192 | graphs = [
Graph(
let={
"n2": Const(0),
"t": Summation(var="k", start=Const(0), end=Ref("n2"), expr=Mul(Pow(Const(-1), Var("k")), Binom(n=Ref("n2"), k=Var("k")))),
"n1": Const(0),
"e": Summation(var="k", start=Const(0), end=Ref("n1"), expr=Mul(Pow(Const(-1), V... | COMB | null | SUM | sympy | BINOMIAL_ALTERNATING | [
"BINOMIAL_ALTERNATING"
] | c21569 | comb_sum_binomial_row_v1 | null | 3 | 2 | [
"BINOMIAL_ALTERNATING"
] | 1 | 0.002 | 2026-02-08T15:54:53.044040Z | {
"verified": true,
"answer": 8192,
"timestamp": "2026-02-08T15:54:53.045635Z"
} | 96d096 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 184,
"completion_tokens": 322
},
"timestamp": "2026-02-24T19:00:05.850Z",
"answer": 8192
},
{
"i... | 2 | [
{
"lemma": "BINOMIAL_ALTERNATING",
"status": "ok"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
... | {
"lo": -10,
"mid": -7.42,
"hi": -4.85
} | ||
9b6aa1 | algebra_vieta_sum_v1_898971024_31 | Let $P(x) = x^4 + 19x^3 + 113x^2 + 245x + 150$. Let $S$ be the set of all integer roots of $P(x) = 0$. Compute the product of all elements of $S$. | 150 | graphs = [
Graph(
let={
"result": ProductOverSet(set=SolutionsSet(var=Var(name='x'), condition=Eq(left=Sum(Pow(base=Var(name='x'), exp=Const(value=4)), Mul(Const(value=19), Pow(base=Var(name='x'), exp=Const(value=3))), Mul(Const(value=113), Pow(base=Var(name='x'), exp=Const(value=2))), Mul(Const... | NT | null | COMPUTE | sympy | MOBIUS_COPRIME | [
"MOBIUS_COPRIME"
] | ac54ac | algebra_vieta_sum_v1 | null | 3 | 0 | [
"MOBIUS_COPRIME"
] | 1 | 0.021 | 2026-02-08T15:09:31.244477Z | {
"verified": true,
"answer": 150,
"timestamp": "2026-02-08T15:09:31.265797Z"
} | 5803a6 | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 1,
"correct": {
"strict": false,
"boxed": false,
"relaxed": true
},
"usage": {
"prompt_tokens": 123,
"completion_tokens": 423
},
"timestamp": "2026-02-16T05:18:00.093Z",
"answer": 30
},
{
"id": 11,
... | 1 | [
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "MOBIUS_COPRIME",
"status": "ok"
},
{
"lemma": "V1",
"status": "no"
}
] | {
"lo": -8.26,
"mid": -5.01,
"hi": -1.76
} | ||
a2dac5 | alg_poly_orbit_hensel_v1_1419126231_1822 | For a non-negative integer $a$, define the sequence $N, M, R$ by $$x_0 = a,\quad x_1 = x_0^4 - 3x_0^3 - 4x_0 + 2 \bmod 3481,\quad x_2 = x_1^4 - 3x_1^3 - 4x_1 + 2 \bmod 3481,\quad x_3 = x_2^4 - 3x_2^3 - 4x_2 + 2 \bmod 3481,$$ so that $N = x_1$, $M = x_2$, $R = x_3$. Find the number of integers $a$ with $0 \leq a \leq 23... | 2,034 | graphs = [
Graph(
let={
"p1": Mod(value=Sum(Pow(Var("a"), Const(4)), Mul(Const(-3), Pow(Var("a"), Const(3))), Mul(Const(-4), Var("a")), Const(2)), modulus=Const(3481)),
"p2": Mod(value=Sum(Pow(Ref("p1"), Const(4)), Mul(Const(-3), Pow(Ref("p1"), Const(3))), Mul(Const(-4), Ref("p1")), ... | ALG | null | COUNT | sympy | POLY_ORBIT_COUNT | [
"POLY_ORBIT_COUNT"
] | 4ad965 | alg_poly_orbit_hensel_v1 | null | 6 | null | [
"POLY_ORBIT_COUNT"
] | 1 | 0.03 | 2026-02-25T11:22:29.048252Z | {
"verified": true,
"answer": 2034,
"timestamp": "2026-02-25T11:22:29.077793Z"
} | 15ba97 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 306,
"completion_tokens": 13971
},
"timestamp": "2026-03-30T14:14:27.206Z",
"answer": 2034
},
{
"... | 1 | [
{
"lemma": "POLY_ORBIT_COUNT",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
}
] | {
"lo": 3.8,
"mid": 6.33,
"hi": 9.49
} | ||
d4f6cf | geo_count_lattice_rect_v1_655260480_6074 | Compute the number of lattice points $(x, y)$ such that $0 \leq x \leq 80$ and $0 \leq y \leq 162$. | 13,203 | graphs = [
Graph(
let={
"a": Const(80),
"b": Const(162),
"result": LatticePointsRect(a=Ref(name='a'), b=Ref(name='b')),
"Q": Ref("result"),
},
goal=Ref("Q"),
)
] | GEOM | null | COUNT | sympy | [] | geo_count_lattice_rect_v1 | null | 2 | 0 | null | null | 0.001 | 2026-02-08T18:48:55.808353Z | {
"verified": true,
"answer": 13203,
"timestamp": "2026-02-08T18:48:55.809445Z"
} | 65c47a | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 81,
"completion_tokens": 518
},
"timestamp": "2026-02-18T19:33:54.455Z",
"answer": 13203
},
{
... | 1 | [] | {
"lo": -7.92,
"mid": -4.6,
"hi": -1.84
} | ||||
b5dcfe | nt_min_coprime_above_v1_809748730_1449 | Let $S$ be the set of all positive integers $t$ such that $9 \leq t \leq 1700$ and there exist positive integers $a \leq 256$ and $b \leq 105$ for which $t = 5a + 4b$. Let $N$ be the number of elements in $S$. Determine the smallest integer $n$ such that $N < n \leq 1912$ and $\gcd(n, 222) = 1$. | 1,681 | graphs = [
Graph(
let={
"start": 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=256)), Geq(left=Var(name='b'), right=Const(v... | NT | null | EXTREMUM | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | nt_min_coprime_above_v1 | null | 5 | 0 | [
"LIN_FORM"
] | 1 | 0.022 | 2026-02-08T12:25:58.047316Z | {
"verified": true,
"answer": 1681,
"timestamp": "2026-02-08T12:25:58.069347Z"
} | 53ec95 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 151,
"completion_tokens": 6564
},
"timestamp": "2026-02-15T01:24:46.015Z",
"answer": 1681
},
{... | 1 | [
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no... | {
"lo": -5.49,
"mid": 0.22,
"hi": 6.51
} | ||
d699de | nt_count_divisors_in_range_v1_1431428450_198 | Let $n = 332640$. Let $a$ be the number of positive integers $k$ with $1 \leq k \leq 6$ such that $2$ divides the $k$-th Fibonacci number. Let $b = 11886$. Compute the number of positive divisors $d$ of $n$ such that $a \leq d \leq b$. | 170 | graphs = [
Graph(
let={
"_n": Const(2),
"n": Const(332640),
"a": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Const(6)), Divides(divisor=Ref("_n"), dividend=Fibonacci(arg=Var(name='n')))))),
"b": Const(11886)... | NT | null | COUNT | sympy | COUNT_FIB_DIVISIBLE | [
"COUNT_FIB_DIVISIBLE"
] | 66de3c | nt_count_divisors_in_range_v1 | null | 5 | 0 | [
"COUNT_FIB_DIVISIBLE"
] | 1 | 0.17 | 2026-02-08T13:17:41.965534Z | {
"verified": true,
"answer": 170,
"timestamp": "2026-02-08T13:17:42.135968Z"
} | f2ce6b | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 125,
"completion_tokens": 2540
},
"timestamp": "2026-02-15T12:04:14.047Z",
"answer": 170
},
{
... | 1 | [
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "ok"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
}
] | {
"lo": -5.49,
"mid": 0.22,
"hi": 6.51
} | ||
ba7907 | comb_binomial_compute_v1_1419126231_654 | Find the number of ordered pairs $(a, b)$ of positive integers with $1 \leq a \leq b \leq 25$ such that $2a^2 + 2b^2 - 4ab = 242$. Let $n$ be this number, and compute $\binom{n}{6}$. | 3,003 | graphs = [
Graph(
let={
"_n": Const(2),
"n": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("a"), Var("b")]), condition=And(Geq(Var("a"), Const(1)), Leq(Var("a"), Const(25)), Geq(Var("b"), Const(1)), Leq(Var("b"), Const(25)), Leq(Var("a"), Var("b")), Eq(Sum(Mul(Const(2), Pow(V... | COMB | null | COMPUTE | sympy | QF_PSD_ORBIT | [
"QF_PSD_ORBIT"
] | 1d37f3 | comb_binomial_compute_v1 | null | 4 | 0 | [
"QF_PSD_ORBIT"
] | 1 | 0.002 | 2026-02-25T10:08:57.141186Z | {
"verified": true,
"answer": 3003,
"timestamp": "2026-02-25T10:08:57.142826Z"
} | 9b18dc | 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": 720
},
"timestamp": "2026-03-30T09:16:15.623Z",
"answer": 3003
},
{
"id... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "QF_PSD_ORBIT",
"status": "ok"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
... | {
"lo": -5.37,
"mid": 0.23,
"hi": 5.22
} | ||
3545c2 | nt_min_coprime_above_v1_1742523217_780 | Let $n$ be a positive integer. Define $\alpha$ to be the number of positive integers $n \leq 8563$ such that $\gcd(n, 30) = 1$. Compute the smallest integer $n > 2026$ such that $n \leq \alpha$ and $\gcd(n, 248) = 1$. | 2,027 | graphs = [
Graph(
let={
"_n": Const(30),
"start": Const(2026),
"upper": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Const(8563)), Eq(GCD(a=Var("n"), b=Ref("_n")), Const(1))))),
"modulus": Const(248),
... | NT | null | EXTREMUM | sympy | C4 | [
"C4"
] | 08d162 | nt_min_coprime_above_v1 | null | 5 | 0 | [
"C4"
] | 1 | 0.024 | 2026-02-08T03:14:41.260890Z | {
"verified": true,
"answer": 2027,
"timestamp": "2026-02-08T03:14:41.284737Z"
} | d88f41 | 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": 1735
},
"timestamp": "2026-02-09T22:41:45.077Z",
"answer": 2027
},
{
"i... | 1 | [
{
"lemma": "C4",
"status": "ok"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
}
] | {
"lo": -5.55,
"mid": -3.02,
"hi": 0.31
} | ||
61836a | nt_min_with_divisor_count_v1_1978505735_1178 | Let $n$ be a positive integer such that $1 \leq n \leq 32768$ and the number of positive divisors of $n$ is exactly 9. Let $S$ be the set of all such integers $n$. Determine the value of the minimum element of $S$, and denote this value by $m$.
Let $T$ be the set of all ordered pairs $(i, j)$ of positive integers such... | 18,369 | graphs = [
Graph(
let={
"upper": Const(32768),
"div_count": Const(9),
"result": MinOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Ref("upper")), Eq(NumDivisors(n=Var("n")), Ref("div_count"))))),
"Q": Mod(value=Sum(M... | NT | null | EXTREMUM | sympy | COUNT_COPRIME_GRID | [
"COUNT_COPRIME_GRID"
] | 283923 | nt_min_with_divisor_count_v1 | two_moduli | 6 | 0 | [
"COUNT_COPRIME_GRID"
] | 1 | 1.481 | 2026-02-08T15:52:50.806644Z | {
"verified": true,
"answer": 18369,
"timestamp": "2026-02-08T15:52:52.287668Z"
} | b33b71 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 216,
"completion_tokens": 1631
},
"timestamp": "2026-02-16T14:51:35.109Z",
"answer": 18369
},
... | 1 | [
{
"lemma": "COUNT_COPRIME_GRID",
"status": "ok"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "V3",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
81fd97 | comb_count_partitions_v1_1520064083_4000 | Let $n = 1633$. Define $s$ to be the number of nonnegative integers $j$ such that $0 \le j \le 1633$ and $\binom{1633}{j}$ is odd. Let $m = s + 7$. Compute the number of integer partitions of $m$. | 31,185 | graphs = [
Graph(
let={
"_n": Const(1633),
"n": Sum(CountOverSet(set=SolutionsSet(var=Var("j"), condition=And(Geq(Var("j"), Const(0)), Leq(Var("j"), Const(1633)), Eq(Mod(value=Binom(n=Ref("_n"), k=Var("j")), modulus=Const(2)), Const(1))), domain='nonnegative_integers')), Const(7)),
... | COMB | null | COUNT | sympy | V8 | [
"V8"
] | 86348e | comb_count_partitions_v1 | null | 7 | 0 | [
"V8"
] | 1 | 0.001 | 2026-02-08T06:01:05.940027Z | {
"verified": true,
"answer": 31185,
"timestamp": "2026-02-08T06:01:05.940962Z"
} | 96b7ea | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 178,
"completion_tokens": 1125
},
"timestamp": "2026-02-24T05:06:35.652Z",
"answer": 31185
},
{
"... | 1 | [
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "V3",
"status": "no"
},
{
"lemma": "V8",
"status": "ok"
}
] | {
"lo": -2.46,
"mid": 0.47,
"hi": 3.59
} | ||
3a8299 | modular_modexp_compute_v1_579913215_162 | Let $S$ be the set of all ordered pairs $(x, y)$ of positive integers such that $xy = 1327104$. Let $e$ be the minimum value of $x + y$ over all such pairs.
Compute the remainder when $19^e$ is divided by $28900$. | 24,821 | graphs = [
Graph(
let={
"a": Const(19),
"e": MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(Mul(Var("x"), Var("y")), Const(1327104)))), expr=Sum(Var("x"), Var("y")))),... | NT | null | COMPUTE | sympy | B3 | [
"B3"
] | 0cd20d | modular_modexp_compute_v1 | null | 6 | 0 | [
"B3"
] | 1 | 0.002 | 2026-02-08T12:55:35.179170Z | {
"verified": true,
"answer": 24821,
"timestamp": "2026-02-08T12:55:35.181243Z"
} | 7c4d0e | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 112,
"completion_tokens": 2879
},
"timestamp": "2026-02-15T07:57:32.384Z",
"answer": 24821
},
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
}
] | {
"lo": -5.49,
"mid": 0.22,
"hi": 6.51
} | ||
023b4a | nt_num_divisors_compute_v1_2051736721_1330 | Let $n = 136$. Define $m$ to be the maximum value of $xy$ over all ordered pairs $(x, y)$ of positive integers such that $x + y = 136$. Compute the number of positive divisors of $m$. | 15 | graphs = [
Graph(
let={
"_n": Const(136),
"n": MaxOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(Sum(Var("x"), Var("y")), Ref("_n")))), expr=Mul(Var("x"), Var("y")))),
... | NT | null | COMPUTE | sympy | B1 | [
"B1"
] | 5b950e | nt_num_divisors_compute_v1 | null | 3 | 0 | [
"B1"
] | 1 | 0.002 | 2026-02-08T15:56:25.764656Z | {
"verified": true,
"answer": 15,
"timestamp": "2026-02-08T15:56:25.766472Z"
} | 7c5182 | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 113,
"completion_tokens": 559
},
"timestamp": "2026-02-16T06:49:58.405Z",
"answer": 21
},
{
"id": 11,
... | 1 | [
{
"lemma": "B1",
"status": "ok"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
}
] | {
"lo": -8.26,
"mid": -5.01,
"hi": -1.76
} | ||
0a867b | antilemma_sum_equals_v1_1918700295_4078 | Let $x$ be the number of ordered pairs $(i, j)$ of positive integers such that $i + j = 96$ and $1 \leq i, j \leq 95$. Compute the value of $x + \phi(|x| + 1) + \tau(|x| + 1)$, where $\phi(n)$ denotes the number of positive integers at most $n$ that are relatively prime to $n$, and $\tau(n)$ denotes the number of posit... | 139 | graphs = [
Graph(
let={
"x": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("i"), Var("j")]), condition=Eq(Sum(Var("i"), Var("j")), Const(96)), domain=CartesianProduct(left=IntegerRange(start=Const(1), end=Const(95)), right=IntegerRange(start=Const(1), end=Const(95))))),
"Q": ... | COMB | GEOM | COMPUTE | sympy | COUNT_SUM_EQUALS | [
"COUNT_SUM_EQUALS"
] | 75ab0f | antilemma_sum_equals_v1 | null | 3 | 0 | [
"COUNT_SUM_EQUALS"
] | 1 | 0.004 | 2026-02-08T09:07:46.332559Z | {
"verified": true,
"answer": 139,
"timestamp": "2026-02-08T09:07:46.337024Z"
} | 0c8dbe | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 220,
"completion_tokens": 932
},
"timestamp": "2026-02-24T10:34:37.050Z",
"answer": 139
},
{
"id"... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "ok"
},
{
"lemma": "V7",
... | {
"lo": -4.92,
"mid": -2.91,
"hi": -0.68
} | ||
4e2c3f | nt_sum_divisors_mod_v1_1978505735_4626 | Let $S$ be the set of all ordered pairs $(x, y)$ of positive integers such that $xy = 396900$. Let $n$ be the minimum value of $x + y$ over all such pairs. Let $\sigma$ denote the sum of all positive divisors of $n$. Compute the remainder when $\sigma$ is divided by $11353$. | 4,368 | graphs = [
Graph(
let={
"n": MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(Mul(Var("x"), Var("y")), Const(396900)))), expr=Sum(Var("x"), Var("y")))),
"M": Const(11353... | NT | null | COMPUTE | sympy | B3 | [
"B3"
] | 0cd20d | nt_sum_divisors_mod_v1 | null | 6 | 0 | [
"B3"
] | 1 | 0.003 | 2026-02-08T18:24:38.749983Z | {
"verified": true,
"answer": 4368,
"timestamp": "2026-02-08T18:24:38.752995Z"
} | 8685cf | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 123,
"completion_tokens": 2991
},
"timestamp": "2026-02-18T16:57:04.159Z",
"answer": 4368
},
{... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
e82d27 | modular_sum_quadratic_residues_v1_601307018_10734 | Let $M$ be the maximum value of $xy$ over all ordered pairs $(x, y)$ of positive integers such that $x + y = 4$. Let $p$ be the largest prime number satisfying $2 \leq p \leq 102$. Compute $\frac{p(p - 1)}{M}$. | 2,525 | graphs = [
Graph(
let={
"_m": Const(2),
"_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(4)))), expr=Mul(Var("x"), Var("y")))),
... | NT | null | SUM | sympy | B1 | [
"B1/MAX_PRIME_BELOW"
] | 2fc9f0 | modular_sum_quadratic_residues_v1 | null | 3 | 0 | [
"B1",
"MAX_PRIME_BELOW"
] | 2 | 0.005 | 2026-03-10T11:13:14.648021Z | {
"verified": true,
"answer": 2525,
"timestamp": "2026-03-10T11:13:14.652797Z"
} | eb0843 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 180,
"completion_tokens": 319
},
"timestamp": "2026-04-19T14:36:54.633Z",
"answer": 2525
},
{
"i... | 2 | [
{
"lemma": "B1",
"status": "ok"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok_later"
},
{
... | {
"lo": -10,
"mid": -5.89,
"hi": -1.79
} | ||
96f3cf_n | alg_poly4_sum_v1_1218484723_731 | A digital artist generates abstract patterns on a $198\times198$ canvas, where each pixel at position $(a,b)$ contributes energy equal to $P a^4 + 296a^3b + 600a^2b^2 + 32ab^3 + 32b^4$, and $P$ is the largest prime number no greater than 339. After rendering the full image, the total energy is recorded modulo $54704$. ... | 21,906 | ALG | null | COMPUTE | sympy | MAX_PRIME_BELOW | [
"MAX_PRIME_BELOW"
] | dc3ad3 | alg_poly4_sum_v1 | null | 5 | null | [
"MAX_PRIME_BELOW"
] | 1 | 0.091 | 2026-02-25T02:28:02.135059Z | null | 3f77fb | 96f3cf | narrative | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 209,
"completion_tokens": 4309
},
"timestamp": "2026-03-30T15:50:17.777Z",
"answer": 34250
},
{
... | 1 | [
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok"
},
{
"lemma": "MOD_FACTORIAL",
"status": "n... | {
"lo": 1.5,
"mid": 4.69,
"hi": 7.23
} | |
1a9a19 | nt_gcd_compute_v1_2051736721_2256 | Let $m = 97$. Let $n$ be the number of positive integers $k$ such that $1 \leq k \leq 1751$ and $17$ divides $k$. Let $a = 584787$ and $b = 1086033$. Let $\text{result} = \gcd(a, b)$. Define
$$
Q = \left( 353702 \cdot (|\text{result}| \bmod m) + 329703 \cdot \left( (|\text{result}|^2 + 1) \bmod d_\text{min} \right) + 2... | 37,527 | graphs = [
Graph(
let={
"_m": Const(97),
"_n": CountOverSet(set=SolutionsSet(var=Var("k"), condition=And(Geq(Var("k"), Const(1)), Leq(Var("k"), Const(1751)), Divides(divisor=Const(17), dividend=Var("k"))), domain='positive_integers')),
"a": Const(584787),
"b":... | NT | null | COMPUTE | sympy | C2 | [
"C2/MIN_PRIME_FACTOR"
] | 83fddd | nt_gcd_compute_v1 | crt_mix_3 | 5 | 0 | [
"C2",
"MIN_PRIME_FACTOR"
] | 2 | 0.006 | 2026-02-08T16:33:08.743334Z | {
"verified": true,
"answer": 37527,
"timestamp": "2026-02-08T16:33:08.749742Z"
} | aed428 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 251,
"completion_tokens": 2525
},
"timestamp": "2026-02-17T06:33:34.101Z",
"answer": 37527
},
... | 1 | [
{
"lemma": "C2",
"status": "ok"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "MIN_PRIME_FACTOR",
"status": "ok_later"
},
... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
031a6c | nt_min_coprime_above_v1_124444284_7669 | Let $A$ be the set of all ordered pairs $(x,y)$ of positive integers such that $xy = 11560000$. Define $S$ to be the set of all values $x + y$ where $(x,y) \in A$. Let $m$ be the minimum element of $S$. Let $n$ be the smallest integer greater than 6724 and at most $m$ such that $\gcd(n, 66) = 1$. Compute $n$. | 6,725 | graphs = [
Graph(
let={
"start": Const(6724),
"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(11560000)))), expr=Sum(Var("x"), V... | NT | null | EXTREMUM | sympy | B3 | [
"B3"
] | 0cd20d | nt_min_coprime_above_v1 | null | 5 | 0 | [
"B3"
] | 1 | 0.01 | 2026-02-08T09:16:35.053522Z | {
"verified": true,
"answer": 6725,
"timestamp": "2026-02-08T09:16:35.063229Z"
} | 919684 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 148,
"completion_tokens": 2006
},
"timestamp": "2026-02-14T02:54:14.594Z",
"answer": 6725
},
{... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
... | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
5bac60 | sequence_fibonacci_compute_v1_458359167_1705 | Let $n$ be the sum of $\phi(d)$ over all positive divisors $d$ of $24$. Define $F_n$ to be the $n$-th Fibonacci number, where $F_1 = 1$, $F_2 = 1$, and $F_k = F_{k-1} + F_{k-2}$ for $k \geq 3$. Compute the remainder when $85846 \cdot F_n$ is divided by $51087$. | 12,636 | graphs = [
Graph(
let={
"_n": Const(24),
"n": SumOverDivisors(n=Ref(name='_n'), var='d', expr=EulerPhi(n=Var(name='d'))),
"result": Fibonacci(arg=Ref(name='n')),
"_c": Const(85846),
"Q": Mod(value=Mul(Ref("_c"), Ref("result")), modulus=Const(51087)... | NT | null | COMPUTE | sympy | K3 | [
"K3"
] | 54c41e | sequence_fibonacci_compute_v1 | null | 4 | 0 | [
"K3"
] | 1 | 0.001 | 2026-02-08T04:48:56.989682Z | {
"verified": true,
"answer": 12636,
"timestamp": "2026-02-08T04:48:56.990566Z"
} | cb0f9d | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 214,
"completion_tokens": 2119
},
"timestamp": "2026-02-11T22:10:23.279Z",
"answer": 12636
},
{
... | 1 | [
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "K3",
"status": "ok"
},
{
"lemma": "V1",
"status": "no"
},
{
"lemma": "V3",
"status": "no"
}
] | {
"lo": -3.42,
"mid": 1.86,
"hi": 7.55
} | ||
24ff48 | modular_min_modexp_v1_397696148_480 | Let $ a = 11 $, and let $ b $ be the number of positive integers $ k $ between 1 and 24037, inclusive, that are divisible by 43. Let $ m = 773 $ and define $ x $ to be a positive integer at most 386 such that $ a^x \equiv b \pmod{m} $. Find the smallest such $ x $. | 104 | graphs = [
Graph(
let={
"a": Const(11),
"b": CountOverSet(set=SolutionsSet(var=Var("k"), condition=And(Geq(Var("k"), Const(1)), Leq(Var("k"), Const(24037)), Divides(divisor=Const(43), dividend=Var("k"))), domain='positive_integers')),
"m": Const(773),
"upper":... | NT | null | EXTREMUM | sympy | B3 | [
"C2"
] | 9685eb | modular_min_modexp_v1 | null | 6 | 0 | [
"B3",
"C2"
] | 2 | 0.04 | 2026-02-08T11:30:52.253903Z | {
"verified": true,
"answer": 104,
"timestamp": "2026-02-08T11:30:52.293585Z"
} | 8c65e0 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 128,
"completion_tokens": 5078
},
"timestamp": "2026-02-14T15:21:35.938Z",
"answer": 104
},
{
... | 1 | [
{
"lemma": "C2",
"status": "ok"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
}
] | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
116e43 | nt_count_digit_sum_v1_2051736721_1608 | Consider the set of all ordered pairs $(x, y)$ of positive integers such that $xy = 225$. Let $s$ be the minimum value of $x + y$ over all such pairs. Let $N$ be the number of positive integers $n$, with $1 \leq n \leq 99999$, such that the sum of the digits of $n$ is equal to $s$. Let $P$ be the largest prime number b... | 9,463 | graphs = [
Graph(
let={
"_n": Const(2),
"upper": Const(99999),
"target_sum": 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(... | NT | null | COUNT | sympy | MAX_PRIME_BELOW | [
"MAX_PRIME_BELOW",
"B3"
] | 3b70ab | nt_count_digit_sum_v1 | quadratic_mod | 6 | 0 | [
"B3",
"MAX_PRIME_BELOW"
] | 2 | 14.878 | 2026-02-08T16:07:25.926796Z | {
"verified": true,
"answer": 9463,
"timestamp": "2026-02-08T16:07:40.804652Z"
} | e202e4 | 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": 2511
},
"timestamp": "2026-02-16T21:16:52.945Z",
"answer": 9463
},
{... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
a556b1 | sequence_count_fib_divisible_v1_151522320_1231 | Let $n$ be a positive integer. Define $A$ as the set of all positive integers $n$ such that $1 \leq n \leq 728$ and $9$ divides the $n$th Fibonacci number $F_n$. Define $B$ as the set of all positive integers $j$ such that $1 \leq j \leq 600$ and $j^3 \leq 216000000$. Compute the number of elements in $B$ minus the num... | 540 | graphs = [
Graph(
let={
"upper": Const(728),
"d": Const(9),
"result": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Ref("upper")), Divides(divisor=Ref("d"), dividend=Fibonacci(arg=Var(name='n')))))),
"_c": Cou... | NT | null | COUNT | sympy | C3 | [
"C3"
] | a45c54 | sequence_count_fib_divisible_v1 | negation_mod | 6 | 0 | [
"C3"
] | 1 | 0.032 | 2026-02-08T03:51:13.496431Z | {
"verified": true,
"answer": 540,
"timestamp": "2026-02-08T03:51:13.528062Z"
} | 484790 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 222,
"completion_tokens": 3283
},
"timestamp": "2026-02-10T15:53:47.092Z",
"answer": 540
},
{
"id... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "C3",
"status": "ok"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "n... | {
"lo": -5.55,
"mid": -3.02,
"hi": 0.31
} | ||
cf1f5b | nt_min_crt_v1_1978505735_2033 | Let $m$ be the smallest divisor of 2695 that is at least 2. Let $k$ be the smallest divisor of 294151 that is at least 2. Determine the smallest positive integer $n$ such that $1 \leq n \leq 55$, $n \equiv 1 \pmod{m}$, and $n \equiv 6 \pmod{k}$. | 6 | graphs = [
Graph(
let={
"_n": Const(2),
"m": MinOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Const(2)), Divides(divisor=Var("d"), dividend=Const(2695))))),
"k": MinOverSet(set=SolutionsSet(var=Var("d1"), condition=And(Geq(Var("d1"), Ref("_n")), Divid... | NT | null | EXTREMUM | sympy | B1 | [
"MIN_PRIME_FACTOR"
] | bc3776 | nt_min_crt_v1 | null | 5 | 0 | [
"B1",
"MIN_PRIME_FACTOR"
] | 2 | 0.256 | 2026-02-08T16:37:35.766819Z | {
"verified": true,
"answer": 6,
"timestamp": "2026-02-08T16:37:36.023317Z"
} | a3d898 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 128,
"completion_tokens": 1028
},
"timestamp": "2026-02-17T08:48:26.511Z",
"answer": 6
},
{
... | 1 | [
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "MIN_PRIME_FACTOR",
"status": "ok"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} |
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