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 |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
40ff6a | lin_form_endings_v1_1520064083_4764 | Let $ a = 98 $ and $ b = 42 $. Let $ g = \gcd(a, b) $. Let $ k = 10420 $. Define $ s = k \cdot g $. Compute the remainder when $ s $ is divided by 68024. | 9,832 | graphs = [
Graph(
let={
"a_coeff": Const(98),
"b_coeff": Const(42),
"_inner_result": GCD(a=Ref("a_coeff"), b=Ref("b_coeff")),
"_scale_k": Const(10420),
"_scaled": Mul(Ref("_scale_k"), Ref("_inner_result")),
"_mod_M": Const(68024),
... | COMB | NT | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | lin_form_endings_v1 | null | 2 | null | [
"LIN_FORM"
] | 1 | 0.001 | 2026-02-08T06:25:38.383706Z | {
"verified": true,
"answer": 9832,
"timestamp": "2026-02-08T06:25:38.384234Z"
} | a588a8 | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 158,
"completion_tokens": 342
},
"timestamp": "2026-02-19T08:14:57.611Z",
"answer": 19560
},
{
"id": 11... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
}
] | {
"lo": -5.92,
"mid": -3.14,
"hi": 0.27
} | ||
86ecab | lin_form_endings_v1_1248542787_965 | Let $a = 75$ and $b = 105$. Let $L$ be the least common multiple of $a$ and $b$. Let $k = 5325$ and let $M = 56622$. Compute the remainder when $k \cdot L$ is divided by $M$. | 21,147 | graphs = [
Graph(
let={
"a_coeff": Const(75),
"b_coeff": Const(105),
"_inner_result": LCM(a=Ref("a_coeff"), b=Ref("b_coeff")),
"_scale_k": Const(5325),
"_scaled": Mul(Ref("_scale_k"), Ref("_inner_result")),
"_mod_M": Const(56622),
... | COMB | NT | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | lin_form_endings_v1 | null | 2 | null | [
"LIN_FORM"
] | 1 | 0 | 2026-02-08T03:31:02.359863Z | {
"verified": true,
"answer": 21147,
"timestamp": "2026-02-08T03:31:02.360194Z"
} | 4d6f2f | 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": 719
},
"timestamp": "2026-02-09T10:37:14.034Z",
"answer": 21147
},
{
"i... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "V8",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
... | {
"lo": -3.46,
"mid": 1.03,
"hi": 5.49
} | ||
da1f1e | comb_count_surjections_v1_1820931509_784 | Let $n = 7$ and $k = 3$. Define $\text{result} = k! \cdot S(n, k)$, where $S(n, k)$ is the Stirling number of the second kind. Let $Q$ be the number of ordered pairs $(a, b)$ of positive integers such that $1 \leq a \leq 96$ and $1 \leq b \leq 96$, minus $\text{result}$. Compute the value of $Q$. | 7,410 | graphs = [
Graph(
let={
"n": Const(7),
"k": Const(3),
"result": Mul(Factorial(Ref("k")), Stirling2(n=Ref(name='n'), k=Ref(name='k'))),
"Q": Sub(CountOverSet(set=CartesianProduct(left=IntegerRange(start=Const(1), end=Const(96)), right=IntegerRange(start=Const(1... | COMB | null | COUNT | sympy | COUNT_CARTESIAN | [
"COUNT_CARTESIAN"
] | 009729 | comb_count_surjections_v1 | negation_mod | 3 | 0 | [
"COUNT_CARTESIAN"
] | 1 | 0.001 | 2026-02-08T11:52:51.461707Z | {
"verified": true,
"answer": 7410,
"timestamp": "2026-02-08T11:52:51.463120Z"
} | be3cb7 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 218,
"completion_tokens": 822
},
"timestamp": "2026-02-24T15:00:57.696Z",
"answer": 7410
},
{
"id... | 1 | [
{
"lemma": "COUNT_CARTESIAN",
"status": "ok"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
},
{
"lemma": "V8_SUM",
"status"... | {
"lo": -4.92,
"mid": -2.91,
"hi": -0.68
} | ||
3e7465 | comb_binomial_compute_v1_601307018_10464 | Let $n$ be the number of ordered pairs $(a, b)$ of positive integers with $1 \le a, b \le 25$ such that $17a^4 + 102a^2b^2 + 68a^3b + 68ab^3 + 17b^4 = 31860737$. Let $M = \binom{n}{7}$. Find the remainder when $44121M$ is divided by $77260$. | 70,932 | graphs = [
Graph(
let={
"_n": Const(102),
"n": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("a"), Var("b")]), condition=And(Geq(Var("a"), Const(1)), Leq(Var("a"), Const(25)), Geq(Var("b"), Const(1)), Leq(Var("b"), Const(25)), Eq(Sum(Mul(Ref("_n"), Pow(Var("a"), Const(2)), Po... | COMB | null | COMPUTE | sympy | POLY4_COUNT | [
"POLY4_COUNT"
] | 861d91 | comb_binomial_compute_v1 | null | 6 | 0 | [
"POLY4_COUNT"
] | 1 | 0.004 | 2026-03-10T10:57:34.537689Z | {
"verified": true,
"answer": 70932,
"timestamp": "2026-03-10T10:57:34.541508Z"
} | a02603 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 211,
"completion_tokens": 2695
},
"timestamp": "2026-04-19T13:51:08.204Z",
"answer": 70932
},
{
... | 1 | [
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "POLY4_COUNT",
"status": "ok"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8_SUM",
... | {
"lo": -5.34,
"mid": 1.1,
"hi": 7.53
} | ||
a02d55 | comb_binomial_compute_v1_677425708_2542 | Let $n$ be the largest prime number at most 13. Compute $\binom{n}{6}$. | 1,716 | graphs = [
Graph(
let={
"_n": Const(13),
"n": MaxOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(2)), Leq(Var("n"), Ref("_n")), IsPrime(Var("n"))))),
"k": Const(6),
"result": Binom(n=Ref("n"), k=Ref("k")),
},
goal=Ref("... | NT | null | COMPUTE | sympy | MAX_PRIME_BELOW | [
"MAX_PRIME_BELOW"
] | dc3ad3 | comb_binomial_compute_v1 | null | 3 | 0 | [
"MAX_PRIME_BELOW"
] | 1 | 0.001 | 2026-02-08T05:06:57.931892Z | {
"verified": true,
"answer": 1716,
"timestamp": "2026-02-08T05:06:57.933205Z"
} | bb9745 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 134,
"completion_tokens": 314
},
"timestamp": "2026-02-11T22:51:43.885Z",
"answer": 1716
},
{
"i... | 1 | [
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "V8",
"stat... | {
"lo": -5.55,
"mid": -3.01,
"hi": 0.33
} | ||
64340f | diophantine_fbi2_min_v1_971394319_392 | Let $m = 21$ and $k = 24$. Let $N$ be the number of positive integers $k_1$ such that $1 \leq k_1 \leq 17136$ and $24$ divides $k_1$. Let $U$ be the number of positive integers $k_2$ such that $1 \leq k_2 \leq N$ and $m$ divides $k_2$. Find the smallest positive integer $d$ such that $6 \leq d \leq U$, $d$ divides $k$,... | 6 | graphs = [
Graph(
let={
"_m": Const(21),
"_n": CountOverSet(set=SolutionsSet(var=Var("k"), condition=And(Geq(Var("k"), Const(1)), Leq(Var("k"), Const(17136)), Divides(divisor=Const(24), dividend=Var("k"))), domain='positive_integers')),
"k": Const(24),
"upper"... | NT | null | EXTREMUM | sympy | ONE_PHI_2 | [
"C2/C2"
] | c8a699 | diophantine_fbi2_min_v1 | null | 4 | 0 | [
"C2",
"ONE_PHI_2"
] | 2 | 0.035 | 2026-02-08T13:03:22.482855Z | {
"verified": true,
"answer": 6,
"timestamp": "2026-02-08T13:03:22.517443Z"
} | 63a284 | 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": 613
},
"timestamp": "2026-02-15T08:51:41.553Z",
"answer": 6
},
{
... | 1 | [
{
"lemma": "C2",
"status": "ok"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
}
] | {
"lo": -6.96,
"mid": -4.56,
"hi": -1.46
} | ||
9022b7 | nt_max_prime_below_v1_784195855_9343 | Let $ S $ be the set of all positive integers $ p $ for which there exists a positive integer $ q $ such that $ p \cdot q = 108 $, $ \gcd(p, q) = 1 $, and $ p < q $. Let $ m $ be the number of elements in $ S $. Let $ T $ be the set of all prime numbers $ n $ such that $ m \leq n \leq 47524 $. Determine the value of $ ... | 51,167 | graphs = [
Graph(
let={
"upper": Const(47524),
"result": MaxOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), CountOverSet(set=SolutionsSet(var=Var("p"), condition=And(IsPositive(arg=Var(name='p')), Exists(var=Var(name='q'), condition=And(Eq(left=Mul(Var(name='p'), V... | NT | null | EXTREMUM | sympy | COPRIME_PAIRS | [
"COPRIME_PAIRS"
] | 2bb3aa | nt_max_prime_below_v1 | null | 4 | 0 | [
"COPRIME_PAIRS"
] | 1 | 1.106 | 2026-02-08T16:43:58.775362Z | {
"verified": true,
"answer": 51167,
"timestamp": "2026-02-08T16:43:59.881677Z"
} | 99e62b | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 166,
"completion_tokens": 2511
},
"timestamp": "2026-02-17T11:29:14.590Z",
"answer": 51167
},
... | 1 | [
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "V1",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
b5474e | comb_bell_compute_v1_124444284_7966 | Let $a$ be the Bell number $B_9$, the number of partitions of a set of 9 elements. Let $c$ be the minimum value of $x + y$ over all ordered pairs of positive integers $(x, y)$ such that $xy = 2500$. Compute the remainder when $c - a$ is divided by 59676. | 38,629 | graphs = [
Graph(
let={
"n": Const(9),
"result": Bell(Ref("n")),
"_c": MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(Mul(Var("x"), Var("y")), Const(2500))... | COMB | null | COMPUTE | sympy | B3 | [
"B3"
] | fc629c | comb_bell_compute_v1 | negation_mod | 5 | 0 | [
"B3"
] | 1 | 0.001 | 2026-02-08T09:29:08.207784Z | {
"verified": true,
"answer": 38629,
"timestamp": "2026-02-08T09:29:08.208828Z"
} | e31d96 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 186,
"completion_tokens": 630
},
"timestamp": "2026-02-24T11:18:56.861Z",
"answer": 38629
},
{
"i... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
}
] | {
"lo": -3.84,
"mid": -1.67,
"hi": 1.32
} | ||
339d48 | nt_min_coprime_above_v1_1978505735_3988 | Let $\text{start} = 50625$ and $\text{upper} = 50772$. Let $d_{\text{min}}$ be the smallest divisor of $58765536377$ that is at least $2$. Find the smallest integer $n$ such that $n > \text{start}$, $n \leq \text{upper}$, and $\gcd(n, d_{\text{min}}) = 1$. | 50,626 | graphs = [
Graph(
let={
"start": Const(50625),
"upper": Const(50772),
"modulus": MinOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Const(2)), Divides(divisor=Var("d"), dividend=Const(58765536377))))),
"result": MinOverSet(set=SolutionsSet(v... | NT | null | EXTREMUM | sympy | MIN_PRIME_FACTOR | [
"MIN_PRIME_FACTOR"
] | bc3776 | nt_min_coprime_above_v1 | null | 4 | 0 | [
"MIN_PRIME_FACTOR"
] | 1 | 0.016 | 2026-02-08T17:58:21.960048Z | {
"verified": true,
"answer": 50626,
"timestamp": "2026-02-08T17:58:21.975732Z"
} | c4b590 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 136,
"completion_tokens": 1768
},
"timestamp": "2026-02-18T10:43:24.557Z",
"answer": 50626
},
... | 1 | [
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "MIN_PRIME_FACTOR",
"status": "ok"
},
{
"lemma": "V5",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
4f2730 | modular_mod_compute_v1_458359167_2407 | Let $S$ be the set of all ordered pairs $(x, y)$ of positive integers such that $x \cdot y = 640000$. Let $n$ be the minimum value of $x + y$ as $(x, y)$ ranges over $S$. Let $a$ be the largest positive divisor $d$ of $2561600$ such that $1 \leq d \leq n$. Let $T$ be the set of all ordered pairs $(x, y)$ of positive in... | 1,600 | graphs = [
Graph(
let={
"_m": Const(98),
"_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(640000)))), expr=Sum(Var("x"), Var("y"))))... | NT | null | COMPUTE | sympy | B3 | [
"B3/MAX_DIVISOR",
"B1"
] | c7fece | modular_mod_compute_v1 | null | 6 | 0 | [
"B1",
"B3",
"MAX_DIVISOR"
] | 3 | 0.005 | 2026-02-08T05:23:33.488170Z | {
"verified": true,
"answer": 1600,
"timestamp": "2026-02-08T05:23:33.493612Z"
} | 2310bf | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 198,
"completion_tokens": 1702
},
"timestamp": "2026-02-12T08:02:48.072Z",
"answer": 1600
},
{... | 1 | [
{
"lemma": "B1",
"status": "ok"
},
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "MAX_DIVISOR",
"status": "ok_later"
},
{
"lemma": "V3",
"status": "no"
},
{
... | {
"lo": -5.55,
"mid": -3.01,
"hi": 0.32
} | ||
074ed8 | modular_modexp_compute_v1_349078426_1611 | Let $T$ be the set of all ordered pairs $(x,y)$ of positive integers such that $xy = 1234321$. Let $s_{\min}$ be the minimum value of $x + y$ over all such pairs. Let $e$ be the number of ordered pairs $(x_1, x_2)$ of positive odd integers such that $x_1 + x_2 = s_{\min}$. Define $a = 19$ and $m = 16900$. Let $r$ be th... | 17,906 | graphs = [
Graph(
let={
"_n": MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(Mul(Var("x"), Var("y")), Const(1234321)))), expr=Sum(Var("x"), Var("y")))),
"a": Const(19)... | NT | null | COMPUTE | sympy | B3 | [
"B3/COMB1"
] | e26f7e | modular_modexp_compute_v1 | null | 6 | 0 | [
"B3",
"COMB1"
] | 2 | 0.014 | 2026-02-08T13:45:55.286665Z | {
"verified": true,
"answer": 17906,
"timestamp": "2026-02-08T13:45:55.300305Z"
} | 5485fe | 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": 2999
},
"timestamp": "2026-02-15T20:48:26.648Z",
"answer": 17906
},
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "COMB1",
"status": "ok_later"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K5",
"sta... | {
"lo": -5.49,
"mid": 0.22,
"hi": 6.51
} | ||
c7a259 | algebra_poly_eval_v1_1978505735_6444 | Let $x = 12$. Compute the value of $x^4 + 2x^3 + 2x^2 + 7x - 7$. Let $c$ be the sum of the integers from 1 to 125. Find the remainder when the product of $c$ and the computed value is divided by 80851. | 71,634 | graphs = [
Graph(
let={
"_n": Const(4),
"x": Const(12),
"result": Sum(Pow(Ref("x"), Ref("_n")), Mul(Const(2), Pow(Ref("x"), Const(3))), Mul(Const(2), Pow(Ref("x"), Const(2))), Mul(Const(7), Ref("x")), Const(-7)),
"_c": Summation(var="k", start=Const(1), end=Co... | NT | null | COMPUTE | sympy | SUM_ARITHMETIC | [
"SUM_ARITHMETIC"
] | 349fee | algebra_poly_eval_v1 | affine_mod | 2 | 0 | [
"SUM_ARITHMETIC"
] | 1 | 0.002 | 2026-02-08T19:36:09.706556Z | {
"verified": true,
"answer": 71634,
"timestamp": "2026-02-08T19:36:09.708871Z"
} | 915b0b | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 120,
"completion_tokens": 1271
},
"timestamp": "2026-02-18T22:56:27.135Z",
"answer": 71634
},
... | 1 | [
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "SUM_ARITHMETIC",
"status": "ok"
},
{
"lemma": "V1",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
866196 | nt_sum_over_divisible_v1_458359167_1886 | Let $n_0 = 2$. Let $u$ be the smallest divisor $d$ of $26009999$ such that $d \geq n_0$. Compute the sum of all positive integers $n$ from $1$ to $u$ that are divisible by $165$. | 76,725 | graphs = [
Graph(
let={
"_n": Const(2),
"upper": MinOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Ref("_n")), Divides(divisor=Var("d"), dividend=Const(26009999))))),
"divisor": Const(165),
"result": SumOverSet(set=SolutionsSet(var=Var("n")... | NT | null | SUM | sympy | MOBIUS_SUM | [
"MIN_PRIME_FACTOR"
] | bc3776 | nt_sum_over_divisible_v1 | null | 3 | 0 | [
"MIN_PRIME_FACTOR",
"MOBIUS_SUM"
] | 2 | 5.243 | 2026-02-08T04:55:23.374117Z | {
"verified": true,
"answer": 76725,
"timestamp": "2026-02-08T04:55:28.617302Z"
} | caea34 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 172,
"completion_tokens": 6175
},
"timestamp": "2026-02-11T22:27:27.738Z",
"answer": 76725
},
{
"... | 1 | [
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "MIN_PRIME_FACTOR",
"status": "ok"
... | {
"lo": -3.45,
"mid": 1.15,
"hi": 6.18
} | ||
a78ab6 | geo_count_lattice_rect_v1_124444284_6387 | Let $ a = 64 $ and $ b = 99 $. Define $ \text{result} $ to be the number of lattice points $ (x, y) $ such that $ 0 \leq x \leq a $ and $ 0 \leq y \leq b $. Let $ c = 73353 $. Compute the remainder when $ c \cdot \text{result} $ is divided by $ 92552 $. | 59,148 | graphs = [
Graph(
let={
"a": Const(64),
"b": Const(99),
"result": LatticePointsRect(a=Ref(name='a'), b=Ref(name='b')),
"_c": Const(73353),
"Q": Mod(value=Mul(Ref("_c"), Ref("result")), modulus=Const(92552)),
},
goal=Ref("Q"),
)
... | GEOM | null | COUNT | sympy | [] | geo_count_lattice_rect_v1 | null | 3 | 0 | null | null | 0.001 | 2026-02-08T08:18:57.246177Z | {
"verified": true,
"answer": 59148,
"timestamp": "2026-02-08T08:18:57.246944Z"
} | 602d89 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 204,
"completion_tokens": 1530
},
"timestamp": "2026-02-24T09:22:08.330Z",
"answer": 59148
},
{
"... | 1 | [] | {
"lo": -2.35,
"mid": 1.22,
"hi": 4.84
} | ||||
594661_l | geo_count_lattice_triangle_v1_50713871_31 | Let $A$ be the absolute value of
$$120\cdot 120 + 225\cdot(0-3).$$
Let $C$ be the value of
$$\sum_{k=0}^{8}(-1)^k\binom{8}{k}.$$
Let $D$ be the number of integers $t$ with $10 \le t \le 246$ for which there exist integers $a$ and $b$ satisfying $1 \le a \le 19$, $1 \le b \le 27$, and
$$t = 3a + 7b.$$
Let $E$ be the nu... | 6,859 | COMB | NT | COUNT | sympy | BINOMIAL_ALTERNATING | [
"BINOMIAL_ALTERNATING",
"COUNT_CARTESIAN",
"LIN_FORM"
] | f7c074 | geo_count_lattice_triangle_v1 | null | 8 | 0 | [
"BINOMIAL_ALTERNATING",
"COUNT_CARTESIAN",
"LIN_FORM"
] | 3 | 0.01 | 2026-02-08T02:43:43.991960Z | {
"verified": false,
"answer": 6853,
"timestamp": "2026-02-08T02:43:44.002382Z"
} | 5e45e8 | 594661 | legacy_text | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 381,
"completion_tokens": 1483
},
"timestamp": "2026-02-08T19:45:09.031Z",
"answer": 6859
},
{
... | 0 | [
{
"lemma": "BINOMIAL_ALTERNATING",
"status": "ok"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "ok"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemm... | {
"lo": 5.41,
"mid": 7.53,
"hi": 10
} | |
c8612a | geo_count_lattice_triangle_v1_1918700295_1170 | Let $m = 100$. Let $n$ be the number of prime numbers between 2 and 26, inclusive. Define the quantity
$$
\text{area}_{2x} = \left| 120 \cdot m + 4 \cdot (0 - 49) \right|.
$$
Define the boundary value as
$$
\text{boundary} = \gcd(|120|, |49|) + \gcd(|4 - 120|, |100 - t_0|) + \gcd(|0 - 4|, |0 - 100|),
$$
where $t_0$ is ... | 11,492 | graphs = [
Graph(
let={
"_m": Const(100),
"_n": SumOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(2)), Leq(Var("n"), Const(26)), IsPrime(Var("n"))))),
"area_2x": Abs(arg=Sum(Mul(Const(value=120), Ref(name='_m')), Mul(Const(value=4), Sub(left=Cons... | NT | null | COUNT | sympy | SUM_PRIMES | [
"SUM_PRIMES/LIN_FORM"
] | 9278c1 | geo_count_lattice_triangle_v1 | null | 6 | 0 | [
"LIN_FORM",
"SUM_PRIMES"
] | 2 | 0.009 | 2026-02-08T05:37:49.132482Z | {
"verified": true,
"answer": 11492,
"timestamp": "2026-02-08T05:37:49.141203Z"
} | 59adc8 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 307,
"completion_tokens": 3480
},
"timestamp": "2026-02-12T11:05:07.045Z",
"answer": 11492
},
... | 1 | [
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok_later"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"... | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
52ec10 | alg_poly_orbit_hensel_v1_1218484723_6065 | For each integer $a$, define
\begin{align*}
N &\equiv a^{2} - 3099 \pmod{6859},\\
M &\equiv N^{2} - 3099 \pmod{6859},\\
R &\equiv M^{2} - 3099 \pmod{6859}.
\end{align*}
Let $Q$ be the number of integers $a$ with $0 \le a \le 8909840$ such that $R = a$, $N \ne a$, and $M \ne a$. Find $Q$. | 3,897 | graphs = [
Graph(
let={
"p1": Mod(value=Sum(Pow(Var("a"), Const(2)), Const(-3099)), modulus=Const(6859)),
"p2": Mod(value=Sum(Pow(Ref("p1"), Const(2)), Const(-3099)), modulus=Const(6859)),
"p3": Mod(value=Sum(Pow(Ref("p2"), Const(2)), Const(-3099)), modulus=Const(6859)),
... | ALG | null | COUNT | sympy | POLY_ORBIT_COUNT | [
"POLY_ORBIT_COUNT"
] | 4ad965 | alg_poly_orbit_hensel_v1 | null | 7 | null | [
"POLY_ORBIT_COUNT"
] | 1 | 0.021 | 2026-02-25T07:41:52.441086Z | {
"verified": true,
"answer": 3897,
"timestamp": "2026-02-25T07:41:52.462484Z"
} | d026a3 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 243,
"completion_tokens": 32768
},
"timestamp": "2026-03-30T00:04:56.227Z",
"answer": null
},
{
... | 1 | [
{
"lemma": "POLY_ORBIT_COUNT",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
}
] | {
"lo": 1.53,
"mid": 4.7,
"hi": 7.23
} | ||
1c4dca | antilemma_k2_v1_124444284_10033 | Let $n = 134$. Compute the sum $\sum_{d \mid n} \phi(d)$, where $\phi$ denotes Euler's totient function. Denote this sum by $m$. Then compute the sum
$$
\sum_{k=1}^{m} \phi(k) \left\lfloor \frac{134}{k} \right\rfloor.
$$
Find the value of this sum. | 9,045 | graphs = [
Graph(
let={
"_n": Const(134),
"x": Summation(var="k", start=Const(1), end=SumOverDivisors(n=Ref(name='_n'), var='d', expr=EulerPhi(n=Var(name='d'))), expr=Mul(EulerPhi(n=Var("k")), Floor(Div(Const(134), Var("k"))))),
},
goal=Ref("x"),
)
] | NT | COMB | COMPUTE | sympy | K3 | [
"K3/K2",
"K2"
] | c7f244 | antilemma_k2_v1 | null | 5 | 0 | [
"K2",
"K3"
] | 2 | 0.001 | 2026-02-08T12:47:34.328270Z | {
"verified": true,
"answer": 9045,
"timestamp": "2026-02-08T12:47:34.329349Z"
} | a80585 | 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": 850
},
"timestamp": "2026-02-15T05:27:43.363Z",
"answer": 9045
},
{
... | 1 | [
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "K2",
"status": "ok"
},
{
"lemma": "K3",
"status": "ok"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "V3",
"status": "no"
},
{
"lemma": "V8_SUM",
"st... | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
cc55b4 | diophantine_fbi2_count_v1_2051736721_3154 | Let $k = 360$. Determine the number of positive integers $d$ such that $5 \leq d \leq 81$, $d$ divides $k$, and the quotient $k/d$ is at least $2$ and at most $\sum_{k_1=1}^{12} k_1$. Compute this number. | 16 | graphs = [
Graph(
let={
"_n": Const(2),
"k": Const(360),
"result": CountOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Const(5)), Leq(Var("d"), Const(81)), Divides(divisor=Var("d"), dividend=Ref("k")), Geq(Div(Ref("k"), Var("d")), Ref("_n")), Leq(Div(R... | NT | null | COUNT | sympy | SUM_ARITHMETIC | [
"SUM_ARITHMETIC"
] | eb34f0 | diophantine_fbi2_count_v1 | null | 4 | 0 | [
"SUM_ARITHMETIC"
] | 1 | 0.012 | 2026-02-08T17:08:41.169883Z | {
"verified": true,
"answer": 16,
"timestamp": "2026-02-08T17:08:41.181724Z"
} | 33ca02 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 117,
"completion_tokens": 1046
},
"timestamp": "2026-02-17T20:43:25.860Z",
"answer": 16
},
{
... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "SUM_ARITHMETIC",
"status": "ok"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
83fcde | modular_inverse_v1_151522320_1540 | Let $S$ be the set of all prime numbers $n$ such that $2 \leq n \leq 1649$. Define $U$ to be the set of all positive integers $n$ such that $1 \leq n \leq \max(S)$ and $\gcd(n, 6) = 1$. Let $m = |U|$. Find the smallest positive integer $x$ such that $1 \leq x \leq m$ and $134x \equiv 1 \pmod{547}$. | 298 | graphs = [
Graph(
let={
"_n": Const(6),
"a": Const(134),
"m": Const(547),
"upper": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), MaxOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(2)),... | NT | null | EXTREMUM | sympy | MAX_PRIME_BELOW | [
"MAX_PRIME_BELOW/C4"
] | a99ef8 | modular_inverse_v1 | null | 6 | 0 | [
"C4",
"MAX_PRIME_BELOW"
] | 2 | 0.052 | 2026-02-08T04:05:03.100170Z | {
"verified": true,
"answer": 298,
"timestamp": "2026-02-08T04:05:03.151882Z"
} | 1a7a9e | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 227,
"completion_tokens": 2093
},
"timestamp": "2026-02-10T15:19:45.226Z",
"answer": 298
},
{
"i... | 1 | [
{
"lemma": "C4",
"status": "ok_later"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "V8_SUM",
"stat... | {
"lo": -3.49,
"mid": 1.84,
"hi": 7.55
} | ||
f294ea | nt_count_divisible_v1_1520064083_638 | Let $d$ be the smallest integer greater than or equal to 2 that divides 5929. Compute the number of positive integers $n$ such that $1 \leq n \leq 45360$ and $n$ is divisible by $d$. | 6,480 | graphs = [
Graph(
let={
"_n": Const(2),
"upper": Const(45360),
"divisor": MinOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Ref("_n")), Divides(divisor=Var("d"), dividend=Const(5929))))),
"result": CountOverSet(set=SolutionsSet(var=Var("n")... | NT | null | COUNT | sympy | MIN_PRIME_FACTOR | [
"MIN_PRIME_FACTOR"
] | bc3776 | nt_count_divisible_v1 | null | 3 | 0 | [
"MIN_PRIME_FACTOR"
] | 1 | 1.449 | 2026-02-08T03:30:43.262230Z | {
"verified": true,
"answer": 6480,
"timestamp": "2026-02-08T03:30:44.711538Z"
} | 2b7841 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 165,
"completion_tokens": 543
},
"timestamp": "2026-02-10T14:39:16.419Z",
"answer": 6480
},
{
"id... | 1 | [
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "MIN_PRIME_FACTOR",
"status": "ok"
},
{
"lemma": "V5",
"status": "no"
},
{
"lemma": "VAL_SUM... | {
"lo": -7.01,
"mid": -4.68,
"hi": -2.15
} | ||
6efecc | nt_sum_over_divisible_v1_1978505735_3006 | Let $d$ be a positive integer such that $1 \leq d \leq 5879$ and $d$ divides $34703737$. Let $\text{upper}$ be the largest such $d$. Determine the sum of all positive integers $n$ such that $1 \leq n \leq \text{upper}$ and $n$ is divisible by $197$. | 85,695 | graphs = [
Graph(
let={
"_n": Const(5879),
"upper": MaxOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Const(1)), Leq(Var("d"), Ref("_n")), Divides(divisor=Var("d"), dividend=Const(34703737))))),
"divisor": Const(197),
"result": SumOverSet(s... | NT | null | SUM | sympy | MAX_PRIME_BELOW | [
"MAX_DIVISOR"
] | 51757e | nt_sum_over_divisible_v1 | null | 3 | 0 | [
"MAX_DIVISOR",
"MAX_PRIME_BELOW"
] | 2 | 3.506 | 2026-02-08T17:18:14.276471Z | {
"verified": true,
"answer": 85695,
"timestamp": "2026-02-08T17:18:17.782619Z"
} | 2723e5 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 125,
"completion_tokens": 1438
},
"timestamp": "2026-02-18T00:28:21.888Z",
"answer": 85695
},
... | 1 | [
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "MAX_DIVISOR",
"status": "ok"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "n... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
fc151b | lin_form_endings_v1_1915831931_1128 | Compute the remainder when $10957 \cdot \text{lcm}(20, 30)$ is divided by $50760$. | 48,300 | graphs = [
Graph(
let={
"a_coeff": Const(20),
"b_coeff": Const(30),
"_inner_result": LCM(a=Ref("a_coeff"), b=Ref("b_coeff")),
"_scale_k": Const(10957),
"_scaled": Mul(Ref("_scale_k"), Ref("_inner_result")),
"_mod_M": Const(50760),
... | COMB | NT | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | lin_form_endings_v1 | null | 2 | null | [
"LIN_FORM"
] | 1 | 0.001 | 2026-02-08T15:54:05.328210Z | {
"verified": true,
"answer": 48300,
"timestamp": "2026-02-08T15:54:05.329318Z"
} | 7b593a | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 73,
"completion_tokens": 1057
},
"timestamp": "2026-02-16T16:32:27.175Z",
"answer": 48300
},
{... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
1fed6c | modular_modexp_compute_v1_124444284_4573 | Let $d$ be an integer divisor of $1573$ such that $d \geq 2$. Let $a$ be the smallest such $d$. Define $e = 377$ and $m = 20000$. Let $r$ be the remainder when $a^e$ is divided by $m$. Compute the remainder when $21147 \cdot r$ is divided by $83275$. | 47,612 | graphs = [
Graph(
let={
"_n": Const(21147),
"a": MinOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Const(2)), Divides(divisor=Var("d"), dividend=Const(1573))))),
"e": Const(377),
"m": Const(20000),
"result": ModExp(base=Ref("a")... | NT | null | COMPUTE | sympy | MIN_PRIME_FACTOR | [
"MIN_PRIME_FACTOR"
] | bc3776 | modular_modexp_compute_v1 | null | 4 | 0 | [
"MIN_PRIME_FACTOR"
] | 1 | 0.003 | 2026-02-08T06:05:27.894725Z | {
"verified": true,
"answer": 47612,
"timestamp": "2026-02-08T06:05:27.897882Z"
} | 7c94ea | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 132,
"completion_tokens": 3493
},
"timestamp": "2026-02-12T20:31:08.464Z",
"answer": 47612
},
... | 1 | [
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "MIN_PRIME_FACTOR",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "V3",
"status": "no"
}
] | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
82524f | comb_factorial_compute_v1_1218484723_6039 | Let $M$ be the number of ordered pairs $(a, b)$ of positive integers with $1 \le a, b \le 35$ such that $10a^2 - 18ab + 25b^2 \le 3617$. Let $n$ be the number of ordered pairs $(a_1, b_1)$ of positive integers with $1 \le a_1 \le b_1 \le 10$ such that $32b_1^2 + 32a_1^2 - 64a_1b_1 = M$. Compute $14884 - n!$. | 9,844 | graphs = [
Graph(
let={
"_m": Const(32),
"_n": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("a"), Var("b")]), condition=And(Geq(Var("a"), Const(1)), Leq(Var("a"), Const(35)), Geq(Var("b"), Const(1)), Leq(Var("b"), Const(35)), Leq(Sum(Mul(Const(10), Pow(Var("a"), Const(2))), ... | COMB | null | COMPUTE | sympy | QF_PSD_COUNT_LEQ | [
"QF_PSD_COUNT_LEQ/QF_PSD_ORBIT"
] | b96baf | comb_factorial_compute_v1 | null | 4 | 0 | [
"QF_PSD_COUNT_LEQ",
"QF_PSD_ORBIT"
] | 2 | 0.007 | 2026-02-25T07:40:07.130380Z | {
"verified": true,
"answer": 9844,
"timestamp": "2026-02-25T07:40:07.137181Z"
} | b1087c | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 241,
"completion_tokens": 23909
},
"timestamp": "2026-03-29T23:58:20.664Z",
"answer": 9844
},
{
"... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "QF_PSD_COUNT_LEQ",
"status": "ok"
},
{
"lemma": "QF_PSD_ORBIT",
"status": "ok_later"
},
{
"lemma": "V7... | {
"lo": -3.33,
"mid": 1.03,
"hi": 5.26
} | ||
039c60_n | comb_count_partitions_v1_1218484723_6648 | A bakery sells gift boxes containing $a$ croissants and $b$ muffins, where $1 \leq a \leq 10$ and $1 \leq b \leq 5$. Each box is assigned a point value $t = 9a + 21b$. Only boxes with $30 \leq t \leq 195$ are eligible for a loyalty reward. Let $n$ be the number of distinct eligible point values. How many ways can $n$ b... | 75,175 | COMB | null | COUNT | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | comb_count_partitions_v1 | null | 5 | null | [
"LIN_FORM"
] | 1 | 0.003 | 2026-02-25T08:10:41.308216Z | null | cc4da1 | 039c60 | narrative | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 226,
"completion_tokens": 10628
},
"timestamp": "2026-03-31T01:40:55.117Z",
"answer": 74574
},
{
... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "V8",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
... | {
"lo": 3.8,
"mid": 6.33,
"hi": 9.49
} | |
289ca8 | comb_sum_binomial_row_v1_153355830_841 | Let $T$ be the set of all integers $t$ such that $14 \leq t \leq 16598$ and there exist positive integers $a$ and $b$ with $1 \leq a \leq 1067$, $1 \leq b \leq 1482$, and $t = 10a + 4b$. Let $m$ be the number of elements in $T$. Define $n$ as the number of nonnegative integers $j \leq m$ for which the binomial coeffici... | 65,536 | graphs = [
Graph(
let={
"_m": Const(2),
"_n": Const(2),
"n": CountOverSet(set=SolutionsSet(var=Var("j"), condition=And(Geq(Var("j"), Const(0)), Leq(Var("j"), CountOverSet(set=SolutionsSet(var=Var("t"), condition=Exists(var=Var(name='a'), condition=Exists(var=Var(name='b')... | ALG | COMB | SUM | sympy | LIN_FORM | [
"LIN_FORM/V8"
] | 654a7e | comb_sum_binomial_row_v1 | null | 7 | 0 | [
"LIN_FORM",
"V8"
] | 2 | 0.002 | 2026-02-08T04:11:34.280174Z | {
"verified": true,
"answer": 65536,
"timestamp": "2026-02-08T04:11:34.282395Z"
} | dbecb7 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 1,
"correct": {
"strict": false,
"boxed": false,
"relaxed": true
},
"usage": {
"prompt_tokens": 244,
"completion_tokens": 32768
},
"timestamp": "2026-02-23T23:45:19.794Z",
"answer": null
},
{
... | 1 | [
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "V8",
"status": "ok_later"
}
] | {
"lo": 1.97,
"mid": 4.36,
"hi": 6.69
} | ||
e79083 | nt_count_intersection_v1_655260480_337 | Let $N = 50000$. Let $S$ be the set of all ordered pairs $(x_1, x_2)$ of positive integers such that $x_1$ and $x_2$ are both odd and $x_1 + x_2 = 28$. Let $M$ be the number of elements in $S$. Now let $T$ be the set of all ordered pairs $(x_1, y_1)$ of positive integers such that $x_1 + y_1 = M$. Let $P$ be the maximu... | 7,143 | graphs = [
Graph(
let={
"N": Const(50000),
"a": Const(3),
"b": MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(Mul(Var("x"), Var("y")), MaxOverSet(set=MapOv... | NT | null | COUNT | sympy | COMB1 | [
"COMB1/B1/B3"
] | 8a5319 | nt_count_intersection_v1 | null | 6 | 0 | [
"B1",
"B3",
"COMB1"
] | 3 | 2.883 | 2026-02-08T15:21:14.290298Z | {
"verified": true,
"answer": 7143,
"timestamp": "2026-02-08T15:21:17.173236Z"
} | 9d42ac | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 276,
"completion_tokens": 1901
},
"timestamp": "2026-02-16T04:40:18.411Z",
"answer": 7143
},
{... | 1 | [
{
"lemma": "B1",
"status": "ok_later"
},
{
"lemma": "B3",
"status": "ok_later"
},
{
"lemma": "COMB1",
"status": "ok"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "M... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
01da9d | algebra_quadratic_discriminant_v1_601307018_8993 | Let $a$ be the number of ordered pairs $(a_1, b_1)$ of positive integers with $1 \leq a_1 \leq 20$ and $1 \leq b_1 \leq 20$ such that $$
68 a_1 b_1^3 + \max \{ d \geq 1 : d \mid 323,\, d^2 \leq 323 \} \cdot b_1^4 + 68 a_1^3 b_1 + 102 a_1^2 b_1^2 + 17 a_1^4 = 15699857.
$$ Let $D = 9^2 - 4a(-2)$ and $S = 2\cdot[D > 0] + ... | 35,318 | graphs = [
Graph(
let={
"_m": Const(68),
"_n": Const(4),
"a": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("a1"), Var("b1")]), condition=And(Geq(Var("a1"), Const(1)), Leq(Var("a1"), Const(20)), Geq(Var("b1"), Const(1)), Leq(Var("b1"), Const(20)), Eq(Sum(Mul(Ref("... | NT | null | COMPUTE | sympy | POLY_ORBIT_COUNT | [
"B3_CLOSEST/POLY4_COUNT"
] | d56cb5 | algebra_quadratic_discriminant_v1 | null | 6 | 0 | [
"B3_CLOSEST",
"POLY4_COUNT",
"POLY_ORBIT_COUNT"
] | 3 | 0.098 | 2026-03-10T09:25:42.835223Z | {
"verified": true,
"answer": 35318,
"timestamp": "2026-03-10T09:25:42.933681Z"
} | 71092d | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 320,
"completion_tokens": 1581
},
"timestamp": "2026-04-19T10:21:52.579Z",
"answer": 35318
},
{
... | 2 | [
{
"lemma": "B3_CLOSEST",
"status": "ok"
},
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
... | {
"lo": -10,
"mid": -5.89,
"hi": -1.79
} | ||
99d5c1 | comb_binomial_compute_v1_153355830_580 | Let $\mathcal{P}$ be the set of all positive integers $p$ for which there exists a positive integer $q$ such that
\begin{itemize}
\item $pq = 6$,
\item $\gcd(p,q) = 1$, and
\item $p < q$.
\end{itemize}
Let $c$ be the number of elements in $\mathcal{P}$.
Let $d$ range over the integers with $d \ge c$ such that $d... | 1,716 | graphs = [
Graph(
let={
"_c": 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=6)), Eq(left=GCD(a=Var(name='p'), b=Var(name='q')), right=Const(value=1)), L... | NT | null | COMPUTE | sympy | COPRIME_PAIRS | [
"COPRIME_PAIRS/MIN_PRIME_FACTOR/L3C/MAX_PRIME_BELOW"
] | 4a978a | comb_binomial_compute_v1 | null | 7 | 0 | [
"COPRIME_PAIRS",
"L3C",
"MAX_PRIME_BELOW",
"MIN_PRIME_FACTOR"
] | 4 | 0.004 | 2026-02-08T03:10:34.150022Z | {
"verified": true,
"answer": 1716,
"timestamp": "2026-02-08T03:10:34.154030Z"
} | 4e47f7 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 359,
"completion_tokens": 7903
},
"timestamp": "2026-02-10T15:15:00.933Z",
"answer": 1716
},
{
"... | 1 | [
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "L3C",
"status": "ok_later"
},
{
"lemma": "LTE_DIFF_P2",
"... | {
"lo": -3.42,
"mid": 1.86,
"hi": 7.55
} | ||
7e9c70 | alg_poly3_min_v1_1218484723_903 | Let $Q$ be the minimum value of $$7344b^3 + 18360ab^2 + 20196a^{\min\{5b_1^2 - 28a_1b_1 + 41a_1^2 : 1 \leq a_1, b_1 \leq 5\}} b + \left(\min\{x + y : x, y > 0,\ xy = 10323369\}\right) a^3$$ over all ordered pairs $(a, b)$ of positive integers with $1 \leq a, b \leq 103$. Find $Q$. | 52,326 | graphs = [
Graph(
let={
"_m": Const(7344),
"_n": Const(3),
"result": MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("a"), Var("b")]), condition=And(Geq(Var("a"), Const(1)), Leq(Var("a"), Const(103)), Geq(Var("b"), Const(1)), Leq(Var("b"), Const(103))))... | ALG | null | COMPUTE | sympy | QF_PSD_MIN | [
"QF_PSD_MIN",
"B3"
] | 8ca15d | alg_poly3_min_v1 | null | 6 | 0 | [
"B3",
"QF_PSD_MIN"
] | 2 | 0.032 | 2026-02-25T02:37:18.278699Z | {
"verified": true,
"answer": 52326,
"timestamp": "2026-02-25T02:37:18.310694Z"
} | aa9b55 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 249,
"completion_tokens": 32768
},
"timestamp": "2026-03-10T02:46:47.506Z",
"answer": null
},
{
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "QF_PSD_MIN",
"status": "ok"
}
] | {
"lo": -0.93,
"mid": 2.04,
"hi": 4.6
} | ||
efd284_n | comb_binomial_compute_v1_1218484723_5406 | A digital lock has a sequence of 4 switches, each representing a power of 2 from $2^0$ to $2^3$. When all switches are set to 'on', the total value is $n$. The lock requires selecting 7 unique codes from a set of $n$ base codes to generate a master key. The number of ways to choose these 7 codes is $R$. If the final se... | 57,105 | COMB | null | COMPUTE | sympy | SUM_GEOM | [
"SUM_GEOM"
] | 04214c | comb_binomial_compute_v1 | null | 2 | null | [
"SUM_GEOM"
] | 1 | 0.001 | 2026-02-25T06:58:37.137733Z | null | 26b360 | efd284 | narrative | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 221,
"completion_tokens": 1612
},
"timestamp": "2026-03-30T23:24:14.354Z",
"answer": 57105
},
{
"... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "SUM_GEOM",
"status": "ok"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
... | {
"lo": -5.37,
"mid": 0.23,
"hi": 5.22
} | |
642574 | modular_mod_compute_v1_1918700295_3805 | Let $a$ be the number of positive integers $p$ such that there exists a positive integer $q$ with $p < q$, $\gcd(p, q) = 1$, and $pq = 806682376500$. Compute the remainder when $a$ is divided by $33489$. | 64 | graphs = [
Graph(
let={
"a": CountOverSet(set=SolutionsSet(var=Var("p"), condition=And(IsPositive(arg=Var(name='p')), Exists(var=Var(name='q'), condition=And(Eq(left=Mul(Var(name='p'), Var(name='q')), right=Const(value=806682376500)), Eq(left=GCD(a=Var(name='p'), b=Var(name='q')), right=Const(va... | NT | null | COMPUTE | sympy | COPRIME_PAIRS | [
"COPRIME_PAIRS"
] | 2bb3aa | modular_mod_compute_v1 | null | 5 | 0 | [
"COPRIME_PAIRS"
] | 1 | 0.002 | 2026-02-08T08:57:33.700714Z | {
"verified": true,
"answer": 64,
"timestamp": "2026-02-08T08:57:33.703193Z"
} | fb9b1a | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 110,
"completion_tokens": 3795
},
"timestamp": "2026-02-13T22:46:53.911Z",
"answer": 64
},
{
... | 1 | [
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
}
] | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
d0bf67 | sequence_lucas_compute_v1_601307018_10459 | Let $n$ be the number of ordered pairs $(a, b)$ of positive integers with $1 \le a \le 20$, $1 \le b \le 20$, and $16b^2 = 64$. Let $Q = L_n$, where $L_n$ denotes the $n$-th Lucas number. Compute $Q$. | 15,127 | graphs = [
Graph(
let={
"_n": Const(2),
"n": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("a"), Var("b")]), condition=And(Geq(Var("a"), Const(1)), Leq(Var("a"), Const(20)), Geq(Var("b"), Const(1)), Leq(Var("b"), Const(20)), Eq(Mul(Const(16), Pow(Var("b"), Ref("_n"))), Const(... | ALG | null | COMPUTE | sympy | QF_PSD_COUNT | [
"QF_PSD_COUNT"
] | 09ce67 | sequence_lucas_compute_v1 | null | 3 | 0 | [
"QF_PSD_COUNT"
] | 1 | 0.002 | 2026-03-10T10:57:28.450009Z | {
"verified": true,
"answer": 15127,
"timestamp": "2026-03-10T10:57:28.452074Z"
} | 2c0199 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 185,
"completion_tokens": 1383
},
"timestamp": "2026-04-19T13:49:01.404Z",
"answer": 15127
},
{
... | 2 | [
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "QF_PSD_COUNT",
"status": "ok"
}
] | {
"lo": -10,
"mid": -5.89,
"hi": -1.79
} | ||
30eb3b | nt_min_crt_v1_1439011603_2006 | Let $m$ be the maximum value of $xy$ over all ordered pairs $(x,y)$ of positive integers such that $x + y = 4$. Let $n$ be a positive integer satisfying $1 \leq n \leq \sum_{k1=1}^{7} k1$, $n \equiv 1 \pmod{m}$, and $n \equiv 2 \pmod{7}$. Compute the minimum possible value of $n$. | 9 | graphs = [
Graph(
let={
"_n": Const(7),
"m": MaxOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(Sum(Var("x"), Var("y")), Const(4)))), expr=Mul(Var("x"), Var("y")))),
... | NT | null | EXTREMUM | sympy | L3B | [
"SUM_ARITHMETIC",
"B1"
] | c1222e | nt_min_crt_v1 | null | 5 | 0 | [
"B1",
"L3B",
"SUM_ARITHMETIC"
] | 3 | 0.268 | 2026-02-08T16:27:23.788110Z | {
"verified": true,
"answer": 9,
"timestamp": "2026-02-08T16:27:24.056184Z"
} | 2e3819 | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 153,
"completion_tokens": 448
},
"timestamp": "2026-02-16T07:25:13.158Z",
"answer": 9
},
{
"id": 11,
"... | 2 | [
{
"lemma": "B1",
"status": "ok"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "SUM_ARITHMETIC",
"status": "ok"... | {
"lo": -10,
"mid": -7.27,
"hi": -4.54
} | ||
32d1a8_n | comb_catalan_compute_v1_1218484723_116 | A game designer creates character levels using combinations of two types of experience tokens: red tokens worth 2 points and blue tokens worth 3 points. Each character must collect between 5 and 17 total points using at least one red and one blue token, with no more than 4 red and 3 blue tokens used. For each valid tot... | 17,177 | COMB | null | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | comb_catalan_compute_v1 | null | 3 | null | [
"LIN_FORM"
] | 1 | 0.002 | 2026-02-25T01:49:49.773172Z | null | 0a7de6 | 32d1a8 | narrative | 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": 2655
},
"timestamp": "2026-03-30T14:53:10.927Z",
"answer": 17177
},
{
"... | 1 | [
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
}
... | {
"lo": -5.37,
"mid": 0.23,
"hi": 5.22
} | |
ae1d42 | modular_inverse_v1_784195855_7873 | Let $a = 537$. Let $m$ be the largest prime number less than or equal to 1050. Define $S$ as the set of all ordered pairs $(x, y)$ of positive integers such that $xy = 274576$. Let $s_{\text{min}}$ be the minimum value of $x + y$ over all pairs $(x, y) \in S$. Let $T$ be the set of all positive integers $x$ such that $... | 46,316 | graphs = [
Graph(
let={
"a": Const(537),
"m": MaxOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(2)), Leq(Var("n"), MaxOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(2)), Leq(Var("n"), Const(1050)), IsPrime(Var("n")))))), IsPrime(Var... | NT | null | EXTREMUM | sympy | MAX_PRIME_BELOW | [
"MAX_PRIME_BELOW/MAX_PRIME_BELOW",
"B3"
] | ca513e | modular_inverse_v1 | null | 6 | 0 | [
"B3",
"MAX_PRIME_BELOW"
] | 2 | 0.093 | 2026-02-08T09:35:38.386457Z | {
"verified": true,
"answer": 46316,
"timestamp": "2026-02-08T09:35:38.479787Z"
} | 562e3d | 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": 3049
},
"timestamp": "2026-02-14T05:17:26.878Z",
"answer": 46316
},
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"l... | {
"lo": -5.49,
"mid": 0.22,
"hi": 6.51
} | ||
d45294 | comb_sum_binomial_row_v1_124444284_6742 | Let $m = 2$. Define $S$ as the set of all integers $d \geq 2$ such that $d$ divides $1859$. Let $n$ be the largest prime number that is at least $m$ and at most the smallest element of $S$. Compute $2^n$. | 2,048 | graphs = [
Graph(
let={
"_m": Const(2),
"_n": Const(2),
"n": MaxOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Ref("_m")), Leq(Var("n"), MinOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Const(2)), Divides(divisor=Var("d"), dividend... | NT | null | SUM | sympy | MIN_PRIME_FACTOR | [
"MIN_PRIME_FACTOR/MAX_PRIME_BELOW"
] | e4e16c | comb_sum_binomial_row_v1 | null | 3 | 0 | [
"MAX_PRIME_BELOW",
"MIN_PRIME_FACTOR"
] | 2 | 0.001 | 2026-02-08T08:36:20.541017Z | {
"verified": true,
"answer": 2048,
"timestamp": "2026-02-08T08:36:20.542476Z"
} | 5652c3 | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 125,
"completion_tokens": 376
},
"timestamp": "2026-02-15T20:17:31.421Z",
"answer": 8
},
{
"id": 11,
... | 1 | [
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok_later"
},
{
"lemma": "MIN_PRIME_FACTOR",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"s... | {
"lo": -7.01,
"mid": -4.68,
"hi": -2.15
} | ||
485b29 | algebra_poly_eval_v1_1218484723_4117 | Let $m = 6$. Define
$$R = 4 \cdot m^{\left|\left\{ (a, b) : 1 \le a \le 40,\ 1 \le b \le 40,\ 16a^{2} - 16ab + \left|\left\{ (a_1, b_1) : 1 \le a_1 \le 35,\ 1 \le b_1 \le 35,\ 2b_1^{4} + 8a_1 b_1^{3} + 2a_1^{4} + 12a_1^{2} b_1^{2} + 8a_1^{3} b_1 = 1620000 \right\}\right| b^{2} = 20000 \right\}|} + 2m^{3} + 5m^{2} + 9m ... | 56,282 | graphs = [
Graph(
let={
"_m": Const(2),
"_n": Const(44121),
"m": Const(6),
"result": Sum(Mul(Const(4), Pow(Ref("m"), CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("a"), Var("b")]), condition=And(Geq(Var("a"), Const(1)), Leq(Var("a"), Const(40)), Geq(Va... | ALG | null | COMPUTE | sympy | QUADRATIC_INEQ | [
"POLY4_COUNT/QF_PSD_COUNT"
] | a8812c | algebra_poly_eval_v1 | null | 7 | 0 | [
"POLY4_COUNT",
"QF_PSD_COUNT",
"QUADRATIC_INEQ"
] | 3 | 0.041 | 2026-02-25T05:45:38.620412Z | {
"verified": true,
"answer": 56282,
"timestamp": "2026-02-25T05:45:38.661428Z"
} | 3bef9d | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 331,
"completion_tokens": 4709
},
"timestamp": "2026-03-29T13:53:00.622Z",
"answer": 56282
},
{
"... | 1 | [
{
"lemma": "POLY4_COUNT",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "QF_PSD_COUNT",
"status": "ok_later"
}
] | {
"lo": -2.45,
"mid": 1.37,
"hi": 5.29
} | ||
967269 | antilemma_k3_v1_1978505735_7516 | Compute $\sum_{d \mid 34547} \varphi(d)$, where $\varphi$ denotes Euler's totient function. | 34,547 | graphs = [
Graph(
let={
"x": SumOverDivisors(n=Const(value=34547), 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 | 0.001 | 2026-02-08T20:17:54.536932Z | {
"verified": true,
"answer": 34547,
"timestamp": "2026-02-08T20:17:54.537512Z"
} | 327e74 | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 1,
"correct": {
"strict": false,
"boxed": false,
"relaxed": true
},
"usage": {
"prompt_tokens": 87,
"completion_tokens": 1237
},
"timestamp": "2026-02-16T18:49:48.562Z",
"answer": 34819
},
{
"id": 11,... | 1 | [
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K3",
"status": "ok"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
}
] | {
"lo": -8.26,
"mid": -5.01,
"hi": -1.76
} | ||
74312a | alg_sum_powers_v1_1419126231_659 | Let $S$ be the number of ordered pairs $(a, b)$ of positive integers with $1 \leq a, b \leq 30$ such that $13a^2 + 2b^2 - 2ab \leq 5125$. Compute the remainder when $\sum_{k=1}^{S} k^3$ is divided by $7572$. | 6,765 | graphs = [
Graph(
let={
"_n": Const(30),
"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(30)), Geq(Var("b"), Const(1)), Leq(Var("b"), Ref("_n"... | 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 | 0.026 | 2026-02-25T10:09:02.849208Z | {
"verified": true,
"answer": 6765,
"timestamp": "2026-02-25T10:09:02.874841Z"
} | 4351a1 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 191,
"completion_tokens": 5880
},
"timestamp": "2026-03-30T09:17:17.234Z",
"answer": 6765
},
{
"i... | 1 | [
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "QF_PSD_COUNT_LEQ",
"status": "ok"
}
] | {
"lo": -5.37,
"mid": 0.23,
"hi": 5.22
} | ||
1edf52 | nt_sum_gcd_range_mod_v1_784195855_9782 | Let $N$ be the number of positive integers $n$ at most $19681$ such that $\gcd(n, 6) = 1$. Let $k = 168$ and $M = 10099$. Compute the remainder when
$$
\sum_{n=1}^{N} \gcd(n, k)
$$
is divided by $M$. | 240 | graphs = [
Graph(
let={
"_n": Const(6),
"N": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Const(19681)), Eq(GCD(a=Var("n"), b=Ref("_n")), Const(1))))),
"k": Const(168),
"M": Const(10099),
"sum": S... | NT | null | COMPUTE | sympy | C4 | [
"C4"
] | 08d162 | nt_sum_gcd_range_mod_v1 | null | 6 | 0 | [
"C4"
] | 1 | 0.467 | 2026-02-08T17:04:01.770239Z | {
"verified": true,
"answer": 240,
"timestamp": "2026-02-08T17:04:02.237674Z"
} | 89fd94 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 121,
"completion_tokens": 2989
},
"timestamp": "2026-02-17T21:15:58.050Z",
"answer": 240
},
{
... | 1 | [
{
"lemma": "C4",
"status": "ok"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
},
{
"lemma": "VAL_SUM_EQ",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
00be08 | comb_catalan_compute_v1_809748730_630 | Let $n$ be the number of ordered pairs $(x_1, x_2)$ of positive odd integers such that $x_1 + x_2 = 22$. Let $C_n$ denote the $n$th Catalan number. Compute the remainder when $44121 \cdot C_n$ is divided by $59008$. | 466 | 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 | 0.003 | 2026-02-08T11:39:28.560339Z | {
"verified": true,
"answer": 466,
"timestamp": "2026-02-08T11:39:28.563251Z"
} | c823a2 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 182,
"completion_tokens": 4186
},
"timestamp": "2026-02-24T14:27:10.114Z",
"answer": 466
},
{
"id... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COMB1",
"status": "ok"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
}
] | {
"lo": 1.15,
"mid": 4.18,
"hi": 6.61
} | ||
8da299 | diophantine_product_count_v1_349078426_1459 | Let $S$ be the set of all ordered pairs of positive integers $(x, y)$ such that $xy = 396900$. For each such pair, compute $x + y$, and let $T$ be the set of all such sums. Let $k$ be the minimum value in $T$. Now, let $A$ be the set of all positive integers $x$ such that $1 \leq x \leq 249$, $x$ divides $k$, and $\fra... | 26 | graphs = [
Graph(
let={
"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")))),
"upper": Const(2... | NT | null | COUNT | sympy | B3 | [
"B3"
] | 0cd20d | diophantine_product_count_v1 | null | 5 | 0 | [
"B3"
] | 1 | 0.022 | 2026-02-08T13:40:05.614489Z | {
"verified": true,
"answer": 26,
"timestamp": "2026-02-08T13:40:05.636247Z"
} | e82dd4 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 167,
"completion_tokens": 1630
},
"timestamp": "2026-02-15T19:09:49.234Z",
"answer": 26
},
{
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
},
{
"lemma": "VAL_SUM_EQ",
"status": "no"
}
] | {
"lo": -5.49,
"mid": 0.22,
"hi": 6.51
} | ||
781c00 | antilemma_sum_equals_v1_898971024_2030 | Let $m = 23$. Consider the set of all ordered triples $(x_1, x_2, x_3)$ of positive odd integers such that $x_1 + x_2 + x_3 = m$. Let $n$ be the number of such triples. Now consider the set of all ordered pairs $(i, j)$ where $i$ is an integer from 1 to 65, inclusive, and $j$ is an integer from 1 to 66, inclusive, such... | 65 | graphs = [
Graph(
let={
"_m": Const(23),
"_n": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x1"), Var("x2"), Var("x3")]), condition=And(IsPositive(arg=Var(name='x1')), IsPositive(arg=Var(name='x2')), IsPositive(arg=Var(name='x3')), IsOdd(arg=Var(name='x1')), IsOdd(arg=Var(n... | COMB | GEOM | COMPUTE | sympy | COMB1 | [
"COMB1/COUNT_SUM_EQUALS",
"COUNT_SUM_EQUALS"
] | 3e1adf | antilemma_sum_equals_v1 | null | 5 | 0 | [
"COMB1",
"COUNT_SUM_EQUALS"
] | 2 | 0.05 | 2026-02-08T16:30:11.484930Z | {
"verified": true,
"answer": 65,
"timestamp": "2026-02-08T16:30:11.534624Z"
} | e99077 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 230,
"completion_tokens": 879
},
"timestamp": "2026-02-24T21:10:08.858Z",
"answer": 65
},
{
"id"... | 2 | [
{
"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": -10,
"mid": -7.42,
"hi": -4.85
} | ||
de5e5c | nt_count_coprime_v1_124444284_8593 | Let $A$ be the number of positive integers $n \leq 19600$ such that $\gcd(n, 13) = 1$. Let $B$ be the number of positive integers $n \leq 423$ that are divisible by $9$ and satisfy $\gcd(n, 10) = 1$. Find the remainder when $B - A$ is divided by $94211$. | 76,137 | graphs = [
Graph(
let={
"_n": Const(94211),
"upper": Const(19600),
"k": Const(13),
"result": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Ref("upper")), Eq(GCD(a=Var("n"), b=Ref("k")), Const(1))))),
... | NT | null | COUNT | sympy | C5 | [
"C5"
] | 92f7e3 | nt_count_coprime_v1 | negation_mod | 4 | 0 | [
"C5"
] | 1 | 1.866 | 2026-02-08T09:48:14.696324Z | {
"verified": true,
"answer": 76137,
"timestamp": "2026-02-08T09:48:16.562144Z"
} | fa155e | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 155,
"completion_tokens": 398
},
"timestamp": "2026-02-16T03:24:43.389Z",
"answer": 75549
},
{
"id": 11... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "C5",
"status": "ok"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
}
] | {
"lo": -6.96,
"mid": -4.56,
"hi": -1.46
} | ||
b77b2f | modular_mod_compute_v1_809748730_997 | Let $m = 212$. Consider the number of ordered pairs $(x_1, x_2)$ of positive odd integers such that $x_1 + x_2 = m$; denote this count by $n$. Let $a$ be the number of positive integers $k$ with $1 \leq k \leq \sum_{i=1}^{n} i$ such that $\gcd(k, 15) = 1$. Find the remainder when $a$ is divided by $81225$. | 3,025 | graphs = [
Graph(
let={
"_m": Const(212),
"_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")), ... | NT | null | COMPUTE | sympy | COMB1 | [
"COMB1/SUM_ARITHMETIC/C4"
] | e9714a | modular_mod_compute_v1 | null | 6 | 0 | [
"C4",
"COMB1",
"SUM_ARITHMETIC"
] | 3 | 0.005 | 2026-02-08T11:59:32.293481Z | {
"verified": true,
"answer": 3025,
"timestamp": "2026-02-08T11:59:32.298751Z"
} | ccac14 | 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": 1201
},
"timestamp": "2026-02-14T21:30:09.674Z",
"answer": 3025
},
{... | 1 | [
{
"lemma": "C4",
"status": "ok_later"
},
{
"lemma": "COMB1",
"status": "ok"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "SUM_ARITHMETIC",
"status": "ok_later"
}... | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
51eac1 | nt_count_coprime_and_v1_1439011603_259 | Let $S$ be the set of all ordered pairs $(a,b)$ of positive integers with $1 \leq a \leq 17$, $1 \leq b \leq 85$, such that $t = 5a + 2b$ satisfies $7 \leq t \leq 255$. Let $n = |S|$. Let $k_2$ be the smallest divisor of $n$ that is at least $2$. Determine the number of positive integers $n'$ such that $1 \leq n' \leq ... | 21,697 | 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=17)), Geq(left=Var(name='b'), right=Const(value... | NT | null | COUNT | sympy | LIN_FORM | [
"LIN_FORM/MIN_PRIME_FACTOR"
] | bb1a13 | nt_count_coprime_and_v1 | null | 7 | 0 | [
"LIN_FORM",
"MIN_PRIME_FACTOR"
] | 2 | 4.171 | 2026-02-08T15:22:38.583658Z | {
"verified": true,
"answer": 21697,
"timestamp": "2026-02-08T15:22:42.754287Z"
} | 864756 | 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": 1830
},
"timestamp": "2026-02-16T05:17:58.716Z",
"answer": 21697
},
... | 1 | [
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "MIN_PRIME_FACTOR",
"status": "ok_later"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "V3",
"s... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
f6545c | nt_lcm_compute_v1_677425708_767 | Let $a = 2431$. Consider the set of all ordered pairs $(x, y)$ of positive integers such that $xy = 506944$. Let $b$ be the minimum value of $x + y$ over all such pairs. Compute the least common multiple of $a$ and $b$. Multiply this value by 44121 and find the remainder when the result is divided by 96244. | 36,296 | graphs = [
Graph(
let={
"a": Const(2431),
"b": MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(Mul(Var("x"), Var("y")), Const(506944)))), expr=Sum(Var("x"), Var("y"))))... | NT | null | COMPUTE | sympy | B3 | [
"B3"
] | 0cd20d | nt_lcm_compute_v1 | null | 6 | 0 | [
"B3"
] | 1 | 0.001 | 2026-02-08T03:43:38.199068Z | {
"verified": true,
"answer": 36296,
"timestamp": "2026-02-08T03:43:38.200560Z"
} | db4282 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 199,
"completion_tokens": 4578
},
"timestamp": "2026-02-08T21:04:31.191Z",
"answer": 36296
},
{
"... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
}
] | {
"lo": -3.46,
"mid": 1.03,
"hi": 5.49
} | ||
950690 | antilemma_k2_v1_784195855_7716 | Let $n = 6$. Define $S$ as the set of all ordered pairs $(k, j)$ of positive integers such that $1 \le k \le 46$ and $1 \le j \le 8$. Let $T$ be the set of all values $\phi(k) \left\lfloor \frac{46}{k} \right\rfloor$ as $(k, j)$ ranges over $S$, where $\phi$ denotes Euler's totient function. Compute the value of
$$
\fr... | 1,081 | graphs = [
Graph(
let={
"_n": Const(6),
"x": Div(Mul(Ref("_n"), SumOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("k"), Var("_j")]), condition=Const(1), domain=CartesianProduct(left=IntegerRange(start=Const(1), end=Const(46)), right=IntegerRange(start=Const(1), end=C... | NT | COMB | COMPUTE | sympy | SUM_INDEPENDENT | [
"SUM_INDEPENDENT/K2",
"K2"
] | ddbc0a | antilemma_k2_v1 | null | 5 | 0 | [
"K2",
"SUM_INDEPENDENT"
] | 2 | 0.001 | 2026-02-08T09:27:59.220156Z | {
"verified": true,
"answer": 1081,
"timestamp": "2026-02-08T09:27:59.221035Z"
} | 29bacb | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 164,
"completion_tokens": 4378
},
"timestamp": "2026-02-14T04:23:04.696Z",
"answer": 1081
},
{... | 1 | [
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "K2",
"status": "ok"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "SUM_INDEPENDENT",
"status": "ok"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
},
{
"lemm... | {
"lo": -5.49,
"mid": 0.22,
"hi": 6.51
} | ||
58e017 | nt_sum_totient_over_divisors_v1_1520064083_9814 | Let $n = 62828$. Define
$$
r = \sum_{d \mid n} \phi(d),
$$
where $\phi$ denotes Euler's totient function. Let $T$ be the set of all real numbers $x$ such that
$$
x^2 - 2116x + 50208 = 0.
$$
Compute the remainder when
$$
r^2 + 4r + \sum T
$$
is divided by $60667$. | 9,322 | graphs = [
Graph(
let={
"_n": Const(2),
"n": Const(62828),
"result": SumOverDivisors(n=Ref(name='n'), var='d', expr=EulerPhi(n=Var(name='d'))),
"Q": Mod(value=Sum(Pow(Ref("result"), Const(2)), Mul(Const(4), Ref("result")), SumOverSet(set=SolutionsSet(var=Var("... | NT | null | COMPUTE | sympy | VIETA_SUM | [
"VIETA_SUM"
] | 833c91 | nt_sum_totient_over_divisors_v1 | quadratic_mod | 5 | 0 | [
"VIETA_SUM"
] | 1 | 0.002 | 2026-02-08T11:00:37.780318Z | {
"verified": true,
"answer": 9322,
"timestamp": "2026-02-08T11:00:37.782183Z"
} | 24fcef | 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": 968
},
"timestamp": "2026-02-14T10:00:29.163Z",
"answer": 9322
},
{
... | 1 | [
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "VIETA_SUM",
"status": "ok"... | {
"lo": -5.49,
"mid": 0.22,
"hi": 6.51
} | ||
efd99a | geo_count_lattice_triangle_v1_1520064083_2450 | A triangle has vertices at $(0,0)$, $(200,25)$, and $(25,100)$. Let $A$ be twice the area of this triangle, and let $B$ be the sum of the greatest common divisors of the absolute values of the differences in coordinates along each side:
\[
\gcd(|200|, |25|) + \gcd(|25 - 200|, |100 - 25|) + \gcd(|0 - 25|, |0 - 100|).
\]... | 9,651 | graphs = [
Graph(
let={
"area_2x": Abs(arg=Sum(Mul(Const(value=200), Const(value=100)), Mul(Const(value=25), Sub(left=Const(value=0), right=Const(value=25))))),
"boundary": Sum(GCD(a=Abs(arg=Const(value=200)), b=Abs(arg=Const(value=25))), GCD(a=Abs(arg=Sub(left=Const(value=25), right... | ALG | NT | COUNT | sympy | [] | geo_count_lattice_triangle_v1 | null | 6 | 0 | null | null | 0.002 | 2026-02-08T04:44:45.349910Z | {
"verified": true,
"answer": 9651,
"timestamp": "2026-02-08T04:44:45.352090Z"
} | ecb4e1 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 238,
"completion_tokens": 965
},
"timestamp": "2026-02-11T21:51:02.494Z",
"answer": 9651
},
{
"i... | 1 | [] | {
"lo": -5.55,
"mid": -3.01,
"hi": 0.33
} | ||||
5d3f80 | nt_euler_phi_compute_v1_151522320_353 | Consider all integers $t$ for which there exist integers $a$ and $b$ satisfying
$$1\le a\le 45,\quad 1\le b\le 37,\quad 14\le t\le 598,\quad t=10a+4b.$$
Let $N$ be the number of such integers $t$.
Consider all ordered pairs $(x,y)$ of positive integers such that $xy=N$. For each such pair, form the sum $x+y$, and let ... | 16,146 | graphs = [
Graph(
let={
"_m": Const(58232),
"_n": Const(4),
"n": Const(48841),
"result": EulerPhi(n=Ref("n")),
"_c": MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), I... | NT | null | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM/B3",
"SUM_ARITHMETIC"
] | 49c1fc | nt_euler_phi_compute_v1 | quadratic_mod | 7 | 0 | [
"B3",
"LIN_FORM",
"SUM_ARITHMETIC"
] | 3 | 0.003 | 2026-02-08T03:09:56.256850Z | {
"verified": true,
"answer": 16146,
"timestamp": "2026-02-08T03:09:56.259922Z"
} | 9ae71d | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 333,
"completion_tokens": 4028
},
"timestamp": "2026-02-09T01:46:17.382Z",
"answer": 16212
},
{
... | 1 | [
{
"lemma": "B3",
"status": "ok_later"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
... | {
"lo": 1.96,
"mid": 5.23,
"hi": 8.52
} | ||
666ff3 | nt_count_divisible_v1_784195855_7005 | Let $d$ be the number of ordered pairs $(i,j)$ of positive integers such that $i + j = 29$ and $1 \leq i, j \leq 28$. Determine the value of the number of positive integers $n$ such that $1 \leq n \leq 30509$ and $n$ is divisible by $d$. | 1,089 | graphs = [
Graph(
let={
"upper": Const(30509),
"divisor": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("i"), Var("j")]), condition=Eq(Sum(Var("i"), Var("j")), Const(29)), domain=CartesianProduct(left=IntegerRange(start=Const(1), end=Const(28)), right=IntegerRange(start=Const... | NT | null | COUNT | sympy | COUNT_SUM_EQUALS | [
"COUNT_SUM_EQUALS"
] | 75ab0f | nt_count_divisible_v1 | null | 3 | 0 | [
"COUNT_SUM_EQUALS"
] | 1 | 2.027 | 2026-02-08T09:03:01.429763Z | {
"verified": true,
"answer": 1089,
"timestamp": "2026-02-08T09:03:03.456324Z"
} | 964483 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 122,
"completion_tokens": 588
},
"timestamp": "2026-02-13T23:52:38.114Z",
"answer": 1089
},
{
... | 1 | [
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "ok"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "V8",
"status": "no"... | {
"lo": -7.01,
"mid": -4.68,
"hi": -2.15
} | ||
636e39 | nt_min_crt_v1_124444284_9999 | Find the smallest positive integer $n$ such that $n \geq 1$, $n \leq 40$, $n \equiv 3 \pmod{5}$, and $n \equiv 3 \pmod{8}$. Let this value be $n_0$. Given that $c = 14039$, compute $c \cdot n_0$. | 42,117 | graphs = [
Graph(
let={
"m": Const(5),
"k": Const(8),
"a": Const(3),
"b": Const(3),
"upper": Const(40),
"result": MinOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Ref("upper")), Eq(Mod(value... | NT | null | EXTREMUM | sympy | SUM_ARITHMETIC | [
"SUM_ARITHMETIC/B1"
] | 844731 | nt_min_crt_v1 | null | 4 | 0 | [
"B1",
"SUM_ARITHMETIC"
] | 2 | 0.043 | 2026-02-08T12:46:08.698191Z | {
"verified": true,
"answer": 42117,
"timestamp": "2026-02-08T12:46:08.740743Z"
} | ee4739 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 123,
"completion_tokens": 429
},
"timestamp": "2026-02-15T04:41:43.544Z",
"answer": 42117
},
{... | 1 | [
{
"lemma": "B1",
"status": "ok_later"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "SUM_ARITHMETIC",
"status": "ok"
},
{
"lemma": "V1",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
},
{
... | {
"lo": -6.96,
"mid": -4.56,
"hi": -1.46
} | ||
ead52c | lin_form_endings_v1_1526740231_83 | Let $n = 105$, $a = 105$, and $b = 75$. Compute $\gcd(a, b)$, and let $k = \left\lfloor \frac{n}{\gcd(a, b)} \right\rfloor$. Multiply $k$ by $18387$, then compute the remainder when this product is divided by $97492$. Find the value of this remainder. | 31,217 | graphs = [
Graph(
let={
"_n": Const(105),
"a_coeff": Const(105),
"b_coeff": Const(75),
"_inner_result": Floor(Div(Ref("_n"), GCD(a=Ref("a_coeff"), b=Ref("b_coeff")))),
"_scale_k": Const(18387),
"_scaled": Mul(Ref("_scale_k"), Ref("_inne... | COMB | NT | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | lin_form_endings_v1 | null | 3 | null | [
"LIN_FORM"
] | 1 | 0.001 | 2026-02-08T11:20:43.352686Z | {
"verified": true,
"answer": 31217,
"timestamp": "2026-02-08T11:20:43.353215Z"
} | 4b2d2e | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 155,
"completion_tokens": 322
},
"timestamp": "2026-02-15T21:43:37.484Z",
"answer": 31267
},
{
"id": 11... | 1 | [
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8",
"status... | {
"lo": -6.96,
"mid": -4.56,
"hi": -1.46
} | ||
283953 | nt_min_coprime_above_v1_1439011603_2358 | Let $a = 2304$, $b = 2335$, and $m = \sum_{k=1}^{6} k$. Let $S$ be the set of all integers $n$ such that $a < n \leq b$ and $\gcd(n, m) = 1$. Let $r$ be the smallest element of $S$. Compute the remainder when $44121 \cdot r$ is divided by $70654$. Find the value of this remainder. | 27,799 | graphs = [
Graph(
let={
"start": Const(2304),
"upper": Const(2335),
"modulus": Summation(var="k", start=Const(1), end=Const(6), expr=Var("k")),
"result": MinOverSet(set=SolutionsSet(var=Var("n"), condition=And(Gt(Var("n"), Ref("start")), Leq(Var("n"), Ref("upp... | NT | null | EXTREMUM | sympy | SUM_ARITHMETIC | [
"SUM_ARITHMETIC"
] | eb34f0 | nt_min_coprime_above_v1 | null | 3 | 0 | [
"SUM_ARITHMETIC"
] | 1 | 0.04 | 2026-02-08T16:44:44.236363Z | {
"verified": true,
"answer": 27799,
"timestamp": "2026-02-08T16:44:44.275970Z"
} | f0b7e1 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 148,
"completion_tokens": 6197
},
"timestamp": "2026-02-17T10:11:44.722Z",
"answer": 27799
},
... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "SUM_ARITHMETIC",
"status": "ok"
},
{
"lemma": "V3",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
d993ac | modular_inverse_v1_151522320_1974 | Let $a = 625$ and $m = 1279$. Let $s$ be the minimum value of $x + y$ over all ordered pairs $(x,y)$ of positive integers such that $xy = 408321$. Let $r$ be the smallest positive integer $x$ such that $1 \leq x \leq s$ and $625x \equiv 1 \pmod{1279}$. Compute the smallest positive integer $k$ such that the $k$th Fibon... | 126 | graphs = [
Graph(
let={
"a": Const(625),
"m": Const(1279),
"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(408321)))... | NT | null | EXTREMUM | sympy | B3 | [
"B3"
] | 0cd20d | modular_inverse_v1 | null | 6 | 0 | [
"B3"
] | 1 | 0.074 | 2026-02-08T04:29:45.994663Z | {
"verified": true,
"answer": 126,
"timestamp": "2026-02-08T04:29:46.068191Z"
} | 9b1dc0 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 236,
"completion_tokens": 3109
},
"timestamp": "2026-02-10T16:49:42.634Z",
"answer": 126
},
{
"i... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"
}
] | {
"lo": -3.49,
"mid": 1.84,
"hi": 7.55
} | ||
e43d42 | nt_num_divisors_compute_v1_1978505735_6436 | Let $S$ be the set of all ordered pairs $(x,y)$ of positive integers such that $xy = 23059204$. Define $n$ to be the minimum value of $x + y$ as $(x,y)$ ranges over $S$. Find the number of positive divisors of $n$. | 15 | graphs = [
Graph(
let={
"n": MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(Mul(Var("x"), Var("y")), Const(23059204)))), expr=Sum(Var("x"), Var("y")))),
"result": NumD... | NT | null | COMPUTE | sympy | B3 | [
"B3"
] | 0cd20d | nt_num_divisors_compute_v1 | null | 4 | 0 | [
"B3"
] | 1 | 0.002 | 2026-02-08T19:35:51.241418Z | {
"verified": true,
"answer": 15,
"timestamp": "2026-02-08T19:35:51.243047Z"
} | 9e9425 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 110,
"completion_tokens": 2433
},
"timestamp": "2026-02-18T22:56:43.724Z",
"answer": 15
},
{
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
d964de | alg_poly4_sum_v1_1218484723_5946 | Find the remainder when
$$
\sum_{\substack{1 \le a \le 40 \\ 1 \le b \le 40}} \left( 312a^2b^2 - 80a^3b + 17a^4 + 40ab^3 + \left(\min\{ d : d \geq 2, d \mid 40811711 \}\right) b^4 \right)
$$
is divided by $70521$. | 48,500 | graphs = [
Graph(
let={
"_n": Const(4),
"result": Mod(value=SumOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("a"), Var("b")]), condition=And(Geq(Var("a"), Const(1)), Leq(Var("a"), Const(40)), Geq(Var("b"), Const(1)), Leq(Var("b"), Const(40)))), expr=Sum(Mul(Const(31... | NT | null | COMPUTE | sympy | MIN_PRIME_FACTOR | [
"MIN_PRIME_FACTOR"
] | bc3776 | alg_poly4_sum_v1 | null | 5 | 0 | [
"MIN_PRIME_FACTOR"
] | 1 | 0.015 | 2026-02-25T07:32:49.545388Z | {
"verified": true,
"answer": 48500,
"timestamp": "2026-02-25T07:32:49.560203Z"
} | 89ad01 | 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": "2026-03-29T23:37:45.945Z",
"answer": null
},
{
... | 1 | [
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "MIN_PRIME_FACTOR",
"status": "ok"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "V3",
"status":... | {
"lo": 1.53,
"mid": 4.7,
"hi": 7.23
} | ||
6151f8 | nt_num_divisors_compute_v1_1978505735_7355 | Let $n$ be the sum of all real solutions to the equation $x^2 - 225x + 10764 = 0$. Let $\text{result}$ be the number of positive divisors of $n$. Find the remainder when $32731 \cdot \text{result}$ is divided by $56510$. | 12,029 | graphs = [
Graph(
let={
"_n": Const(56510),
"n": SumOverSet(set=SolutionsSet(var=Var("x"), condition=Eq(Sum(Pow(Var("x"), Const(2)), Mul(Const(-225), Var("x")), Const(10764)), Const(0)))),
"result": NumDivisors(n=Ref("n")),
"Q": Mod(value=Mul(Const(32731), Ref... | NT | null | COMPUTE | sympy | VIETA_SUM | [
"VIETA_SUM"
] | b33a7a | nt_num_divisors_compute_v1 | null | 4 | 0 | [
"VIETA_SUM"
] | 1 | 0.001 | 2026-02-08T20:13:08.523524Z | {
"verified": true,
"answer": 12029,
"timestamp": "2026-02-08T20:13:08.524422Z"
} | 0f2d3c | 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": 706
},
"timestamp": "2026-02-19T00:08:00.110Z",
"answer": 12029
},
{... | 1 | [
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
},
{
"lemma": "VIETA_SUM",
"status": "ok"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
a07f52 | antilemma_count_primes_v1_1742523217_891 | Let $n$ be an integer such that $2 \leq n \leq 1307$. Compute the number of prime values of $n$. | 214 | graphs = [
Graph(
let={
"_n": Const(1307),
"x": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(2)), Leq(Var("n"), Ref("_n")), IsPrime(Var("n"))))),
},
goal=Ref("x"),
)
] | NT | null | COMPUTE | sympy | COUNT_PRIMES | [
"COUNT_PRIMES"
] | 07c874 | antilemma_count_primes_v1 | null | 4 | 0 | [
"COUNT_PRIMES"
] | 1 | 0 | 2026-02-08T03:20:00.086614Z | {
"verified": true,
"answer": 214,
"timestamp": "2026-02-08T03:20:00.087026Z"
} | 56b46b | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 142,
"completion_tokens": 2269
},
"timestamp": "2026-02-10T00:13:42.098Z",
"answer": 214
},
{
"id... | 1 | [
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_PRIMES",
"status": "ok"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
... | {
"lo": -6.5,
"mid": -0.2,
"hi": 6.11
} | ||
b29379 | diophantine_product_count_v1_784195855_7847 | Let $n = 57600$. Consider the set of all ordered pairs $(x, y)$ of positive integers such that $xy = n$. For each such pair, compute $x + y$, and let $k$ be the minimum value of $x + y$ over all such pairs.
Let $p$ be the smallest prime divisor of $583573$. Determine the number of positive integers $x$ such that $1 \l... | 12 | graphs = [
Graph(
let={
"_n": Const(57600),
"k": MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(Mul(Var("x"), Var("y")), Ref("_n")))), expr=Sum(Var("x"), Var("y")))),
... | NT | null | COUNT | sympy | MIN_PRIME_FACTOR | [
"MIN_PRIME_FACTOR",
"B3"
] | 6c6c26 | diophantine_product_count_v1 | null | 5 | 0 | [
"B3",
"MIN_PRIME_FACTOR"
] | 2 | 0.012 | 2026-02-08T09:33:34.767843Z | {
"verified": true,
"answer": 12,
"timestamp": "2026-02-08T09:33:34.780171Z"
} | de2dcf | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 160,
"completion_tokens": 2052
},
"timestamp": "2026-02-14T05:03:38.283Z",
"answer": 12
},
{
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "MIN_PRIME_FACTOR",
"status": "ok"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
... | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
84d27f | antilemma_sum_equals_v1_677425708_2660 | Let $c = 86$. Compute the number of ordered pairs $(x_1, x_2)$ of positive odd integers such that $x_1 + x_2 = c$. Denote this number by $m$. Compute the number of ordered pairs $(i,j)$ of positive integers with $1 \leq i \leq 41$ and $1 \leq j \leq 42$ such that $i + j = m$. Denote this number by $n$. Find the number ... | 38 | graphs = [
Graph(
let={
"_c": Const(86),
"_m": 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")), R... | COMB | GEOM | COMPUTE | sympy | COUNT_SUM_EQUALS | [
"COUNT_SUM_EQUALS/COUNT_SUM_EQUALS",
"COMB1/COUNT_SUM_EQUALS",
"COUNT_SUM_EQUALS"
] | a57484 | antilemma_sum_equals_v1 | null | 4 | 0 | [
"COMB1",
"COUNT_SUM_EQUALS"
] | 2 | 0.014 | 2026-02-08T05:10:50.356394Z | {
"verified": true,
"answer": 38,
"timestamp": "2026-02-08T05:10:50.370533Z"
} | b6da90 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 261,
"completion_tokens": 1499
},
"timestamp": "2026-02-11T23:04:19.188Z",
"answer": 38
},
{
"id"... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COMB1",
"status": "ok"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS... | {
"lo": -2.46,
"mid": 0.47,
"hi": 3.59
} | ||
47da3f | nt_count_with_divisor_count_v1_151522320_1923 | Let $n$ be the largest prime number satisfying $2 \leq n \leq 5$. Define $$d = \sum_{k=1}^{n} \phi(k) \left\lfloor \frac{5}{k} \right\rfloor,$$ where $\phi$ denotes Euler's totient function. Let $r$ be the number of positive integers $m$ with $1 \leq m \leq 70000$ such that $m$ has exactly $d$ positive divisors. Comput... | 65,094 | graphs = [
Graph(
let={
"_n": MaxOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(2)), Leq(Var("n"), Const(5)), IsPrime(Var("n"))))),
"upper": Const(70000),
"div_count": Summation(var="k", start=Const(1), end=Ref("_n"), expr=Mul(EulerPhi(n=Var("k")... | NT | null | COUNT | sympy | MAX_PRIME_BELOW | [
"MAX_PRIME_BELOW/K2"
] | 7eb1ee | nt_count_with_divisor_count_v1 | null | 6 | 0 | [
"K2",
"MAX_PRIME_BELOW"
] | 2 | 3.618 | 2026-02-08T04:27:37.421872Z | {
"verified": true,
"answer": 65094,
"timestamp": "2026-02-08T04:27:41.039736Z"
} | 226422 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 239,
"completion_tokens": 3387
},
"timestamp": "2026-02-10T16:48:18.127Z",
"answer": 65094
},
{
... | 1 | [
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "K2",
"status": "ok_later"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok"
},
{
"lemma": "V1",
"s... | {
"lo": -3.42,
"mid": 1.86,
"hi": 7.55
} | ||
f188c9 | nt_min_coprime_above_v1_397696148_1127 | Let $S$ be the set of all prime numbers $n$ such that $2 \leq n \leq 1657$. Let $m$ be the number of elements in $S$. Let $T$ be the set of all integers $n$ such that $14161 < n \leq 14431$ and $\gcd(n, m) = 1$. Let $r$ be the smallest element of $T$. Compute the remainder when $27755 \cdot r$ is divided by $58416$. | 12,801 | graphs = [
Graph(
let={
"start": Const(14161),
"upper": Const(14431),
"modulus": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(2)), Leq(Var("n"), Const(1657)), IsPrime(Var("n"))))),
"result": MinOverSet(set=SolutionsSet(var=Var(... | NT | null | EXTREMUM | sympy | COUNT_PRIMES | [
"COUNT_PRIMES"
] | 07c874 | nt_min_coprime_above_v1 | null | 4 | 0 | [
"COUNT_PRIMES"
] | 1 | 0.031 | 2026-02-08T12:22:27.847845Z | {
"verified": true,
"answer": 12801,
"timestamp": "2026-02-08T12:22:27.878439Z"
} | 74db7f | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 154,
"completion_tokens": 2740
},
"timestamp": "2026-02-15T00:29:35.070Z",
"answer": 12801
},
... | 1 | [
{
"lemma": "COUNT_PRIMES",
"status": "ok"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "V3",
"status": "no"
},
{
"lemma": "V5",
"status": "no"... | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
c11d48 | modular_mod_compute_v1_2051736721_2011 | Let $S$ be the set of all ordered pairs $(x, y)$ of positive integers such that $xy = 777924$. Let $a$ be the minimum value of $x + y$ as $(x, y)$ ranges over $S$. Let $r$ be the remainder when $a$ is divided by 7000. Compute the remainder when $89077 \cdot r$ is divided by 80694. | 20,610 | graphs = [
Graph(
let={
"_n": Const(80694),
"a": MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(Mul(Var("x"), Var("y")), Const(777924)))), expr=Sum(Var("x"), Var("y"))... | NT | null | COMPUTE | sympy | B3 | [
"B3"
] | 0cd20d | modular_mod_compute_v1 | null | 4 | 0 | [
"B3"
] | 1 | 0.002 | 2026-02-08T16:24:59.204151Z | {
"verified": true,
"answer": 20610,
"timestamp": "2026-02-08T16:24:59.206526Z"
} | 45a949 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 136,
"completion_tokens": 1446
},
"timestamp": "2026-02-17T04:08:54.650Z",
"answer": 20610
},
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
b9a771 | modular_count_residue_v1_1915831931_2382 | Let $S$ be the set of all integers $t$ such that $14 \leq t \leq 852$ and there exist positive integers $a$ and $b$ with $1 \leq a \leq 99$, $1 \leq b \leq 10$, and $t = 8a + 6b$. Let $d$ be a positive divisor of $|S|$, and let $m$ be the largest such $d$ satisfying $1 \leq d \leq 18$. Find the number of positive integ... | 2,990 | graphs = [
Graph(
let={
"upper": Const(53824),
"m": MaxOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Const(1)), Leq(Var("d"), Const(18)), Divides(divisor=Var("d"), dividend=CountOverSet(set=SolutionsSet(var=Var("t"), condition=Exists(var=Var(name='a'), condition=... | NT | null | COUNT | sympy | LIN_FORM | [
"LIN_FORM/MAX_DIVISOR"
] | 8c55ae | modular_count_residue_v1 | null | 5 | 0 | [
"LIN_FORM",
"MAX_DIVISOR"
] | 2 | 3.619 | 2026-02-08T16:45:51.593004Z | {
"verified": true,
"answer": 2990,
"timestamp": "2026-02-08T16:45:55.211848Z"
} | 07c45b | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 185,
"completion_tokens": 4994
},
"timestamp": "2026-02-17T12:19:13.445Z",
"answer": 2990
},
{... | 1 | [
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "MAX_DIVISOR",
"statu... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
e03a86 | comb_factorial_compute_v1_124444284_535 | Let $n$ be the smallest integer $d \geq 2$ that divides $847$. Compute $n!$, and let $A = n!$. Define
\[
Q = A + \varphi\left(|A| + \varphi(2)\right) + \tau\left(|A| + \varphi(2)\right),
\]
where $\varphi$ is Euler's totient function and $\tau(m)$ is the number of positive divisors of $m$. Find the value of $Q$. | 10,013 | 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(847))))),
"result": Factorial(Ref("n")),
"Q": Sum(Ref("result"), EulerPhi(n=Sum(Abs(arg=Ref(... | NT | null | COMPUTE | sympy | MIN_PRIME_FACTOR | [
"MIN_PRIME_FACTOR",
"ONE_PHI_2"
] | 99e59d | comb_factorial_compute_v1 | null | 3 | 0 | [
"MIN_PRIME_FACTOR",
"ONE_PHI_2"
] | 2 | 0.002 | 2026-02-08T03:20:53.563849Z | {
"verified": true,
"answer": 10013,
"timestamp": "2026-02-08T03:20:53.565673Z"
} | eae1ca | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 222,
"completion_tokens": 780
},
"timestamp": "2026-02-09T18:54:45.544Z",
"answer": 10013
},
{
"i... | 1 | [
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "MIN_PRIME_FACTOR",
"status": "ok"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "ONE_PHI_2",... | {
"lo": -6.51,
"mid": -0.31,
"hi": 5.43
} | ||
85fb2d | sequence_lucas_compute_v1_601307018_5676 | Let $n$ be the number of ordered pairs $(a, b)$ of positive integers with $1 \le a, b \le 25$ such that $10ab + 5a^2 + 5b^2 = 3920$. Let $R = L_n$, where $L_n$ denotes the $n$-th Lucas number. Find the remainder when $16129 - R$ is divided by $78259$. | 30,309 | graphs = [
Graph(
let={
"_n": Const(78259),
"n": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("a"), Var("b")]), condition=And(Geq(Var("a"), Const(1)), Leq(Var("a"), Const(25)), Geq(Var("b"), Const(1)), Leq(Var("b"), Const(25)), Eq(Sum(Mul(Const(10), Var("a"), Var("b")), Mul(... | ALG | null | COMPUTE | sympy | QF_PSD_COUNT | [
"QF_PSD_COUNT"
] | 09ce67 | sequence_lucas_compute_v1 | null | 3 | 0 | [
"QF_PSD_COUNT"
] | 1 | 0.004 | 2026-03-10T06:15:01.758280Z | {
"verified": true,
"answer": 30309,
"timestamp": "2026-03-10T06:15:01.762433Z"
} | a4f021 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 202,
"completion_tokens": 926
},
"timestamp": "2026-04-19T02:40:25.803Z",
"answer": 30309
},
{
"... | 1 | [
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "QF_PSD_COUNT",
"status": "ok"
}
] | {
"lo": -5.35,
"mid": 0.52,
"hi": 5.84
} | ||
b12af7 | antilemma_sum_factor_cartesian_v1_1248542787_837 | Let $d$ be a positive divisor of $\gcd(12, 25)$. Define $w = \sum_{d \mid \gcd(12,25)} \mu(d)$, where $\mu$ is the M\"obius function. Let $S$ be the set of all ordered pairs $(i,j)$ of integers with $1 \leq i \leq 9$ and $1 \leq j \leq 11$. Define $x$ to be the sum of $i \cdot j$ over all pairs $(i,j)$ in $S$. Compute ... | 19,774 | graphs = [
Graph(
let={
"x": SumOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("i"), Var("j")]), condition=SumOverDivisors(n=GCD(a=Const(value=12), b=Const(value=25)), var='d', expr=MoebiusMu(n=Var(name='d'))), domain=CartesianProduct(left=IntegerRange(start=Const(1), end=Const(... | NT | null | COMPUTE | sympy | SUM_FACTOR_CARTESIAN | [
"SUM_FACTOR_CARTESIAN",
"MOBIUS_COPRIME"
] | 1428b5 | antilemma_sum_factor_cartesian_v1 | null | 2 | 0 | [
"MOBIUS_COPRIME",
"SUM_FACTOR_CARTESIAN"
] | 2 | 0.001 | 2026-02-08T03:27:05.471611Z | {
"verified": true,
"answer": 19774,
"timestamp": "2026-02-08T03:27:05.472436Z"
} | 2ea311 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 257,
"completion_tokens": 1583
},
"timestamp": "2026-02-09T08:55:18.881Z",
"answer": 19774
},
{
"... | 1 | [
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MOBIUS_COPRIME",
"status": "ok"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "SUM_FACTOR_CART... | {
"lo": -6.51,
"mid": -0.31,
"hi": 5.43
} | ||
1f6141 | antilemma_k2_v1_898971024_644 | Let $x$ be the sum
$$
\sum_{k=1}^{58} \phi(k) \cdot \left\lfloor \frac{s_k}{k} \right\rfloor,
$$
where $s_k$ is the sum of all real solutions $x_1$ to the equation $x_1^2 - 58x_1 - 1463 = 0$. Compute $x$. | 1,711 | graphs = [
Graph(
let={
"_n": Const(2),
"x": Summation(var="k", start=Const(1), end=Const(58), expr=Mul(EulerPhi(n=Var("k")), Floor(Div(SumOverSet(set=SolutionsSet(var=Var("x1"), condition=Eq(Sum(Pow(Var("x1"), Ref("_n")), Mul(Const(-58), Var("x1")), Const(-1463)), Const(0)))), Var("... | NT | COMB | COMPUTE | sympy | VIETA_SUM | [
"VIETA_SUM/K2",
"K2"
] | 6be084 | antilemma_k2_v1 | null | 5 | 0 | [
"K2",
"VIETA_SUM"
] | 2 | 0.002 | 2026-02-08T15:34:27.405661Z | {
"verified": true,
"answer": 1711,
"timestamp": "2026-02-08T15:34:27.407428Z"
} | 53b507 | 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": 979
},
"timestamp": "2026-02-16T08:07:51.033Z",
"answer": 1711
},
{
... | 1 | [
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "K2",
"status": "ok"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
},
... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
f397f5 | sequence_count_fib_divisible_v1_677425708_2148 | Let $N = 800$. Let $u$ be the largest prime number not exceeding $N$. Compute the number of positive integers $n$ such that $n \leq u$ and the $n$-th Fibonacci number is divisible by $15$. | 39 | graphs = [
Graph(
let={
"_n": Const(800),
"upper": MaxOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(2)), Leq(Var("n"), Ref("_n")), IsPrime(Var("n"))))),
"d": Const(15),
"result": CountOverSet(set=SolutionsSet(var=Var("n"), condition=... | NT | null | COUNT | sympy | MIN_PRIME_FACTOR | [
"MAX_PRIME_BELOW"
] | dc3ad3 | sequence_count_fib_divisible_v1 | null | 6 | 0 | [
"MAX_PRIME_BELOW",
"MIN_PRIME_FACTOR"
] | 2 | 0.661 | 2026-02-08T04:48:53.322233Z | {
"verified": true,
"answer": 39,
"timestamp": "2026-02-08T04:48:53.983575Z"
} | ebdb70 | 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": 2220
},
"timestamp": "2026-02-10T06:30:37.269Z",
"answer": 39
},
{
"id"... | 1 | [
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
}
] | {
"lo": -5.55,
"mid": -3.02,
"hi": 0.32
} | ||
766348 | antilemma_k2_v1_260342960_30 | Let $n = 44121$. Let $d_1, d_2, \dots, d_k$ be the positive divisors of $228$. For each divisor $d_i$, compute $\phi(d_i)$, and let $T = \sum_{i=1}^k \phi(d_i)$. Define
$$
x = \sum_{k=1}^{T} \phi(k) \left\lfloor \frac{228}{k} \right\rfloor.
$$
Compute the remainder when $n \cdot x$ is divided by $62687$. | 11,888 | graphs = [
Graph(
let={
"_n": Const(44121),
"x": Summation(var="k", start=Const(1), end=SumOverDivisors(n=Const(value=228), var='d', expr=EulerPhi(n=Var(name='d'))), expr=Mul(EulerPhi(n=Var("k")), Floor(Div(Const(228), Var("k"))))),
"Q": Mod(value=Mul(Ref("_n"), Ref("x"))... | NT | COMB | COMPUTE | sympy | K13 | [
"K3/K2",
"K2"
] | c7f244 | antilemma_k2_v1 | null | 6 | 0 | [
"K13",
"K2",
"K3"
] | 3 | 0.002 | 2026-02-08T11:11:21.992738Z | {
"verified": true,
"answer": 11888,
"timestamp": "2026-02-08T11:11:21.994439Z"
} | 2bb372 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 238,
"completion_tokens": 2252
},
"timestamp": "2026-02-08T20:27:35.401Z",
"answer": 11888
},
{
"... | 1 | [
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "K2",
"status": "ok"
},
{
"lemma": "K3",
"status": "ok"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
},
{
"lemma": "V7",
... | {
"lo": -0.14,
"mid": 2.22,
"hi": 4.26
} | ||
1aa8e1 | comb_binomial_compute_v1_865884756_4605 | Let $n = 14$. Let $k$ be the largest integer $d$ with $1 \leq d \leq 8$ such that $d$ divides the number of prime numbers between $2$ and $457$, inclusive. Compute $\binom{n}{k}$. | 3,003 | graphs = [
Graph(
let={
"_n": Const(457),
"n": Const(14),
"k": MaxOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Const(1)), Leq(Var("d"), Const(8)), Divides(divisor=Var("d"), dividend=CountOverSet(set=SolutionsSet(var=Var("n1"), condition=And(Geq(Var("... | NT | null | COMPUTE | sympy | COUNT_PRIMES | [
"COUNT_PRIMES/MAX_DIVISOR"
] | 3db9d0 | comb_binomial_compute_v1 | null | 4 | 0 | [
"COUNT_PRIMES",
"MAX_DIVISOR"
] | 2 | 0.003 | 2026-02-08T18:00:19.514002Z | {
"verified": true,
"answer": 3003,
"timestamp": "2026-02-08T18:00:19.516919Z"
} | f880f8 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 104,
"completion_tokens": 1003
},
"timestamp": "2026-02-18T11:49:45.240Z",
"answer": 3003
},
{... | 1 | [
{
"lemma": "COUNT_PRIMES",
"status": "ok"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MAX_DIVISOR",
"status": "ok_later"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "POLY_PADIC_... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
940de7 | diophantine_fbi2_min_v1_153355830_2618 | Let $k = 360$. Let $S$ be the set of all ordered pairs $(a,b)$ where $a$ is an integer with $1 \le a \le 10$ and $b$ is an integer with $1 \le b \le 37$. Define $u$ to be the number of elements in $S$. Determine the value of the smallest integer $d$ such that $3 \le d \le u$, $d$ divides $k$, and $\frac{k}{d} \ge 7$. | 3 | graphs = [
Graph(
let={
"k": Const(360),
"upper": CountOverSet(set=CartesianProduct(left=IntegerRange(start=Const(1), end=Const(10)), right=IntegerRange(start=Const(1), end=Const(37)))),
"result": MinOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Const... | NT | null | EXTREMUM | sympy | MAX_PRIME_BELOW | [
"COUNT_CARTESIAN"
] | 409d7d | diophantine_fbi2_min_v1 | null | 4 | 0 | [
"COUNT_CARTESIAN",
"MAX_PRIME_BELOW"
] | 2 | 0.163 | 2026-02-08T07:14:47.859188Z | {
"verified": true,
"answer": 3,
"timestamp": "2026-02-08T07:14:48.022247Z"
} | 5f86ab | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 159,
"completion_tokens": 789
},
"timestamp": "2026-02-13T09:07:25.020Z",
"answer": 3
},
{
... | 1 | [
{
"lemma": "COUNT_CARTESIAN",
"status": "ok"
},
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"sta... | {
"lo": -7.01,
"mid": -4.68,
"hi": -2.15
} | ||
02f009 | nt_count_divisible_v1_1520064083_3586 | Let $d$ be the number of integers $t$ such that $7 \leq t \leq 33$ and there exist positive integers $a \leq 3$ and $b \leq 9$ for which $t = 5a + 2b$. Let $s$ be the number of integers $n$ with $1 \leq n \leq 67600$ such that
$$
n \equiv \sum_{k=0}^{8} (-1)^k \binom{8}{k} \pmod{d}.
$$
Compute the remainder when $17825... | 78,811 | graphs = [
Graph(
let={
"upper": Const(67600),
"divisor": CountOverSet(set=SolutionsSet(var=Var("t"), condition=Exists(var=Var(name='a'), condition=Exists(var=Var(name='b'), condition=And(Geq(left=Var(name='a'), right=Const(value=1)), Leq(left=Var(name='a'), right=Const(value=3)), Ge... | COMB | null | COUNT | sympy | BINOMIAL_ALTERNATING | [
"BINOMIAL_ALTERNATING",
"LIN_FORM"
] | 10f694 | nt_count_divisible_v1 | null | 5 | 0 | [
"BINOMIAL_ALTERNATING",
"LIN_FORM"
] | 2 | 2.428 | 2026-02-08T05:45:11.273037Z | {
"verified": true,
"answer": 78811,
"timestamp": "2026-02-08T05:45:13.700847Z"
} | 866506 | 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": 3547
},
"timestamp": "2026-02-24T04:27:42.919Z",
"answer": 78811
},
{
"... | 1 | [
{
"lemma": "BINOMIAL_ALTERNATING",
"status": "ok"
},
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "V7",
"stat... | {
"lo": -0.06,
"mid": 2.89,
"hi": 5.27
} | ||
272133 | nt_count_coprime_v1_717093673_1316 | Let $m$ be the number of positive integers $p$ for which there exists a positive integer $q$ such that $pq = 18$, $\gcd(p, q) = 1$, and $p < q$. Let $k$ be the largest integer such that $m^k \leq 34651624384$. Let $S$ be the set of all positive integers $n$ such that $1 \leq n \leq 56644$ and $\gcd(n, k) = 1$. Let $\el... | 1 | graphs = [
Graph(
let={
"_m": CountOverSet(set=SolutionsSet(var=Var("p"), condition=And(IsPositive(arg=Var(name='p')), Exists(var=Var(name='q'), condition=And(Eq(left=Mul(Var(name='p'), Var(name='q')), right=Const(value=18)), Eq(left=GCD(a=Var(name='p'), b=Var(name='q')), right=Const(value=1)), ... | NT | COMB | COUNT | sympy | MAX_PRIME_BELOW | [
"MAX_PRIME_BELOW",
"COPRIME_PAIRS/MAX_VAL"
] | 05d06b | nt_count_coprime_v1 | bell_mod | 6 | 0 | [
"COPRIME_PAIRS",
"MAX_PRIME_BELOW",
"MAX_VAL"
] | 3 | 6.447 | 2026-02-08T15:59:29.706700Z | {
"verified": true,
"answer": 1,
"timestamp": "2026-02-08T15:59:36.154085Z"
} | ebf070 | 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": 1023
},
"timestamp": "2026-02-16T18:53:16.728Z",
"answer": 1
},
{
... | 1 | [
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok"
},
{
"lemma": "MAX_VAL",
"status": "ok_later"
}... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
e397ce | modular_mod_compute_v1_601307018_7074 | Let $m$ be the smallest positive divisor of $2082233$. Find the remainder when $56616$ is divided by $m$. | 495 | graphs = [
Graph(
let={
"_n": Const(2),
"a": Const(56616),
"m": MinOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Ref("_n")), Divides(divisor=Var("d"), dividend=Const(2082233))))),
"result": Mod(value=Ref("a"), modulus=Ref("m")),
},... | NT | null | COMPUTE | sympy | MIN_PRIME_FACTOR | [
"MIN_PRIME_FACTOR"
] | bc3776 | modular_mod_compute_v1 | null | 2 | 0 | [
"MIN_PRIME_FACTOR"
] | 1 | 0.003 | 2026-03-10T07:44:05.762272Z | {
"verified": true,
"answer": 495,
"timestamp": "2026-03-10T07:44:05.765054Z"
} | fd866e | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 139,
"completion_tokens": 11480
},
"timestamp": "2026-04-19T05:57:40.603Z",
"answer": 495
},
{
"... | 1 | [
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MIN_PRIME_FACTOR",
"status": "ok"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
}
] | {
"lo": -5.34,
"mid": 1.1,
"hi": 7.53
} | ||
481a3e | modular_modexp_compute_v1_153355830_2443 | Let $a = 3$, $e = 676$, and $m = 68121$. Define $r$ to be the remainder when $a^e$ is divided by $m$. Let $c$ be the sum of $\phi(d)$ over all positive divisors $d$ of $361$. Find the remainder when $c - r$ is divided by $84006$. | 56,098 | graphs = [
Graph(
let={
"_n": Const(361),
"a": Const(3),
"e": Const(676),
"m": Const(68121),
"result": ModExp(base=Ref("a"), exp=Ref("e"), mod=Ref("m")),
"_c": SumOverDivisors(n=Ref(name='_n'), var='d', expr=EulerPhi(n=Var(name='d'))),
... | NT | null | COMPUTE | sympy | K3 | [
"K3"
] | 91dc2d | modular_modexp_compute_v1 | negation_mod | 4 | 0 | [
"K3"
] | 1 | 0.002 | 2026-02-08T07:07:59.878213Z | {
"verified": true,
"answer": 56098,
"timestamp": "2026-02-08T07:07:59.879976Z"
} | 3e51c9 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 127,
"completion_tokens": 4349
},
"timestamp": "2026-02-13T08:20:57.631Z",
"answer": 56098
},
... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "K3",
"status": "ok"
},
{
"lemma": "V8_SUM",
"status": "no"
}
] | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
21cee8 | nt_min_coprime_above_v1_1353956133_617 | Let $a = 48841$ and $b = 48898$. Let $d$ be the smallest divisor of $2491$ that is at least $2$. Define $S$ as the set of all integers $n$ such that $a < n \leq b$ and $\gcd(n, d) = 1$. Let $m$ be the smallest element of $S$. Compute the value of
$$
\sum_{i=0}^{\lfloor \log_{10} |m| \rfloor} \left( \text{the } i\text{-... | 25,282 | graphs = [
Graph(
let={
"start": Const(48841),
"upper": Const(48898),
"modulus": MinOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Const(2)), Divides(divisor=Var("d"), dividend=Const(2491))))),
"result": MinOverSet(set=SolutionsSet(var=Var(... | NT | null | EXTREMUM | sympy | MIN_PRIME_FACTOR | [
"MIN_PRIME_FACTOR"
] | bc3776 | nt_min_coprime_above_v1 | null | 4 | 0 | [
"MIN_PRIME_FACTOR"
] | 1 | 0.018 | 2026-02-08T11:43:55.203791Z | {
"verified": true,
"answer": 25282,
"timestamp": "2026-02-08T11:43:55.222278Z"
} | dfc871 | 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": 1497
},
"timestamp": "2026-02-14T17:50:19.322Z",
"answer": 25282
},
... | 1 | [
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "MIN_PRIME_FACTOR",
"status": "ok"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
... | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
7774de | comb_count_partitions_v1_784195855_3930 | Let $M$ be the number of integers $n$ with $1 \le n \le 799$ such that the sum of the decimal digits of $n$ is odd.
Consider all ordered pairs $(x,y)$ of positive integers such that $xy = M$. For each such pair, form the sum $x+y$. Let $N$ be the smallest possible value of $x+y$ over all such pairs.
Let $P$ be the nu... | 55,226 | graphs = [
Graph(
let={
"_m": Const(98935),
"_n": Const(39567),
"n": MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(Mul(Var("x"), Var("y")), CountOverSet(s... | COMB | null | COUNT | sympy | L3B | [
"L3B/B3"
] | f2ec8b | comb_count_partitions_v1 | null | 8 | 0 | [
"B3",
"L3B"
] | 2 | 0.004 | 2026-02-08T06:42:34.577909Z | {
"verified": true,
"answer": 55226,
"timestamp": "2026-02-08T06:42:34.581924Z"
} | 376c94 | 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": 4440
},
"timestamp": "2026-02-24T06:53:01.667Z",
"answer": 55226
},
{
"... | 1 | [
{
"lemma": "B3",
"status": "ok_later"
},
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "L3B",
"status": "ok"
},
{
"lemma": "V8",
"status": "no"
}... | {
"lo": -2.46,
"mid": 0.47,
"hi": 3.59
} | ||
50ddf3 | sequence_count_fib_divisible_v1_784195855_734 | Let $n$ be a positive integer. Consider the set of all ordered pairs $(x,y)$ of positive integers such that $xy = 7744$. Let $S$ be the set of all values of $x + y$ for such pairs. Let $m$ be the minimum element of $S$. Define $u$ to be the largest prime number $n$ such that $2 \leq n \leq m$. Determine the number of p... | 28 | graphs = [
Graph(
let={
"_n": Const(2),
"upper": MaxOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Ref("_n")), Leq(Var("n"), MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositiv... | NT | null | COUNT | sympy | B3 | [
"B3/MAX_PRIME_BELOW"
] | f253c0 | sequence_count_fib_divisible_v1 | null | 7 | 0 | [
"B3",
"MAX_PRIME_BELOW"
] | 2 | 0.01 | 2026-02-08T04:34:28.602867Z | {
"verified": true,
"answer": 28,
"timestamp": "2026-02-08T04:34:28.612917Z"
} | 323899 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 241,
"completion_tokens": 1845
},
"timestamp": "2026-02-10T17:04:44.362Z",
"answer": 28
},
{
"id... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok_later"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
... | {
"lo": -3.42,
"mid": 1.86,
"hi": 7.55
} | ||
7ba672 | comb_factorial_compute_v1_151522320_1762 | Let $n$ be the number of nonnegative integers $j$ such that $0 \leq j \leq 33028$ and $\binom{33028}{j}$ is odd. Compute $n!$. | 40,320 | graphs = [
Graph(
let={
"_n": Const(33028),
"n": CountOverSet(set=SolutionsSet(var=Var("j"), condition=And(Geq(Var("j"), Const(0)), Leq(Var("j"), Const(33028)), Eq(Mod(value=Binom(n=Ref("_n"), k=Var("j")), modulus=Const(2)), Const(1))), domain='nonnegative_integers')),
"r... | ALG | COMB | COMPUTE | sympy | V8 | [
"V8"
] | 86348e | comb_factorial_compute_v1 | null | 6 | 0 | [
"V8"
] | 1 | 0.002 | 2026-02-08T04:20:57.458574Z | {
"verified": true,
"answer": 40320,
"timestamp": "2026-02-08T04:20:57.460367Z"
} | 02dfda | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 157,
"completion_tokens": 1052
},
"timestamp": "2026-02-24T00:21:24.896Z",
"answer": 40320
},
{
"... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "V1",
"status": "no"
},
{
"lemma": "V8",
"status": "ok"
}
] | {
"lo": -2.46,
"mid": 0.47,
"hi": 3.59
} | ||
195bae | diophantine_product_count_v1_677425708_925 | Let $k = 720$ and $U = 453$. Define $S$ to be the set of all positive integers $x$ such that $1 \le x \le 453$, $x$ divides $720$, and $\frac{720}{x} \le 453$. Compute the number of elements in $S$. Determine the value of this count. | 28 | graphs = [
Graph(
let={
"k": Const(720),
"upper": Const(453),
"result": CountOverSet(set=SolutionsSet(var=Var("x"), condition=And(Geq(Var("x"), Const(1)), Leq(Var("x"), Ref("upper")), Divides(divisor=Var("x"), dividend=Ref("k")), Leq(Div(Ref("k"), Var("x")), Ref("upper"))... | NT | null | COUNT | sympy | B3 | [
"LIN_FORM"
] | 7b2633 | diophantine_product_count_v1 | null | 5 | 0 | [
"B3",
"LIN_FORM"
] | 2 | 0.172 | 2026-02-08T03:52:33.601070Z | {
"verified": true,
"answer": 28,
"timestamp": "2026-02-08T03:52:33.773081Z"
} | f2f8ac | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 191,
"completion_tokens": 3837
},
"timestamp": "2026-02-09T14:08:55.216Z",
"answer": 28
},
{
"id"... | 1 | [
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "V5",
"status"... | {
"lo": -3.46,
"mid": 1.03,
"hi": 5.49
} | ||
4f6bff | nt_count_primes_v1_1470522791_581 | Let $S$ be the set of all positive integers $p$ such that there exists a positive integer $q$ satisfying $pq = 18$, $\gcd(p, q) = 1$, and $p < q$. Let $L$ be the number of elements in $S$. Let $T$ be the set of all prime numbers $n$ such that $L \leq n \leq 21025$. Compute the number of elements in $T$. | 2,366 | graphs = [
Graph(
let={
"upper": Const(21025),
"result": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), CountOverSet(set=SolutionsSet(var=Var("p"), condition=And(IsPositive(arg=Var(name='p')), Exists(var=Var(name='q'), condition=And(Eq(left=Mul(Var(name='p'),... | NT | null | COUNT | sympy | COPRIME_PAIRS | [
"COPRIME_PAIRS"
] | 2bb3aa | nt_count_primes_v1 | null | 3 | 0 | [
"COPRIME_PAIRS"
] | 1 | 4.568 | 2026-02-08T13:07:45.957266Z | {
"verified": true,
"answer": 2366,
"timestamp": "2026-02-08T13:07:50.525272Z"
} | 032b9e | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 143,
"completion_tokens": 1869
},
"timestamp": "2026-02-15T09:54:32.327Z",
"answer": 2366
},
{... | 1 | [
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
}
] | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
08c363 | alg_poly3_min_v1_1218484723_3883 | Let $B$ be the set of integers $b$ with $1 \le b \le 25$ for which there exist integers $a_1, b_1 \in [1,25]$ such that
\[
384a_1^2b_1 + 128b_1^3 + 128a_1^3 + C \cdot a_1b_1^2 = 2000000,
\]
where $C$ is the number of integer pairs $(a_2,b_2) \in [1,35]^2$ satisfying $13a_2^2 - 2a_2b_2 + 2b_2^2 \le 2297$. Find the minim... | 831 | graphs = [
Graph(
let={
"_m": Const(2),
"_n": Const(2),
"result": Mod(value=MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("a"), Var("b"), Var("c")]), condition=And(Geq(Var("a"), Const(1)), Leq(Var("a"), Const(24)), Geq(Var("b"), Const(1)), Leq(Var("b"... | ALG | null | COMPUTE | sympy | QF_PSD_COUNT_LEQ | [
"QF_PSD_COUNT_LEQ/POLY3_COUNT"
] | 1c021d | alg_poly3_min_v1 | null | 5 | 0 | [
"POLY3_COUNT",
"QF_PSD_COUNT_LEQ"
] | 2 | 0.054 | 2026-02-25T05:30:53.646974Z | {
"verified": true,
"answer": 831,
"timestamp": "2026-02-25T05:30:53.700998Z"
} | d1f117 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 375,
"completion_tokens": 32768
},
"timestamp": "2026-03-29T12:45:33.044Z",
"answer": null
},
{
... | 1 | [
{
"lemma": "POLY3_COUNT",
"status": "ok_later"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "QF_PSD_COUNT_LEQ",
"status": "ok"
}
] | {
"lo": 3.81,
"mid": 6.33,
"hi": 9.49
} | ||
e6b84e | nt_sum_divisors_mod_v1_1520064083_7292 | Let $S$ be the set of all ordered pairs $(x, y)$ of positive integers such that $xy = 705600$. For each such pair, compute $x + y$. Let $n$ be the smallest value of $x + y$ over all such pairs.
Let $\sigma(n)$ denote the sum of the positive divisors of $n$. Compute the remainder when $\sigma(n)$ is divided by $10601$. | 5,952 | graphs = [
Graph(
let={
"n": MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(Mul(Var("x"), Var("y")), Const(705600)))), expr=Sum(Var("x"), Var("y")))),
"M": Const(10601... | NT | null | COMPUTE | sympy | B3 | [
"B3"
] | 0cd20d | nt_sum_divisors_mod_v1 | null | 4 | 0 | [
"B3"
] | 1 | 0.001 | 2026-02-08T08:53:17.653257Z | {
"verified": true,
"answer": 5952,
"timestamp": "2026-02-08T08:53:17.654636Z"
} | 1e5852 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 136,
"completion_tokens": 1413
},
"timestamp": "2026-02-13T22:53:05.098Z",
"answer": 5952
},
{... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "V3",
"status": "no"
}
] | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
95c03c | modular_sum_quadratic_residues_v1_865884756_7142 | Let $P$ be the set of all positive integers $p_1$ for which there exists a positive integer $q$ such that $p_1 q = 72$, $\gcd(p_1, q) = 1$, and $p_1 < q$. Let $n$ be the number of elements in $P$.
Let $p$ be the smallest divisor of $394399573$ that is at least $n$. Compute the remainder when $30335 \cdot \frac{p(p-1)}... | 11,220 | graphs = [
Graph(
let={
"_m": Const(4),
"_n": CountOverSet(set=SolutionsSet(var=Var("p1"), condition=And(IsPositive(arg=Var(name='p1')), Exists(var=Var(name='q'), condition=And(Eq(left=Mul(Var(name='p1'), Var(name='q')), right=Const(value=72)), Eq(left=GCD(a=Var(name='p1'), b=Var(nam... | NT | null | SUM | sympy | COPRIME_PAIRS | [
"COPRIME_PAIRS/MIN_PRIME_FACTOR"
] | 52cee2 | modular_sum_quadratic_residues_v1 | null | 6 | 0 | [
"COPRIME_PAIRS",
"MIN_PRIME_FACTOR"
] | 2 | 0.002 | 2026-02-08T19:38:09.603429Z | {
"verified": true,
"answer": 11220,
"timestamp": "2026-02-08T19:38:09.605540Z"
} | 331d0c | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 163,
"completion_tokens": 3509
},
"timestamp": "2026-02-18T23:00:57.979Z",
"answer": 11220
},
... | 1 | [
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "MIN_PRIME_FACTOR",
"status": "ok_later"
},
{
"lemma": "... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
bcee5c | algebra_quadratic_discriminant_v1_1918700295_169 | Let $a = 1$, $b = -2$, and $c = -48$. Let $k$ be the number of positive integers $p$ for which there exists a positive integer $q$ such that $p < q$, $pq = 18$, and $\gcd(p, q) = 1$. Compute $b^k - 4ac$. | 196 | graphs = [
Graph(
let={
"_n": Const(4),
"a": Const(1),
"b": Const(-2),
"c": Const(-48),
"result": Sub(Pow(Ref("b"), CountOverSet(set=SolutionsSet(var=Var("p"), condition=And(IsPositive(arg=Var(name='p')), Exists(var=Var(name='q'), condition=And(Eq(... | NT | null | COMPUTE | sympy | COPRIME_PAIRS | [
"COPRIME_PAIRS"
] | 2bb3aa | algebra_quadratic_discriminant_v1 | null | 5 | 0 | [
"COPRIME_PAIRS"
] | 1 | 0.003 | 2026-02-08T03:01:44.036483Z | {
"verified": true,
"answer": 196,
"timestamp": "2026-02-08T03:01:44.039425Z"
} | 4cca0a | 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": 735
},
"timestamp": "2026-02-10T12:37:03.757Z",
"answer": 196
},
{
"id"... | 1 | [
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
}
] | {
"lo": -5.55,
"mid": -3.02,
"hi": 0.3
} | ||
20bb8f | nt_sum_divisors_mod_v1_809748730_819 | Let $n$ be the sum of Euler's totient function $\phi(d)$ over all positive divisors $d$ of $5040$. Let $\sigma$ denote the sum of all positive divisors of $n$. Let $M = 11903$, and let $r$ be the remainder when $\sigma$ is divided by $M$. Compute $62001 - r$. | 54,560 | graphs = [
Graph(
let={
"n": SumOverDivisors(n=Const(value=5040), var='d', expr=EulerPhi(n=Var(name='d'))),
"M": Const(11903),
"sigma": SumDivisors(n=Ref("n")),
"result": Mod(value=Ref("sigma"), modulus=Ref("M")),
"_c": Const(62001),
"Q... | NT | null | COMPUTE | sympy | K3 | [
"K3"
] | 54c41e | nt_sum_divisors_mod_v1 | null | 4 | 0 | [
"K3"
] | 1 | 0.001 | 2026-02-08T11:46:07.669233Z | {
"verified": true,
"answer": 54560,
"timestamp": "2026-02-08T11:46:07.670390Z"
} | 8a0223 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 123,
"completion_tokens": 1109
},
"timestamp": "2026-02-14T18:31:02.727Z",
"answer": 54560
},
... | 1 | [
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "K3",
"status": "ok"
},
{
"lemma": "V1",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
}
] | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
58a748 | sequence_fibonacci_compute_v1_1125832087_1549 | Let $ t $ be an integer. Let $ A $ be the set of all integers $ t $ such that $ 8 \leq t \leq 1311 $ and there exist positive integers $ a \leq 392 $ and $ b \leq 27 $ satisfying $ t = 3a + 5b $. Let $ N $ be the number of elements in $ A $. Let $ F_{24} $ be the 24th Fibonacci number. Compute the remainder when $ N - ... | 17,438 | graphs = [
Graph(
let={
"n": Const(24),
"result": Fibonacci(arg=Ref(name='n')),
"Q": Mod(value=Sub(CountOverSet(set=SolutionsSet(var=Var("t"), condition=Exists(var=Var(name='a'), condition=Exists(var=Var(name='b'), condition=And(Geq(left=Var(name='a'), right=Const(value=1... | NT | null | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM"
] | 324ba4 | sequence_fibonacci_compute_v1 | negation_mod | 4 | 0 | [
"LIN_FORM"
] | 1 | 0.001 | 2026-02-08T03:47:25.257735Z | {
"verified": true,
"answer": 17438,
"timestamp": "2026-02-08T03:47:25.258869Z"
} | 8179c2 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 229,
"completion_tokens": 8040
},
"timestamp": "2026-02-10T15:42:45.957Z",
"answer": 17442
},
{
... | 1 | [
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
}
] | {
"lo": 1.71,
"mid": 5.04,
"hi": 8.38
} | ||
71cf92 | nt_num_divisors_compute_v1_151522320_2129 | Let $p$ and $q$ be positive integers such that $pq = 36$, $\gcd(p, q) = 1$, and $p < q$. Define $\mathcal{S}$ as the set of all such integers $p$. Let $n$ be the sum of all real solutions $x$ to the equation $x^{|\mathcal{S}|} - 16x - 4032 = 0$. Determine the value of $\tau(n)$, the number of positive divisors of $n$. | 5 | graphs = [
Graph(
let={
"_n": CountOverSet(set=SolutionsSet(var=Var("p"), condition=And(IsPositive(arg=Var(name='p')), Exists(var=Var(name='q'), condition=And(Eq(left=Mul(Var(name='p'), Var(name='q')), right=Const(value=36)), Eq(left=GCD(a=Var(name='p'), b=Var(name='q')), right=Const(value=1)), ... | NT | null | COMPUTE | sympy | B1 | [
"COPRIME_PAIRS/VIETA_SUM"
] | 815fe1 | nt_num_divisors_compute_v1 | null | 5 | 0 | [
"B1",
"COPRIME_PAIRS",
"VIETA_SUM"
] | 3 | 0.006 | 2026-02-08T04:37:49.350853Z | {
"verified": true,
"answer": 5,
"timestamp": "2026-02-08T04:37:49.356669Z"
} | 030a48 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 221,
"completion_tokens": 1050
},
"timestamp": "2026-02-11T21:38:28.798Z",
"answer": 5
},
{
"id"... | 1 | [
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
... | {
"lo": -5.55,
"mid": -3.01,
"hi": 0.33
} | ||
419110 | antilemma_sum_equals_v1_784195855_1500 | Let $m = 67$. Let $n$ be the number of ordered pairs $(i, j)$ with $1 \le i \le 66$, $1 \le j \le 67$, and $i + j = m$. Compute the number of ordered pairs $(i, j)$ with $1 \le i \le 64$, $1 \le j \le 65$, and $i + j = n$. | 64 | graphs = [
Graph(
let={
"_m": Const(67),
"_n": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("i"), Var("j")]), condition=Eq(Sum(Var("i"), Var("j")), Ref("_m")), domain=CartesianProduct(left=IntegerRange(start=Const(1), end=Const(66)), right=IntegerRange(start=Const(1), end=Co... | COMB | GEOM | COMPUTE | sympy | COUNT_SUM_EQUALS | [
"COUNT_SUM_EQUALS/COUNT_SUM_EQUALS",
"COUNT_SUM_EQUALS"
] | ae9919 | antilemma_sum_equals_v1 | null | 3 | 0 | [
"COUNT_SUM_EQUALS"
] | 1 | 0.111 | 2026-02-08T05:03:11.225909Z | {
"verified": true,
"answer": 64,
"timestamp": "2026-02-08T05:03:11.336781Z"
} | 50aa09 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 201,
"completion_tokens": 32768
},
"timestamp": "2026-02-24T02:50:57.727Z",
"answer": 64
},
{
"id... | 2 | [
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "ok"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8_SU... | {
"lo": -9.23,
"mid": -6.18,
"hi": -4.06
} | ||
71e45b | antilemma_count_primes_v1_784195855_54 | Let $c = 2$. Let $S$ be the set of all nonnegative integers $j$ with $0 \leq j \leq 44$ such that $\binom{44}{j}$ is odd. Let $\text{sum}_S$ be the sum of all elements in $S$. Let $\text{_n}$ be the largest prime number $n$ such that $2 \leq n \leq \text{sum}_S$. Let $x$ be the number of prime numbers $n$ such that $2 ... | 82 | graphs = [
Graph(
let={
"_c": Const(2),
"_m": Const(2),
"_n": MaxOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(2)), Leq(Var("n"), SumOverSet(set=SolutionsSet(var=Var("j"), condition=And(Geq(Var("j"), Const(0)), Leq(Var("j"), Const(44)), Eq(Mod(v... | NT | null | COMPUTE | sympy | V8 | [
"V8/MAX_PRIME_BELOW/COUNT_PRIMES",
"COUNT_PRIMES"
] | 3e1a55 | antilemma_count_primes_v1 | null | 5 | 0 | [
"COUNT_PRIMES",
"MAX_PRIME_BELOW",
"V8"
] | 3 | 0.003 | 2026-02-08T02:55:32.477965Z | {
"verified": true,
"answer": 82,
"timestamp": "2026-02-08T02:55:32.480696Z"
} | 3c329c | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 294,
"completion_tokens": 1608
},
"timestamp": "2026-02-08T22:19:17.382Z",
"answer": 82
},
{
"id... | 1 | [
{
"lemma": "COUNT_PRIMES",
"status": "ok"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok_later"
},
{
"lemma": "MAX_VAL",
"status": "no"... | {
"lo": -6.49,
"mid": 0.51,
"hi": 7.52
} | ||
5a8db5 | algebra_quadratic_discriminant_v1_784195855_5721 | Let $a = 1$, $c = 100$, and let $b$ be the minimum value of $x + y$ over all pairs of positive integers $(x, y)$ such that $xy = 100$. Compute $b^2 - 4ac$. | 0 | graphs = [
Graph(
let={
"_n": Const(4),
"a": Const(1),
"b": MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(Mul(Var("x"), Var("y")), Const(100)))), expr=Sum... | NT | null | COMPUTE | sympy | B3 | [
"B3"
] | 0cd20d | algebra_quadratic_discriminant_v1 | null | 3 | 0 | [
"B3"
] | 1 | 0.014 | 2026-02-08T08:05:16.127345Z | {
"verified": true,
"answer": 0,
"timestamp": "2026-02-08T08:05:16.141374Z"
} | 83674b | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 117,
"completion_tokens": 387
},
"timestamp": "2026-02-15T19:09:55.491Z",
"answer": 0
},
{
"id": 11,
"... | 2 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
}
] | {
"lo": -10,
"mid": -7.73,
"hi": -5.46
} | ||
a06f3b | comb_count_derangements_v1_151522320_331 | Let $n_2 = 8$. Define
$$
s = \sum_{k=0}^{8} (-1)^k \binom{8}{k}.
$$
Let $n_1 = 3 + s$. Define
$$
h = \sum_{k=0}^{n_1} (-1)^k \binom{n_1}{k}.
$$
Let $n = 7 + h$.
Compute the number of derangements of $n$ elements. | 1,854 | graphs = [
Graph(
let={
"n2": Const(8),
"s": Summation(var="k", start=Sub(Binom(n=Const(1), k=Const(1)), Const(1)), end=Ref("n2"), expr=Mul(Pow(Const(-1), Var("k")), Binom(n=Ref("n2"), k=Var("k")))),
"n1": Sum(Const(3), Ref("s")),
"h": Summation(var="k", start... | COMB | null | COUNT | sympy | BINOMIAL_ALTERNATING | [
"BINOMIAL_ALTERNATING",
"ZERO_BINOM_N"
] | ba7829 | comb_count_derangements_v1 | null | 5 | 2 | [
"BINOMIAL_ALTERNATING",
"ZERO_BINOM_N"
] | 2 | 0.002 | 2026-02-08T03:09:38.565386Z | {
"verified": true,
"answer": 1854,
"timestamp": "2026-02-08T03:09:38.567771Z"
} | 8db2d9 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 214,
"completion_tokens": 896
},
"timestamp": "2026-02-10T13:26:16.140Z",
"answer": 1854
},
{
"id... | 1 | [
{
"lemma": "BINOMIAL_ALTERNATING",
"status": "ok"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
},
{
"lemma": "V8_SUM",
"sta... | {
"lo": -5.97,
"mid": -3.96,
"hi": -1.93
} | ||
c04660 | nt_count_divisors_in_range_v1_124444284_2338 | Let $n = 166320$. Let $S$ be the set of all ordered pairs $(x,y)$ of positive integers such that $xy = 3426201$. Let $b$ be the minimum value of $x + y$ as $(x,y)$ ranges over $S$.
Compute the number of positive divisors $d$ of $n$ such that $6 \leq d \leq b$. | 126 | graphs = [
Graph(
let={
"n": Const(166320),
"a": Const(6),
"b": MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(Mul(Var("x"), Var("y")), Const(3426201)))), ... | NT | null | COUNT | sympy | MAX_PRIME_BELOW | [
"B3"
] | 0cd20d | nt_count_divisors_in_range_v1 | null | 4 | 0 | [
"B3",
"MAX_PRIME_BELOW"
] | 2 | 0.057 | 2026-02-08T04:35:58.862292Z | {
"verified": true,
"answer": 126,
"timestamp": "2026-02-08T04:35:58.918990Z"
} | 83b4ef | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 132,
"completion_tokens": 5613
},
"timestamp": "2026-02-12T01:45:05.969Z",
"answer": 126
},
{
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "LTE_DIFF",
... | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
848617 | comb_count_permutations_fixed_v1_2051736721_2654 | Let $k$ be the smallest divisor of $847$ that is at least $2$. Compute $\binom{10}{k} \cdot ! (10 - k)$, where $!m$ denotes the number of derangements of $m$ elements. | 240 | graphs = [
Graph(
let={
"_n": Const(2),
"n": Const(10),
"k": MinOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Ref("_n")), Divides(divisor=Var("d"), dividend=Const(847))))),
"result": Mul(Binom(n=Ref("n"), k=Ref("k")), Subfactorial(arg=Sub(... | NT | COMB | COUNT | sympy | MIN_PRIME_FACTOR | [
"MIN_PRIME_FACTOR"
] | bc3776 | comb_count_permutations_fixed_v1 | null | 3 | 0 | [
"MIN_PRIME_FACTOR"
] | 1 | 0.003 | 2026-02-08T16:49:57.550260Z | {
"verified": true,
"answer": 240,
"timestamp": "2026-02-08T16:49:57.553703Z"
} | 5e9de7 | 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": 603
},
"timestamp": "2026-02-17T13:10:48.203Z",
"answer": 240
},
{
... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MIN_PRIME_FACTOR",
"status": "ok"
},
{
"lemma": "MOD_SUB",
"stat... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
cdd332 | antilemma_k2_v1_2051736721_3143 | Let $m = 349$. Let $n$ be the sum of $\phi(d)$ over all positive divisors $d$ of $350$, where $\phi$ denotes Euler's totient function. Define
$$
x = \sum_{k=1}^{n} \phi(k) \left\lfloor \frac{1}{k} \cdot s \right\rfloor,
$$
where $s$ is the sum of all real solutions to the equation $x_1^2 - 350x_1 + m = 0$. Compute $x$. | 61,425 | graphs = [
Graph(
let={
"_m": Const(349),
"_n": SumOverDivisors(n=Const(value=350), var='d', expr=EulerPhi(n=Var(name='d'))),
"x": Summation(var="k", start=Const(1), end=Ref("_n"), expr=Mul(EulerPhi(n=Var("k")), Floor(Div(SumOverSet(set=SolutionsSet(var=Var("x1"), conditi... | NT | COMB | COMPUTE | sympy | VIETA_SUM | [
"VIETA_SUM/K2",
"K3/K2",
"K2"
] | 4108ea | antilemma_k2_v1 | null | 6 | 0 | [
"K2",
"K3",
"VIETA_SUM"
] | 3 | 0.002 | 2026-02-08T17:08:21.943974Z | {
"verified": true,
"answer": 61425,
"timestamp": "2026-02-08T17:08:21.945692Z"
} | 6b574d | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 161,
"completion_tokens": 783
},
"timestamp": "2026-02-17T20:41:10.700Z",
"answer": 61425
},
{... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "K2",
"status": "ok"
},
{
"lemma": "K3",
"status": "ok"
},
{
"lemma": ... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} |
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