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 |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
05699e | nt_max_prime_below_v1_1431428450_876 | Let $P$ be the set of all positive integers $p$ for which there exists a positive integer $q$ such that $p \cdot q = 6$, $\gcd(p, q) = 1$, and $p < q$. Let $m = |P|$. Let $S$ be the set of all prime numbers $n$ such that $m \le n \le 33856$. Determine the value of the largest element in $S$. | 33,851 | graphs = [
Graph(
let={
"upper": Const(33856),
"result": MaxOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), CountOverSet(set=SolutionsSet(var=Var("p"), condition=And(IsPositive(arg=Var(name='p')), Exists(var=Var(name='q'), condition=And(Eq(left=Mul(Var(name='p'), V... | NT | null | EXTREMUM | sympy | COPRIME_PAIRS | [
"COPRIME_PAIRS"
] | 2bb3aa | nt_max_prime_below_v1 | null | 4 | 0 | [
"COPRIME_PAIRS"
] | 1 | 2.167 | 2026-02-08T13:45:36.815105Z | {
"verified": true,
"answer": 33851,
"timestamp": "2026-02-08T13:45:38.981643Z"
} | d2519e | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 144,
"completion_tokens": 2737
},
"timestamp": "2026-02-15T20:27:19.302Z",
"answer": 33851
},
... | 1 | [
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "V1",
"status": "no"
},
{
"lemma": "V3",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
}
] | {
"lo": -5.49,
"mid": 0.22,
"hi": 6.51
} | ||
d6014e | sequence_fibonacci_compute_v1_458359167_3822 | Let $T$ be the set of all integers $t$ such that $8 \le t \le 38$ and there exist positive integers $a$ and $b$ with $1 \le a \le 4$, $1 \le b \le 6$, and
$$
t = 5a + 3b.
$$
Let $n$ be the number of elements in $T$. Compute the $n$-th Fibonacci number, where the Fibonacci sequence is defined by $F_1 = 1$, $F_2 = 1$, a... | 28,657 | graphs = [
Graph(
let={
"n": CountOverSet(set=SolutionsSet(var=Var("t"), condition=Exists(var=Var(name='a'), condition=Exists(var=Var(name='b'), condition=And(Geq(left=Var(name='a'), right=Const(value=1)), Leq(left=Var(name='a'), right=Const(value=4)), Geq(left=Var(name='b'), right=Const(value=1... | NT | null | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | sequence_fibonacci_compute_v1 | null | 4 | 0 | [
"LIN_FORM"
] | 1 | 0.003 | 2026-02-08T11:22:46.323658Z | {
"verified": true,
"answer": 28657,
"timestamp": "2026-02-08T11:22:46.326260Z"
} | 258c42 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 190,
"completion_tokens": 1810
},
"timestamp": "2026-02-14T12:41:27.658Z",
"answer": 28657
},
... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status":... | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
d4c0ea | nt_count_digit_sum_v1_1918700295_3520 | Let $n$ be a positive integer such that $1 \leq n \leq 309136$ and the sum of the decimal digits of $n$ is $24$. Let $S$ be the set of all such integers $n$. Compute the number of elements in $S$, take the absolute value of that number, and let $d$ be the smallest integer greater than or equal to $2$ that divides $143$... | 37,326 | graphs = [
Graph(
let={
"_n": Const(2),
"upper": Const(309136),
"target_sum": Const(24),
"result": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Ref("upper")), Eq(DigitSum(Var("n")), Ref("target_sum"))))),
... | NT | COMB | COUNT | sympy | COPRIME_PAIRS | [
"MIN_PRIME_FACTOR"
] | 58d7e9 | nt_count_digit_sum_v1 | bell_mod | 4 | 0 | [
"COPRIME_PAIRS",
"MIN_PRIME_FACTOR"
] | 2 | 31.461 | 2026-02-08T08:40:34.980440Z | {
"verified": true,
"answer": 37326,
"timestamp": "2026-02-08T08:41:06.441875Z"
} | 7b140a | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 177,
"completion_tokens": 4910
},
"timestamp": "2026-02-13T21:08:42.571Z",
"answer": 37326
},
... | 1 | [
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MIN_PRIME_FACTOR",
"status": "ok"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "n... | {
"lo": -3.51,
"mid": 1.33,
"hi": 6.56
} | ||
d81001 | antilemma_cartesian_v1_1742523217_1993 | Let $x$ be the number of ordered pairs $(a, b)$ where $a$ is an integer from 1 to 29, inclusive, and $b$ is an integer from 1 to 30, inclusive. Find the remainder when $44121 \cdot x$ is divided by $59926$. | 32,630 | graphs = [
Graph(
let={
"x": CountOverSet(set=CartesianProduct(left=IntegerRange(start=Const(1), end=Const(29)), right=IntegerRange(start=Const(1), end=Const(30)))),
"Q": Mod(value=Mul(Const(44121), Ref("x")), modulus=Const(59926)),
},
goal=Ref("Q"),
)
] | COMB | GEOM | COMPUTE | sympy | COUNT_CARTESIAN | [
"COUNT_CARTESIAN"
] | 409d7d | antilemma_cartesian_v1 | null | 2 | 0 | [
"COUNT_CARTESIAN"
] | 1 | 0.001 | 2026-02-08T04:23:07.458750Z | {
"verified": true,
"answer": 32630,
"timestamp": "2026-02-08T04:23:07.459377Z"
} | 4f4bde | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 176,
"completion_tokens": 6950
},
"timestamp": "2026-02-24T00:29:01.934Z",
"answer": 32630
},
{
"... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "ok"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
}
] | {
"lo": -2.46,
"mid": 0.47,
"hi": 3.59
} | ||
d01a52 | comb_count_derangements_v1_48377204_2795 | Let $S$ be the set of all positive integers $p$ for which there exists a positive integer $q$ such that $pq = 31500$, $\gcd(p, q) = 1$, and $p < q$. Let $n$ be the number of elements in $S$. The subfactorial of $n$, denoted $!n$, is the number of derangements of $n$ elements. Compute the remainder when $44121 \cdot !n$... | 31,217 | graphs = [
Graph(
let={
"_n": Const(80812),
"n": CountOverSet(set=SolutionsSet(var=Var("p"), condition=And(IsPositive(arg=Var(name='p')), Exists(var=Var(name='q'), condition=And(Eq(left=Mul(Var(name='p'), Var(name='q')), right=Const(value=31500)), Eq(left=GCD(a=Var(name='p'), b=Var(n... | NT | COMB | COUNT | sympy | COPRIME_PAIRS | [
"COPRIME_PAIRS"
] | 2bb3aa | comb_count_derangements_v1 | null | 6 | 0 | [
"COPRIME_PAIRS"
] | 1 | 0.002 | 2026-02-08T16:57:53.422523Z | {
"verified": true,
"answer": 31217,
"timestamp": "2026-02-08T16:57:53.424410Z"
} | 7c0f13 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 153,
"completion_tokens": 2521
},
"timestamp": "2026-02-17T17:53:06.849Z",
"answer": 31217
},
... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
85d2d8 | modular_mod_compute_v1_1918700295_3230 | Let $n = 63991$. Define $m$ to be the number of nonnegative integers $j$ such that $$
\sum_{k=0}^{1} (-1)^k \binom{1}{k} \leq j \leq n$$ and $$
\binom{63991}{j} \equiv 1 \pmod{2}.
$$ Let $a = -4$. Compute the remainder when $a$ is divided by $m$. | 8,188 | graphs = [
Graph(
let={
"_n": Const(63991),
"a": Const(-4),
"m": CountOverSet(set=SolutionsSet(var=Var("j"), condition=And(Geq(Var("j"), Summation(var="k", start=Const(0), end=Const(1), expr=Mul(Pow(Const(-1), Var("k")), Binom(n=Const(1), k=Var("k"))))), Leq(Var("j"), Ref... | COMB | null | COMPUTE | sympy | BINOMIAL_ALTERNATING | [
"BINOMIAL_ALTERNATING",
"V8"
] | efe7d7 | modular_mod_compute_v1 | null | 4 | 0 | [
"BINOMIAL_ALTERNATING",
"V8"
] | 2 | 0.002 | 2026-02-08T08:27:49.476323Z | {
"verified": true,
"answer": 8188,
"timestamp": "2026-02-08T08:27:49.477992Z"
} | ba3c78 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 211,
"completion_tokens": 1927
},
"timestamp": "2026-02-24T09:34:30.826Z",
"answer": 8188
},
{
"i... | 1 | [
{
"lemma": "BINOMIAL_ALTERNATING",
"status": "ok"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
},
{
"lemma": "V7",
"status": ... | {
"lo": -2.35,
"mid": 1.22,
"hi": 4.84
} | ||
fe8000 | sequence_lucas_compute_v1_124444284_10050 | Let $n$ be the smallest integer at least $2$ that divides $444889$. Compute the $n$th Lucas number. | 64,079 | graphs = [
Graph(
let={
"_n": Const(2),
"n": MinOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Ref("_n")), Divides(divisor=Var("d"), dividend=Const(444889))))),
"result": Lucas(arg=Ref(name='n')),
},
goal=Ref("result"),
)
] | NT | null | COMPUTE | sympy | MIN_PRIME_FACTOR | [
"MIN_PRIME_FACTOR"
] | bc3776 | sequence_lucas_compute_v1 | null | 3 | 0 | [
"MIN_PRIME_FACTOR"
] | 1 | 0.001 | 2026-02-08T12:47:42.462539Z | {
"verified": true,
"answer": 64079,
"timestamp": "2026-02-08T12:47:42.463645Z"
} | afea2d | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 75,
"completion_tokens": 990
},
"timestamp": "2026-02-15T05:30:24.237Z",
"answer": 64079
},
{
... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "MIN_PRIME_FACTOR",
"status": "ok"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
}
... | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
e531b6 | nt_count_divisors_in_range_v1_655260480_2719 | Let $n$ be the number of ordered pairs $(i,j)$ of positive integers with $1 \leq i \leq 21$, $1 \leq j \leq 64$, and $\gcd(i,j) = 1$. Compute the number of positive divisors $d$ of $n$ such that $1 \leq d \leq 122$. Let this count be $c$. Find the remainder when $45344 \cdot c$ is divided by 74205. | 65,869 | graphs = [
Graph(
let={
"_n": Const(74205),
"n": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("i"), Var("j")]), condition=Eq(GCD(a=Var("i"), b=Var("j")), Const(1)), domain=CartesianProduct(left=IntegerRange(start=Const(1), end=Const(21)), right=IntegerRange(start=Const(1), e... | NT | null | COUNT | sympy | COUNT_COPRIME_GRID | [
"COUNT_COPRIME_GRID"
] | 20ec03 | nt_count_divisors_in_range_v1 | null | 4 | 0 | [
"COUNT_COPRIME_GRID"
] | 1 | 0.009 | 2026-02-08T16:55:34.922781Z | {
"verified": true,
"answer": 65869,
"timestamp": "2026-02-08T16:55:34.932147Z"
} | 0881ca | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 145,
"completion_tokens": 2760
},
"timestamp": "2026-02-17T15:15:49.060Z",
"answer": 65869
},
... | 1 | [
{
"lemma": "COUNT_COPRIME_GRID",
"status": "ok"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "V1",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
0759ad | comb_sum_binomial_row_v1_1248542787_327 | Let $n$ be the number of ordered pairs $(i,j)$ of positive integers with $1 \leq i \leq 2$ and $1 \leq j \leq 9$ such that $\gcd(i,j) = 1$. Compute $37636 - 2^n$. | 21,252 | graphs = [
Graph(
let={
"_n": Const(2),
"n": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("i"), Var("j")]), condition=Eq(GCD(a=Var("i"), b=Var("j")), Const(1)), domain=CartesianProduct(left=IntegerRange(start=Const(1), end=Const(2)), right=IntegerRange(start=Const(1), end=Co... | NT | null | SUM | sympy | COUNT_COPRIME_GRID | [
"COUNT_COPRIME_GRID"
] | 20ec03 | comb_sum_binomial_row_v1 | null | 3 | 0 | [
"COUNT_COPRIME_GRID"
] | 1 | 0.001 | 2026-02-08T03:03:40.136375Z | {
"verified": true,
"answer": 21252,
"timestamp": "2026-02-08T03:03:40.137380Z"
} | 17a577 | 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": 385
},
"timestamp": "2026-02-09T02:55:50.760Z",
"answer": 21252
},
{
"i... | 2 | [
{
"lemma": "COUNT_COPRIME_GRID",
"status": "ok"
},
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "... | {
"lo": -10,
"mid": -7.73,
"hi": -5.46
} | ||
e4d532 | modular_mod_compute_v1_1874849503_1518 | Let $n = 146$. Consider the set of all ordered pairs $(x,y)$ of positive integers such that $x + y = 146$. Let $P$ be the set of all values of $xy$ as $(x,y)$ ranges over these pairs. Define $a = \max(P)$.
Compute the remainder when $a$ is divided by $36864$. | 5,329 | graphs = [
Graph(
let={
"_n": Const(146),
"a": 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 | modular_mod_compute_v1 | null | 4 | 0 | [
"B1"
] | 1 | 0.001 | 2026-02-08T13:56:42.473267Z | {
"verified": true,
"answer": 5329,
"timestamp": "2026-02-08T13:56:42.474479Z"
} | 6f5000 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 188,
"completion_tokens": 280
},
"timestamp": "2026-02-10T05:00:15.430Z",
"answer": 5329
},
{
"id... | 2 | [
{
"lemma": "B1",
"status": "ok"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
}
] | {
"lo": -10,
"mid": -7.27,
"hi": -4.54
} | ||
63f918 | algebra_poly_eval_v1_1918700295_1723 | Let $y = 29$. Define $\text{result} = \frac{1}{70} \left( 16y^3 + \left( \sum_{k=1}^{12} k \right) y^2 - 122y - 84 \right)$. Let $Q = |\text{result}|$. Find the value of $Q$. | 6,460 | graphs = [
Graph(
let={
"_n": Const(12),
"y": Const(29),
"result": Div(Sum(Mul(Const(16), Pow(Ref("y"), Const(3))), Mul(Summation(var="k", start=Const(1), end=Ref("_n"), expr=Var("k")), Pow(Ref("y"), Const(2))), Mul(Const(-122), Ref("y")), Const(-84)), Const(70)),
... | NT | null | COMPUTE | sympy | SUM_ARITHMETIC | [
"SUM_ARITHMETIC"
] | eb34f0 | algebra_poly_eval_v1 | null | 2 | 0 | [
"SUM_ARITHMETIC"
] | 1 | 0.005 | 2026-02-08T05:58:31.574870Z | {
"verified": true,
"answer": 6460,
"timestamp": "2026-02-08T05:58:31.579511Z"
} | 2b3c6f | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 124,
"completion_tokens": 709
},
"timestamp": "2026-02-12T17:44:17.789Z",
"answer": 6460
},
{
... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "SUM_ARITHMETIC",
"status": "ok"
... | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
8c98cb | comb_count_permutations_fixed_v1_784195855_4783 | Let $n$ be the largest integer such that $11^n$ divides $99!$. Compute the value of $\binom{n}{5} \cdot !(n-5)$, where $!k$ denotes the number of derangements of $k$ elements. | 1,134 | graphs = [
Graph(
let={
"_n": Const(99),
"n": MaxKDivides(target=Factorial(Ref("_n")), base=Const(11)),
"k": Const(5),
"result": Mul(Binom(n=Ref("n"), k=Ref("k")), Subfactorial(arg=Sub(left=Ref(name='n'), right=Ref(name='k')))),
},
goal=Ref("re... | NT | COMB | COUNT | sympy | COPRIME_PAIRS | [
"V1"
] | dae96f | comb_count_permutations_fixed_v1 | null | 5 | 0 | [
"COPRIME_PAIRS",
"V1"
] | 2 | 0.011 | 2026-02-08T07:20:28.366917Z | {
"verified": true,
"answer": 1134,
"timestamp": "2026-02-08T07:20:28.377885Z"
} | c97227 | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 152,
"completion_tokens": 500
},
"timestamp": "2026-02-20T02:21:47.119Z",
"answer": 1134
}
] | 2 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "K5",
"status": "same_pattern_wrong"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"... | {
"lo": -10,
"mid": -6.47,
"hi": -2.95
} | ||
a00324 | comb_binomial_compute_v1_458359167_439 | Let $m = 56908$. Let $P$ be the set of all positive integers $p$ for which there exists a positive integer $q$ such that $p \cdot q = 1543500$, $\gcd(p, q) = 1$, and $p < q$. Let $\mathcal{N}$ be the number of elements in $P$. Define $n$ to be the maximum value of $x \cdot y$ over all pairs of positive integers $(x, y)... | 37,832 | graphs = [
Graph(
let={
"_m": Const(56908),
"_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=1543500)), Eq(left=GCD(a=Var(name='p'), b=Va... | NT | null | COMPUTE | sympy | COPRIME_PAIRS | [
"COPRIME_PAIRS/B1",
"L3C"
] | ff8179 | comb_binomial_compute_v1 | null | 6 | 0 | [
"B1",
"COPRIME_PAIRS",
"L3C"
] | 3 | 0.003 | 2026-02-08T03:18:29.462315Z | {
"verified": true,
"answer": 37832,
"timestamp": "2026-02-08T03:18:29.465606Z"
} | 89ded6 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 1,
"correct": {
"strict": false,
"boxed": false,
"relaxed": true
},
"usage": {
"prompt_tokens": 315,
"completion_tokens": 3029
},
"timestamp": "2026-02-10T14:05:54.282Z",
"answer": null
},
{
... | 1 | [
{
"lemma": "B1",
"status": "ok_later"
},
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "L3C",
"sta... | {
"lo": 3.24,
"mid": 5.68,
"hi": 8.81
} | ||
8adaf4 | comb_catalan_compute_v1_1915831931_3044 | Let $n$ be the number of ordered pairs $(x_1, x_2)$ of positive odd integers such that $x_1 + x_2 = 22$. Let $r$ be the $n$-th Catalan number. Compute $62500 - r$. Find the value of this expression. | 3,714 | graphs = [
Graph(
let={
"_n": Const(22),
"n": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x1"), Var("x2")]), condition=And(IsPositive(arg=Var(name='x1')), IsPositive(arg=Var(name='x2')), IsOdd(arg=Var(name='x1')), IsOdd(arg=Var(name='x2')), Eq(Sum(Var("x1"), Var("x2")), Re... | COMB | null | COMPUTE | sympy | COMB1 | [
"COMB1"
] | 567f58 | comb_catalan_compute_v1 | null | 4 | 0 | [
"COMB1"
] | 1 | 0.004 | 2026-02-08T17:19:47.573531Z | {
"verified": true,
"answer": 3714,
"timestamp": "2026-02-08T17:19:47.577266Z"
} | a10a09 | 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": 1166
},
"timestamp": "2026-02-17T23:57:26.233Z",
"answer": 3714
},
{... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COMB1",
"status": "ok"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
}
] | {
"lo": -5.64,
"mid": -3.17,
"hi": -0.81
} | ||
d8bcac | lin_form_endings_v1_458359167_4542 | Let $a = 70$ and $b = 98$. Let $L$ be the least common multiple of $a$ and $b$. Define $x = 3L + a + b$. Compute $x$. | 1,638 | graphs = [
Graph(
let={
"a_coeff": Const(70),
"b_coeff": Const(98),
"k_val": Const(3),
"lcm_node": LCM(a=Ref("a_coeff"), b=Ref("b_coeff")),
"x": Sum(Mul(Ref("k_val"), Ref("lcm_node")), Ref("a_coeff"), Ref("b_coeff")),
},
goal=Ref("x... | COMB | NT | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | lin_form_endings_v1 | null | 2 | null | [
"LIN_FORM"
] | 1 | 0.001 | 2026-02-08T11:51:57.784496Z | {
"verified": true,
"answer": 1638,
"timestamp": "2026-02-08T11:51:57.785060Z"
} | d38da5 | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 104,
"completion_tokens": 249
},
"timestamp": "2026-02-16T03:25:54.015Z",
"answer": 1638
},
{
"id": 11,
... | 2 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "V8_SUM",
... | {
"lo": -10,
"mid": -7.71,
"hi": -5.43
} | ||
11a555_n | alg_telescope_v1_1218484723_5454 | A data analyst is studying two different production systems.
For the first system, she looks at all integer pairs $(a, b)$ with $1 \le a \le 20$ and $1 \le b \le 20$. A pair is labeled *stable* if the quantity $-12ab + 41a^{2} + 20b^{2}$ does not exceed a threshold $B$, where $B$ is the number of distinct totals $t$ ... | 1,805 | ALG | null | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM/QF_PSD_COUNT_LEQ"
] | 77251b | alg_telescope_v1 | null | 7 | null | [
"LIN_FORM",
"QF_PSD_COUNT_LEQ"
] | 2 | 0.014 | 2026-02-25T07:00:40.135748Z | null | efd421 | 11a555 | narrative | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 463,
"completion_tokens": 32768
},
"timestamp": "2026-03-30T23:28:14.128Z",
"answer": null
},
{
... | 1 | [
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "QF_PSD_COUNT_LEQ",
"status": "ok_later"
}
] | {
"lo": 3.8,
"mid": 6.33,
"hi": 9.49
} | |
d253fa | antilemma_cartesian_v1_124444284_7823 | Compute the number of ordered pairs $(x, y)$ such that $1 \le x \le 12$ and $1 \le y \le 18$. | 216 | graphs = [
Graph(
let={
"x": CountOverSet(set=CartesianProduct(left=IntegerRange(start=Const(1), end=Const(12)), right=IntegerRange(start=Const(1), end=Const(18)))),
},
goal=Ref("x"),
)
] | COMB | GEOM | COMPUTE | sympy | COUNT_CARTESIAN | [
"COUNT_CARTESIAN"
] | 409d7d | antilemma_cartesian_v1 | null | 2 | 0 | [
"COUNT_CARTESIAN"
] | 1 | 0 | 2026-02-08T09:23:02.861897Z | {
"verified": true,
"answer": 216,
"timestamp": "2026-02-08T09:23:02.862296Z"
} | 2abf5b | 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": 175
},
"timestamp": "2026-02-24T11:12:57.872Z",
"answer": 216
},
{
"id"... | 2 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "ok"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "V8",
... | {
"lo": -10,
"mid": -7.79,
"hi": -5.57
} | ||
74d356 | diophantine_product_count_v1_784195855_1603 | Let $n = 360$. Define $k$ to be the sum of $\phi(d)$ over all positive divisors $d$ of $n$. Let $u = 261$. Consider the set of all positive integers $x$ such that $1 \le x \le u$, $x$ divides $k$, and $\frac{k}{x} \le u$. Compute the number of elements in this set. | 22 | graphs = [
Graph(
let={
"_n": Const(360),
"k": SumOverDivisors(n=Ref(name='_n'), var='d', expr=EulerPhi(n=Var(name='d'))),
"upper": Const(261),
"result": CountOverSet(set=SolutionsSet(var=Var("x"), condition=And(Geq(Var("x"), Const(1)), Leq(Var("x"), Ref("uppe... | NT | null | COUNT | sympy | LIN_FORM | [
"K3"
] | 54c41e | diophantine_product_count_v1 | null | 6 | 0 | [
"K3",
"LIN_FORM"
] | 2 | 0.087 | 2026-02-08T05:10:16.366178Z | {
"verified": true,
"answer": 22,
"timestamp": "2026-02-08T05:10:16.453514Z"
} | d1f29d | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 197,
"completion_tokens": 1870
},
"timestamp": "2026-02-11T23:02:20.307Z",
"answer": 22
},
{
"id... | 1 | [
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "K3",
"status": "ok"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "V3",
"status": "no"
}
] | {
"lo": -3.42,
"mid": 1.86,
"hi": 7.55
} | ||
a4884d | antilemma_k3_v1_1978505735_2884 | Compute the sum of $\phi(d)$ over all positive divisors $d$ of $56127$, where $\phi$ denotes Euler's totient function. | 56,127 | graphs = [
Graph(
let={
"x": SumOverDivisors(n=Const(value=56127), var='d', expr=EulerPhi(n=Var(name='d'))),
},
goal=Ref("x"),
)
] | NT | COMB | COMPUTE | sympy | K3 | [
"K3"
] | 54c41e | antilemma_k3_v1 | null | 3 | 0 | [
"K3"
] | 1 | 0 | 2026-02-08T17:14:15.056339Z | {
"verified": true,
"answer": 56127,
"timestamp": "2026-02-08T17:14:15.056791Z"
} | 36eb27 | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 1,
"correct": {
"strict": false,
"boxed": false,
"relaxed": true
},
"usage": {
"prompt_tokens": 93,
"completion_tokens": 725
},
"timestamp": "2026-02-16T09:11:32.853Z",
"answer": 18709
},
{
"id": 11,
... | 1 | [
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K3",
"status": "ok"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "V3",
"status": "no"
},
{
"lemma": "VAL_SUM_EQ",
"status": "no"
}
] | {
"lo": -8.26,
"mid": -5.01,
"hi": -1.76
} | ||
a4702b | geo_visible_lattice_v1_1218484723_4599 | Let $B_n$ denote the $n$-th Bell number. Let $N$ be the number of lattice points $(x,y)$ with $1 \leq x, y \leq 157$ such that $\gcd(x,y) = 1$. Compute $B_{N \bmod 11}$. | 52 | graphs = [
Graph(
let={
"n": Const(157),
"result": VisibleLatticePoints(n=Ref(name='n')),
"Q": Bell(Mod(value=Abs(arg=Ref(name='result')), modulus=Const(11))),
},
goal=Ref("Q"),
)
] | GEOM | GEOM | COUNT | sympy | [] | geo_visible_lattice_v1 | null | 4 | 0 | null | null | 2.357 | 2026-02-25T06:16:14.019591Z | {
"verified": true,
"answer": 52,
"timestamp": "2026-02-25T06:16:16.376243Z"
} | c495da | 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": 19786
},
"timestamp": "2026-03-29T16:29:44.878Z",
"answer": 52
},
{
"id... | 1 | [] | {
"lo": 1.53,
"mid": 4.7,
"hi": 7.23
} | ||||
de67ab | lte_diff_endings_v1_168721529_79 | Let $a = 86$, $b = 11$, and $n = 30$. Let $d = a^n - b^n$, and let $v_5$ be the largest integer $k$ such that $5^k$ divides $d$. Compute the remainder when $11983 \cdot v_5$ is divided by $100000$. | 35,949 | graphs = [
Graph(
let={
"a_val": Const(86),
"b_val": Const(11),
"p_val": Const(5),
"n_val": Const(30),
"a_pow": Pow(Ref("a_val"), Ref("n_val")),
"b_pow": Pow(Ref("b_val"), Ref("n_val")),
"pow_diff": Sub(Ref("a_pow"), Ref("b_... | NT | null | COMPUTE | sympy | LTE_DIFF | [
"LTE_DIFF"
] | cf8260 | lte_diff_endings_v1 | null | 7 | null | [
"LTE_DIFF"
] | 1 | 0.001 | 2026-02-08T12:48:01.367267Z | {
"verified": true,
"answer": 35949,
"timestamp": "2026-02-08T12:48:01.368423Z"
} | d9cff3 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 192,
"completion_tokens": 594
},
"timestamp": "2026-02-08T21:02:52.993Z",
"answer": 35949
},
{
"i... | 1 | [
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "ok"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "V5",
"status":... | {
"lo": -2.06,
"mid": 1.85,
"hi": 5.2
} | ||
1301e3 | antilemma_k2_v1_2051736721_1618 | Let $m = 2$. Let $S$ be the set of all real numbers $x_1$ such that $x_1^m - 160x_1 - 11024 = 0$. Let $n$ be the sum of all elements in $S$. Define
$$
x = \sum_{k=1}^{n} \phi(k) \cdot \left\lfloor \frac{160}{k} \right\rfloor,
$$
where $\phi(k)$ denotes Euler's totient function. Find the remainder when $44121 \cdot x$ i... | 38,030 | graphs = [
Graph(
let={
"_m": Const(2),
"_n": SumOverSet(set=SolutionsSet(var=Var("x1"), condition=Eq(Sum(Pow(Var("x1"), Ref("_m")), Mul(Const(-160), Var("x1")), Const(-11024)), Const(0)))),
"x": Summation(var="k", start=Const(1), end=Ref("_n"), expr=Mul(EulerPhi(n=Var("k... | NT | COMB | COMPUTE | sympy | VIETA_SUM | [
"VIETA_SUM/K2",
"K2"
] | 6be084 | antilemma_k2_v1 | null | 6 | 0 | [
"K2",
"VIETA_SUM"
] | 2 | 0.002 | 2026-02-08T16:07:58.635345Z | {
"verified": true,
"answer": 38030,
"timestamp": "2026-02-08T16:07:58.637224Z"
} | a78036 | 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": 1520
},
"timestamp": "2026-02-16T21:15:41.922Z",
"answer": 38030
},
... | 1 | [
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "K2",
"status": "ok"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "VAL_SUM_EQ",
"status": "no"
},
{
... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
e5a635 | comb_count_partitions_v1_124444284_607 | Let $m = 19$ and $n_0 = 3$. Define $n$ to be the smallest positive integer such that the largest power of $n_0$ dividing $n!$ is at least the sum of all positive integers $k \le m$ that are divisible by 19. Let $p(n)$ denote the number of integer partitions of $n$. Compute the remainder when $58771 \cdot p(n)$ is divid... | 21,976 | graphs = [
Graph(
let={
"_m": Const(19),
"_n": Const(3),
"n": MinOverSet(set=SolutionsSet(var=Var("n"), condition=Geq(MaxKDivides(target=Factorial(Var("n")), base=Ref("_n")), SumOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Re... | NT | COMB | COUNT | sympy | SUM_DIVISIBLE | [
"SUM_DIVISIBLE/V5"
] | 7f4b43 | comb_count_partitions_v1 | null | 6 | 0 | [
"SUM_DIVISIBLE",
"V5"
] | 2 | 0.002 | 2026-02-08T03:23:46.728295Z | {
"verified": true,
"answer": 21976,
"timestamp": "2026-02-08T03:23:46.729851Z"
} | 58295d | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 209,
"completion_tokens": 2704
},
"timestamp": "2026-02-09T19:42:58.713Z",
"answer": 21976
},
{
"... | 1 | [
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "SUM_DIVISIBLE",
"status": "ok"
},
{
"lemma": "V3",
"status": "no"
},
{
... | {
"lo": 1.69,
"mid": 5.03,
"hi": 8.38
} | ||
b310f1 | comb_count_partitions_v1_601307018_4441 | Let $M = \sum_{k=1}^{15} k$ and $R = p(43)$, where $p(n)$ denotes the number of integer partitions of $n$, and $d(R)$ denotes the number of digits of $R$. Compute $$\sum_{i=\binom{3}{0} - 1}^{d(R) - 1} d_i(R) \cdot \left(i + \binom{6}{6}\right)^2 + M,$$ where $d_i(R)$ is the $i$-th digit of $R$ (with $i=0$ being the un... | 361 | graphs = [
Graph(
let={
"_n": Const(15),
"n": Const(43),
"result": Partition(arg=Ref(name='n')),
"_c": Summation(var="k", start=Const(1), end=Ref("_n"), expr=Var("k")),
"Q": Sum(Summation(var="i", start=Sub(Binom(n=Const(3), k=Const(0)), Const(1)),... | COMB | null | COUNT | sympy | SUM_ARITHMETIC | [
"SUM_ARITHMETIC",
"ZERO_BINOM_0",
"ONE_BINOM_N"
] | 0212a0 | comb_count_partitions_v1 | digits_weighted_mod | 5 | 0 | [
"ONE_BINOM_N",
"SUM_ARITHMETIC",
"ZERO_BINOM_0"
] | 3 | 0.008 | 2026-03-10T05:00:00.463974Z | {
"verified": true,
"answer": 361,
"timestamp": "2026-03-10T05:00:00.472259Z"
} | 91cf5d | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 244,
"completion_tokens": 1419
},
"timestamp": "2026-03-29T12:14:38.398Z",
"answer": 361
},
{
"id... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "ONE_BINOM_N",
"status": "ok"
},
{
"lemma": "SUM_ARITHMETI... | {
"lo": 1.19,
"mid": 4.27,
"hi": 6.7
} | ||
3157e0 | comb_count_surjections_v1_397696148_660 | Let $u = 4$ and $n_2 = u + 1$. Define
$$
t = \sum_{k=0}^{n_2} (-1)^k \binom{n_2}{k}.
$$
Let $u' = 9$ and $n_1 = u' + 1$. Define
$$
v = \sum_{k=0}^{n_1} (-1)^k \binom{n_1}{k}.
$$
Let $n = 8 + v$ and $k = 3 + t$. Compute the value of $k! \cdot S(n, k)$, where $S(n, k)$ denotes the Stirling number of the second kind. | 5,796 | graphs = [
Graph(
let={
"u1": Const(4),
"n2": Sum(Ref("u1"), Const(1)),
"t": Summation(var="k", start=Const(0), end=Ref("n2"), expr=Mul(Pow(Const(-1), Var("k")), Binom(n=Ref("n2"), k=Var("k")))),
"u": Const(9),
"n1": Sum(Ref("u"), Const(1)),
... | COMB | null | COUNT | sympy | BINOMIAL_ALTERNATING | [
"BINOMIAL_ALTERNATING"
] | c21569 | comb_count_surjections_v1 | null | 5 | 2 | [
"BINOMIAL_ALTERNATING"
] | 1 | 0.001 | 2026-02-08T11:39:20.974131Z | {
"verified": true,
"answer": 5796,
"timestamp": "2026-02-08T11:39:20.974976Z"
} | 78cd33 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 265,
"completion_tokens": 1164
},
"timestamp": "2026-02-24T14:29:57.038Z",
"answer": 5796
},
{
"i... | 1 | [
{
"lemma": "BINOMIAL_ALTERNATING",
"status": "ok"
},
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "V8_... | {
"lo": -3.84,
"mid": -1.67,
"hi": 1.32
} | ||
515672 | nt_sum_gcd_range_mod_v1_168721529_317 | Let $N = 98$. Define $N'$ to be the maximum value of $xy$ over all pairs of positive integers $(x, y)$ such that $x + y = N$. Let $k = 504$ and $M = 10321$. Compute the remainder when $\sum_{n=1}^{N'} \gcd(n, k)$ is divided by $M$. | 5,121 | graphs = [
Graph(
let={
"_n": Const(98),
"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_sum_gcd_range_mod_v1 | null | 6 | 0 | [
"B1"
] | 1 | 0.179 | 2026-02-08T12:59:23.554790Z | {
"verified": true,
"answer": 5121,
"timestamp": "2026-02-08T12:59:23.733633Z"
} | 2eef77 | CC BY 4.0 | [
{
"id": 4,
"model": "NousResearch/Hermes-4-405B",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 138,
"completion_tokens": 444
},
"timestamp": "2026-02-09T15:23:51.789Z",
"answer": 6299
},
... | 1 | [
{
"lemma": "B1",
"status": "ok"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
}
] | {
"lo": -1.9,
"mid": 2.34,
"hi": 6.68
} | ||
91fbb2 | comb_count_derangements_v1_1125832087_1193 | Let $n$ be the number of nonnegative integers $j$ such that $0 \le j \le 5136$ and $\binom{5136}{j}$ is odd. Let $r$ be the number of derangements of $n$ elements. Compute the remainder when $44121 \cdot r$ is divided by $77800$. | 70,993 | graphs = [
Graph(
let={
"_n": Const(2),
"n": CountOverSet(set=SolutionsSet(var=Var("j"), condition=And(Geq(Var("j"), Const(0)), Leq(Var("j"), Const(5136)), Eq(Mod(value=Binom(n=Const(5136), k=Var("j")), modulus=Ref("_n")), Const(1))), domain='nonnegative_integers')),
"res... | COMB | null | COUNT | sympy | V8 | [
"V8"
] | 86348e | comb_count_derangements_v1 | null | 6 | 0 | [
"V8"
] | 1 | 0.001 | 2026-02-08T03:36:42.408902Z | {
"verified": true,
"answer": 70993,
"timestamp": "2026-02-08T03:36:42.410074Z"
} | 0762ef | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 185,
"completion_tokens": 2287
},
"timestamp": "2026-02-10T15:09:06.008Z",
"answer": 70993
},
{
"... | 1 | [
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "V1",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
},
{
"lemma": "V8",
"status": "ok"
}
] | {
"lo": 1.97,
"mid": 4.36,
"hi": 6.69
} | ||
a8de8c | sequence_fibonacci_compute_v1_1918700295_1977 | Let $n$ be the maximum value of $xy$ over all pairs of positive integers $(x, y)$ such that $x + y = 10$. Let $F_n$ denote the $n$th Fibonacci number, with $F_1 = F_2 = 1$. Compute the remainder when $92215 \cdot F_n$ is divided by $62181$. | 47,953 | graphs = [
Graph(
let={
"_n": Const(62181),
"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(10)))), expr=Mul(Var("x"), Var("y")))),
... | NT | null | COMPUTE | sympy | B1 | [
"B1"
] | 5b950e | sequence_fibonacci_compute_v1 | null | 3 | 0 | [
"B1"
] | 1 | 0.001 | 2026-02-08T07:36:05.243065Z | {
"verified": true,
"answer": 47953,
"timestamp": "2026-02-08T07:36:05.244003Z"
} | 737f8b | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 126,
"completion_tokens": 1526
},
"timestamp": "2026-02-13T11:26:56.704Z",
"answer": 47953
},
... | 1 | [
{
"lemma": "B1",
"status": "ok"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
}
] | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
20d440 | nt_sum_gcd_range_mod_v1_865884756_6536 | Let $N$ be the number of integers $n$ with $1 \leq n \leq 21000$ such that $n \equiv \left\lfloor \frac{n}{2} \right\rfloor \pmod{7}$.
Let $k$ be the number of ordered pairs $(x_1, x_2)$ of positive odd integers such that $x_1 + x_2 = 192$.
Let $\displaystyle \text{sum} = \sum_{n_1=1}^{N} \gcd(n_1, k)$, and let $M = ... | 6,559 | graphs = [
Graph(
let={
"N": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Const(21000)), Congruent(a=Var(name='n'), b=Floor(arg=Div(left=Var(name='n'), right=Const(value=2))), modulus=Const(value=7))))),
"k": CountOverSet(set=Soluti... | NT | null | COMPUTE | sympy | COMB1 | [
"COMB1",
"L3C"
] | 942b13 | nt_sum_gcd_range_mod_v1 | null | 6 | 0 | [
"COMB1",
"L3C"
] | 2 | 0.133 | 2026-02-08T19:16:54.140209Z | {
"verified": true,
"answer": 6559,
"timestamp": "2026-02-08T19:16:54.273656Z"
} | 8aa387 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 187,
"completion_tokens": 2655
},
"timestamp": "2026-02-18T21:49:07.236Z",
"answer": 6559
},
{... | 1 | [
{
"lemma": "COMB1",
"status": "ok"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "L3C",
"status": "ok"
},
{
"lemma": "M... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
5b6236 | nt_count_gcd_equals_v1_1742523217_2767 | Let $k$ be the number of integers $t$ with $5 \leq t \leq 371$ for which there exist positive integers $a$ and $b$ such that $1 \leq a \leq 27$, $1 \leq b \leq 145$, and $t = 3a + 2b$. Let $r$ be the number of positive integers $n$ with $1 \leq n \leq 16653$ such that $\gcd(n, k) = 1$. Compute the remainder when $73417... | 53,160 | graphs = [
Graph(
let={
"_n": Const(90196),
"upper": Const(16653),
"k": CountOverSet(set=SolutionsSet(var=Var("t"), condition=Exists(var=Var(name='a'), condition=Exists(var=Var(name='b'), condition=And(Geq(left=Var(name='a'), right=Const(value=1)), Leq(left=Var(name='a'),... | NT | null | COUNT | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | nt_count_gcd_equals_v1 | null | 6 | 0 | [
"LIN_FORM"
] | 1 | 1.294 | 2026-02-08T05:20:05.565366Z | {
"verified": true,
"answer": 53160,
"timestamp": "2026-02-08T05:20:06.858997Z"
} | 3f5849 | 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": 4559
},
"timestamp": "2026-02-12T06:28:22.113Z",
"answer": 53160
},
... | 1 | [
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "V1",
"status": "no"
}
] | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
edabc7 | alg_poly_orbit_hensel_v1_1218484723_3367 | Let $f(x) = x^2 - 41 \bmod 2809$. For a non-negative integer $a$, define the sequence $N = f(a)$, $M = f(N)$, $R = f(M)$, $S = f(R)$, $T = f(S)$. Find the number of integers $a$ with $0 \leq a \leq 3556193$ such that $T = a$ but $a$ does not appear in the sequence $N, M, R, S$. | 6,330 | graphs = [
Graph(
let={
"p1": Mod(value=Sum(Pow(Var("a"), Const(2)), Const(-41)), modulus=Const(2809)),
"p2": Mod(value=Sum(Pow(Ref("p1"), Const(2)), Const(-41)), modulus=Const(2809)),
"p3": Mod(value=Sum(Pow(Ref("p2"), Const(2)), Const(-41)), modulus=Const(2809)),
... | ALG | null | COUNT | sympy | POLY_ORBIT_COUNT | [
"POLY_ORBIT_COUNT"
] | 4ad965 | alg_poly_orbit_hensel_v1 | null | 6 | null | [
"POLY_ORBIT_COUNT"
] | 1 | 0.034 | 2026-02-25T05:04:50.271409Z | {
"verified": true,
"answer": 6330,
"timestamp": "2026-02-25T05:04:50.305706Z"
} | a86441 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 224,
"completion_tokens": 32768
},
"timestamp": "2026-03-29T09:55:10.042Z",
"answer": null
},
{
... | 1 | [
{
"lemma": "POLY_ORBIT_COUNT",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
}
] | {
"lo": 3.81,
"mid": 6.33,
"hi": 9.49
} | ||
85e231 | alg_poly4_count_v1_1218484723_2905 | Let $V$ be the number of integers $v$ with $45 \le v \le 23805$ for which there exist positive integers $a, b$ with $1 \le a, b \le 23$ such that $17a^2 + 20ab + 8b^2 = v$. Let $W$ be the number of ordered pairs $(a_1, b_1)$ with $1 \le a_1, b_1 \le 40$ satisfying $34a_1^2 + 22a_1b_1 + 25b_1^2 \le 49365$. Find the numb... | 365 | graphs = [
Graph(
let={
"_m": Const(22),
"_n": Const(2),
"result": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("a"), Var("b")]), condition=And(Geq(Var("a"), Const(1)), Leq(Var("a"), Const(495)), Geq(Var("b"), Const(1)), Leq(Var("b"), CountOverSet(set=SolutionsSe... | ALG | null | COUNT | sympy | MIN_PRIME_FACTOR | [
"QF_PSD_COUNT_LEQ",
"QF_PSD_DISTINCT"
] | f25d80 | alg_poly4_count_v1 | null | 7 | 0 | [
"MIN_PRIME_FACTOR",
"QF_PSD_COUNT_LEQ",
"QF_PSD_DISTINCT"
] | 3 | 1.252 | 2026-02-25T04:40:02.222456Z | {
"verified": true,
"answer": 365,
"timestamp": "2026-02-25T04:40:03.474247Z"
} | e5aa8f | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 1,
"correct": {
"strict": false,
"boxed": false,
"relaxed": true
},
"usage": {
"prompt_tokens": 330,
"completion_tokens": 32768
},
"timestamp": "2026-03-29T07:15:59.640Z",
"answer": null
},
{
... | 1 | [
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "QF_PSD_COUNT_LEQ",
"status": "ok"
},
{
"lemma": "QF_PSD_DISTINCT",
"status": "ok"
}
] | {
"lo": 3.81,
"mid": 6.33,
"hi": 9.49
} | ||
ab7c2f | nt_count_intersection_v1_1353956133_685 | Let $N$ be the number of positive integers $k$ at most 125000 that are divisible by 25. Determine the number of positive integers $n$ at most $N$ that are divisible by 7 and relatively prime to 10. | 286 | graphs = [
Graph(
let={
"_n": Const(25),
"N": CountOverSet(set=SolutionsSet(var=Var("k"), condition=And(Geq(Var("k"), Const(1)), Leq(Var("k"), Const(125000)), Divides(divisor=Ref("_n"), dividend=Var("k"))), domain='positive_integers')),
"a": Const(7),
"b": Con... | NT | null | COUNT | sympy | C2 | [
"C2"
] | 9685eb | nt_count_intersection_v1 | null | 4 | 0 | [
"C2"
] | 1 | 0.184 | 2026-02-08T11:47:03.130412Z | {
"verified": true,
"answer": 286,
"timestamp": "2026-02-08T11:47:03.313960Z"
} | 548b87 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 99,
"completion_tokens": 951
},
"timestamp": "2026-02-14T18:53:33.810Z",
"answer": 286
},
{
... | 1 | [
{
"lemma": "C2",
"status": "ok"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"statu... | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
87df23 | alg_poly3_sum_v1_1218484723_2539 | Let $d = \left|\{ (a_1, b_1) : 1 \leq a_1, b_1 \leq 40,\ 34a_1^2 - 2a_1b_1 + 5b_1^2 = 8450 \}\right|$. Compute the remainder when
$$
\sum_{\substack{1 \leq a \leq 192 \\ 1 \leq b \leq 192}} \left( -56a^d + 192a^2b - 192ab^2 + 64b^3 \right)
$$
is divided by $84190$. | 47,594 | 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(192)), Geq(Var("b"), Const(1)), Leq(Var("b"), Const(192)))), expr=Sum(Mul(Const(... | ALG | null | COMPUTE | sympy | QF_PSD_COUNT | [
"QF_PSD_COUNT"
] | 09ce67 | alg_poly3_sum_v1 | null | 5 | 0 | [
"QF_PSD_COUNT"
] | 1 | 0.071 | 2026-02-25T04:16:56.270592Z | {
"verified": true,
"answer": 47594,
"timestamp": "2026-02-25T04:16:56.341584Z"
} | 8fbc50 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 254,
"completion_tokens": 26787
},
"timestamp": "2026-03-29T05:18:25.059Z",
"answer": 47594
},
{
... | 1 | [
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "QF_PSD_COUNT",
"status": "ok"
}
] | {
"lo": -2.45,
"mid": 1.37,
"hi": 5.29
} | ||
b65f49 | alg_sum_powers_v1_1218484723_6914 | Let $C = \left|\{ (a, b) \mid 1 \le a, b \le 40,\ 17a^2 - 32ab + 16b^2 \le 19616 \}\right|$. Let $M = \left( \sum_{k=1}^{C} k^3 \right) \bmod 8309$. Find the remainder when $80759M$ is divided by $65768$. | 53,763 | graphs = [
Graph(
let={
"_n": Const(19616),
"result": Mod(value=Summation(var="k", start=Const(1), end=CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("a"), Var("b")]), condition=And(Geq(Var("a"), Const(1)), Leq(Var("a"), Const(40)), Geq(Var("b"), Const(1)), Leq(Var("b"), Const... | ALG | null | COMPUTE | sympy | QF_PSD_COUNT_LEQ | [
"QF_PSD_COUNT_LEQ"
] | 009d0f | alg_sum_powers_v1 | null | 4 | 0 | [
"QF_PSD_COUNT_LEQ"
] | 1 | 0.069 | 2026-02-25T08:22:14.980537Z | {
"verified": true,
"answer": 53763,
"timestamp": "2026-02-25T08:22:15.049165Z"
} | 67d953 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 207,
"completion_tokens": 21211
},
"timestamp": "2026-03-30T03:10:20.921Z",
"answer": 51692
},
{
... | 1 | [
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "QF_PSD_COUNT_LEQ",
"status": "ok"
}
] | {
"lo": 3.81,
"mid": 6.33,
"hi": 9.49
} | ||
75d558 | antilemma_sum_equals_v1_1248542787_909 | Let $n = 67$. Define $x$ to be the number of ordered pairs $(i, j)$ of positive integers such that $i + j = n$ and $1 \leq i, j \leq 66$.
Let $c = 3001$. Let $S$ be the set of all ordered pairs $(x_1, x_2)$ of positive odd integers such that $x_1 + x_2 = 794$. Define $y$ to be the number of elements in $S$.
Compute t... | 43,312 | graphs = [
Graph(
let={
"_n": Const(67),
"x": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("i"), Var("j")]), condition=Eq(Sum(Var("i"), Var("j")), Ref("_n")), domain=CartesianProduct(left=IntegerRange(start=Const(1), end=Const(66)), right=IntegerRange(start=Const(1), end=Con... | COMB | GEOM | COMPUTE | sympy | COMB1 | [
"COMB1",
"COUNT_SUM_EQUALS"
] | 128824 | antilemma_sum_equals_v1 | two_moduli | 4 | 0 | [
"COMB1",
"COUNT_SUM_EQUALS"
] | 2 | 0.006 | 2026-02-08T03:28:48.546034Z | {
"verified": true,
"answer": 43312,
"timestamp": "2026-02-08T03:28:48.551897Z"
} | ec5b81 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 262,
"completion_tokens": 1242
},
"timestamp": "2026-02-09T09:52:59.733Z",
"answer": 43312
},
{
"... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COMB1",
"status": "ok"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "ok"
},
{
"lemma": "V7",
"statu... | {
"lo": -4.92,
"mid": -2.9,
"hi": -0.7
} | ||
4ce9db | comb_count_derangements_v1_48377204_3208 | Let $A$ be the set of all positive integers $p$ for which there exists a positive integer $q$ such that $pq = 6$, $\gcd(p, q) = 1$, and $p < q$. Let $d_0 = |A|$. Let $n$ be the smallest divisor of $13013$ that is at least $d_0$. Let $c$ be the number of ordered pairs $(i,j)$ with $1 \leq i \leq 14$ and $1 \leq j \leq 5... | 89,260 | graphs = [
Graph(
let={
"_n": Const(90670),
"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 | COMB | COUNT | sympy | COUNT_COPRIME_GRID | [
"COUNT_COPRIME_GRID",
"COPRIME_PAIRS/MIN_PRIME_FACTOR"
] | 90cb91 | comb_count_derangements_v1 | negation_mod | 7 | 0 | [
"COPRIME_PAIRS",
"COUNT_COPRIME_GRID",
"MIN_PRIME_FACTOR"
] | 3 | 0.004 | 2026-02-08T17:14:20.574132Z | {
"verified": true,
"answer": 89260,
"timestamp": "2026-02-08T17:14:20.578113Z"
} | 57ffa4 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 208,
"completion_tokens": 2278
},
"timestamp": "2026-02-17T21:49:00.423Z",
"answer": 89260
},
... | 1 | [
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "ok"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "MIN_PRIME_FACTOR",
"status": "ok_later"
},
{
"lemma": "MOD_MUL",
... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
b3dfd1 | diophantine_sum_product_min_v1_1978505735_4835 | Let $ S = 42 $ and $ P = 272 $. Consider the set of all integers $ x $ such that $ 1 \leq x \leq 41 $ and $ x(S - x) = P $. Determine the minimum value of $ x $ in this set. | 8 | graphs = [
Graph(
let={
"S": Const(42),
"P": Const(272),
"result": MinOverSet(set=SolutionsSet(var=Var("x"), condition=And(Geq(Var("x"), Const(1)), Leq(Var("x"), Const(41)), Eq(Mul(Var("x"), Sub(Ref("S"), Var("x"))), Ref("P"))))),
},
goal=Ref("result"),
... | NT | null | EXTREMUM | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | diophantine_sum_product_min_v1 | null | 3 | 0 | [
"LIN_FORM"
] | 1 | 0.025 | 2026-02-08T18:35:53.783122Z | {
"verified": true,
"answer": 8,
"timestamp": "2026-02-08T18:35:53.807652Z"
} | a6bb61 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 105,
"completion_tokens": 450
},
"timestamp": "2026-02-18T17:59:12.817Z",
"answer": 8
},
{
... | 1 | [
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "V3",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
350dbd | diophantine_product_count_v1_1742523217_1930 | Let $k = 180$ and let the upper bound be the number of ordered pairs $(i, j)$ such that $1 \leq i \leq 4$ and $1 \leq j \leq 11$. Compute the number of positive integers $x$ satisfying $1 \leq x \leq \text{upper}$, $x$ divides $k$, and $\frac{k}{x} \leq \text{upper}$. | 10 | graphs = [
Graph(
let={
"k": Const(180),
"upper": CountOverSet(set=CartesianProduct(left=IntegerRange(start=Const(1), end=Const(4)), right=IntegerRange(start=Const(1), end=Const(11)))),
"result": CountOverSet(set=SolutionsSet(var=Var("x"), condition=And(Geq(Var("x"), Cons... | NT | null | COUNT | sympy | LIN_FORM | [
"COUNT_CARTESIAN"
] | 409d7d | diophantine_product_count_v1 | null | 5 | 0 | [
"COUNT_CARTESIAN",
"LIN_FORM"
] | 2 | 0.047 | 2026-02-08T04:21:13.101820Z | {
"verified": true,
"answer": 10,
"timestamp": "2026-02-08T04:21:13.148848Z"
} | 0c366e | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 208,
"completion_tokens": 1210
},
"timestamp": "2026-02-10T16:24:24.514Z",
"answer": 10
},
{
"id... | 1 | [
{
"lemma": "COUNT_CARTESIAN",
"status": "ok"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
}
] | {
"lo": -3.42,
"mid": 1.86,
"hi": 7.55
} | ||
ee5776 | antilemma_k2_v1_898971024_2281 | Let $m = 13430$. Consider the quadratic equation $x^2 - 249x + m = 0$. Let $n$ be the sum of all positive integer roots of this equation. Compute $$
\sum_{k=1}^{249} \phi(k) \left\lfloor \frac{n}{k} \right\rfloor,
$$where $\phi(k)$ denotes Euler's totient function. | 31,125 | graphs = [
Graph(
let={
"_m": Const(13430),
"_n": SumOverSet(set=SolutionsSet(var=Var("x1"), condition=Eq(Sum(Pow(Var("x1"), Const(2)), Mul(Const(-249), Var("x1")), Ref("_m")), Const(0)))),
"x": Summation(var="k", start=Const(1), end=Const(249), expr=Mul(EulerPhi(n=Var("k... | NT | COMB | COMPUTE | sympy | VIETA_SUM | [
"VIETA_SUM/K2",
"K2"
] | 6be084 | antilemma_k2_v1 | null | 5 | 0 | [
"K2",
"VIETA_SUM"
] | 2 | 0.001 | 2026-02-08T16:38:28.356884Z | {
"verified": true,
"answer": 31125,
"timestamp": "2026-02-08T16:38:28.357792Z"
} | 9b9321 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 130,
"completion_tokens": 1267
},
"timestamp": "2026-02-17T09:37:29.003Z",
"answer": 31125
},
... | 1 | [
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "K2",
"status": "ok"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
074a4a | nt_sum_divisors_mod_v1_1742523217_1219 | Let $ n = 55440 $. Compute $ \sigma(n) $, the sum of all positive divisors of $ n $, and let $ r $ be the remainder when $ \sigma(n) $ is divided by 11777. Let $ P $ be the set of all products $ xy $ where $ x $ and $ y $ are positive integers satisfying $ x + y = 138 $. Let $ m $ be the maximum element of $ P $. Let $... | 1,601 | graphs = [
Graph(
let={
"_n": Const(71059),
"n": Const(55440),
"M": Const(11777),
"sigma": SumDivisors(n=Ref("n")),
"result": Mod(value=Ref("sigma"), modulus=Ref("M")),
"Q": Mod(value=Sum(Pow(Ref("result"), Const(2)), Mul(Const(2), Ref(... | NT | null | COMPUTE | sympy | B1 | [
"B1/MAX_DIVISOR"
] | f9a2b6 | nt_sum_divisors_mod_v1 | quadratic_mod | 6 | 0 | [
"B1",
"MAX_DIVISOR"
] | 2 | 0.005 | 2026-02-08T03:32:17.661694Z | {
"verified": true,
"answer": 1601,
"timestamp": "2026-02-08T03:32:17.666349Z"
} | 041f27 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 256,
"completion_tokens": 5631
},
"timestamp": "2026-02-10T05:15:41.437Z",
"answer": 1601
},
{
"i... | 1 | [
{
"lemma": "B1",
"status": "ok"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "MAX_DIVISOR",
"status": "ok_later"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "MOD_SU... | {
"lo": -3.46,
"mid": 1.03,
"hi": 5.49
} | ||
d0c7e1 | geo_count_lattice_rect_v1_48377204_1669 | Compute the number of lattice points $(x, y)$ such that $0 \le x \le 193$ and $0 \le y \le 87$. Let $R$ be this number. Find the remainder when $31193 \cdot R$ is divided by $59506$. | 7,702 | graphs = [
Graph(
let={
"a": Const(193),
"b": Const(87),
"result": LatticePointsRect(a=Ref(name='a'), b=Ref(name='b')),
"Q": Mod(value=Mul(Const(31193), Ref("result")), modulus=Const(59506)),
},
goal=Ref("Q"),
)
] | GEOM | null | COUNT | sympy | [] | geo_count_lattice_rect_v1 | null | 2 | 0 | null | null | 0.003 | 2026-02-08T16:18:09.092512Z | {
"verified": true,
"answer": 7702,
"timestamp": "2026-02-08T16:18:09.095423Z"
} | 7648af | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 171,
"completion_tokens": 999
},
"timestamp": "2026-02-24T20:33:10.943Z",
"answer": 7702
},
{
"i... | 1 | [] | {
"lo": -2.4,
"mid": 1.57,
"hi": 5.75
} | ||||
9e88ba | sequence_fibonacci_compute_v1_458359167_2384 | Let $n$ be the number of positive integers $k$ such that $1 \leq k \leq 176$ and $7$ divides the $k$-th Fibonacci number. Compute the $n$-th Fibonacci number. | 17,711 | graphs = [
Graph(
let={
"_n": Const(176),
"n": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Ref("_n")), Divides(divisor=Const(7), dividend=Fibonacci(arg=Var(name='n')))))),
"result": Fibonacci(arg=Ref(name='n')),
... | ALG | NT | COMPUTE | sympy | COUNT_FIB_DIVISIBLE | [
"COUNT_FIB_DIVISIBLE"
] | 66de3c | sequence_fibonacci_compute_v1 | null | 4 | 0 | [
"COUNT_FIB_DIVISIBLE"
] | 1 | 0.001 | 2026-02-08T05:22:17.049478Z | {
"verified": true,
"answer": 17711,
"timestamp": "2026-02-08T05:22:17.050255Z"
} | 72ee96 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 94,
"completion_tokens": 1886
},
"timestamp": "2026-02-12T08:02:41.469Z",
"answer": 17711
},
{... | 1 | [
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "ok"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "MOD_SUB",
... | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
d14ce6 | comb_count_surjections_v1_2051736721_3862 | Let $n$ be the number of integers $t$ such that $5 \leq t \leq 14$ and there exist integers $a$ and $b$ with $1 \leq a \leq 2$, $1 \leq b \leq 4$, and $t = 3a + 2b$. Let $k$ be the number of ordered triples $(x_1, x_2, x_3)$ of positive odd integers such that $x_1 + x_2 + x_3 = 5$. Compute $k! \cdot S(n, k)$, where $S(... | 5,796 | graphs = [
Graph(
let={
"_n": Const(5),
"n": CountOverSet(set=SolutionsSet(var=Var("t"), condition=Exists(var=Var(name='a'), condition=Exists(var=Var(name='b'), condition=And(Geq(left=Var(name='a'), right=Const(value=1)), Leq(left=Var(name='a'), right=Const(value=2)), Geq(left=Var(na... | COMB | null | COUNT | sympy | COUNT_CARTESIAN | [
"LIN_FORM",
"COMB1"
] | 3d1461 | comb_count_surjections_v1 | null | 6 | 0 | [
"COMB1",
"COUNT_CARTESIAN",
"LIN_FORM"
] | 3 | 0.046 | 2026-02-08T17:36:29.112079Z | {
"verified": true,
"answer": 5796,
"timestamp": "2026-02-08T17:36:29.157948Z"
} | 48b118 | 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": 1236
},
"timestamp": "2026-02-18T04:30:16.417Z",
"answer": 5796
},
{... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COMB1",
"status": "ok"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "V7",
"status": "no"... | {
"lo": -5.64,
"mid": -3.17,
"hi": -0.81
} | ||
4c531b | nt_count_primes_v1_784195855_1360 | Let $A$ be the number of ordered pairs of positive integers $(p, q)$ such that $pq = 6$, $\gcd(p, q) = 1$, and $p < q$. Determine the number of prime numbers $n$ such that $A \leq n \leq 10080$. | 1,237 | graphs = [
Graph(
let={
"upper": Const(10080),
"result": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), CountOverSet(set=SolutionsSet(var=Var("p"), condition=And(IsPositive(arg=Var(name='p')), Exists(var=Var(name='q'), condition=And(Eq(left=Mul(Var(name='p'),... | NT | null | COUNT | sympy | COPRIME_PAIRS | [
"COPRIME_PAIRS"
] | 2bb3aa | nt_count_primes_v1 | null | 5 | 0 | [
"COPRIME_PAIRS"
] | 1 | 0.234 | 2026-02-08T04:59:21.809319Z | {
"verified": true,
"answer": 1237,
"timestamp": "2026-02-08T04:59:22.043555Z"
} | 85221d | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 177,
"completion_tokens": 6797
},
"timestamp": "2026-02-11T22:35:17.450Z",
"answer": 1238
},
{
... | 1 | [
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "V1",
"status": "no"
}
] | {
"lo": 1.96,
"mid": 5.23,
"hi": 8.52
} | ||
10dfe7 | nt_max_prime_below_v1_677425708_1915 | Let $S$ be the set of all positive integers $p$ for which there exists a positive integer $q$ such that $pq = 24$, $\gcd(p, q) = 1$, and $p < q$. Let $L$ be the number of elements in $S$. Compute the largest prime number $n$ such that $L \leq n \leq 25200$. | 25,189 | graphs = [
Graph(
let={
"upper": Const(25200),
"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 | 2.538 | 2026-02-08T04:38:56.182358Z | {
"verified": true,
"answer": 25189,
"timestamp": "2026-02-08T04:38:58.720715Z"
} | 61d8d9 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 195,
"completion_tokens": 3354
},
"timestamp": "2026-02-10T03:01:04.026Z",
"answer": 25189
},
{
"... | 1 | [
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "MOD_ADD",
"stat... | {
"lo": -3.45,
"mid": 1.15,
"hi": 6.18
} | ||
4582c0 | modular_mod_compute_v1_601307018_4995 | Let $m$ be the number of non-negative integers $j$ with $0 \le j \le 59829$ such that $\binom{59829}{j} \bmod 2 = 1$. Let $N = 43 \bmod m$. Find the remainder when $84557N$ is divided by $69184€. | 38,383 | graphs = [
Graph(
let={
"a": Const(43),
"m": CountOverSet(set=SolutionsSet(var=Var("j"), condition=And(Geq(Var("j"), Const(0)), Leq(Var("j"), Const(59829)), Eq(Mod(value=Binom(n=Const(59829), k=Var("j")), modulus=Const(2)), Const(1))), domain='nonnegative_integers')),
"re... | NT | COMB | COMPUTE | sympy | V8 | [
"V8"
] | 86348e | modular_mod_compute_v1 | null | 5 | 0 | [
"V8"
] | 1 | 0.006 | 2026-03-10T05:40:43.452707Z | {
"verified": true,
"answer": 38383,
"timestamp": "2026-03-10T05:40:43.458687Z"
} | bd9595 | 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": 1394
},
"timestamp": "2026-04-19T00:38:34.966Z",
"answer": 38383
},
{
... | 1 | [
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "V1",
"status": "no"
},
{
"lemma": "V8",
"status": "... | {
"lo": -3.31,
"mid": 1.32,
"hi": 5.87
} | ||
1b93e9_l | comb_count_permutations_fixed_v1_1915831931_3016 | Let $n = 10$ and let $k$ be the number of nonnegative integers $j \leq 6208$ such that $\binom{6208}{j}$ is odd. Compute $\binom{n}{k} \cdot !(n - k)$, where $!m$ denotes the number of derangements of $m$ elements. | 0 | COMB | null | COUNT | sympy | K14 | [
"V8"
] | 86348e | comb_count_permutations_fixed_v1 | null | 6 | 0 | [
"K14",
"V8"
] | 2 | 0.01 | 2026-02-08T17:18:01.696374Z | {
"verified": false,
"answer": 45,
"timestamp": "2026-02-08T17:18:01.706534Z"
} | 3a264a | 1b93e9 | legacy_text | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
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"relaxed": true
},
"usage": {
"prompt_tokens": 119,
"completion_tokens": 1326
},
"timestamp": "2026-02-17T23:52:44.630Z",
"answer": 45
},
{
... | 1 | [
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "V8",
"status": "ok"
},
{
"lemma": "V8_SUM",
"status": "no"
},
{
"lemma": "VAL_SUM_EQ",
"status": "no"
}
] | {
"lo": -2.38,
"mid": 1.74,
"hi": 6.59
} | |
2c2998 | nt_max_prime_below_v1_655260480_5881 | Let $c$ be the number of positive integers $p$ for which there exists a positive integer $q$ such that $pq = 2250$, $\gcd(p, q) = 1$, and $p < q$.
Let $S$ be the set of all ordered pairs $(x_1, x_2)$ of positive odd integers such that $x_1 + x_2 = c$.
Let $m$ be the number of elements in $S$.
Let $r$ be the largest ... | 10,867 | graphs = [
Graph(
let={
"upper": Const(10878),
"result": MaxOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x1"), Var("x2")]), condition=And(IsPositive(arg=Var(name='x1')), IsPositive(arg=Var(name='x2')), IsOdd... | NT | null | EXTREMUM | sympy | COPRIME_PAIRS | [
"COPRIME_PAIRS/COMB1"
] | 5f6aea | nt_max_prime_below_v1 | null | 5 | 0 | [
"COMB1",
"COPRIME_PAIRS"
] | 2 | 0.263 | 2026-02-08T18:41:55.209037Z | {
"verified": true,
"answer": 10867,
"timestamp": "2026-02-08T18:41:55.471614Z"
} | f7a029 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 174,
"completion_tokens": 3258
},
"timestamp": "2026-02-18T19:01:08.137Z",
"answer": 10867
},
... | 1 | [
{
"lemma": "COMB1",
"status": "ok_later"
},
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "V3",
"status": "no"
},... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
0fe4dc | antilemma_k3_v1_655260480_4387 | Let $x = \sum_{d \mid 58725} \phi(d)$, where $\phi$ denotes Euler's totient function. Compute the remainder when $\left( (x \bmod 317) + 5003 \cdot (x \bmod 313) \right)$ is divided by $99259$. | 77,331 | graphs = [
Graph(
let={
"_n": Const(58725),
"x": SumOverDivisors(n=Ref(name='_n'), var='d', expr=EulerPhi(n=Var(name='d'))),
"Q": Mod(value=Sum(Mod(value=Ref("x"), modulus=Const(317)), Mul(Const(5003), Mod(value=Ref("x"), modulus=Const(313)))), modulus=Const(99259)),
... | NT | COMB | COMPUTE | sympy | K3 | [
"K3"
] | 54c41e | antilemma_k3_v1 | null | 3 | 0 | [
"K3"
] | 1 | 0.001 | 2026-02-08T17:54:32.832725Z | {
"verified": true,
"answer": 77331,
"timestamp": "2026-02-08T17:54:32.833520Z"
} | 34428e | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 114,
"completion_tokens": 578
},
"timestamp": "2026-02-18T09:39:38.742Z",
"answer": 77331
},
{... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "K3",
"status": "ok"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "VAL_SUM_EQ",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
b9ea17 | algebra_poly_eval_v1_601307018_6273 | Let $M = 10 \cdot 13^{3} + 13^{2} - 9 \cdot 13 + \max\{ x_1 y : x_1 > 0,\ y > 0,\ x_1 + y = 6 \}$. Find the remainder when $90023 \cdot M$ is divided by $96537$. | 40,585 | graphs = [
Graph(
let={
"x": Const(13),
"result": Sum(Mul(Const(10), Pow(Ref("x"), Const(3))), Pow(Ref("x"), Const(2)), Mul(Const(-9), Ref("x")), MaxOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x1"), Var("y")]), condition=And(IsPositive(arg=Var(name='x1')), IsPosi... | ALG | null | COMPUTE | sympy | B1 | [
"B1"
] | 5b950e | algebra_poly_eval_v1 | null | 2 | 0 | [
"B1"
] | 1 | 0.005 | 2026-03-10T06:52:30.265246Z | {
"verified": true,
"answer": 40585,
"timestamp": "2026-03-10T06:52:30.270441Z"
} | c72cef | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 190,
"completion_tokens": 1201
},
"timestamp": "2026-04-19T04:02:58.379Z",
"answer": 40585
},
{
... | 1 | [
{
"lemma": "B1",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
}
] | {
"lo": -5.35,
"mid": 0.52,
"hi": 5.84
} | ||
9fff8d | sequence_lucas_compute_v1_1520064083_9623 | Let $c=7$. Let $N$ be the number of integers $n$ such that $1\le n\le 18865$, $c$ divides $n$, and $\gcd(n,6)=1$.
Let $p$ be a positive integer for which there exists a positive integer $q$ satisfying
$$pq=108,\quad \gcd(p,q)=1,\quad p<q.$$
Let $k$ be the number of such integers $p$.
Let $L_{n}$ denote the $n$th Luca... | 7,295 | graphs = [
Graph(
let={
"_c": Const(7),
"_m": Const(22),
"_n": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Const(18865)), Divides(divisor=Ref("_c"), dividend=Var("n")), Eq(GCD(a=Var("n"), b=Const(6)), Const(1))))),
... | NT | null | COMPUTE | sympy | C5 | [
"C5/MIN_PRIME_FACTOR",
"COPRIME_PAIRS"
] | ba3786 | sequence_lucas_compute_v1 | quadratic_mod | 6 | 0 | [
"C5",
"COPRIME_PAIRS",
"MIN_PRIME_FACTOR"
] | 3 | 0.006 | 2026-02-08T10:56:00.236047Z | {
"verified": true,
"answer": 7295,
"timestamp": "2026-02-08T10:56:00.242523Z"
} | 8c9890 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 293,
"completion_tokens": 2446
},
"timestamp": "2026-02-14T09:28:43.113Z",
"answer": 7295
},
{... | 1 | [
{
"lemma": "C5",
"status": "ok"
},
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "MIN_PRIME_FACTOR",
"status": "ok_later"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
... | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
4da6fa | diophantine_sum_product_min_v1_1918700295_4201 | Let $S = 62$. Let $P$ be the minimum value of $x + y$ over all pairs of positive integers $(x, y)$ such that $xy = 28224$. Let $r$ be the smallest positive integer $x$ such that $1 \leq x \leq 61$ and $x(S - x) = P$. Compute $r^2 + 3r + M$, where $M$ is the minimum value of $x + y$ over all pairs of positive integers $... | 134 | graphs = [
Graph(
let={
"_n": Const(2),
"S": Const(62),
"P": 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(28224)))), expr=... | NT | null | EXTREMUM | sympy | B3 | [
"B3"
] | d720b5 | diophantine_sum_product_min_v1 | quadratic_mod | 4 | 0 | [
"B3"
] | 1 | 0.008 | 2026-02-08T09:13:35.879655Z | {
"verified": true,
"answer": 134,
"timestamp": "2026-02-08T09:13:35.887656Z"
} | bc954e | 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": 928
},
"timestamp": "2026-02-14T01:50:24.178Z",
"answer": 134
},
{
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "V1",
"status": "no"
}
] | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
5d4f25 | alg_qf_psd_count_v1_1218484723_1401 | Let $Q$ be the number of ordered pairs $(a, b)$ of positive integers with $1 \le a, b \le 150$ such that
$$
-1728ab + \left|\left\{ (a_1, b_1) : 1 \le a_1 \le \left|\left\{ (a_2, b_2) : 1 \le a_2, b_2 \le 40,\ 16b_2^2 = 16 \right\}\right|,\ 1 \le b_1 \le 40,\ 10a_1^2 - 18a_1b_1 + 25b_1^2 \le 20725 \right\}\right| \cdot... | 12 | graphs = [
Graph(
let={
"_m": Const(150),
"_n": Const(2),
"result": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("a"), Var("b")]), condition=And(Geq(Var("a"), Const(1)), Leq(Var("a"), Ref("_m")), Geq(Var("b"), Const(1)), Leq(Var("b"), Const(150)), Eq(Sum(Mul(Cons... | ALG | null | COUNT | sympy | QF_PSD_COUNT | [
"QF_PSD_COUNT/QF_PSD_COUNT_LEQ"
] | 89ab91 | alg_qf_psd_count_v1 | null | 6 | 0 | [
"QF_PSD_COUNT",
"QF_PSD_COUNT_LEQ"
] | 2 | 0.681 | 2026-02-25T03:08:18.035219Z | {
"verified": true,
"answer": 12,
"timestamp": "2026-02-25T03:08:18.716095Z"
} | 7bb926 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 1,
"correct": {
"strict": false,
"boxed": false,
"relaxed": true
},
"usage": {
"prompt_tokens": 295,
"completion_tokens": 32768
},
"timestamp": "2026-03-10T06:55:58.847Z",
"answer": null
},
{
... | 1 | [
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "QF_PSD_COUNT",
"status": "ok"
},
{
"lemma": "QF_PSD_COUNT_LEQ",
"status": "ok_later"
}
] | {
"lo": 3.14,
"mid": 5.37,
"hi": 7.61
} | ||
ee56e9 | geo_count_lattice_rect_v1_153355830_757 | Compute the number of lattice points in the rectangle $[0, 200] \times [0, 103]$. | 20,904 | graphs = [
Graph(
let={
"a": Const(200),
"b": Const(103),
"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 | 2026-02-08T04:09:50.290355Z | {
"verified": true,
"answer": 20904,
"timestamp": "2026-02-08T04:09:50.291842Z"
} | 496f2f | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 135,
"completion_tokens": 272
},
"timestamp": "2026-02-23T23:39:51.113Z",
"answer": 20904
},
{
"i... | 1 | [] | {
"lo": -7.18,
"mid": -4.99,
"hi": -3
} | ||||
87efec | antilemma_sum_equals_v1_784195855_5586 | Let $m = 154$. Define $n$ to be the number of ordered pairs $(x_1, x_2)$ of positive odd integers such that $x_1 + x_2 = m$. Compute the number of ordered pairs $(i, j)$ with $1 \le i \le 76$ and $1 \le j \le 77$ such that $i + j = n$. | 76 | graphs = [
Graph(
let={
"_m": Const(154),
"_n": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x1"), Var("x2")]), condition=And(IsPositive(arg=Var(name='x1')), IsPositive(arg=Var(name='x2')), IsOdd(arg=Var(name='x1')), IsOdd(arg=Var(name='x2')), Eq(Sum(Var("x1"), Var("x2")), ... | COMB | GEOM | COMPUTE | sympy | COUNT_SUM_EQUALS | [
"COMB1/COUNT_SUM_EQUALS",
"COUNT_SUM_EQUALS"
] | 3e1adf | antilemma_sum_equals_v1 | null | 3 | 0 | [
"COMB1",
"COUNT_SUM_EQUALS"
] | 2 | 0.015 | 2026-02-08T07:59:15.193705Z | {
"verified": true,
"answer": 76,
"timestamp": "2026-02-08T07:59:15.208785Z"
} | aca99e | 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": 3928
},
"timestamp": "2026-02-24T08:40:05.498Z",
"answer": 76
},
{
"id"... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COMB1",
"status": "ok"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "ok"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
},
{
... | {
"lo": -5.97,
"mid": -3.97,
"hi": -1.93
} | ||
ae8e06 | nt_sum_totient_over_divisors_v1_677425708_3449 | Let $n$ be the number of integers $t$ such that $5 \leq t \leq 1771$ and there exist positive integers $a$ and $b$ with $1 \leq a \leq 614$, $1 \leq b \leq 181$, and $t = 2a + 3b$. Compute $$\sum_{d \mid n} \phi(d),$$ where $\phi$ denotes Euler's totient function. | 1,765 | graphs = [
Graph(
let={
"n": CountOverSet(set=SolutionsSet(var=Var("t"), condition=Exists(var=Var(name='a'), condition=Exists(var=Var(name='b'), condition=And(Geq(left=Var(name='a'), right=Const(value=1)), Leq(left=Var(name='a'), right=Const(value=614)), Geq(left=Var(name='b'), right=Const(value... | NT | null | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | nt_sum_totient_over_divisors_v1 | null | 6 | 0 | [
"LIN_FORM"
] | 1 | 0.004 | 2026-02-08T05:43:35.184083Z | {
"verified": true,
"answer": 1765,
"timestamp": "2026-02-08T05:43:35.188213Z"
} | 9a2eb4 | 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": 2861
},
"timestamp": "2026-02-12T14:00:05.550Z",
"answer": 1765
},
{... | 1 | [
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "V8_SUM",
... | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
b51d4d | nt_sum_over_divisible_v1_898971024_443 | Let $d$ be the number of integers $n$ such that $1 \leq n \leq 320$ and $n \equiv \left\lfloor \frac{n}{2} \right\rfloor \pmod{5}$. Let $S$ be the sum of all positive integers $n_1 \leq 24336$ that are divisible by $d$. Compute the remainder when $66759 \cdot S$ is divided by $69382$. | 3,220 | graphs = [
Graph(
let={
"_n": Const(320),
"upper": Const(24336),
"divisor": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Ref("_n")), Congruent(a=Var(name='n'), b=Floor(arg=Div(left=Var(name='n'), right=Const(value=2))), ... | NT | null | SUM | sympy | L3C | [
"L3C"
] | 73f8b0 | nt_sum_over_divisible_v1 | null | 7 | 0 | [
"L3C"
] | 1 | 0.793 | 2026-02-08T15:27:21.961485Z | {
"verified": true,
"answer": 3220,
"timestamp": "2026-02-08T15:27:22.754149Z"
} | d09922 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 142,
"completion_tokens": 1838
},
"timestamp": "2026-02-16T07:18:37.674Z",
"answer": 3220
},
{... | 1 | [
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "L3C",
"status": "ok"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
3581d9 | antilemma_k3_v1_784195855_4675 | Define $x = \sum_{d \mid 65086} \phi(d)$, where $\phi$ denotes Euler's totient function. Compute the value of $x$. | 65,086 | graphs = [
Graph(
let={
"x": SumOverDivisors(n=Const(value=65086), var='d', expr=EulerPhi(n=Var(name='d'))),
},
goal=Ref("x"),
)
] | NT | COMB | COMPUTE | sympy | K3 | [
"K3"
] | 54c41e | antilemma_k3_v1 | null | 3 | 0 | [
"K3"
] | 1 | 0 | 2026-02-08T07:16:07.300791Z | {
"verified": true,
"answer": 65086,
"timestamp": "2026-02-08T07:16:07.301140Z"
} | 4d0b3c | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 134,
"completion_tokens": 353
},
"timestamp": "2026-02-20T02:04:21.468Z",
"answer": 65086
},
{
"id": 11,
... | 1 | [
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "K3",
"status": "ok"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
}
] | {
"lo": -8.32,
"mid": -5.11,
"hi": -2.37
} | ||
7f552b | comb_factorial_compute_v1_784195855_2638 | Let $n_2 = 0$. Define $s = \sum_{k=0}^{n_2} (-1)^k \binom{n_2}{k}$. Let $u = 9$ and $n_1 = u + 1$. Define $h = \sum_{k=0}^{n_1} (-1)^k \binom{n_1}{k}$. Let $n = 8s + h$. Compute $n!$. | 40,320 | graphs = [
Graph(
let={
"n2": Const(0),
"s": Summation(var="k", start=Const(0), end=Ref("n2"), expr=Mul(Pow(Const(-1), Var("k")), Binom(n=Ref("n2"), k=Var("k")))),
"u": Const(9),
"n1": Sum(Ref("u"), Const(1)),
"h": Summation(var="k", start=Const(0)... | COMB | null | COMPUTE | sympy | BINOMIAL_ALTERNATING | [
"BINOMIAL_ALTERNATING"
] | c21569 | comb_factorial_compute_v1 | null | 3 | 2 | [
"BINOMIAL_ALTERNATING"
] | 1 | 0.001 | 2026-02-08T05:54:46.790297Z | {
"verified": true,
"answer": 40320,
"timestamp": "2026-02-08T05:54:46.791135Z"
} | 8280f7 | 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": 410
},
"timestamp": "2026-02-24T04:48:18.729Z",
"answer": 40320
},
{
"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": "V8",
"status": "no"
},
{
"lemma": "V... | {
"lo": -9.23,
"mid": -6.18,
"hi": -4.06
} | ||
2828eb | comb_catalan_compute_v1_1742523217_3328 | Let $n = 11$. Define $C_n$ to be the $n$-th Catalan number, given by the formula
$$
C_n = \frac{1}{n+1} \binom{2n}{n}.
$$
Compute the value of $Q = (19 - C_n) \bmod 87939$. | 29,172 | graphs = [
Graph(
let={
"n": Const(11),
"result": Catalan(Ref("n")),
"Q": Mod(value=Sub(Const(19), Ref("result")), modulus=Const(87939)),
},
goal=Ref("Q"),
)
] | COMB | null | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM/COUNT_SUM_EQUALS"
] | 8d684a | comb_catalan_compute_v1 | negation_mod | 2 | 0 | [
"COUNT_SUM_EQUALS",
"LIN_FORM"
] | 2 | 0.032 | 2026-02-08T05:46:50.815917Z | {
"verified": true,
"answer": 29172,
"timestamp": "2026-02-08T05:46:50.847875Z"
} | 3388a4 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 184,
"completion_tokens": 416
},
"timestamp": "2026-02-24T04:35:50.673Z",
"answer": 29172
},
{
"i... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "ok_later"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "V7",
... | {
"lo": -4.93,
"mid": -2.91,
"hi": -0.71
} | ||
740227 | nt_sum_over_divisible_v1_2080023795_163 | Let $n = 2275$ and let $d$ be the largest integer $k$ such that $13^k$ divides $2275!$. Let $S$ be the set of all positive integers $m$ such that $1 \leq m \leq 16129$ and $m$ is divisible by $d$. Compute the sum of all elements in $S$. Let this sum be $A$. Determine the value of $$
A + \varphi(|A|+1) + \tau(|A|+1) \pm... | 8,903 | graphs = [
Graph(
let={
"_n": Const(2275),
"upper": Const(16129),
"divisor": MaxKDivides(target=Factorial(Ref("_n")), base=Const(13)),
"result": SumOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Ref("upper")), Eq(Mo... | NT | null | SUM | sympy | V1 | [
"V1"
] | dae96f | nt_sum_over_divisible_v1 | null | 6 | 0 | [
"V1"
] | 1 | 0.528 | 2026-02-08T11:35:13.844531Z | {
"verified": true,
"answer": 8903,
"timestamp": "2026-02-08T11:35:14.372807Z"
} | e97d10 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 280,
"completion_tokens": 2633
},
"timestamp": "2026-02-08T20:47:50.100Z",
"answer": 23548
},
{
... | 1 | [
{
"lemma": "K5",
"status": "same_pattern_wrong"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "V1",
"status": "ok"
},
{
"lemma": "V3",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
},
... | {
"lo": 3.26,
"mid": 5.68,
"hi": 8.81
} | ||
1fa0ff | nt_count_gcd_equals_v1_1520064083_2378 | Let $s$ be the smallest sum $x + y$ where $x$ and $y$ are positive integers such that $xy = 7986276$. Let $k$ be the number of positive integers $n$ such that $1 \le n \le s$ and $12$ divides the $n$-th Fibonacci number. Let $S$ be the set of all positive integers $n$ such that $1 \le n \le 47961$ and $\gcd(n, k) = 3$.... | 15,886 | graphs = [
Graph(
let={
"upper": Const(47961),
"k": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPos... | NT | null | COUNT | sympy | B3 | [
"B3/COUNT_FIB_DIVISIBLE"
] | 9b7a57 | nt_count_gcd_equals_v1 | null | 7 | 0 | [
"B3",
"COUNT_FIB_DIVISIBLE"
] | 2 | 5.777 | 2026-02-08T04:41:25.569995Z | {
"verified": true,
"answer": 15886,
"timestamp": "2026-02-08T04:41:31.346858Z"
} | b0003b | 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": 3669
},
"timestamp": "2026-02-11T21:49:57.890Z",
"answer": 15886
},
{
"... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "ok_later"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"... | {
"lo": -3.45,
"mid": 1.15,
"hi": 6.18
} | ||
6d0a73 | diophantine_sum_product_min_v1_124444284_5448 | Let $S = 74$ and $P = 585$. Determine the value of the smallest positive integer $x \le 73$ such that $x(S - x) = P$. | 9 | graphs = [
Graph(
let={
"S": Const(74),
"P": Const(585),
"result": MinOverSet(set=SolutionsSet(var=Var("x"), condition=And(Geq(Var("x"), Const(1)), Leq(Var("x"), Const(73)), Eq(Mul(Var("x"), Sub(Ref("S"), Var("x"))), Ref("P"))))),
},
goal=Ref("result"),
... | NT | null | EXTREMUM | sympy | MIN_PRIME_FACTOR | [
"MIN_PRIME_FACTOR",
"VIETA_SUM",
"ONE_PHI_1",
"B3"
] | d48c08 | diophantine_sum_product_min_v1 | null | 3 | 0 | [
"B3",
"MIN_PRIME_FACTOR",
"ONE_PHI_1",
"VIETA_SUM"
] | 4 | 0.045 | 2026-02-08T06:35:35.804519Z | {
"verified": true,
"answer": 9,
"timestamp": "2026-02-08T06:35:35.849978Z"
} | 08f912 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 87,
"completion_tokens": 500
},
"timestamp": "2026-02-13T02:22:32.317Z",
"answer": 9
},
{
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MIN_PRIME_FACTOR",
"status": "ok"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
... | {
"lo": -7.01,
"mid": -4.68,
"hi": -2.15
} | ||
e62b80 | modular_sum_quadratic_residues_v1_1742523217_2508 | Let $d$ be the smallest prime divisor of $1573$, and let $p$ be the smallest prime divisor of $12432181$. Define $r = \frac{p(p-1)}{4}$. Let $n$ be the absolute value of $r$, and let $m$ be the smallest prime divisor of $1573$. Compute the Bell number $B_k$, where $k$ is the remainder when $n$ is divided by $m$. | 877 | graphs = [
Graph(
let={
"_m": Const(1573),
"_n": MinOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Const(2)), Divides(divisor=Var("d"), dividend=Ref("_m"))))),
"p": MinOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Const(2)), Divide... | NT | COMB | SUM | sympy | MIN_PRIME_FACTOR | [
"MIN_PRIME_FACTOR/MIN_PRIME_FACTOR"
] | 6f8539 | modular_sum_quadratic_residues_v1 | bell_mod | 6 | 0 | [
"MIN_PRIME_FACTOR"
] | 1 | 0.004 | 2026-02-08T04:48:42.773402Z | {
"verified": true,
"answer": 877,
"timestamp": "2026-02-08T04:48:42.777044Z"
} | 507f67 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 208,
"completion_tokens": 4672
},
"timestamp": "2026-02-11T22:05:24.825Z",
"answer": 877
},
{
"i... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "MIN_PRIME_FACTOR",
"status": "ok"
},
{
"lemma": "MOD_FACTORIAL",
"status": ... | {
"lo": -3.42,
"mid": 1.86,
"hi": 7.55
} | ||
9222dc | nt_num_divisors_compute_v1_168721529_1609 | Let $n = 333$. Compute the number of positive divisors of $n$. Let $c$ be the number of positive integers $j \leq 47$ such that $j^4 \leq 4879681$. Find the value of $c$ minus the number of positive divisors of $333$. | 41 | graphs = [
Graph(
let={
"_n": Const(47),
"n": Const(333),
"result": NumDivisors(n=Ref("n")),
"_c": CountOverSet(set=SolutionsSet(var=Var("j"), condition=And(Geq(Var("j"), Const(1)), Leq(Var("j"), Ref("_n")), Leq(Pow(Var("j"), Const(4)), Const(4879681))), domai... | NT | null | COMPUTE | sympy | B3 | [
"C3"
] | a45c54 | nt_num_divisors_compute_v1 | negation_mod | 3 | 0 | [
"B3",
"C3"
] | 2 | 0.108 | 2026-02-08T13:48:26.184281Z | {
"verified": true,
"answer": 41,
"timestamp": "2026-02-08T13:48:26.292597Z"
} | 1f2996 | 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": 1061
},
"timestamp": "2026-02-09T19:25:55.091Z",
"answer": 41
},
{
"id"... | 1 | [
{
"lemma": "C3",
"status": "ok"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
... | {
"lo": -5.49,
"mid": 0.03,
"hi": 6.12
} | ||
ed5632 | diophantine_product_count_v1_458359167_1197 | Let $k$ be the sum of all positive integers $n$ such that $1 \leq n \leq 320$ and $n$ is divisible by $160$. Let $\text{result}$ be the number of positive integers $x$ such that $1 \leq x \leq 466$, $x$ divides $k$, and $\frac{k}{x} \leq 466$. Find the remainder when $98948 \cdot \text{result}$ is divided by $88461$. | 53,792 | graphs = [
Graph(
let={
"_n": Const(98948),
"k": SumOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Const(320)), Eq(Mod(value=Var("n"), modulus=Const(160)), Const(0))))),
"upper": Const(466),
"result": CountOverSet(s... | NT | null | COUNT | sympy | SUM_DIVISIBLE | [
"SUM_DIVISIBLE"
] | 02dbe3 | diophantine_product_count_v1 | null | 5 | 0 | [
"SUM_DIVISIBLE"
] | 1 | 0.016 | 2026-02-08T04:29:19.587030Z | {
"verified": true,
"answer": 53792,
"timestamp": "2026-02-08T04:29:19.603159Z"
} | 31e888 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 219,
"completion_tokens": 1180
},
"timestamp": "2026-02-10T16:53:33.679Z",
"answer": 53792
},
{
... | 1 | [
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "SUM_DIVISIBLE",
"status": "ok"
},
{
"lemma": "V8",
"status": "no"
}
] | {
"lo": -3.42,
"mid": 1.86,
"hi": 7.55
} | ||
4e11e5 | nt_count_coprime_v1_1742523217_153 | Let $T$ be the set of all integers $t$ such that $5 \leq t \leq 31$ and there exist positive integers $a$ and $b$ with $1 \leq a \leq 3$, $1 \leq b \leq 11$, and $t = 3a + 2b$. Let $k$ be the largest prime number less than or equal to the number of elements in $T$. Compute the number of positive integers $n$ such that ... | 66,957 | graphs = [
Graph(
let={
"_n": Const(2),
"upper": Const(70000),
"k": MaxOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Ref("_n")), Leq(Var("n"), CountOverSet(set=SolutionsSet(var=Var("t"), condition=Exists(var=Var(name='a'), condition=Exists(var=Var(nam... | NT | null | COUNT | sympy | LIN_FORM | [
"LIN_FORM/MAX_PRIME_BELOW"
] | 47006e | nt_count_coprime_v1 | null | 6 | 0 | [
"LIN_FORM",
"MAX_PRIME_BELOW"
] | 2 | 9.418 | 2026-02-08T02:53:55.850258Z | {
"verified": true,
"answer": 66957,
"timestamp": "2026-02-08T02:54:05.268679Z"
} | 85c7ea | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 248,
"completion_tokens": 2340
},
"timestamp": "2026-02-09T14:10:20.174Z",
"answer": 66957
},
{
"... | 1 | [
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok_later"
},
{
"lemma": "MAX_VA... | {
"lo": 0.58,
"mid": 2.47,
"hi": 4.15
} | ||
980a18 | nt_gcd_compute_v1_2051736721_3042 | Let $a = 450884$ and $b = 837356$. Let $\text{result} = \gcd(a, b)$. Let $\mathcal{S}$ be the set of all ordered pairs $(x, y)$ of positive integers such that $xy = 22500$. Let $\mathcal{T}$ be the set of all values $x + y$ where $(x, y) \in \mathcal{S}$. Let $_c$ be the minimum element of $\mathcal{T}$. Let $Q$ be the... | 80,528 | graphs = [
Graph(
let={
"_m": Const(22500),
"_n": Const(83866),
"a": Const(450884),
"b": Const(837356),
"result": GCD(a=Ref("a"), b=Ref("b")),
"_c": MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), co... | NT | null | COMPUTE | sympy | SUM_ARITHMETIC | [
"SUM_ARITHMETIC",
"B3"
] | ea8ff9 | nt_gcd_compute_v1 | quadratic_mod | 3 | 0 | [
"B3",
"SUM_ARITHMETIC"
] | 2 | 0.002 | 2026-02-08T17:04:49.235320Z | {
"verified": true,
"answer": 80528,
"timestamp": "2026-02-08T17:04:49.237365Z"
} | e379ff | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 186,
"completion_tokens": 2044
},
"timestamp": "2026-02-17T18:58:48.527Z",
"answer": 80528
},
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "SUM_ARITHMETIC",
"status": "ok"
},
{
"lemma": "V5",
"status": "no"
},
{
"lemm... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
db8f00 | geo_count_lattice_rect_v1_1520064083_3512 | Let $a = 99$ and $b = 53$. Define $R$ as the number of lattice points $(x, y)$ such that $0 \leq x \leq a$ and $0 \leq y \leq b$. Compute $73984 - R$. Determine the value of this difference. | 68,584 | graphs = [
Graph(
let={
"a": Const(99),
"b": Const(53),
"result": LatticePointsRect(a=Ref(name='a'), b=Ref(name='b')),
"Q": Sub(Const(73984), Ref("result")),
},
goal=Ref("Q"),
)
] | GEOM | null | COUNT | sympy | [] | geo_count_lattice_rect_v1 | null | 4 | 0 | null | null | 0.002 | 2026-02-08T05:43:32.390307Z | {
"verified": true,
"answer": 68584,
"timestamp": "2026-02-08T05:43:32.391934Z"
} | 0d9493 | 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": 557
},
"timestamp": "2026-02-24T04:27:09.466Z",
"answer": 68584
},
{
"i... | 1 | [] | {
"lo": -5.98,
"mid": -3.97,
"hi": -1.94
} | ||||
6f7650 | diophantine_fbi2_count_v1_677425708_3079 | Let $n = 171$. Consider the set of all ordered pairs $(x, y)$ of positive integers such that $xy = 396900$. For each such pair, compute $x + y$, and let $k$ be the smallest value among all such sums. Define $S$ to be the set of all integers $d$ such that $4 \leq d \leq 172$, $d$ divides $k$, and $3 \leq \frac{k}{d} \le... | 30,818 | graphs = [
Graph(
let={
"_n": Const(171),
"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(396900)))), expr=Sum(Var("x"), Var("y"))))... | NT | null | COUNT | sympy | B3 | [
"B3"
] | 0cd20d | diophantine_fbi2_count_v1 | null | 6 | 0 | [
"B3"
] | 1 | 0.018 | 2026-02-08T05:28:50.451356Z | {
"verified": true,
"answer": 30818,
"timestamp": "2026-02-08T05:28:50.469218Z"
} | ccf428 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 183,
"completion_tokens": 1978
},
"timestamp": "2026-02-12T09:00:32.251Z",
"answer": 30818
},
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"statu... | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
477e30 | diophantine_product_count_v1_397696148_303 | Let $k = 420$ and let $\text{upper}$ be the largest prime number less than or equal to $192$. Define $\text{result}$ to be the number of positive integers $x$ such that $1 \leq x \leq \text{upper}$, $x$ divides $k$, and $\frac{k}{x} \leq \text{upper}$. Compute $\text{result}$. | 20 | graphs = [
Graph(
let={
"k": Const(420),
"upper": MaxOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(2)), Leq(Var("n"), Const(192)), IsPrime(Var("n"))))),
"result": CountOverSet(set=SolutionsSet(var=Var("x"), condition=And(Geq(Var("x"), Const(1)),... | NT | null | COUNT | sympy | MAX_VAL | [
"MAX_PRIME_BELOW"
] | dc3ad3 | diophantine_product_count_v1 | null | 3 | 0 | [
"MAX_PRIME_BELOW",
"MAX_VAL"
] | 2 | 0.036 | 2026-02-08T11:25:19.100345Z | {
"verified": true,
"answer": 20,
"timestamp": "2026-02-08T11:25:19.136271Z"
} | 2a817d | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 131,
"completion_tokens": 1965
},
"timestamp": "2026-02-14T13:39:09.745Z",
"answer": 20
},
{
... | 1 | [
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok"
},
{
"lemma": "V8_SUM",
"status": "no"
},
{
"lemma": "VAL_SUM_EQ",
... | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
be744c | lin_form_endings_v1_458359167_2702 | Let $a = 9$ and $b = 6$. Let $g = \gcd(a, b)$. Define $a' = \left\lfloor \frac{a}{g} \right\rfloor$ and $b' = \left\lfloor \frac{b}{g} \right\rfloor$. Let $A = 29$ and $B = 30$. Compute the value of
$$
( a' A + b' B - a' b' ) \times 19987 \mod 88770,
$$
defined as the unique integer $x$ with $0 \leq x < 88770$ such tha... | 66,297 | graphs = [
Graph(
let={
"a_coeff": Const(9),
"b_coeff": Const(6),
"A_val": Const(29),
"B_val": Const(30),
"g_step": GCD(a=Ref("a_coeff"), b=Ref("b_coeff")),
"ap_node": Floor(Div(Ref("a_coeff"), Ref("g_step"))),
"bp_node": Fl... | COMB | NT | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | lin_form_endings_v1 | null | 3 | null | [
"LIN_FORM"
] | 1 | 0.002 | 2026-02-08T06:44:21.250770Z | {
"verified": true,
"answer": 66297,
"timestamp": "2026-02-08T06:44:21.252558Z"
} | a0e9ca | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 208,
"completion_tokens": 1166
},
"timestamp": "2026-02-13T03:58:43.597Z",
"answer": 66297
},
... | 1 | [
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "V8",
"status": "no"
},
{
"lemma": "V8_SUM",
... | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
86a38b | algebra_quadratic_discriminant_v1_1520064083_6888 | Let $a$ be the number of positive integers $p$ for which there exists a positive integer $q$ such that $p \cdot q = 22050$, $\gcd(p, q) = 1$, and $p < q$. Let $n = 2$, $b = -9$, and $c = 0$. Define $\text{result} = b^n - 4ac$. Compute the remainder when $42947 \cdot \text{result}$ is divided by $93186$. | 30,825 | graphs = [
Graph(
let={
"_n": Const(2),
"a": CountOverSet(set=SolutionsSet(var=Var("p"), condition=And(IsPositive(arg=Var(name='p')), Exists(var=Var(name='q'), condition=And(Eq(left=Mul(Var(name='p'), Var(name='q')), right=Const(value=22050)), Eq(left=GCD(a=Var(name='p'), b=Var(name=... | NT | null | COMPUTE | sympy | COPRIME_PAIRS | [
"COPRIME_PAIRS"
] | 2bb3aa | algebra_quadratic_discriminant_v1 | null | 5 | 0 | [
"COPRIME_PAIRS"
] | 1 | 0.012 | 2026-02-08T08:23:21.647192Z | {
"verified": true,
"answer": 30825,
"timestamp": "2026-02-08T08:23:21.659036Z"
} | eab28b | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 153,
"completion_tokens": 1448
},
"timestamp": "2026-02-13T18:08:19.804Z",
"answer": 30825
},
... | 1 | [
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
}
] | {
"lo": -3.51,
"mid": 1.33,
"hi": 6.56
} | ||
b33423 | geo_count_lattice_triangle_v1_1742523217_4569 | Let $A = (0,0)$, $B = (191,128)$, and $C = (88,289)$. The quantity $2 \cdot \text{area}$ of triangle $ABC$ is given by
$$
|191 \cdot 128 + 88 \cdot (0 - 289)|.
$$
The number of lattice points on the boundary of triangle $ABC$ is
$$
\gcd(191, 289) + \gcd(|88 - 191|, |128 - 289|) + \gcd(88, 128).
$$
Using Pick's Theorem,... | 26,749 | graphs = [
Graph(
let={
"_n": Const(128),
"area_2x": Abs(arg=Sum(Mul(Const(value=191), Const(value=128)), Mul(Const(value=88), Sub(left=Const(value=0), right=Const(value=289))))),
"boundary": Sum(GCD(a=Abs(arg=Const(value=191)), b=Abs(arg=Const(value=289))), GCD(a=Abs(arg... | ALG | NT | COUNT | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | geo_count_lattice_triangle_v1 | null | 7 | 0 | [
"LIN_FORM"
] | 1 | 0.01 | 2026-02-08T08:58:21.057657Z | {
"verified": true,
"answer": 26749,
"timestamp": "2026-02-08T08:58:21.067431Z"
} | 7e900c | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 235,
"completion_tokens": 2471
},
"timestamp": "2026-02-13T22:37:52.365Z",
"answer": 26749
},
... | 1 | [
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
}
] | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
dee4fc | comb_sum_binomial_mod_v1_153355830_2023 | Let $T$ be the set of all ordered pairs $(x,y)$ of positive integers such that $xy = 32400$. Define $s$ to be the minimum value of $x + y$ over all such pairs. Compute the sum $$
\sum_{k=39}^{355} \binom{s}{k},
$$ and let $r$ be the remainder when this sum is divided by $11503$. Let $Q = 38416 - r$. Find the value of $... | 34,796 | graphs = [
Graph(
let={
"_n": Const(11503),
"sum": Summation(var="k", start=Const(39), end=Const(355), expr=Binom(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(... | ALG | COMB | COMPUTE | sympy | B3 | [
"B3"
] | 0cd20d | comb_sum_binomial_mod_v1 | null | 6 | 0 | [
"B3"
] | 1 | 0.031 | 2026-02-08T06:51:14.582867Z | {
"verified": true,
"answer": 34796,
"timestamp": "2026-02-08T06:51:14.613372Z"
} | 2223ce | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 214,
"completion_tokens": 32768
},
"timestamp": "2026-02-24T07:12:25.655Z",
"answer": null
},
{
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
}
] | {
"lo": 3.43,
"mid": 5.73,
"hi": 8.84
} | ||
7d9086 | nt_sum_divisors_mod_v1_2051736721_1210 | Let $n = 180$ and let $\sigma$ be the sum of the positive divisors of $n$. Let $r$ be the remainder when $\sigma$ is divided by $11833$. Let $p_{\text{max}}$ be the largest prime number $p$ such that $2 \le p \le 12$. Compute the Bell number $B_{|r| \bmod p_{\text{max}}}$ and determine its value. | 877 | graphs = [
Graph(
let={
"_n": Const(2),
"n": Const(180),
"M": Const(11833),
"sigma": SumDivisors(n=Ref("n")),
"result": Mod(value=Ref("sigma"), modulus=Ref("M")),
"Q": Bell(Mod(value=Abs(arg=Ref(name='result')), modulus=MaxOverSet(set=S... | NT | COMB | COMPUTE | sympy | MAX_PRIME_BELOW | [
"MAX_PRIME_BELOW"
] | 88ea9c | nt_sum_divisors_mod_v1 | bell_mod | 4 | 0 | [
"MAX_PRIME_BELOW"
] | 1 | 0.006 | 2026-02-08T15:54:12.913642Z | {
"verified": true,
"answer": 877,
"timestamp": "2026-02-08T15:54:12.919715Z"
} | 357bd4 | 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": 737
},
"timestamp": "2026-02-16T15:58:41.978Z",
"answer": 877
},
{
... | 1 | [
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok"
},
{
"lemma": "MOD_MUL",
"status": "no"
}
... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
e605cc | comb_count_surjections_v1_1520064083_7295 | Let $T$ be the set of all integers $t$ such that $27 \leq t \leq 54$ and there exist integers $a, b$ with $1 \leq a \leq 2$, $1 \leq b \leq 4$, satisfying
$$
t = 9a + 6b + 12.
$$
Let $s$ be the number of elements in $T$.
Let $k$ be the number of ordered pairs $(x_1, x_2)$ of positive odd integers such that $x_1 + x_2 ... | 8,400 | graphs = [
Graph(
let={
"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(Sum(Var("x1"), Var("x2")), Coun... | COMB | null | COUNT | sympy | LIN_FORM | [
"LIN_FORM/COMB1"
] | 268a62 | comb_count_surjections_v1 | null | 6 | 0 | [
"COMB1",
"LIN_FORM"
] | 2 | 0.002 | 2026-02-08T08:53:27.403655Z | {
"verified": true,
"answer": 8400,
"timestamp": "2026-02-08T08:53:27.405990Z"
} | 2a78bd | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 273,
"completion_tokens": 1723
},
"timestamp": "2026-02-24T10:14:12.831Z",
"answer": 8400
},
{
"i... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COMB1",
"status": "ok_later"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "LIN_FORM",
... | {
"lo": -2.35,
"mid": 1.22,
"hi": 4.84
} | ||
a1a5af | diophantine_sum_product_min_v1_124444284_10035 | Let $S_1$ be the set of all ordered pairs $(x, y)$ of positive integers such that $xy = 81$. For each such pair, compute $x + y$, and let $n$ be the smallest value of $x + y$ over all such pairs. Now consider all ordered pairs $(x, y)$ of positive integers such that $x + y = n$, and for each such pair compute $xy$. Let... | 80,967 | graphs = [
Graph(
let={
"_m": Const(17),
"_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(81)))), expr=Sum(Var("x"), Var("y")))),
... | NT | null | EXTREMUM | sympy | B3 | [
"B3/B1"
] | 7f76f7 | diophantine_sum_product_min_v1 | null | 6 | 0 | [
"B1",
"B3"
] | 2 | 0.007 | 2026-02-08T12:47:36.053767Z | {
"verified": true,
"answer": 80967,
"timestamp": "2026-02-08T12:47:36.060717Z"
} | fc1b2d | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 211,
"completion_tokens": 811
},
"timestamp": "2026-02-15T05:27:42.515Z",
"answer": 80967
},
{... | 1 | [
{
"lemma": "B1",
"status": "ok_later"
},
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
},
{
"lemma": "... | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
64defe | algebra_poly_eval_v1_1218484723_4969 | Let $x = 23$. Let $A = \min\{ 4a_1^2 + 16b_1^2 : a_1, b_1 \in \mathbb{Z}^+,\ 1 \leq a_1, b_1 \leq 26 \}$. Let $B = \left|\{ (a_2, b_2) : 1 \leq a_2, b_2 \leq 35,\ 13a_2^2 - 2a_2b_2 + 2b_2^2 \leq 4058 \}\right|$. Compute $$5x^2 + \left|\left\{ (a, b) : 1 \leq a \leq b \leq 20,\ a \leq A,\ 2b^2 - 4ab + 2a^2 = B \right\}\... | 2,711 | graphs = [
Graph(
let={
"_c": Const(13),
"_m": Const(2),
"_n": Const(2),
"x": Const(23),
"result": Sum(Mul(Const(5), Pow(Ref("x"), Ref("_n"))), Mul(CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("a"), Var("b")]), condition=And(Geq(Var("a"), ... | ALG | null | COMPUTE | sympy | QF_PSD_COUNT_LEQ | [
"QF_PSD_COUNT_LEQ/QF_PSD_ORBIT",
"QF_PSD_MIN/QF_PSD_ORBIT"
] | d8e126 | algebra_poly_eval_v1 | null | 6 | 0 | [
"QF_PSD_COUNT_LEQ",
"QF_PSD_MIN",
"QF_PSD_ORBIT"
] | 3 | 0.016 | 2026-02-25T06:35:36.889016Z | {
"verified": true,
"answer": 2711,
"timestamp": "2026-02-25T06:35:36.904990Z"
} | 970918 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 322,
"completion_tokens": 13400
},
"timestamp": "2026-03-29T18:48:37.694Z",
"answer": 2711
},
{
"... | 1 | [
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "QF_PSD_COUNT_LEQ",
"status": "ok"
},
{
"lemma": "QF_PSD_MIN",
"status": "ok"
},
{
"lemma": "QF_PSD_ORBIT",
"status": "ok_later"
}
] | {
"lo": -3.33,
"mid": 1.03,
"hi": 5.26
} | ||
7cc151 | nt_count_divisible_and_v1_677425708_1672 | Let $n = 5$. Compute $d_2 = \sum_{k=1}^{n} k$. Determine the number of integers $n$ such that $\phi(2) \leq n \leq 269400$, $n$ is divisible by $12$, and $n$ is divisible by $d_2$. Find the value of this count. | 4,490 | graphs = [
Graph(
let={
"_n": Const(5),
"upper": Const(269400),
"d1": Const(12),
"d2": Summation(var="k", start=Const(1), end=Ref("_n"), expr=Var("k")),
"result": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), EulerPhi(n=Co... | NT | null | COUNT | sympy | SUM_ARITHMETIC | [
"SUM_ARITHMETIC",
"ONE_PHI_2"
] | f42bcb | nt_count_divisible_and_v1 | null | 3 | 0 | [
"ONE_PHI_2",
"SUM_ARITHMETIC"
] | 2 | 9.432 | 2026-02-08T04:22:03.804798Z | {
"verified": true,
"answer": 4490,
"timestamp": "2026-02-08T04:22:13.236720Z"
} | df23fb | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 188,
"completion_tokens": 808
},
"timestamp": "2026-02-09T23:10:06.734Z",
"answer": 4490
},
{
"id... | 2 | [
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "ONE_PHI_2",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "SUM_ARITHMETIC",
"status": "ok"
},
{
"lemma": "V8",
... | {
"lo": -10,
"mid": -6.47,
"hi": -2.95
} | ||
202e3c | nt_num_divisors_compute_v1_1915831931_1849 | Let $n = 95481$. Compute the number of positive divisors of $n$. | 9 | graphs = [
Graph(
let={
"n": Const(95481),
"result": NumDivisors(n=Ref("n")),
},
goal=Ref("result"),
)
] | NT | null | COMPUTE | sympy | LTE_DIFF_P2 | [
"EULER_TOTIENT_SUM"
] | 58c2f4 | nt_num_divisors_compute_v1 | null | 2 | 0 | [
"EULER_TOTIENT_SUM",
"LTE_DIFF_P2"
] | 2 | 0.031 | 2026-02-08T16:29:14.926349Z | {
"verified": true,
"answer": 9,
"timestamp": "2026-02-08T16:29:14.956859Z"
} | e4003c | 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": 855
},
"timestamp": "2026-02-17T04:45:35.244Z",
"answer": 9
},
{
... | 1 | [
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "EULER_TOTIENT_SUM",
"status": "ok"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "V... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
2534a5 | alg_qf_psd_orbit_v1_1218484723_4605 | Find the number of ordered pairs $(a, b)$ of positive integers with $1 \leq a \leq b \leq 481$ such that $32b^2 + 64ab + 32a^2 = 1634432$. | 113 | graphs = [
Graph(
let={
"_n": Const(481),
"result": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("a"), Var("b")]), condition=And(Geq(Var("a"), Const(1)), Leq(Var("a"), CountOverSet(set=SolutionsSet(var=Var("v"), condition=And(Geq(Var("v"), Const(34)), Leq(Var("v"), Const(179... | ALG | null | COUNT | sympy | COPRIME_PAIRS | [
"QF_PSD_DISTINCT"
] | a8f9cb | alg_qf_psd_orbit_v1 | null | 6 | 0 | [
"COPRIME_PAIRS",
"QF_PSD_DISTINCT"
] | 2 | 6.293 | 2026-02-25T06:16:18.666555Z | {
"verified": true,
"answer": 113,
"timestamp": "2026-02-25T06:16:24.959062Z"
} | cc26fa | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 164,
"completion_tokens": 1825
},
"timestamp": "2026-03-29T16:29:56.127Z",
"answer": 113
},
{
"id... | 2 | [
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "QF_PSD_DISTINCT",
"status": "ok"
}
] | {
"lo": -10,
"mid": -6.24,
"hi": -2.48
} | ||
4431a5 | comb_count_derangements_v1_601307018_4632 | Let $D_n$ denote the number of derangements of $n$ elements. For each integer $a$ with $0 \le a \le 168$, define $S = (a^5 - 3a^4 - 4a^3 - 3a^2 + 4a - 3) \bmod 169$, and $T = (S^5 - 3S^4 - 4S^3 - 3S^2 + 4S - 3) \bmod 169$. Let $c = \left| \{ a : 0 \le a \le 168,\ T = a,\ S \ne a \} \right|$, and let $k = \binom{c}{14} ... | 52,623 | graphs = [
Graph(
let={
"_m": Const(169),
"_n": Const(73189),
"n": Summation(var="k", start=Sub(Binom(n=CountOverSet(set=SolutionsSet(var=Var("a"), condition=And(Geq(Var("a"), Const(0)), Leq(Var("a"), Const(168)), Eq(Ref("_po_p2"), Var("a")), Neq(Ref("_po_p1"), Var("a")))... | COMB | null | COUNT | sympy | POLY_ORBIT_HENSEL | [
"POLY_ORBIT_HENSEL/ZERO_BINOM_N/SUM_GEOM"
] | fe677c | comb_count_derangements_v1 | null | 6 | 0 | [
"POLY_ORBIT_HENSEL",
"SUM_GEOM",
"ZERO_BINOM_N"
] | 3 | 0.005 | 2026-03-10T05:16:54.416567Z | {
"verified": true,
"answer": 52623,
"timestamp": "2026-03-10T05:16:54.421902Z"
} | 412e4b | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 332,
"completion_tokens": 23202
},
"timestamp": "2026-03-29T12:55:40.456Z",
"answer": 23122
},
{
... | 0 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "POLY_ORBIT_HENSEL",
"status": "ok"
},
{
"lemma": "SUM_GEOM",
"status": "ok_later"
},
{
"lemma": "V7",
... | {
"lo": 3.34,
"mid": 5.77,
"hi": 8.89
} | ||
ca6ab8 | alg_qf_psd_min_v1_601307018_1427 | Let $S$ be the set of ordered pairs $(a_1, b_1)$ of positive integers with $1 \leq a_1, b_1 \leq 35$ such that $9a_1^2 + 30a_1b_1 + 25b_1^2 = 17689$, and let $A = |S|$. Let $T$ be the set of ordered pairs $(a_2, b_2)$ of positive integers with $1 \leq a_2, b_2 \leq 25$ such that $27b_2^3 + 144a_2^2b_2 + k a_2b_2^2 + 64... | 51,646 | graphs = [
Graph(
let={
"_m": Const(17689),
"_n": Const(35),
"result": MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("a"), Var("b"), Var("c")]), condition=And(Geq(Var("a"), Const(1)), Leq(Var("a"), CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var... | ALG | null | COMPUTE | sympy | B3 | [
"B3/POLY3_COUNT",
"QF_PSD_COUNT"
] | aa9f70 | alg_qf_psd_min_v1 | null | 7 | 0 | [
"B3",
"POLY3_COUNT",
"QF_PSD_COUNT"
] | 3 | 0.033 | 2026-03-10T02:08:24.212045Z | {
"verified": true,
"answer": 51646,
"timestamp": "2026-03-10T02:08:24.244923Z"
} | 8572a0 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 1,
"correct": {
"strict": false,
"boxed": false,
"relaxed": true
},
"usage": {
"prompt_tokens": 409,
"completion_tokens": 32768
},
"timestamp": "2026-03-29T02:13:01.251Z",
"answer": null
},
{
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "POLY3_COUNT",
"status": "ok_later"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "QF_PSD_COUNT",
"status": "ok"
}
] | {
"lo": -0.92,
"mid": 2.07,
"hi": 4.68
} | ||
e34f9e | lin_form_endings_v1_124444284_8364 | Let $S$ be the set of all integers $t$ such that $108 \le t \le 1656$ and there exist positive integers $a \le 12$ and $b \le 18$ for which $t = 48a + 60b$. Let $k$ be the number of elements in $S$. Compute the remainder when $13703 \cdot k$ is divided by $74427$. Determine the value of this remainder. | 53,987 | graphs = [
Graph(
let={
"_inner_result": CountOverSet(set=SolutionsSet(var=Var("t"), condition=Exists(var=Var(name='a'), condition=Exists(var=Var(name='b'), condition=And(Geq(left=Var(name='a'), right=Const(value=1)), Leq(left=Var(name='a'), right=Const(value=12)), Geq(left=Var(name='b'), right=... | COMB | null | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | lin_form_endings_v1 | null | 4 | null | [
"LIN_FORM"
] | 1 | 0.001 | 2026-02-08T09:39:24.835602Z | {
"verified": true,
"answer": 53987,
"timestamp": "2026-02-08T09:39:24.836721Z"
} | 791647 | 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": 13565
},
"timestamp": "2026-02-24T11:41:00.820Z",
"answer": 53987
},
{
... | 1 | [
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
... | {
"lo": 1.15,
"mid": 4.18,
"hi": 6.61
} | ||
ffa064 | algebra_quadratic_discriminant_v1_677425708_2302 | Let $a = -5$, $b = 9$, and $c = 2$. Let $D = b^2 - 4ac$. Define $r = 2$ if $D > 0$, $r = 1$ if $D = 0$, and $r = 0$ otherwise. Let $Q$ be the number of positive integers $t$ such that $9 \le t \le 3930$ and $t = 7a' + 2b'$ for some positive integers $a' \le 176$ and $b' \le 1349$, minus $r$. Compute the value of $Q$. | 3,914 | graphs = [
Graph(
let={
"a": Const(-5),
"b": Const(9),
"c": Const(2),
"D": Sub(Pow(Ref("b"), Const(2)), Mul(Const(4), Ref("a"), Ref("c"))),
"result": Sum(Mul(Const(2), Iverson(condition=Gt(Ref("D"), Const(0)))), Iverson(condition=Eq(Ref("D"), Const... | NT | null | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM"
] | 324ba4 | algebra_quadratic_discriminant_v1 | negation_mod | 4 | 0 | [
"LIN_FORM"
] | 1 | 0.002 | 2026-02-08T04:58:48.102892Z | {
"verified": true,
"answer": 3914,
"timestamp": "2026-02-08T04:58:48.105000Z"
} | d13213 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 250,
"completion_tokens": 3566
},
"timestamp": "2026-02-11T22:38:21.292Z",
"answer": 3917
},
{
... | 1 | [
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
... | {
"lo": 3.24,
"mid": 5.68,
"hi": 8.81
} | ||
e20b9e | alg_qf_psd_count_leq_v1_601307018_4022 | Let $A = \left|\left\{ n \ge 1 : n \le 749 \text{ and } n \equiv \left\lfloor \frac{n}{2} \right\rfloor \pmod{3} \right\}\right|$. Find the number of ordered pairs $(a, b)$ of positive integers with $1 \le a \le A$ and $1 \le b \le 249$ such that $29a^2 + 29b^2 - 58ab \le 1328084$. | 60,811 | graphs = [
Graph(
let={
"_n": Const(2),
"result": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("a"), Var("b")]), condition=And(Geq(Var("a"), Const(1)), Leq(Var("a"), CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Const(749)),... | NT | null | COUNT | sympy | L3C | [
"L3C"
] | 73f8b0 | alg_qf_psd_count_leq_v1 | null | 5 | 0 | [
"L3C"
] | 1 | 0.127 | 2026-03-10T04:37:34.709746Z | {
"verified": true,
"answer": 60811,
"timestamp": "2026-03-10T04:37:34.836810Z"
} | dcfa74 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 229,
"completion_tokens": 3265
},
"timestamp": "2026-03-29T10:47:52.099Z",
"answer": 60811
},
{
"... | 1 | [
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "L3C",
"status": "ok"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "V3",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
}
] | {
"lo": -3.34,
"mid": 0.9,
"hi": 4.9
} | ||
7cf739 | comb_factorial_compute_v1_784195855_7735 | Let $ S $ be the set of all positive integers $ n $ such that $ 1 \leq n \leq 32 $ and $ 3 $ divides the $ n $-th Fibonacci number, where $ F_1 = 1 $, $ F_2 = 1 $, and $ F_n = F_{n-1} + F_{n-2} $ for $ n \geq 3 $. Let $ k $ be the number of elements in $ S $. Compute the remainder when $ 19698 \cdot k! $ is divided by ... | 60,616 | graphs = [
Graph(
let={
"_n": Const(93563),
"n": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Const(32)), Divides(divisor=Const(3), dividend=Fibonacci(arg=Var(name='n')))))),
"result": Factorial(Ref("n")),
"Q... | ALG | NT | COMPUTE | sympy | COUNT_FIB_DIVISIBLE | [
"COUNT_FIB_DIVISIBLE"
] | 66de3c | comb_factorial_compute_v1 | null | 5 | 0 | [
"COUNT_FIB_DIVISIBLE"
] | 1 | 0.001 | 2026-02-08T09:28:50.425910Z | {
"verified": true,
"answer": 60616,
"timestamp": "2026-02-08T09:28:50.427042Z"
} | 3cc7a3 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 169,
"completion_tokens": 1785
},
"timestamp": "2026-02-14T04:24:16.201Z",
"answer": 60616
},
... | 1 | [
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "ok"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "n... | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
f4efb8 | algebra_poly_eval_v1_784195855_10016 | Let $d$ be the smallest integer greater than or equal to $2$ that divides $157757$. Compute the value of $2d^3 - 4d^2 + 2d + 8$. | 12,320 | 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(157757))))),
"result": Sum(Mul(Ref("_n"), Pow(Ref("m"), Const(3))), Mul(Const(-4), Pow(Ref("m"), Const(2)... | NT | null | COMPUTE | sympy | MIN_PRIME_FACTOR | [
"MIN_PRIME_FACTOR"
] | bc3776 | algebra_poly_eval_v1 | null | 3 | 0 | [
"MIN_PRIME_FACTOR"
] | 1 | 0.002 | 2026-02-08T17:22:27.940267Z | {
"verified": true,
"answer": 12320,
"timestamp": "2026-02-08T17:22:27.942347Z"
} | d66b0d | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 92,
"completion_tokens": 702
},
"timestamp": "2026-02-18T00:44:02.915Z",
"answer": 12320
},
{
... | 1 | [
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "MIN_PRIME_FACTOR",
"status": "ok"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "V3",
"status": "no... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
21a31e | antilemma_k2_v1_124444284_3664 | Let $m = 347$ and let $n = \sum_{d \mid 347} \phi(d)$, where $\phi$ denotes Euler's totient function. Compute
\[
\sum_{k=1}^{347} \phi(k) \left\lfloor \frac{n}{k} \right\rfloor.
\] | 60,378 | graphs = [
Graph(
let={
"_m": Const(347),
"_n": SumOverDivisors(n=Const(value=347), var='d', expr=EulerPhi(n=Var(name='d'))),
"x": Summation(var="k", start=Const(1), end=Ref("_m"), expr=Mul(EulerPhi(n=Var("k")), Floor(Div(Ref("_n"), Var("k"))))),
},
goal=R... | NT | COMB | COMPUTE | sympy | K3 | [
"K3/K2",
"K2"
] | c7f244 | antilemma_k2_v1 | null | 6 | 0 | [
"K2",
"K3"
] | 2 | 0.001 | 2026-02-08T05:32:36.102162Z | {
"verified": true,
"answer": 60378,
"timestamp": "2026-02-08T05:32:36.102930Z"
} | 5cd51c | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 114,
"completion_tokens": 798
},
"timestamp": "2026-02-12T10:24:56.165Z",
"answer": 60378
},
{... | 1 | [
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "K2",
"status": "ok"
},
{
"lemma": "K3",
"status": "ok"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW... | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
0afd2f | nt_max_prime_below_v1_1439011603_1674 | Let $S$ be the set of all positive integers $p$ for which there exists a positive integer $q$ such that $pq = 12$, $\gcd(p, q) = 1$, and $p < q$. Let $m$ be the number of elements in $S$. Determine the largest prime number $n$ such that $m \leq n \leq 33124$. | 33,119 | graphs = [
Graph(
let={
"upper": Const(33124),
"result": MaxOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), CountOverSet(set=SolutionsSet(var=Var("p"), condition=And(IsPositive(arg=Var(name='p')), Exists(var=Var(name='q'), condition=And(Eq(left=Mul(Var(name='p'), V... | NT | null | EXTREMUM | sympy | COPRIME_PAIRS | [
"COPRIME_PAIRS"
] | 2bb3aa | nt_max_prime_below_v1 | null | 4 | 0 | [
"COPRIME_PAIRS"
] | 1 | 0.883 | 2026-02-08T16:12:50.849202Z | {
"verified": true,
"answer": 33119,
"timestamp": "2026-02-08T16:12:51.732486Z"
} | b522fd | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 129,
"completion_tokens": 2542
},
"timestamp": "2026-02-16T22:59:27.139Z",
"answer": 33119
},
... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "V3",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
7d92d9 | alg_poly_preperiod_count_v1_601307018_2894 | For a non-negative integer $a$, define $f(x) = x^4 - 4x^3 + 5x^2 + 4x - 2$. Let $N = f(a) \bmod 41$, $M = f(N) \bmod 41$, $R = f(M) \bmod 41$, $S = f(R) \bmod 41$, and $T = f(S) \bmod 41$. Find the number of integers $a$ with $0 \le a \le 73963$ such that $T = M$, $R \ne M$, and $S \ne M$. | 25,256 | graphs = [
Graph(
let={
"p1": Mod(value=Sum(Pow(Var("a"), Const(4)), Mul(Const(-4), Pow(Var("a"), Const(3))), Mul(Const(5), Pow(Var("a"), Const(2))), Mul(Const(4), Var("a")), Const(-2)), modulus=Const(41)),
"p2": Mod(value=Sum(Pow(Ref("p1"), Const(4)), Mul(Const(-4), Pow(Ref("p1"), C... | ALG | null | COUNT | sympy | POLY_ORBIT_COUNT | [
"POLY_ORBIT_COUNT"
] | 4ad965 | alg_poly_preperiod_count_v1 | null | 7 | null | [
"POLY_ORBIT_COUNT"
] | 1 | 0.245 | 2026-03-10T03:31:03.411369Z | {
"verified": true,
"answer": 25256,
"timestamp": "2026-03-10T03:31:03.656661Z"
} | 9028d2 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 249,
"completion_tokens": 32768
},
"timestamp": "2026-03-29T06:51:36.866Z",
"answer": 25256
},
{
... | 1 | [
{
"lemma": "POLY_ORBIT_COUNT",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
}
] | {
"lo": 1.23,
"mid": 4.27,
"hi": 6.7
} | ||
b7ae52 | comb_count_permutations_fixed_v1_1915831931_3979 | Let $n$ be the number of ordered pairs $(i,j)$ of positive integers such that $i + j = 11$ and $1 \leq i, j \leq 11$. Let $k = 7$. Compute $\binom{n}{k} \cdot !(n - k)$, where $!m$ denotes the number of derangements of $m$ elements. Find the value of this expression. | 240 | graphs = [
Graph(
let={
"_n": Const(11),
"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(11)), right=IntegerRange(start=Const(1), end=Con... | COMB | null | COUNT | sympy | COUNT_SUM_EQUALS | [
"COUNT_SUM_EQUALS"
] | 75ab0f | comb_count_permutations_fixed_v1 | null | 4 | 0 | [
"COUNT_SUM_EQUALS"
] | 1 | 0.014 | 2026-02-08T18:02:22.624430Z | {
"verified": true,
"answer": 240,
"timestamp": "2026-02-08T18:02:22.638854Z"
} | aff4f4 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 133,
"completion_tokens": 647
},
"timestamp": "2026-02-18T12:02:04.848Z",
"answer": 240
},
{
... | 1 | [
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "ok"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
},
{
"lemma": "V8_SUM",
"status":... | {
"lo": -8,
"mid": -4.75,
"hi": -2.28
} | ||
f60d34 | comb_binomial_compute_v1_397696148_747 | Let $P$ be the maximum value of $xy$ over all pairs of positive integers $(x, y)$ such that $x + y = 14$. Let $s$ be the minimum value of $x + y$ over all pairs of positive integers $(x, y)$ such that $xy = P$. Compute $\binom{s}{7}$. | 3,432 | graphs = [
Graph(
let={
"_n": MaxOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(Sum(Var("x"), Var("y")), Const(14)))), expr=Mul(Var("x"), Var("y")))),
"n": MinOverSet(set... | ALG | COMB | COMPUTE | sympy | B1 | [
"B1/B3"
] | 80b49d | comb_binomial_compute_v1 | null | 4 | 0 | [
"B1",
"B3"
] | 2 | 0.004 | 2026-02-08T11:43:03.920868Z | {
"verified": true,
"answer": 3432,
"timestamp": "2026-02-08T11:43:03.924429Z"
} | f02d1b | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 184,
"completion_tokens": 1228
},
"timestamp": "2026-02-24T14:34:46.255Z",
"answer": 3432
},
{
"i... | 1 | [
{
"lemma": "B1",
"status": "ok"
},
{
"lemma": "B3",
"status": "ok_later"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
}
] | {
"lo": -7.18,
"mid": -5,
"hi": -3.01
} | ||
b785c6 | algebra_poly_eval_v1_1915831931_1407 | Let $a = 8$. Let $s$ be the minimum value of $x + y$ over all ordered pairs $(x, y)$ of positive integers such that $xy = 3025$. Compute the value of
\[
\frac{24 \cdot a^3 - 74 \cdot a^2 + s \cdot a - 72}{40}.
\]
Then, compute the sum of $\phi(n)$ for $n$ from 1 to the absolute value of the result just computed, where ... | 13,366 | graphs = [
Graph(
let={
"_n": Const(2),
"a": Const(8),
"result": Div(Sum(Mul(Const(24), Pow(Ref("a"), Const(3))), Mul(Const(-74), Pow(Ref("a"), Ref("_n"))), Mul(MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(a... | NT | null | COMPUTE | sympy | B3 | [
"B3"
] | 0cd20d | algebra_poly_eval_v1 | null | 5 | 0 | [
"B3"
] | 1 | 0.012 | 2026-02-08T16:04:16.061799Z | {
"verified": true,
"answer": 13366,
"timestamp": "2026-02-08T16:04:16.074037Z"
} | cc0383 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 162,
"completion_tokens": 2340
},
"timestamp": "2026-02-16T21:45:40.038Z",
"answer": 13366
},
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
d4fcba | antilemma_sum_equals_v1_349078426_614 | Let $T$ be the set of all integers $t$ with $7 \leq t \leq 56$ for which there exist integers $a$ and $b$ such that $1 \leq a \leq 4$, $1 \leq b \leq 18$, and $t = 5a + 2b$. Let $m = |T|$. Let $P$ be the set of all ordered pairs $(i, j)$ of integers with $1 \leq i \leq 45$ and $1 \leq j \leq 45$ such that $i + j = m$. ... | 44 | graphs = [
Graph(
let={
"_m": CountOverSet(set=SolutionsSet(var=Var("t"), condition=Exists(var=Var(name='a'), condition=Exists(var=Var(name='b'), condition=And(Geq(left=Var(name='a'), right=Const(value=1)), Leq(left=Var(name='a'), right=Const(value=4)), Geq(left=Var(name='b'), right=Const(value=... | COMB | GEOM | COMPUTE | sympy | COMB1 | [
"COUNT_SUM_EQUALS/COUNT_SUM_EQUALS",
"LIN_FORM/COUNT_SUM_EQUALS",
"COUNT_SUM_EQUALS"
] | b43a9c | antilemma_sum_equals_v1 | null | 6 | 0 | [
"COMB1",
"COUNT_SUM_EQUALS",
"LIN_FORM"
] | 3 | 0.025 | 2026-02-08T13:10:13.868641Z | {
"verified": true,
"answer": 44,
"timestamp": "2026-02-08T13:10:13.893377Z"
} | a90dc4 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 317,
"completion_tokens": 4009
},
"timestamp": "2026-02-24T17:23:31.235Z",
"answer": 44
},
{
"id"... | 1 | [
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "ok"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8",
"st... | {
"lo": -3.84,
"mid": -1.67,
"hi": 1.32
} | ||
1cc6ae | nt_min_phi_inverse_v1_784195855_9336 | Let $m = 44$ and $n = 20$. Define $\text{upper}$ to be the maximum value of $xy$ over all ordered pairs $(x, y)$ of positive integers such that $x + y = 20$. Define $k$ to be the number of positive integers $n$ with $1 \leq n \leq 44$ such that $\gcd(n, 15) = 1$. Let $\text{result}$ be the smallest positive integer $n$... | 131 | graphs = [
Graph(
let={
"_m": Const(44),
"_n": Const(20),
"upper": MaxOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(Sum(Var("x"), Var("y")), Ref("_n")))), ex... | NT | null | EXTREMUM | sympy | B1 | [
"B1",
"C4"
] | b060fb | nt_min_phi_inverse_v1 | null | 6 | 0 | [
"B1",
"C4"
] | 2 | 0.012 | 2026-02-08T16:42:41.446120Z | {
"verified": true,
"answer": 131,
"timestamp": "2026-02-08T16:42:41.457743Z"
} | 12d913 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 205,
"completion_tokens": 3238
},
"timestamp": "2026-02-17T11:31:24.717Z",
"answer": 131
},
{
... | 1 | [
{
"lemma": "B1",
"status": "ok"
},
{
"lemma": "C4",
"status": "ok"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"le... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
93eff5 | nt_count_phi_equals_v1_458359167_965 | Let $S$ be the set of all ordered pairs $(x,y)$ of positive integers such that $xy = 6250000$. Let $T$ be the set of all values $x + y$ where $(x,y) \in S$. Let $m$ be the minimum value in $T$. Determine the number of positive integers $n$ such that $1 \leq n \leq m$ and $\phi(n) = 238$. | 2 | graphs = [
Graph(
let={
"upper": MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(Mul(Var("x"), Var("y")), Const(6250000)))), expr=Sum(Var("x"), Var("y")))),
"k": Const(... | NT | null | COUNT | sympy | K3 | [
"B3"
] | 0cd20d | nt_count_phi_equals_v1 | null | 7 | 0 | [
"B3",
"K3"
] | 2 | 0.496 | 2026-02-08T04:12:29.011429Z | {
"verified": true,
"answer": 2,
"timestamp": "2026-02-08T04:12:29.507658Z"
} | b5ee4d | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 205,
"completion_tokens": 4403
},
"timestamp": "2026-02-10T15:52:36.106Z",
"answer": 2
},
{
"id"... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
... | {
"lo": -3.42,
"mid": 1.86,
"hi": 7.55
} | ||
1dcdf7 | geo_visible_lattice_v1_153355830_1471 | Let $n = 73$. Define a visible lattice point $(x, y)$ to be a point with integer coordinates such that $1 \leq x, y \leq n$ and $\gcd(x, y) = 1$. Let $r$ be the number of visible lattice points for this $n$. Compute the remainder when $95249 \cdot r$ is divided by $86778$. | 85,955 | graphs = [
Graph(
let={
"n": Const(73),
"result": VisibleLatticePoints(n=Ref(name='n')),
"_c": Const(95249),
"Q": Mod(value=Mul(Ref("_c"), Ref("result")), modulus=Const(86778)),
},
goal=Ref("Q"),
)
] | GEOM | null | COUNT | sympy | [] | geo_visible_lattice_v1 | null | 5 | 0 | null | null | 0.716 | 2026-02-08T06:25:59.544417Z | {
"verified": true,
"answer": 85955,
"timestamp": "2026-02-08T06:26:00.260646Z"
} | 3dede5 | 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": 9447
},
"timestamp": "2026-02-24T06:14:33.931Z",
"answer": 85955
},
{
"... | 1 | [] | {
"lo": -0.06,
"mid": 2.89,
"hi": 5.27
} |
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