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 |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
ba33f7 | sequence_lucas_compute_v1_1742523217_4896 | Let $n$ be the number of prime numbers between 2 and 71, inclusive. Compute the $n$-th Lucas number. | 15,127 | graphs = [
Graph(
let={
"_n": Const(2),
"n": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Ref("_n")), Leq(Var("n"), Const(71)), IsPrime(Var("n"))))),
"result": Lucas(arg=Ref(name='n')),
},
goal=Ref("result"),
)
] | NT | null | COMPUTE | sympy | COUNT_PRIMES | [
"COUNT_PRIMES"
] | 07c874 | sequence_lucas_compute_v1 | null | 3 | 0 | [
"COUNT_PRIMES"
] | 1 | 0.001 | 2026-02-08T09:20:19.082445Z | {
"verified": true,
"answer": 15127,
"timestamp": "2026-02-08T09:20:19.083635Z"
} | f9af7f | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 75,
"completion_tokens": 826
},
"timestamp": "2026-02-14T02:47:53.970Z",
"answer": 15127
},
{
... | 1 | [
{
"lemma": "COUNT_PRIMES",
"status": "ok"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status"... | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
9233c3_n | algebra_poly_eval_v1_601307018_2331 | A computer program evaluates the expression $3x^3 - 8x^2 - x - 9$ where $x$ is set to $16$. The exponent $3$ comes from summing the first two positive integers: $1 + 2$. What value does the program output? | 10,215 | ALG | null | COMPUTE | sympy | SUM_ARITHMETIC | [
"SUM_ARITHMETIC"
] | eb34f0 | algebra_poly_eval_v1 | null | 2 | null | [
"SUM_ARITHMETIC"
] | 1 | 0.004 | 2026-03-10T02:59:02.860816Z | null | d3c78f | 9233c3 | narrative | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 171,
"completion_tokens": 216
},
"timestamp": "2026-03-29T16:04:51.781Z",
"answer": 10215
},
{
"i... | 2 | [
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "SUM_ARITHMETIC",
"status": "ok"
}
] | {
"lo": -10,
"mid": -5.89,
"hi": -1.79
} | |
e07794 | nt_count_divisible_v1_784195855_4500 | Let $n$ be a positive integer such that $1 \leq n \leq 62001$. Let $d = \sum_{d \mid 45} \mu(d)$, where $\mu$ denotes the M\"obius function. Compute the number of such integers $n$ for which $n \equiv d \pmod{30}$. | 2,066 | graphs = [
Graph(
let={
"upper": Const(62001),
"divisor": Const(30),
"result": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Ref("upper")), Eq(Mod(value=Var("n"), modulus=Ref("divisor")), SumOverDivisors(n=Const(value=45)... | NT | null | COUNT | sympy | MOBIUS_SUM | [
"MOBIUS_SUM"
] | 518e32 | nt_count_divisible_v1 | null | 5 | 0 | [
"MOBIUS_SUM"
] | 1 | 4.252 | 2026-02-08T07:08:48.954490Z | {
"verified": true,
"answer": 2066,
"timestamp": "2026-02-08T07:08:53.206181Z"
} | ec910a | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 171,
"completion_tokens": 734
},
"timestamp": "2026-02-20T00:02:44.585Z",
"answer": 2066
}
] | 2 | [
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "MOBIUS_SUM",
"status": "ok"
},
{
"lemma": "MOD_SUB",
"status": "... | {
"lo": -10,
"mid": -6.47,
"hi": -2.95
} | ||
d90954 | alg_qf_psd_orbit_v1_601307018_5245 | Let $M$ be the largest positive integer $d$ such that $d^2 \leq 142125$ and $d \mid 142125$. Let $T$ be the number of integer pairs $(a_1, b_1)$ with $1 \leq a_1 \leq 1369$, $1 \leq b_1 \leq 386$ such that $6a_1 + 15b_1$ lies between $21$ and $14004$, inclusive. Let $B = \left|\{ (a_1, b_1) : 1 \leq a_1, b_1 \leq 35,\ ... | 6 | graphs = [
Graph(
let={
"_c": Const(35),
"_m": MaxOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Const(1)), Divides(divisor=Var("d"), dividend=Const(142125)), Leq(Mul(Var("d"), Var("d")), Const(142125))))),
"_n": Const(2),
"result": CountOv... | NT | null | COUNT | sympy | B3_DIFF | [
"LIN_FORM/QF_PSD_COUNT_LEQ",
"B3_CLOSEST/LIN_FORM"
] | 9c4a29 | alg_qf_psd_orbit_v1 | null | 7 | 0 | [
"B3_CLOSEST",
"B3_DIFF",
"LIN_FORM",
"QF_PSD_COUNT_LEQ"
] | 4 | 4.222 | 2026-03-10T05:55:46.453628Z | {
"verified": true,
"answer": 6,
"timestamp": "2026-03-10T05:55:50.675416Z"
} | 10d905 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 1,
"correct": {
"strict": false,
"boxed": false,
"relaxed": true
},
"usage": {
"prompt_tokens": 336,
"completion_tokens": 3524
},
"timestamp": "2026-04-19T01:36:29.967Z",
"answer": 2
},
{
"i... | 0 | [
{
"lemma": "B3_CLOSEST",
"status": "ok"
},
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "QF_PSD_COUNT_LEQ",
"status": "ok_... | {
"lo": 2.12,
"mid": 5.37,
"hi": 8.63
} | ||
bf152c | alg_qf_psd_orbit_v1_1218484723_4818 | Let $M$ be the number of ordered pairs $(a, b)$ of positive integers with $1 \le a, b \le 30$ such that
$$17b^{4} + 17a^{4} + 102a^{2}b^{2} + 68ab^{3} + 68a^{3}b = 48037937.$$
Let $Q$ be the number of ordered pairs $(a_1, b_1)$ of positive integers with $1 \le a_1 \le b_1$ and $1 \le b_1 \le 472$ such that
$$20b_1^{2} ... | 7 | graphs = [
Graph(
let={
"_m": Const(2),
"_n": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("a"), Var("b")]), condition=And(Geq(Var("a"), Const(1)), Leq(Var("a"), Const(30)), Geq(Var("b"), Const(1)), Leq(Var("b"), Const(30)), Eq(Sum(Mul(Const(17), Pow(Var("b"), Const(4))), Mu... | ALG | null | COUNT | sympy | QF_PSD_DISTINCT | [
"POLY4_COUNT/QF_PSD_DISTINCT"
] | 4a1af1 | alg_qf_psd_orbit_v1 | null | 7 | 0 | [
"POLY4_COUNT",
"QF_PSD_DISTINCT"
] | 2 | 1.412 | 2026-02-25T06:28:00.990052Z | {
"verified": true,
"answer": 7,
"timestamp": "2026-02-25T06:28:02.401710Z"
} | 687884 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 1,
"correct": {
"strict": false,
"boxed": false,
"relaxed": true
},
"usage": {
"prompt_tokens": 277,
"completion_tokens": 32768
},
"timestamp": "2026-03-29T17:51:13.873Z",
"answer": null
},
{
... | 1 | [
{
"lemma": "POLY4_COUNT",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "QF_PSD_DISTINCT",
"status": "ok_later"
}
] | {
"lo": 3.81,
"mid": 6.33,
"hi": 9.49
} | ||
ebf752 | comb_sum_binomial_row_v1_677425708_1934 | Let $m = 50$ and let $n_0$ be the largest integer such that $2^{n_0}$ divides $50!$. Let $n$ be the largest integer such that $47^n$ divides $n_0^{14}$. Let $S$ be the set of all positive integers $p$ for which there exists a positive integer $q$ such that $pq = 18$, $\gcd(p, q) = 1$, and $p < q$. Compute the remainder... | 83,436 | graphs = [
Graph(
let={
"_m": Const(50),
"_n": MaxKDivides(target=Factorial(Ref("_m")), base=Const(2)),
"n": MaxKDivides(target=Pow(Ref("_n"), Const(14)), base=Const(47)),
"result": Pow(CountOverSet(set=SolutionsSet(var=Var("p"), condition=And(IsPositive(arg=V... | NT | null | SUM | sympy | COPRIME_PAIRS | [
"COPRIME_PAIRS",
"V1/K14"
] | 68f5b2 | comb_sum_binomial_row_v1 | null | 6 | 0 | [
"COPRIME_PAIRS",
"K14",
"V1"
] | 3 | 0.003 | 2026-02-08T04:39:55.111006Z | {
"verified": true,
"answer": 83436,
"timestamp": "2026-02-08T04:39:55.113761Z"
} | e71d7e | 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": 1987
},
"timestamp": "2026-02-10T03:20:40.324Z",
"answer": 83436
},
{
"... | 1 | [
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K14",
"status": "ok_later"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "K5",
"status": "same_pattern_wr... | {
"lo": -6.5,
"mid": -0.2,
"hi": 6.11
} | ||
676396 | antilemma_sum_equals_v1_1520064083_7093 | Let $n = 20$. Compute the number of ordered pairs $(i, j)$ of positive integers such that $1 \leq i \leq 18$, $1 \leq j \leq 19$, and $i + j = n$. | 18 | graphs = [
Graph(
let={
"_n": Const(20),
"x": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("i"), Var("j")]), condition=Eq(Sum(Var("i"), Var("j")), Ref("_n")), domain=CartesianProduct(left=IntegerRange(start=Const(1), end=Const(18)), right=IntegerRange(start=Const(1), end=Con... | COMB | GEOM | COMPUTE | sympy | COUNT_SUM_EQUALS | [
"COUNT_SUM_EQUALS"
] | 75ab0f | antilemma_sum_equals_v1 | null | 3 | 0 | [
"COUNT_SUM_EQUALS"
] | 1 | 0.072 | 2026-02-08T08:45:34.208840Z | {
"verified": true,
"answer": 18,
"timestamp": "2026-02-08T08:45:34.280502Z"
} | ce9422 | 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": 352
},
"timestamp": "2026-02-24T09:58:42.923Z",
"answer": 18
},
{
"id":... | 2 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "ok"
},
{
"lemma": "V8",
"status": "no"
},
{
"lemma": "V8_SUM",
"stat... | {
"lo": -10,
"mid": -7.79,
"hi": -5.57
} | ||
8538ef | comb_bell_compute_v1_784195855_2960 | Let $T$ be the set of all integers $t$ such that $15 \leq t \leq 45$ and there exist integers $a$ and $b$ with $1 \leq a \leq 3$, $1 \leq b \leq 3$, and $t = 6a + 9b$. Let $n$ be the number of elements in $T$. Compute the remainder when $44121 \cdot B_n$ is divided by $74590$, where $B_n$ denotes the $n$th Bell number. | 55,067 | graphs = [
Graph(
let={
"_n": Const(44121),
"n": CountOverSet(set=SolutionsSet(var=Var("t"), condition=Exists(var=Var(name='a'), condition=Exists(var=Var(name='b'), condition=And(Geq(left=Var(name='a'), right=Const(value=1)), Leq(left=Var(name='a'), right=Const(value=3)), Geq(left=Va... | COMB | null | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | comb_bell_compute_v1 | null | 6 | 0 | [
"LIN_FORM"
] | 1 | 0.002 | 2026-02-08T06:09:32.051247Z | {
"verified": true,
"answer": 55067,
"timestamp": "2026-02-08T06:09:32.052923Z"
} | c188be | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 232,
"completion_tokens": 1791
},
"timestamp": "2026-02-24T05:23:59.323Z",
"answer": 55067
},
{
"... | 1 | [
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8",
"statu... | {
"lo": -2.46,
"mid": 0.47,
"hi": 3.59
} | ||
fd1f32 | comb_sum_binomial_row_v1_784195855_8051 | Let $n$ be the number of integers $t$ such that $12 \leq t \leq 25$ and there exist positive integers $a$ and $b$ with $1 \leq a \leq 5$, $1 \leq b \leq 2$, and $t = 2a + 5b + 5$. Compute $2^n$. | 1,024 | graphs = [
Graph(
let={
"_n": Const(2),
"n": CountOverSet(set=SolutionsSet(var=Var("t"), condition=Exists(var=Var(name='a'), condition=Exists(var=Var(name='b'), condition=And(Geq(left=Var(name='a'), right=Const(value=1)), Leq(left=Var(name='a'), right=Const(value=5)), Geq(left=Var(na... | NT | null | SUM | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | comb_sum_binomial_row_v1 | null | 4 | 0 | [
"LIN_FORM"
] | 1 | 0.001 | 2026-02-08T09:43:36.662958Z | {
"verified": true,
"answer": 1024,
"timestamp": "2026-02-08T09:43:36.663940Z"
} | 61766c | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 124,
"completion_tokens": 1161
},
"timestamp": "2026-02-14T08:33:28.941Z",
"answer": 1024
},
{... | 1 | [
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "V5",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "VAL_SUM_EQ",
"status": "no"
}
] | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
6f009b | comb_sum_binomial_row_v1_1978505735_1870 | Let $ c $ be the minimum value of $ x + y $ over all pairs of positive integers $ (x, y) $ such that $ x \cdot y = 419904 $. Let $ r = 2^{13} $. Compute the remainder when $ c - r $ is divided by $ 88545 $. | 81,649 | graphs = [
Graph(
let={
"_n": Const(88545),
"n": Const(13),
"result": Pow(Const(2), 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'))... | NT | null | SUM | sympy | B3 | [
"B3"
] | fc629c | comb_sum_binomial_row_v1 | negation_mod | 4 | 0 | [
"B3"
] | 1 | 0.003 | 2026-02-08T16:30:15.275642Z | {
"verified": true,
"answer": 81649,
"timestamp": "2026-02-08T16:30:15.278716Z"
} | 827e84 | 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": 1016
},
"timestamp": "2026-02-17T04:57:52.545Z",
"answer": 81649
},
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "V1",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
1e8f25 | nt_count_divisible_v1_124444284_8802 | Let $S$ be the set of all ordered pairs $(k, j)$ of positive integers such that $1 \leq k \leq 5$ and $1 \leq j \leq 5$. Define
$$
d = \frac{6}{30} \sum_{(k,j) \in S} \varphi(k) \left\lfloor \frac{5}{k} \right\rfloor.
$$
Let $N$ be the number of positive integers $n$ such that $1 \leq n \leq 56644$ and $n$ is divisible... | 3,776 | graphs = [
Graph(
let={
"upper": Const(56644),
"divisor": Div(Mul(Const(6), SumOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("k"), Var("_j")]), condition=Const(1), domain=CartesianProduct(left=IntegerRange(start=Const(1), end=Const(5)), right=IntegerRange(start=Cons... | NT | null | COUNT | sympy | SUM_INDEPENDENT | [
"SUM_INDEPENDENT",
"K2"
] | d64c9f | nt_count_divisible_v1 | null | 5 | 0 | [
"K2",
"SUM_INDEPENDENT"
] | 2 | 2.025 | 2026-02-08T11:54:50.238976Z | {
"verified": true,
"answer": 3776,
"timestamp": "2026-02-08T11:54:52.263809Z"
} | b9c8a6 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 172,
"completion_tokens": 1189
},
"timestamp": "2026-02-14T20:30:48.695Z",
"answer": 3776
},
{... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "K2",
"status": "ok"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{... | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
3dc9cf | antilemma_k2_v1_1248542787_707 | Compute the value of $$
\sum_{k=1}^{286} \phi(k) \left\lfloor \frac{286}{k} \right\rfloor.
$$ | 41,041 | graphs = [
Graph(
let={
"x": Summation(var="k", start=Div(Const(29), Const(29)), end=Const(286), expr=Mul(EulerPhi(n=Var("k")), Floor(Div(Const(286), Var("k"))))),
},
goal=Ref("x"),
)
] | NT | COMB | COMPUTE | sympy | K13 | [
"IDENTITY_DIV_SELF",
"K2"
] | 39e678 | antilemma_k2_v1 | null | 7 | 0 | [
"IDENTITY_DIV_SELF",
"K13",
"K2"
] | 3 | 0.002 | 2026-02-08T03:20:17.590785Z | {
"verified": true,
"answer": 41041,
"timestamp": "2026-02-08T03:20:17.592443Z"
} | 4d6b7d | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 152,
"completion_tokens": 582
},
"timestamp": "2026-02-09T07:16:28.695Z",
"answer": 41041
},
{
"i... | 1 | [
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "IDENTITY_DIV_SELF",
"status": "ok"
},
{
"lemma": "K2",
"status": "ok"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
... | {
"lo": -0.54,
"mid": 1.59,
"hi": 3.43
} | ||
9641ca | antilemma_k3_v1_865884756_4639 | Let $n = 44552$. Compute the sum of Euler's totient function $\phi(d)$ over all positive divisors $d$ of $n$. That is, compute $\sum_{d \mid n} \phi(d)$. | 44,552 | graphs = [
Graph(
let={
"x": SumOverDivisors(n=Const(value=44552), var='d', expr=EulerPhi(n=Var(name='d'))),
},
goal=Ref("x"),
)
] | NT | COMB | COMPUTE | sympy | K3 | [
"K3"
] | 54c41e | antilemma_k3_v1 | null | 3 | 0 | [
"K3"
] | 1 | 0 | 2026-02-08T18:01:35.772118Z | {
"verified": true,
"answer": 44552,
"timestamp": "2026-02-08T18:01:35.772439Z"
} | 31d5d8 | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 1,
"correct": {
"strict": false,
"boxed": false,
"relaxed": true
},
"usage": {
"prompt_tokens": 111,
"completion_tokens": 622
},
"timestamp": "2026-02-16T11:51:58.158Z",
"answer": 1436
},
{
"id": 11,
... | 1 | [
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "K3",
"status": "ok"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
}
] | {
"lo": -8.26,
"mid": -5.01,
"hi": -1.76
} | ||
dab716 | nt_sum_gcd_range_mod_v1_124444284_1045 | Let $N$ be the smallest positive integer $n$ such that the exponent of the largest power of $2$ dividing $n!$ is at least $1758$. Let $k = 144$ and $M = 10531$. Compute the remainder when $\sum_{n=1}^{N} \gcd(n, k)$ is divided by $M$. | 1,773 | graphs = [
Graph(
let={
"N": MinOverSet(set=SolutionsSet(var=Var("n"), condition=Geq(MaxKDivides(target=Factorial(Var("n")), base=Const(2)), Const(1758)), domain='Z_{>0}')),
"k": Const(144),
"M": Const(10531),
"sum": Summation(var="n", start=Const(1), end=Ref(... | NT | null | COMPUTE | sympy | V5 | [
"V5"
] | 79df37 | nt_sum_gcd_range_mod_v1 | null | 7 | 0 | [
"V5"
] | 1 | 0.3 | 2026-02-08T03:40:02.262038Z | {
"verified": true,
"answer": 1773,
"timestamp": "2026-02-08T03:40:02.562062Z"
} | 8d8ed7 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 187,
"completion_tokens": 6920
},
"timestamp": "2026-02-10T01:59:19.765Z",
"answer": 1773
},
{
"i... | 1 | [
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "V5",
"status": "ok"
},
{
"lemma": "V8_SUM",
"status": "no"
}
] | {
"lo": -6.5,
"mid": -0.2,
"hi": 6.11
} | ||
544f8b | sequence_fibonacci_compute_v1_124444284_6689 | Let $n$ be the minimum value of $x + y$ over all pairs of positive integers $(x, y)$ such that $xy = 121$. Define $r$ to be the $n$-th Fibonacci number, where $F_1 = 1$, $F_2 = 1$, and $F_k = F_{k-1} + F_{k-2}$ for $k \geq 3$. Compute $53824 - r$. | 36,113 | graphs = [
Graph(
let={
"_n": Const(121),
"n": MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(Mul(Var("x"), Var("y")), Ref("_n")))), expr=Sum(Var("x"), Var("y")))),
... | NT | null | COMPUTE | sympy | B3 | [
"B3"
] | 0cd20d | sequence_fibonacci_compute_v1 | null | 5 | 0 | [
"B3"
] | 1 | 0.001 | 2026-02-08T08:35:08.626178Z | {
"verified": true,
"answer": 36113,
"timestamp": "2026-02-08T08:35:08.627502Z"
} | 82b76b | 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": 664
},
"timestamp": "2026-02-13T19:47:36.562Z",
"answer": 36113
},
{... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"
}
] | {
"lo": -7.01,
"mid": -4.68,
"hi": -2.15
} | ||
8b9513 | nt_min_coprime_above_v1_717093673_691 | Let $T$ be the set of all positive integers $t$ such that $9 \leq t \leq 971$ and there exist positive integers $a$, $b$ with $1 \leq a \leq 14$, $1 \leq b \leq 183$, satisfying $t = 4a + 5b$.
Let $m$ be the number of positive integers $n$ such that $1 \leq n \leq |T|$ and the sum of the decimal digits of $n$ is divis... | 72,296 | graphs = [
Graph(
let={
"_m": Const(77975),
"_n": Const(2),
"start": Const(37249),
"upper": Const(37734),
"modulus": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), CountOverSet(set=SolutionsSet(var=... | NT | null | EXTREMUM | sympy | LIN_FORM | [
"LIN_FORM/L3B"
] | db250f | nt_min_coprime_above_v1 | null | 7 | 0 | [
"L3B",
"LIN_FORM"
] | 2 | 0.118 | 2026-02-08T15:36:11.269503Z | {
"verified": true,
"answer": 72296,
"timestamp": "2026-02-08T15:36:11.387066Z"
} | d54e33 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 232,
"completion_tokens": 7269
},
"timestamp": "2026-02-16T10:40:16.604Z",
"answer": 72296
},
... | 1 | [
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "L3B",
"status": "ok_later"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "V3",
"status": "... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
020c7d | alg_qf_psd_min_v1_1218484723_5794 | Let $A$ be the number of ordered pairs $(a_1, b_1)$ of positive integers with $1 \le a_1, b_1 \le 30$ such that $10a_1^2 - 18a_1b_1 + 25b_1^2 \leq 3805$. Find the minimum value of $115674b^2 - 80082ab + 22245a^2$ over all ordered pairs $(a, b)$ of positive integers with $1 \le a \le A$ and $1 \le b \le 302$. | 44,490 | graphs = [
Graph(
let={
"_n": Const(10),
"result": MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("a"), Var("b")]), condition=And(Geq(Var("a"), Const(1)), Leq(Var("a"), CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("a1"), Var("b1")]), condition=And(Geq(Var... | ALG | null | COMPUTE | sympy | ONE_PHI_2 | [
"QF_PSD_COUNT_LEQ"
] | 009d0f | alg_qf_psd_min_v1 | null | 4 | 0 | [
"ONE_PHI_2",
"QF_PSD_COUNT_LEQ"
] | 2 | 0.192 | 2026-02-25T07:23:15.989172Z | {
"verified": true,
"answer": 44490,
"timestamp": "2026-02-25T07:23:16.181302Z"
} | 4a32e7 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 239,
"completion_tokens": 32768
},
"timestamp": "2026-03-29T22:47:32.485Z",
"answer": null
},
{
... | 1 | [
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "QF_PSD_COUNT_LEQ",
"status": "ok"
}
] | {
"lo": 1.53,
"mid": 4.7,
"hi": 7.23
} | ||
85216c | comb_count_permutations_fixed_v1_784195855_5722 | Let $j$ be a nonnegative integer. Define $n$ to be the number of integers $j$ with $0 \leq j \leq 16424$ such that $\binom{16424}{j}$ is odd, plus 3. Compute the value of $\binom{n}{7} \cdot !(n - 7)$, where $!k$ denotes the number of derangements of $k$ elements. | 2,970 | graphs = [
Graph(
let={
"_n": Const(3),
"n": Sum(CountOverSet(set=SolutionsSet(var=Var("j"), condition=And(Geq(Var("j"), Const(0)), Leq(Var("j"), Const(16424)), Eq(Mod(value=Binom(n=Const(16424), k=Var("j")), modulus=Const(2)), Const(1))), domain='nonnegative_integers')), Ref("_n")),... | COMB | null | COUNT | sympy | V8 | [
"V8"
] | 86348e | comb_count_permutations_fixed_v1 | null | 7 | 0 | [
"V8"
] | 1 | 0.003 | 2026-02-08T08:05:16.148634Z | {
"verified": true,
"answer": 2970,
"timestamp": "2026-02-08T08:05:16.151319Z"
} | dfdf8b | 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": 1217
},
"timestamp": "2026-02-24T08:47:31.772Z",
"answer": 2970
},
{
"i... | 1 | [
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "V8",
"status": "ok"
}
] | {
"lo": -2.35,
"mid": 1.22,
"hi": 4.84
} | ||
e17238 | comb_catalan_compute_v1_601307018_6144 | Let $n = \sum_{k=1}^{4} \varphi(k) \cdot \left\lfloor \frac{4}{k} \right\rfloor$, and let $R = C_n$ where $C_n$ denotes the $n$-th Catalan number. Compute $21316 - R$. | 4,520 | graphs = [
Graph(
let={
"_n": Const(4),
"n": Summation(var="k", start=Const(1), end=Const(4), expr=Mul(EulerPhi(n=Var("k")), Floor(Div(Ref("_n"), Var("k"))))),
"result": Catalan(Ref("n")),
"_c": Const(21316),
"Q": Sub(Ref("_c"), Ref("result")),
... | COMB | NT | COMPUTE | sympy | K13 | [
"K2"
] | 6897ab | comb_catalan_compute_v1 | null | 4 | 0 | [
"K13",
"K2"
] | 2 | 15.002 | 2026-03-10T06:43:59.668454Z | {
"verified": true,
"answer": 4520,
"timestamp": "2026-03-10T06:44:14.670315Z"
} | d56f88 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 180,
"completion_tokens": 711
},
"timestamp": "2026-04-19T03:43:23.144Z",
"answer": 4520
},
{
"i... | 2 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "K2",
"status": "ok"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
}
] | {
"lo": -10,
"mid": -5.89,
"hi": -1.79
} | ||
dcc3a4 | antilemma_cartesian_v1_865884756_4665 | Compute $33333$ minus the number of ordered pairs $(a,b)$ where $a$ is an integer from 1 to 42 and $b$ is an integer from 1 to 47. | 31,359 | graphs = [
Graph(
let={
"x": CountOverSet(set=CartesianProduct(left=IntegerRange(start=Const(1), end=Const(42)), right=IntegerRange(start=Const(1), end=Const(47)))),
"Q": Sub(Const(33333), Ref("x")),
},
goal=Ref("Q"),
)
] | COMB | GEOM | COMPUTE | sympy | COUNT_CARTESIAN | [
"COUNT_CARTESIAN"
] | 409d7d | antilemma_cartesian_v1 | null | 2 | 0 | [
"COUNT_CARTESIAN"
] | 1 | 0.001 | 2026-02-08T18:02:20.425223Z | {
"verified": true,
"answer": 31359,
"timestamp": "2026-02-08T18:02:20.426210Z"
} | 1ca38d | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 89,
"completion_tokens": 675
},
"timestamp": "2026-02-24T23:25:43.498Z",
"answer": 31359
},
{
... | 1 | [
{
"lemma": "COUNT_CARTESIAN",
"status": "ok"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8",
... | {
"lo": -8.52,
"mid": -5.43,
"hi": -3.2
} | ||
7a8226 | nt_count_divisible_and_v1_677425708_1750 | Let $m$ be the sum of $\mu(d)$ over all positive divisors $d$ of $1$. Let $u = 19260 \cdot m$. Let $d_1$ be the minimum value of $x + y$ over all ordered pairs $(x, y)$ of positive integers such that $x y = 25$. Let $d_2$ be $\omega(23)$ multiplied by the number of positive integers $j$ with $1 \leq j \leq 15$ and $j^4... | 60 | graphs = [
Graph(
let={
"_m": Const(4),
"_n": Const(19260),
"n1": Const(23),
"c": SmallOmega(n=Ref(name='n1')),
"n": Const(1),
"m": SumOverDivisors(n=Ref(name='n'), var='d', expr=MoebiusMu(n=Var(name='d'))),
"upper": Mul(Ref... | NT | null | COUNT | sympy | C3 | [
"C3/OMEGA_ONE",
"MOBIUS_SUM",
"B3"
] | 0f4b5d | nt_count_divisible_and_v1 | null | 7 | 2 | [
"B3",
"C3",
"MOBIUS_SUM",
"OMEGA_ONE"
] | 4 | 1.323 | 2026-02-08T04:24:47.477721Z | {
"verified": true,
"answer": 60,
"timestamp": "2026-02-08T04:24:48.800633Z"
} | c390c8 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 307,
"completion_tokens": 1390
},
"timestamp": "2026-02-10T00:22:41.885Z",
"answer": 60
},
{
"id"... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "C3",
"status": "ok"
},
{
"lemma": "MOBIUS_SUM",
"status": "ok"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "OMEGA_ONE",
"status": "ok_later"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"statu... | {
"lo": -6.5,
"mid": -0.2,
"hi": 6.11
} | ||
e5d573 | geo_count_lattice_triangle_v1_48377204_1257 | Let $A$ be the area of a triangle with vertices at $(0,0)$, $(128,144)$, and $(9,128)$, multiplied by $2$. Let $B$ be the sum of the greatest common divisors of the lengths of the sides of this triangle, computed as follows:
- $\gcd(128, 144)$,
- $\gcd(|9 - 128|, |128 - 144|)$,
- $\gcd(9, C)$, where $C$ is the number ... | 65,454 | graphs = [
Graph(
let={
"_m": Const(128),
"_n": Const(9),
"area_2x": Abs(arg=Sum(Mul(Const(value=128), Const(value=128)), Mul(Ref(name='_n'), Sub(left=Const(value=0), right=Const(value=144))))),
"boundary": Sum(GCD(a=Abs(arg=Const(value=128)), b=Abs(arg=Const(... | NT | null | COUNT | sympy | COPRIME_PAIRS | [
"COPRIME_PAIRS",
"LIN_FORM"
] | 67610e | geo_count_lattice_triangle_v1 | null | 6 | 0 | [
"COPRIME_PAIRS",
"LIN_FORM"
] | 2 | 0.018 | 2026-02-08T16:00:14.350974Z | {
"verified": true,
"answer": 65454,
"timestamp": "2026-02-08T16:00:14.368725Z"
} | ef6c34 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 231,
"completion_tokens": 2499
},
"timestamp": "2026-02-16T18:27:20.544Z",
"answer": 65454
},
... | 1 | [
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
6cc120 | v7_endings_v1_677425708_186 | For each integer $k$ with $0 \leq k \leq 995$, let $e_k$ be the largest integer $e$ such that $7^e$ divides $\binom{995}{k}$. Let $E$ be the maximum value of $e_k$ over all such $k$. Compute the value of $14128 \cdot E \bmod 96027$. | 42,384 | graphs = [
Graph(
let={
"_inner_result": MaxOverSet(set=MapOverSet(set=SolutionsSet(var=Var("k"), condition=And(Geq(Var("k"), Const(0)), Leq(Var("k"), Const(995)))), expr=MaxKDivides(target=Binom(n=Const(995), k=Var("k")), base=Const(7)))),
"_scale_k": Const(14128),
"_sca... | NT | null | COMPUTE | sympy | V7 | [
"V7"
] | 0672d4 | v7_endings_v1 | null | 7 | null | [
"V7"
] | 1 | 0.002 | 2026-02-08T03:07:00.022425Z | {
"verified": true,
"answer": 42384,
"timestamp": "2026-02-08T03:07:00.024316Z"
} | c7b7bd | 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": 3299
},
"timestamp": "2026-02-08T20:20:21.977Z",
"answer": 42384
},
{
"... | 1 | [
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "V7",
"status": "ok"
},
{
"lemma": "V8_SUM",
"stat... | {
"lo": -6.51,
"mid": -0.53,
"hi": 4.75
} | ||
8760b4 | lin_form_endings_v1_865884756_6578 | Let $a = 60$, $b = 48$, and $k = 82$. Define $d = \gcd(a, b)$ and $e = \gcd(k, d)$. Let $r = \left\lfloor \frac{k}{e} \right\rfloor$. Compute the remainder when $12693 \cdot r$ is divided by $72068$. | 15,937 | graphs = [
Graph(
let={
"a_coeff": Const(60),
"b_coeff": Const(48),
"k_val": Const(82),
"step": GCD(a=Ref("a_coeff"), b=Ref("b_coeff")),
"_inner_result": Floor(Div(Ref("k_val"), GCD(a=Ref("k_val"), b=Ref("step")))),
"_scale_k": Const(12... | COMB | NT | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | lin_form_endings_v1 | null | 3 | null | [
"LIN_FORM"
] | 1 | 0.001 | 2026-02-08T19:18:13.934972Z | {
"verified": true,
"answer": 15937,
"timestamp": "2026-02-08T19:18:13.936011Z"
} | e68da7 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 124,
"completion_tokens": 980
},
"timestamp": "2026-02-18T21:49:35.162Z",
"answer": 15937
},
{... | 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": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
dada0f_n | alg_sum_powers_v1_1218484723_5345 | A designer considers all possible rectangular tiles labeled by integer coordinates $(a, b)$ with $1 \le a \le 25$ and $1 \le b \le 25$. A tile is called *acceptable* if its dimensions satisfy
$$25b^{2} + 10a^{2} - 18ab \le 7786.$$
She numbers the acceptable tiles from $1$ up to the total number of acceptable tiles, $|S... | 4,516 | ALG | null | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM/ABS_INEQ",
"QF_PSD_COUNT_LEQ"
] | 3219f5 | alg_sum_powers_v1 | null | 7 | null | [
"ABS_INEQ",
"LIN_FORM",
"QF_PSD_COUNT_LEQ"
] | 3 | 0.028 | 2026-02-25T06:57:03.075072Z | null | 27ea45 | dada0f | narrative | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 417,
"completion_tokens": 32768
},
"timestamp": "2026-03-30T23:22:47.440Z",
"answer": null
},
{
... | 1 | [
{
"lemma": "ABS_INEQ",
"status": "ok_later"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "QF_PSD_COUNT_LEQ",
"status": "ok"
}
] | {
"lo": 1.5,
"mid": 4.69,
"hi": 7.23
} | |
c630c9 | sequence_count_fib_divisible_v1_1440796553_1210 | Let $A$ be the number of positive integers $n \leq 11460$ for which the $n$th Fibonacci number is divisible by $16$. Let $B$ be the number of positive integers $n \leq A$ for which the $n$th Fibonacci number is divisible by $9$. Let $Q$ be the remainder when $45408 \cdot B$ is divided by $89299$. Find the value of $Q$. | 15,272 | graphs = [
Graph(
let={
"upper": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Const(11460)), Divides(divisor=Const(16), dividend=Fibonacci(arg=Var(name='n')))))),
"d": Const(9),
"result": CountOverSet(set=SolutionsSet(va... | NT | null | COUNT | sympy | COUNT_FIB_DIVISIBLE | [
"COUNT_FIB_DIVISIBLE"
] | 66de3c | sequence_count_fib_divisible_v1 | null | 5 | 0 | [
"COUNT_FIB_DIVISIBLE"
] | 1 | 0.051 | 2026-02-08T12:14:23.364175Z | {
"verified": true,
"answer": 15272,
"timestamp": "2026-02-08T12:14:23.414978Z"
} | dcf227 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 140,
"completion_tokens": 1433
},
"timestamp": "2026-02-15T18:26:18.362Z",
"answer": 15272
},
... | 1 | [
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "ok"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "V1",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
}
] | {
"lo": -5.49,
"mid": 0.22,
"hi": 6.51
} | ||
90eb40 | diophantine_fbi2_min_v1_1915831931_3669 | Let $k = \sum_{k_1=1}^{8} k_1$. Determine the smallest positive integer $d$ such that $6 \leq d \leq 46$, $d$ divides $k$, and $\frac{k}{d} \geq 2$. Compute this value of $d$. | 6 | graphs = [
Graph(
let={
"k": Summation(var="k1", start=Const(1), end=Const(8), expr=Var("k1")),
"upper": Const(46),
"result": MinOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Const(6)), Leq(Var("d"), Ref("upper")), Divides(divisor=Var("d"), dividend=R... | NT | null | EXTREMUM | sympy | SUM_ARITHMETIC | [
"SUM_ARITHMETIC"
] | eb34f0 | diophantine_fbi2_min_v1 | null | 3 | 0 | [
"SUM_ARITHMETIC"
] | 1 | 0.017 | 2026-02-08T17:48:14.320285Z | {
"verified": true,
"answer": 6,
"timestamp": "2026-02-08T17:48:14.337027Z"
} | 1ca093 | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 124,
"completion_tokens": 289
},
"timestamp": "2026-02-16T11:38:32.613Z",
"answer": 6
},
{
"id": 11,
"... | 2 | [
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "SUM_ARITHMETIC",
"status": "ok"
},
{
"lemma": "V5",
"status": "no"
},
{
"lemma": "V8",
"status": "no... | {
"lo": -10,
"mid": -7.27,
"hi": -4.54
} | ||
69aa42 | lin_form_endings_v1_865884756_1129 | Compute the remainder when $5006 \cdot \gcd(45, 18)$ is divided by $67087$. | 45,054 | graphs = [
Graph(
let={
"a_coeff": Const(45),
"b_coeff": Const(18),
"_inner_result": GCD(a=Ref("a_coeff"), b=Ref("b_coeff")),
"_scale_k": Const(5006),
"_scaled": Mul(Ref("_scale_k"), Ref("_inner_result")),
"_mod_M": Const(67087),
... | COMB | NT | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | lin_form_endings_v1 | null | 2 | null | [
"LIN_FORM"
] | 1 | 0.001 | 2026-02-08T15:47:51.034658Z | {
"verified": true,
"answer": 45054,
"timestamp": "2026-02-08T15:47:51.035352Z"
} | ee6036 | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 87,
"completion_tokens": 301
},
"timestamp": "2026-02-16T06:20:36.396Z",
"answer": 45054
},
{
"id": 11,
... | 2 | [
{
"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": -10,
"mid": -7.27,
"hi": -4.54
} | ||
0bad28 | nt_num_divisors_compute_v1_1470522791_595 | Let $n = 55555$ and let $\tau(n)$ denote the number of positive divisors of $n$. Let $C$ be the number of positive integers $p$ for which there exists an integer $q > p$ such that $pq = 76264588600200$ and $\gcd(p, q) = 1$. Compute $C - \tau(n)$. | 120 | graphs = [
Graph(
let={
"n": Const(55555),
"result": NumDivisors(n=Ref("n")),
"Q": Sub(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(v... | NT | null | COMPUTE | sympy | COPRIME_PAIRS | [
"COPRIME_PAIRS"
] | c90628 | nt_num_divisors_compute_v1 | negation_mod | 6 | 0 | [
"COPRIME_PAIRS"
] | 1 | 0.002 | 2026-02-08T13:08:04.958445Z | {
"verified": true,
"answer": 120,
"timestamp": "2026-02-08T13:08:04.960061Z"
} | e5230e | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 126,
"completion_tokens": 2448
},
"timestamp": "2026-02-15T09:55:34.812Z",
"answer": 120
},
{
... | 1 | [
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"
... | {
"lo": -5.49,
"mid": 0.22,
"hi": 6.51
} | ||
b40722 | nt_max_prime_below_v1_809748730_442 | Let $p_{\max}$ be the largest prime number $p$ such that $2 \le p \le 16384$. Let $C$ be the number of positive integers $n$ with $1 \le n \le 15487$ such that the sum of the decimal digits of $n$ is odd. Find the remainder when $C - p_{\max}$ is divided by 65226. | 56,589 | graphs = [
Graph(
let={
"upper": Const(16384),
"result": MaxOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(2)), Leq(Var("n"), Ref("upper")), IsPrime(Var("n"))))),
"Q": Mod(value=Sub(CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Va... | NT | null | EXTREMUM | sympy | L3B | [
"L3B"
] | f8a865 | nt_max_prime_below_v1 | negation_mod | 4 | 0 | [
"L3B"
] | 1 | 0.374 | 2026-02-08T11:30:58.344233Z | {
"verified": true,
"answer": 56589,
"timestamp": "2026-02-08T11:30:58.718459Z"
} | ede587 | 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": 3510
},
"timestamp": "2026-02-14T15:33:51.691Z",
"answer": 56589
},
... | 1 | [
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "L3B",
"status": "ok"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
}
] | {
"lo": -5.49,
"mid": 0.22,
"hi": 6.51
} | ||
0efca8 | diophantine_fbi2_count_v1_1874849503_1419 | Let $A$ be the set of all positive integers $t$ such that there exist positive integers $a$ and $b$ with $1 \leq a \leq 21$, $1 \leq b \leq 17$, $t = 4a + 3b$, and $7 \leq t \leq 135$. Let $B$ be the set of all positive integers $t$ such that there exist positive integers $a$ and $b$ with $1 \leq a \leq 14$, $1 \leq b ... | 37 | graphs = [
Graph(
let={
"_n": Const(4),
"k": Const(240),
"result": CountOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Ref("_n")), Leq(Var("d"), CountOverSet(set=SolutionsSet(var=Var("t"), condition=Exists(var=Var(name='a'), condition=Exists(var=Var(na... | NT | null | COUNT | sympy | ONE_PHI_1 | [
"LIN_FORM"
] | 7b2633 | diophantine_fbi2_count_v1 | null | 6 | 0 | [
"LIN_FORM",
"ONE_PHI_1"
] | 2 | 0.072 | 2026-02-08T13:53:33.114695Z | {
"verified": true,
"answer": 37,
"timestamp": "2026-02-08T13:53:33.186434Z"
} | be15fb | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 394,
"completion_tokens": 7468
},
"timestamp": "2026-02-11T08:02:50.703Z",
"answer": 37
},
{
"id... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "VAL_SUM_EQ",
"st... | {
"lo": -5.48,
"mid": 0.74,
"hi": 7.52
} | ||
95ed3c | modular_modexp_compute_v1_1520064083_2969 | Let $a = 37$. Let $e$ be the sum of all real solutions $x$ to the equation $x^2 - 9999x + 219494 = 0$. Let $m = 71289$. Define $\text{result} = a^e \bmod m$, and let $Q = (67525 \cdot \text{result}) \bmod 80444$. Find the value of $Q$. | 72,288 | graphs = [
Graph(
let={
"a": Const(37),
"e": SumOverSet(set=SolutionsSet(var=Var("x"), condition=Eq(Sum(Pow(Var("x"), Const(2)), Mul(Const(-9999), Var("x")), Const(219494)), Const(0)))),
"m": Const(71289),
"result": ModExp(base=Ref("a"), exp=Ref("e"), mod=Ref(... | NT | null | COMPUTE | sympy | VIETA_SUM | [
"VIETA_SUM"
] | b33a7a | modular_modexp_compute_v1 | null | 5 | 0 | [
"VIETA_SUM"
] | 1 | 0.002 | 2026-02-08T05:21:33.158961Z | {
"verified": true,
"answer": 72288,
"timestamp": "2026-02-08T05:21:33.160727Z"
} | a7aa0b | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 140,
"completion_tokens": 3646
},
"timestamp": "2026-02-12T07:11:07.228Z",
"answer": 72288
},
... | 1 | [
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "VIETA_SUM",
"status": "ok"
... | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
4207f2 | diophantine_fbi2_min_v1_1915831931_812 | Let $k = 8$ and let $u = 18$. Find the smallest divisor $d$ of $k$ such that $d \geq 2$, $d \leq u$, and
$$
\frac{k}{d} \geq \min\{ d_1 \mid d_1 \geq 2 \text{ and } d_1 \text{ divides } 105 \}.
$$ | 2 | graphs = [
Graph(
let={
"k": Const(8),
"upper": Const(18),
"result": MinOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Const(2)), Leq(Var("d"), Ref("upper")), Divides(divisor=Var("d"), dividend=Ref("k")), Geq(Div(Ref("k"), Var("d")), MinOverSet(set=Sol... | NT | null | EXTREMUM | sympy | MIN_PRIME_FACTOR | [
"MIN_PRIME_FACTOR",
"COPRIME_PAIRS"
] | a3b634 | diophantine_fbi2_min_v1 | null | 4 | 0 | [
"COPRIME_PAIRS",
"MIN_PRIME_FACTOR"
] | 2 | 0.005 | 2026-02-08T15:41:08.893799Z | {
"verified": true,
"answer": 2,
"timestamp": "2026-02-08T15:41:08.898825Z"
} | 0f0b86 | 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": 639
},
"timestamp": "2026-02-16T11:29:06.803Z",
"answer": 2
},
{
... | 1 | [
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "MIN_PRIME_FACTOR",
"status": "ok"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
003104 | alg_poly4_min_v1_1218484723_7652 | Find the minimum value of $4320a^2b^2 + 1280a^4 + 3840a^3b + \max \{ d : d \geq 1,\ d \leq 2160,\ d \mid 4758480 \} \cdot ab^3 + 410b^4$ over all ordered pairs $(a, b)$ of positive integers with $1 \le a, b \le 155$. | 12,010 | graphs = [
Graph(
let={
"_n": Const(4),
"result": MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("a"), Var("b")]), condition=And(Geq(Var("a"), Const(1)), Leq(Var("a"), Const(155)), Geq(Var("b"), Const(1)), Leq(Var("b"), Const(155)))), expr=Sum(Mul(Const(4320), Pow... | NT | null | COMPUTE | sympy | MAX_DIVISOR | [
"MAX_DIVISOR"
] | 51757e | alg_poly4_min_v1 | null | 5 | 0 | [
"MAX_DIVISOR"
] | 1 | 0.062 | 2026-02-25T09:06:34.925011Z | {
"verified": true,
"answer": 12010,
"timestamp": "2026-02-25T09:06:34.986804Z"
} | e38f61 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 208,
"completion_tokens": 2854
},
"timestamp": "2026-03-30T05:43:41.950Z",
"answer": 12010
},
{
"... | 1 | [
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "MAX_DIVISOR",
"status": "ok"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
}
] | {
"lo": -3.33,
"mid": 1.03,
"hi": 5.26
} | ||
639c31 | alg_sum_ap_v1_1218484723_4202 | Let $T$ be the number of integer pairs $(a, b)$ with $1 \le a, b \le 40$ satisfying $41a^2 + 20b^2 - 12ab \le 27881$. Find the remainder when $\sum_{k=0}^{T} (5k + 74)$ is divided by $4220$. | 2,484 | graphs = [
Graph(
let={
"_n": Const(2),
"result": Mod(value=Summation(var="k", start=Const(0), end=CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("a"), Var("b")]), condition=And(Geq(Var("a"), Const(1)), Leq(Var("a"), Const(40)), Geq(Var("b"), Const(1)), Leq(Var("b"), Const(40)... | ALG | null | COMPUTE | sympy | QF_PSD_COUNT_LEQ | [
"QF_PSD_COUNT_LEQ"
] | 009d0f | alg_sum_ap_v1 | null | 4 | 0 | [
"QF_PSD_COUNT_LEQ"
] | 1 | 0.011 | 2026-02-25T05:52:10.645166Z | {
"verified": true,
"answer": 2484,
"timestamp": "2026-02-25T05:52:10.655929Z"
} | 5b4cc8 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 187,
"completion_tokens": 28148
},
"timestamp": "2026-03-29T14:19:05.460Z",
"answer": 2484
},
{
"... | 1 | [
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "QF_PSD_COUNT_LEQ",
"status": "ok"
}
] | {
"lo": -2.45,
"mid": 1.37,
"hi": 5.29
} | ||
9d6e1b | nt_count_digit_sum_v1_655260480_3732 | Let $A$ be the number of positive integers $n$ such that $n \leq 99999$ and the sum of the digits of $n$ is $16$. Let $B$ be the number of positive integers $n_1$ such that $n_1 \leq 6007$ and $\gcd(n_1, 12) = 1$. Let $C$ be the largest prime number less than or equal to $316$. Compute the remainder when $A$ is divided... | 78,425 | graphs = [
Graph(
let={
"_m": Const(316),
"_n": Const(317),
"upper": Const(99999),
"target_sum": Const(16),
"result": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Ref("upper")), Eq(DigitSum(Var("n... | NT | null | COUNT | sympy | MAX_PRIME_BELOW | [
"MAX_PRIME_BELOW",
"C4"
] | 1c2bf9 | nt_count_digit_sum_v1 | two_moduli | 6 | 0 | [
"C4",
"MAX_PRIME_BELOW"
] | 2 | 3.718 | 2026-02-08T17:30:54.014750Z | {
"verified": true,
"answer": 78425,
"timestamp": "2026-02-08T17:30:57.732928Z"
} | 5a1f7c | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 196,
"completion_tokens": 1661
},
"timestamp": "2026-02-18T03:26:32.093Z",
"answer": 78425
},
... | 1 | [
{
"lemma": "C4",
"status": "ok"
},
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
b12985 | comb_binomial_compute_v1_458359167_2570 | Let $n$ be the largest prime number such that $2 \leq n \leq 16$. Let $k = \sum_{i=1}^{3} i$. Compute $\binom{n}{k}$. | 1,716 | graphs = [
Graph(
let={
"_n": Const(2),
"n": MaxOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Ref("_n")), Leq(Var("n"), Const(16)), IsPrime(Var("n"))))),
"k": Summation(var="k", start=Const(1), end=Const(3), expr=Var("k")),
"result": Binom... | NT | null | COMPUTE | sympy | MAX_PRIME_BELOW | [
"MAX_PRIME_BELOW",
"SUM_ARITHMETIC"
] | 15f63b | comb_binomial_compute_v1 | null | 3 | 0 | [
"MAX_PRIME_BELOW",
"SUM_ARITHMETIC"
] | 2 | 0.003 | 2026-02-08T06:20:18.851552Z | {
"verified": true,
"answer": 1716,
"timestamp": "2026-02-08T06:20:18.854954Z"
} | f5daa9 | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 101,
"completion_tokens": 325
},
"timestamp": "2026-02-15T17:39:17.632Z",
"answer": 1716
},
{
"id": 11,
... | 2 | [
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "SUM_ARITHMETIC",
"status":... | {
"lo": -10,
"mid": -7.73,
"hi": -5.46
} | ||
a43224 | algebra_poly_eval_v1_865884756_4538 | Let $t = 12$. Let $A$ be the number of positive integers $n \leq 469$ for which the sum of the decimal digits of $n$ is even. Compute the value of
$$
\frac{36 \cdot t^6 + A \cdot t^5 - 376 \cdot t^4 - 110 \cdot t^3 + 452 \cdot t^2 - 282 \cdot t + 60}{4556}.
$$ | 34,635 | graphs = [
Graph(
let={
"_n": Const(2),
"t": Const(12),
"result": Div(Sum(Mul(Const(36), Pow(Ref("t"), Const(6))), Mul(CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Const(469)), Eq(Mod(value=DigitSum(Var("n")), modulus=Co... | NT | null | COMPUTE | sympy | L3B | [
"L3B"
] | cc148f | algebra_poly_eval_v1 | null | 3 | 0 | [
"L3B"
] | 1 | 0.008 | 2026-02-08T17:58:39.324191Z | {
"verified": true,
"answer": 34635,
"timestamp": "2026-02-08T17:58:39.332309Z"
} | 0beb93 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 145,
"completion_tokens": 2517
},
"timestamp": "2026-02-18T10:35:00.028Z",
"answer": 34635
},
... | 1 | [
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "L3B",
"status": "ok"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
b5174b | alg_poly4_count_v1_601307018_9561 | Let $S$ be the set of ordered pairs $(a_1, b_1)$ of positive integers with $1 \le a_1, b_1 \le 35$ such that $13a_1^2 + 2b_1^2 - 2a_1b_1 \le 2768$, and let $B = |S|$. Find the number of ordered pairs $(a, b)$ with $1 \le a \le 447$ and $1 \le b \le B$ satisfying
$$
1024a b^3 + 1536 a^2 b^2 + 1024 a^3 b + m a^4 + 256 b^... | 36 | graphs = [
Graph(
let={
"_m": Const(35),
"_n": Const(35),
"result": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("a"), Var("b")]), condition=And(Geq(Var("a"), Const(1)), Leq(Var("a"), Const(447)), Geq(Var("b"), Const(1)), Leq(Var("b"), CountOverSet(set=SolutionsS... | NT | null | COUNT | sympy | QF_PSD_COUNT_LEQ | [
"QF_PSD_COUNT_LEQ",
"B3_CLOSEST"
] | cf330f | alg_poly4_count_v1 | null | 6 | 0 | [
"B3_CLOSEST",
"QF_PSD_COUNT_LEQ"
] | 2 | 2.272 | 2026-03-10T09:59:13.471381Z | {
"verified": true,
"answer": 36,
"timestamp": "2026-03-10T09:59:15.743077Z"
} | f31c43 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 296,
"completion_tokens": 4709
},
"timestamp": "2026-04-19T11:33:54.502Z",
"answer": 36
},
{
"id... | 1 | [
{
"lemma": "B3_CLOSEST",
"status": "ok"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma... | {
"lo": -5.34,
"mid": 1.1,
"hi": 7.53
} | ||
beadb9 | comb_count_partitions_v1_1218484723_453 | Let $S = \{ t = 7a + 2b \mid a,b \in \mathbb{Z},\ 1 \le a \le 4,\ 1 \le b \le 12,\ 9 \le t \le 52 \}$. Let $n = |S|$ and $M = p(n)$, where $p(n)$ denotes the number of integer partitions of $n$. Find the remainder when $95813 \cdot M$ is divided by $92661$. | 86,956 | graphs = [
Graph(
let={
"n": CountOverSet(set=SolutionsSet(var=Var("t"), condition=Exists(var=Var(name='a'), condition=Exists(var=Var(name='b'), condition=And(Geq(left=Var(name='a'), right=Const(value=1)), Leq(left=Var(name='a'), right=Const(value=4)), Geq(left=Var(name='b'), right=Const(value=1... | COMB | null | COUNT | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | comb_count_partitions_v1 | null | 4 | 0 | [
"LIN_FORM"
] | 1 | 0.001 | 2026-02-25T02:09:42.758844Z | {
"verified": true,
"answer": 86956,
"timestamp": "2026-02-25T02:09:42.760310Z"
} | 8d6013 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 220,
"completion_tokens": 4636
},
"timestamp": "2026-03-28T22:39:10.510Z",
"answer": 86956
},
{
"... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "V8",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
... | {
"lo": 3.81,
"mid": 5.7,
"hi": 7.82
} | ||
b05c82 | diophantine_fbi2_count_v1_898971024_2175 | Let $k = 60$. Define $d_{\text{min}}$ to be the smallest integer $d_1 \geq 2$ that divides $20602567$. Let $D$ be the set of all integers $d$ such that $2 \leq d \leq d_{\text{min}}$, $d$ divides $k$, and $5 \leq \frac{k}{d} \leq 64$. Let $r$ be the number of elements in $D$. Compute the remainder when $44121 \cdot r$ ... | 34,319 | graphs = [
Graph(
let={
"k": Const(60),
"result": CountOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Const(2)), Leq(Var("d"), MinOverSet(set=SolutionsSet(var=Var("d1"), condition=And(Geq(Var("d1"), Const(2)), Divides(divisor=Var("d1"), dividend=Const(20602567))))... | NT | null | COUNT | sympy | MIN_PRIME_FACTOR | [
"MIN_PRIME_FACTOR"
] | bc3776 | diophantine_fbi2_count_v1 | null | 5 | 0 | [
"MIN_PRIME_FACTOR"
] | 1 | 0.013 | 2026-02-08T16:35:14.509676Z | {
"verified": true,
"answer": 34319,
"timestamp": "2026-02-08T16:35:14.522456Z"
} | fff581 | 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": 1700
},
"timestamp": "2026-02-17T07:48:27.205Z",
"answer": 34319
},
... | 1 | [
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "MIN_PRIME_FACTOR",
"status": "ok"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
},
{
"lemma": "VAL_SUM_EQ",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
1349ec | alg_poly_orbit_legendre_v1_601307018_1874 | Let $a$ be a non-negative integer with $0 \le a \le 92440$. Define the sequence:
\[
\begin{aligned}
N &= a^{48} \bmod 97, \\
M &= (a^2 + a + 17) \bmod 97, \\
R &= M^{48} \bmod 97, \\
S &= (M^2 + M + 17) \bmod 97, \\
T &= S^{48} \bmod 97, \\
K &= (S^2 + S + 17) \bmod 97, \\
L &= K^{48} \bmod 97, \\
P &= (N + R + T + L) ... | 3,812 | graphs = [
Graph(
let={
"p1": Mod(value=Sum(Pow(Var("a"), Const(2)), Var("a"), Const(17)), modulus=Const(97)),
"p2": Mod(value=Sum(Pow(Ref("p1"), Const(2)), Ref("p1"), Const(17)), modulus=Const(97)),
"p3": Mod(value=Sum(Pow(Ref("p2"), Const(2)), Ref("p2"), Const(17)), mod... | NT | null | COUNT | sympy | POLY_ORBIT_LEGENDRE_COUNT | [
"POLY_ORBIT_LEGENDRE_COUNT"
] | b47831 | alg_poly_orbit_legendre_v1 | null | 7 | null | [
"POLY_ORBIT_LEGENDRE_COUNT"
] | 1 | 0.038 | 2026-03-10T02:37:19.943860Z | {
"verified": true,
"answer": 3812,
"timestamp": "2026-03-10T02:37:19.981397Z"
} | 3ac0e5 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 356,
"completion_tokens": 32768
},
"timestamp": "2026-03-29T03:42:47.024Z",
"answer": null
},
{
... | 1 | [
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "POLY_ORBIT_LEGENDRE_COUNT",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CO... | {
"lo": 3.99,
"mid": 6.11,
"hi": 9.15
} | ||
40d55e | antilemma_cartesian_v1_784195855_6114 | Let $A$ be the set of all ordered pairs $(x_1, x_2)$ of positive integers such that $x_1$ is odd, $x_2$ is odd, and $x_1 + x_2 = 4$. Let $c$ be the number of elements in $A$. Let $x$ be the number of ordered pairs $(i, j)$ where $i$ is an integer with $1 \leq i \leq 28$ and $j$ is an integer with $1 \leq j \leq 41$. Co... | 45,616 | graphs = [
Graph(
let={
"_n": Const(4),
"x": CountOverSet(set=CartesianProduct(left=IntegerRange(start=Const(1), end=Const(28)), right=IntegerRange(start=Const(1), end=Const(41)))),
"_c": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x1"), Var("x2")]), condition=... | COMB | GEOM | COMPUTE | sympy | COMB1 | [
"COMB1",
"COUNT_CARTESIAN"
] | 217b64 | antilemma_cartesian_v1 | quadratic_mod | 2 | 0 | [
"COMB1",
"COUNT_CARTESIAN"
] | 2 | 0.001 | 2026-02-08T08:20:41.155371Z | {
"verified": true,
"answer": 45616,
"timestamp": "2026-02-08T08:20:41.156434Z"
} | 1eae4a | 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": 1200
},
"timestamp": "2026-02-24T09:28:10.355Z",
"answer": 45616
},
{
"... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COMB1",
"status": "ok"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "ok"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS... | {
"lo": -3.84,
"mid": -1.67,
"hi": 1.32
} | ||
471987 | lin_form_endings_v1_458359167_3117 | Let $a = 12$ and $b = 18$. Let $g$ be the greatest common divisor of $a$ and $b$. Define $a' = \left\lfloor \frac{a}{g} \right\rfloor$ and $b' = \left\lfloor \frac{b}{g} \right\rfloor$. Let $A = 10$ and $B = 35$. Compute the value of $15374 \cdot (a' \cdot A + b' \cdot B - a' \cdot b')$ modulo $98293$. | 60,232 | graphs = [
Graph(
let={
"a_coeff": Const(12),
"b_coeff": Const(18),
"A_val": Const(10),
"B_val": Const(35),
"g_step": GCD(a=Ref("a_coeff"), b=Ref("b_coeff")),
"ap_node": Floor(Div(Ref("a_coeff"), Ref("g_step"))),
"bp_node": ... | COMB | NT | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | lin_form_endings_v1 | null | 2 | null | [
"LIN_FORM"
] | 1 | 0.001 | 2026-02-08T06:57:18.157889Z | {
"verified": true,
"answer": 60232,
"timestamp": "2026-02-08T06:57:18.158422Z"
} | fc01b3 | 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": 779
},
"timestamp": "2026-02-13T07:02:06.521Z",
"answer": 60232
},
{... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
}
] | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
40a6f1 | nt_num_divisors_compute_v1_124444284_7327 | Let $n = 87025$. Compute the number of positive divisors of $n$. | 9 | graphs = [
Graph(
let={
"n": Const(87025),
"result": NumDivisors(n=Ref("n")),
},
goal=Ref("result"),
)
] | NT | null | COMPUTE | sympy | MAX_PRIME_BELOW | [
"MAX_PRIME_BELOW"
] | dc3ad3 | nt_num_divisors_compute_v1 | null | 2 | 0 | [
"MAX_PRIME_BELOW"
] | 1 | 0.005 | 2026-02-08T09:01:17.115841Z | {
"verified": true,
"answer": 9,
"timestamp": "2026-02-08T09:01:17.120387Z"
} | 0d3f92 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 65,
"completion_tokens": 389
},
"timestamp": "2026-02-13T23:45:56.941Z",
"answer": 9
},
{
... | 1 | [
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "V3",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
}
] | {
"lo": -5.55,
"mid": -3.01,
"hi": 0.32
} | ||
898b6e | comb_count_partitions_v1_784195855_9852 | Let $p$ be a positive integer such that there exists a positive integer $q$ with $p < q$, $pq = 216$, and $\gcd(p, q) = 1$. Let $\_n$ be the number of such integers $p$. Let $n$ be the smallest integer $d \geq \_n$ that divides the number of integers $t$ with $7 \leq t \leq 2031$ such that $t = 5a + 2b$ for some intege... | 63,261 | 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=216)), Eq(left=GCD(a=Var(name='p'), b=Var(name='q')), right=Const(value=1)),... | NT | COMB | COUNT | sympy | COPRIME_PAIRS | [
"COPRIME_PAIRS/MIN_PRIME_FACTOR",
"LIN_FORM/MIN_PRIME_FACTOR"
] | c75b83 | comb_count_partitions_v1 | null | 7 | 0 | [
"COPRIME_PAIRS",
"LIN_FORM",
"MIN_PRIME_FACTOR"
] | 3 | 0.003 | 2026-02-08T17:14:34.587493Z | {
"verified": true,
"answer": 63261,
"timestamp": "2026-02-08T17:14:34.590357Z"
} | ff5505 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 197,
"completion_tokens": 4706
},
"timestamp": "2026-02-18T00:03:24.946Z",
"answer": 63261
},
... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "MIN_PRIME_FACTOR",
"sta... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
3818b9 | sequence_lucas_compute_v1_655260480_1433 | Let $n$ be two more than the number of nonnegative integers $j \le 12816$ for which the binomial coefficient $\binom{12816}{j}$ is odd. Compute the $n$-th Lucas number, where $L_1 = 1$, $L_2 = 3$, and $L_k = L_{k-1} + L_{k-2}$ for $k \ge 3$. | 5,778 | graphs = [
Graph(
let={
"_n": Const(12816),
"n": Sum(CountOverSet(set=SolutionsSet(var=Var("j"), condition=And(Geq(Var("j"), Const(0)), Leq(Var("j"), Ref("_n")), Eq(Mod(value=Binom(n=Const(12816), k=Var("j")), modulus=Const(2)), Const(1))), domain='nonnegative_integers')), Const(2)),... | ALG | COMB | COMPUTE | sympy | C3 | [
"V8"
] | 86348e | sequence_lucas_compute_v1 | null | 6 | 0 | [
"C3",
"V8"
] | 2 | 0.028 | 2026-02-08T16:08:24.883971Z | {
"verified": true,
"answer": 5778,
"timestamp": "2026-02-08T16:08:24.911631Z"
} | c8f34d | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 203,
"completion_tokens": 1190
},
"timestamp": "2026-02-24T19:56:21.119Z",
"answer": 5778
},
{
"... | 1 | [
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "V3",
"status": "no"
},
{
"lemma": "V8",
"status": "ok"
}
] | {
"lo": -2.4,
"mid": 1.57,
"hi": 5.75
} | ||
fe63a2 | antilemma_sum_equals_v1_655260480_3987 | Let $t$ be an integer such that $22 \leq t \leq 156$. A pair of positive integers $(a, b)$ with $1 \leq a \leq 6$ and $1 \leq b \leq 17$ is called *valid* if $t = 14a + 4b + 4$. Let $N$ be the number of values of $t$ for which there exists at least one valid pair $(a, b)$. Determine the number of ordered pairs $(i, j)$... | 61 | 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=6)), Geq(left=Var(name='b'), right=Const(value=... | COMB | GEOM | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM/COUNT_SUM_EQUALS",
"COUNT_SUM_EQUALS"
] | ada383 | antilemma_sum_equals_v1 | null | 5 | 0 | [
"COUNT_SUM_EQUALS",
"LIN_FORM"
] | 2 | 0.007 | 2026-02-08T17:38:54.052946Z | {
"verified": true,
"answer": 61,
"timestamp": "2026-02-08T17:38:54.059566Z"
} | ee1c6d | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 189,
"completion_tokens": 3522
},
"timestamp": "2026-02-18T05:13:26.968Z",
"answer": 61
},
{
... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "ok"
},
{
"lemma": "LIN_F... | {
"lo": -4.1,
"mid": -1.76,
"hi": 1.32
} | ||
8fb466 | nt_min_with_divisor_count_v1_124444284_301 | Let $\phi(n)$ denote Euler's totient function. Define $\text{upper} = \sum_{d \mid 6561} \phi(d)$. Let $\text{div\_count} = 2$. Define $\text{result}$ to be the smallest positive integer $n$ such that $1 \leq n \leq \text{upper}$ and the number of positive divisors of $n$ is equal to $\text{div\_count}$. Compute $\text... | 2 | graphs = [
Graph(
let={
"upper": SumOverDivisors(n=Const(value=6561), var='d', expr=EulerPhi(n=Var(name='d'))),
"div_count": Const(2),
"result": MinOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Ref("upper")), Eq(NumDivisors(n=... | NT | null | EXTREMUM | sympy | B3 | [
"K3"
] | 54c41e | nt_min_with_divisor_count_v1 | null | 4 | 0 | [
"B3",
"K3"
] | 2 | 11.973 | 2026-02-08T03:09:09.110301Z | {
"verified": true,
"answer": 2,
"timestamp": "2026-02-08T03:09:21.083782Z"
} | 28b9fd | 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": 627
},
"timestamp": "2026-02-09T15:51:24.683Z",
"answer": 2
},
{
"id": ... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "K3",
"status": "ok"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
}
] | {
"lo": -5.55,
"mid": -3.02,
"hi": 0.31
} | ||
9dfde4 | nt_count_phi_equals_v1_1915831931_3632 | Let $N = 55119$. Let $u$ be the number of nonnegative integers $j$ such that $0 \leq j \leq 55119$ and the binomial coefficient $\binom{55119}{j}$ is odd. Let $r$ be the number of positive integers $n$ such that $1 \leq n \leq u$ and $\phi(n) = 670$, where $\phi$ denotes Euler's totient function.
Determine the value o... | 0 | graphs = [
Graph(
let={
"_n": Const(55119),
"upper": CountOverSet(set=SolutionsSet(var=Var("j"), condition=And(Geq(Var("j"), Const(0)), Leq(Var("j"), Const(55119)), Eq(Mod(value=Binom(n=Ref("_n"), k=Var("j")), modulus=Const(2)), Const(1))), domain='nonnegative_integers')),
... | NT | null | COUNT | sympy | V1 | [
"V8"
] | 86348e | nt_count_phi_equals_v1 | null | 6 | 0 | [
"V1",
"V8"
] | 2 | 0.948 | 2026-02-08T17:47:34.927298Z | {
"verified": true,
"answer": 0,
"timestamp": "2026-02-08T17:47:35.875663Z"
} | e94052 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 147,
"completion_tokens": 4081
},
"timestamp": "2026-02-18T08:07:03.525Z",
"answer": 0
},
{
... | 1 | [
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "V1",
"status": "no"
},
{
"lemma": "V8",
"status": ... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
32c3a1 | sequence_lucas_compute_v1_1116507919_89 | Let $m = 3$ and $n = 6$. Define
$$
a = \sum_{k=1}^{\sum_{k=1}^{m} \phi(k) \left\lfloor \frac{3}{k} \right\rfloor} \phi(k) \left\lfloor \frac{n}{k} \right\rfloor.
$$
Compute the value of the $a$-th Lucas number. | 24,476 | graphs = [
Graph(
let={
"_m": Const(3),
"_n": Const(6),
"n": Summation(var="k", start=Const(1), end=Summation(var="k", start=Const(1), end=Ref("_m"), expr=Mul(EulerPhi(n=Var("k")), Floor(Div(Const(3), Var("k"))))), expr=Mul(EulerPhi(n=Var("k")), Floor(Div(Ref("_n"), Var("... | NT | null | COMPUTE | sympy | K2 | [
"K2/K2"
] | ddede2 | sequence_lucas_compute_v1 | null | 6 | 0 | [
"K2"
] | 1 | 0.001 | 2026-02-08T02:25:23.273836Z | {
"verified": true,
"answer": 24476,
"timestamp": "2026-02-08T02:25:23.274840Z"
} | 772aff | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 209,
"completion_tokens": 1311
},
"timestamp": "2026-02-08T19:01:55.566Z",
"answer": 24476
},
{
"... | 1 | [
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K2",
"status": "ok"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
}
] | {
"lo": -2.84,
"mid": -0.89,
"hi": 0.95
} | ||
e62573 | comb_catalan_compute_v1_1978505735_4985 | Compute the 10th Catalan number. Let this number be $C$.
Let $S$ be the set of all ordered pairs $(x_1, x_2)$ of positive odd integers such that $x_1 + x_2 = T$, where $T$ is the number of positive integers $t$ for which there exist positive integers $a$ and $b$ with $1 \leq a \leq 2$, $1 \leq b \leq 8$, $14 \leq t \l... | 71,875 | graphs = [
Graph(
let={
"n": Const(10),
"result": Catalan(Ref("n")),
"_c": 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... | COMB | null | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM/COMB1"
] | 866223 | comb_catalan_compute_v1 | negation_mod | 4 | 0 | [
"COMB1",
"LIN_FORM"
] | 2 | 0.002 | 2026-02-08T18:42:08.798244Z | {
"verified": true,
"answer": 71875,
"timestamp": "2026-02-08T18:42:08.800550Z"
} | f195c5 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 219,
"completion_tokens": 1487
},
"timestamp": "2026-02-18T18:51:44.476Z",
"answer": 71875
},
... | 1 | [
{
"lemma": "COMB1",
"status": "ok_later"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "V7"... | {
"lo": -3.12,
"mid": 1.47,
"hi": 6.57
} | ||
3c2d1c | sequence_fibonacci_compute_v1_238844314_606 | Let $n = 21$. Define $F_n$ to be the $n$th Fibonacci number, where $F_1 = 1$, $F_2 = 1$, and $F_k = F_{k-1} + F_{k-2}$ for $k \geq 3$. Let $Q$ be the remainder when $44121 \cdot F_n$ is divided by $62162$. Compute $Q$. | 11,888 | graphs = [
Graph(
let={
"n": Const(21),
"result": Fibonacci(arg=Ref(name='n')),
"Q": Mod(value=Mul(Const(44121), Ref("result")), modulus=Const(62162)),
},
goal=Ref("Q"),
)
] | NT | null | COMPUTE | sympy | LTE_DIFF | [
"LTE_DIFF"
] | cf8260 | sequence_fibonacci_compute_v1 | null | 3 | 0 | [
"LTE_DIFF"
] | 1 | 0.007 | 2026-02-08T13:25:40.113744Z | {
"verified": true,
"answer": 11888,
"timestamp": "2026-02-08T13:25:40.120441Z"
} | f341d2 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 139,
"completion_tokens": 1173
},
"timestamp": "2026-02-15T15:20:25.473Z",
"answer": 11888
},
... | 1 | [
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "ok"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
}
] | {
"lo": -5.49,
"mid": 0.22,
"hi": 6.51
} | ||
70c33c | antilemma_v1_legendre_1742523217_3657 | Let $ m = 2 $. Define $ n $ to be the largest prime number such that $ m \leq n \leq 4 $. Consider the set of all ordered pairs $ (x, y) $ of positive integers such that $ xy = 7551504 $. Let $ s $ be the minimum value of $ x + y $ over all such pairs. Let $ x $ be the largest integer $ k $ such that $ n^k $ divides $ ... | 16,578 | graphs = [
Graph(
let={
"_m": Const(2),
"_n": MaxOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Ref("_m")), Leq(Var("n"), Const(4)), IsPrime(Var("n"))))),
"x": MaxKDivides(target=Factorial(MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[... | NT | null | COMPUTE | sympy | MAX_PRIME_BELOW | [
"MAX_PRIME_BELOW/B3/V1",
"V1"
] | e05ecb | antilemma_v1_legendre | null | 6 | 0 | [
"B3",
"MAX_PRIME_BELOW",
"V1"
] | 3 | 0.003 | 2026-02-08T06:00:52.398606Z | {
"verified": true,
"answer": 16578,
"timestamp": "2026-02-08T06:00:52.401470Z"
} | 726c53 | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 208,
"completion_tokens": 671
},
"timestamp": "2026-02-18T22:17:47.149Z",
"answer": 16578
}
] | 2 | [
{
"lemma": "B3",
"status": "ok_later"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K5",
"status": "same_pattern_wrong"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "MOD_MUL",... | {
"lo": -10,
"mid": -6.47,
"hi": -2.95
} | ||
b3308a | sequence_fibonacci_compute_v1_124444284_10268 | Let $n$ be the number of integers $t$ with $30 \leq t \leq 126$ such that there exist integers $a$ and $b$ satisfying $1 \leq a \leq 7$, $1 \leq b \leq 3$, and $t = 9a + 21b$. Let $\text{result} = F_n$, the $n$-th Fibonacci number. Compute $82165 \cdot \text{result} \bmod 76532$. Find the value of the result. | 50,558 | graphs = [
Graph(
let={
"_n": Const(82165),
"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=7)), Geq(left=Va... | NT | null | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | sequence_fibonacci_compute_v1 | null | 5 | 0 | [
"LIN_FORM"
] | 1 | 0.003 | 2026-02-08T12:56:03.906394Z | {
"verified": true,
"answer": 50558,
"timestamp": "2026-02-08T12:56:03.909504Z"
} | f20568 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 158,
"completion_tokens": 2246
},
"timestamp": "2026-02-15T07:49:22.438Z",
"answer": 50558
},
... | 1 | [
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "V1",
"status": "no"
}
] | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
d08726 | diophantine_fbi2_min_v1_124444284_8214 | Let $k$ be the number of integers $t$ with $10 \le t \le 24$ for which there exist positive integers $a$ and $b$ such that $1 \le a \le 2$, $1 \le b \le 3$, and $t = 6a + 4b$. Let $d$ be a positive integer such that $3 \le d \le 16$, $d$ divides $k$, and $\frac{k}{d} \ge 2$. Determine the smallest possible value of $d$... | 3 | graphs = [
Graph(
let={
"_n": Const(2),
"k": CountOverSet(set=SolutionsSet(var=Var("t"), condition=Exists(var=Var(name='a'), condition=Exists(var=Var(name='b'), condition=And(Geq(left=Var(name='a'), right=Const(value=1)), Leq(left=Var(name='a'), right=Const(value=2)), Geq(left=Var(na... | NT | null | EXTREMUM | sympy | MAX_PRIME_BELOW | [
"COPRIME_PAIRS",
"LIN_FORM"
] | 67610e | diophantine_fbi2_min_v1 | null | 4 | 0 | [
"COPRIME_PAIRS",
"LIN_FORM",
"MAX_PRIME_BELOW"
] | 3 | 0.053 | 2026-02-08T09:36:24.582447Z | {
"verified": true,
"answer": 3,
"timestamp": "2026-02-08T09:36:24.635015Z"
} | f30f8e | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 165,
"completion_tokens": 635
},
"timestamp": "2026-02-14T05:10:21.486Z",
"answer": 3
},
{
... | 1 | [
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "n... | {
"lo": -6.96,
"mid": -4.56,
"hi": -1.46
} | ||
edc6bd | comb_count_surjections_v1_971394319_2039 | Let $n$ be the number of elements in the Cartesian product of the sets $\{1, 2\}$ and $\{1, 2, 3\}$. Let $k$ be the number of ordered pairs $(i, j)$ of integers with $1 \leq i \leq 3$ and $1 \leq j \leq 3$ such that $i + j = 5$. Compute $k! \cdot S(n, k)$, where $S(n, k)$ denotes the Stirling number of the second kind.... | 62 | graphs = [
Graph(
let={
"_n": Const(5),
"n": CountOverSet(set=CartesianProduct(left=IntegerRange(start=Const(1), end=Const(2)), right=IntegerRange(start=Const(1), end=Const(3)))),
"k": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("i"), Var("j")]), condition=Eq(Su... | COMB | null | COUNT | sympy | COUNT_SUM_EQUALS | [
"COUNT_SUM_EQUALS",
"COUNT_CARTESIAN"
] | e4fc6a | comb_count_surjections_v1 | null | 4 | 0 | [
"COUNT_CARTESIAN",
"COUNT_SUM_EQUALS"
] | 2 | 0.018 | 2026-02-08T14:05:41.923501Z | {
"verified": true,
"answer": 62,
"timestamp": "2026-02-08T14:05:41.941808Z"
} | 1f7b77 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 237,
"completion_tokens": 642
},
"timestamp": "2026-02-24T19:50:45.434Z",
"answer": 62
},
{
"id":... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "ok"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "ok"
},
{
"lemma": "V8",
... | {
"lo": -8,
"mid": -4.75,
"hi": -2.29
} | ||
170b08 | comb_bell_compute_v1_458359167_3099 | Let $n = 9$. Compute the Bell number $B_n$, which is the number of ways to partition a set of $n$ elements.
Let $p$ be the largest prime number less than or equal to $18$.
Let $Q$ be the remainder when $p - B_9$ is divided by $88901$. Find $Q$. | 67,771 | graphs = [
Graph(
let={
"_n": Const(88901),
"n": Const(9),
"result": Bell(Ref("n")),
"_c": MaxOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(2)), Leq(Var("n"), Const(18)), IsPrime(Var("n"))))),
"Q": Mod(value=Sub(Ref("_c")... | NT | COMB | COMPUTE | sympy | MAX_PRIME_BELOW | [
"MAX_PRIME_BELOW"
] | 2ed1de | comb_bell_compute_v1 | negation_mod | 2 | 0 | [
"MAX_PRIME_BELOW"
] | 1 | 0.001 | 2026-02-08T06:56:53.736940Z | {
"verified": true,
"answer": 67771,
"timestamp": "2026-02-08T06:56:53.738318Z"
} | c23fd2 | 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": 2073
},
"timestamp": "2026-02-13T06:57:33.389Z",
"answer": 67771
},
... | 1 | [
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "VAL_SUM_EQ",
"statu... | {
"lo": -7.01,
"mid": -4.68,
"hi": -2.15
} | ||
0e8f31 | nt_count_divisors_in_range_v1_1520064083_5403 | Let $a$ be the number of positive integers $k$ such that $1 \leq k \leq 3402$ and $81$ divides $k$.
Let $n = 15120$ and $b = 1012$. Define $d$ as a positive divisor of $n$ such that $a \leq d \leq b$.
Determine the number of such divisors $d$. | 44 | graphs = [
Graph(
let={
"_n": Const(81),
"n": Const(15120),
"a": CountOverSet(set=SolutionsSet(var=Var("k"), condition=And(Geq(Var("k"), Const(1)), Leq(Var("k"), Const(3402)), Divides(divisor=Ref("_n"), dividend=Var("k"))), domain='positive_integers')),
"b": C... | NT | null | COUNT | sympy | C2 | [
"C2"
] | 9685eb | nt_count_divisors_in_range_v1 | null | 4 | 0 | [
"C2"
] | 1 | 0.049 | 2026-02-08T06:46:38.206634Z | {
"verified": true,
"answer": 44,
"timestamp": "2026-02-08T06:46:38.255691Z"
} | 0b4d50 | 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": 2550
},
"timestamp": "2026-02-13T09:36:58.039Z",
"answer": 44
},
{
... | 1 | [
{
"lemma": "C2",
"status": "ok"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
... | {
"lo": -3.51,
"mid": 1.33,
"hi": 6.56
} | ||
f4cf90 | nt_lcm_compute_v1_1874849503_444 | Let $S$ be the set of all integers $t$ such that $5 \le t \le 2179$ and there exist positive integers $a \le 531$ and $b \le 293$ satisfying $t = 3a + 2b$. Let $a$ be the sum of $\phi(d)$ over all positive divisors $d$ of $|S|$. Let $b = 2064$. Let $c = 36463$, and let $\text{result} = \text{LCM}(a, b)$. Compute the re... | 65,790 | graphs = [
Graph(
let={
"a": SumOverDivisors(n=CountOverSet(set=SolutionsSet(var=Var(name='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=531)), Geq(left=Var(name=... | NT | null | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM/K3"
] | c7df50 | nt_lcm_compute_v1 | null | 6 | 0 | [
"K3",
"LIN_FORM"
] | 2 | 0.003 | 2026-02-08T13:03:56.775258Z | {
"verified": true,
"answer": 65790,
"timestamp": "2026-02-08T13:03:56.778278Z"
} | f41b81 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 250,
"completion_tokens": 4400
},
"timestamp": "2026-02-11T07:33:14.307Z",
"answer": 41151
},
{
... | 1 | [
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "K3",
"status": "ok_later"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "V5",
"sta... | {
"lo": 1.94,
"mid": 5.23,
"hi": 8.52
} | ||
98a5d4 | comb_count_permutations_fixed_v1_1915831931_2601 | Let $m = 2$ and $n = 9$. Define $A$ to be the set of all positive integers $j$ such that $1 \leq j \leq m$ and $j^4 \leq 16$. Let $s$ be the number of elements in $A$. Let $k$ be the largest prime number satisfying $s \leq k \leq 6$. Compute $\binom{n}{k} \cdot !(n - k)$, where $!m$ denotes the number of derangements o... | 1,134 | graphs = [
Graph(
let={
"_m": Const(2),
"_n": Const(6),
"n": Const(9),
"k": MaxOverSet(set=SolutionsSet(var=Var("n1"), condition=And(Geq(Var("n1"), CountOverSet(set=SolutionsSet(var=Var("j"), condition=And(Geq(Var("j"), Const(1)), Leq(Var("j"), Ref("_m")), Leq... | NT | COMB | COUNT | sympy | C3 | [
"C3/MAX_PRIME_BELOW"
] | d11855 | comb_count_permutations_fixed_v1 | null | 5 | 0 | [
"C3",
"MAX_PRIME_BELOW"
] | 2 | 0.003 | 2026-02-08T16:58:07.390710Z | {
"verified": true,
"answer": 1134,
"timestamp": "2026-02-08T16:58:07.393837Z"
} | bd0e13 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 162,
"completion_tokens": 731
},
"timestamp": "2026-02-17T17:13:53.491Z",
"answer": 1134
},
{
... | 1 | [
{
"lemma": "C3",
"status": "ok"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok_later"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "V1",
"status": "no"... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
09c41e | comb_count_partitions_v1_1742523217_139 | Let $n = 33301$. Let $m$ be the number of nonnegative integers $j$ such that $0 \leq j \leq 33301$ and $\binom{n}{j}$ is odd. Define $N = m + 7$. Find the value of the number of integer partitions of $N$. | 31,185 | graphs = [
Graph(
let={
"_n": Const(33301),
"n": Sum(CountOverSet(set=SolutionsSet(var=Var("j"), condition=And(Geq(Var("j"), Const(0)), Leq(Var("j"), Const(33301)), Eq(Mod(value=Binom(n=Ref("_n"), k=Var("j")), modulus=Const(2)), Const(1))), domain='nonnegative_integers')), Const(7)),... | COMB | null | COUNT | sympy | V8 | [
"V8"
] | 86348e | comb_count_partitions_v1 | null | 7 | 0 | [
"V8"
] | 1 | 0.001 | 2026-02-08T02:53:24.388201Z | {
"verified": true,
"answer": 31185,
"timestamp": "2026-02-08T02:53:24.389039Z"
} | 76e059 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 185,
"completion_tokens": 2788
},
"timestamp": "2026-02-09T14:03:08.625Z",
"answer": 31185
},
{
"... | 1 | [
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "V8",
"status": "ok"
},
{
"lemma": "V8_SUM",
"status": "no"
},
{
"lemma": "VAL_SUM_EQ",
"status": "no"
}
] | {
"lo": -0.89,
"mid": 0.92,
"hi": 2.5
} | ||
2e5a03 | antilemma_k2_v1_238844314_841 | Let $n = 2$. Consider the quadratic equation $x^2 - 308x - 37293 = 0$. Let $k$ be the sum of all positive integer solutions $x$ to this equation. Compute $\sum_{k=1}^{k} \phi(k) \left\lfloor \frac{308}{k} \right\rfloor$, where $\phi$ denotes Euler's totient function. (Note: The upper limit of summation is the value of ... | 47,586 | graphs = [
Graph(
let={
"_n": Const(2),
"x": Summation(var="k", start=Const(1), end=SumOverSet(set=SolutionsSet(var=Var("x"), condition=Eq(Sum(Pow(Var("x"), Ref("_n")), Mul(Const(-308), Var("x")), Const(-37293)), Const(0)))), expr=Mul(EulerPhi(n=Var("k")), Floor(Div(Const(308), Var("... | NT | COMB | COMPUTE | sympy | VIETA_SUM | [
"VIETA_SUM/K2",
"K2"
] | 6be084 | antilemma_k2_v1 | null | 6 | 0 | [
"K2",
"VIETA_SUM"
] | 2 | 0.001 | 2026-02-08T13:38:47.844551Z | {
"verified": true,
"answer": 47586,
"timestamp": "2026-02-08T13:38:47.845983Z"
} | bda8a7 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 151,
"completion_tokens": 1746
},
"timestamp": "2026-02-15T18:40:03.498Z",
"answer": 47586
},
... | 1 | [
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K2",
"status": "ok"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "VAL_SUM_EQ",
"status": "no"
... | {
"lo": -5.49,
"mid": 0.22,
"hi": 6.51
} | ||
697f46 | nt_sum_totient_over_divisors_v1_1431428450_903 | Let $n = 61659$. Define $\text{result}$ to be the sum of $\phi(d)$ over all positive divisors $d$ of $n$, where $\phi$ denotes Euler's totient function. Let $m$ be the smallest integer $d \geq 2$ that divides $1859$. Define $Q$ to be the Bell number of $|\text{result}| \mod m$. Compute $Q$. | 15 | graphs = [
Graph(
let={
"_n": Const(2),
"n": Const(61659),
"result": SumOverDivisors(n=Ref(name='n'), var='d', expr=EulerPhi(n=Var(name='d'))),
"Q": Bell(Mod(value=Abs(arg=Ref(name='result')), modulus=MinOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq... | NT | COMB | COMPUTE | sympy | MIN_PRIME_FACTOR | [
"MIN_PRIME_FACTOR"
] | 58d7e9 | nt_sum_totient_over_divisors_v1 | bell_mod | 5 | 0 | [
"MIN_PRIME_FACTOR"
] | 1 | 0.002 | 2026-02-08T13:46:38.684962Z | {
"verified": true,
"answer": 15,
"timestamp": "2026-02-08T13:46:38.686976Z"
} | 0e5b45 | 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": 726
},
"timestamp": "2026-02-15T20:30:05.045Z",
"answer": 15
},
{
... | 1 | [
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "MIN_PRIME_FACTOR",
"status": "ok"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
}
] | {
"lo": -5.49,
"mid": 0.22,
"hi": 6.51
} | ||
849039 | nt_count_squarefree_v1_1116507919_314 | Let $ U = 41616 $. Let $ A $ be the set of all positive integers $ n $ such that $ 1 \leq n \leq U $ and $ \mu(n)^2 = 1 $, where $ \mu $ denotes the M\"obius function. Let $ r $ be the number of elements in $ A $. Define $ S = \sum_{n=\phi(2)}^{r} \phi(n) $, where $ \phi $ denotes Euler's totient function. Compute the ... | 57,460 | graphs = [
Graph(
let={
"upper": Const(41616),
"result": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Ref("upper")), Eq(Mul(MoebiusMu(n=Var(name='n')), MoebiusMu(n=Var(name='n'))), Const(1))))),
"Q": Mod(value=Summation(... | NT | null | COUNT | sympy | ONE_PHI_2 | [
"ONE_PHI_2"
] | e19278 | nt_count_squarefree_v1 | null | 5 | 0 | [
"ONE_PHI_2"
] | 1 | 16.386 | 2026-02-08T02:30:46.172404Z | {
"verified": true,
"answer": 57460,
"timestamp": "2026-02-08T02:31:02.558594Z"
} | 3e3626 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 167,
"completion_tokens": 5838
},
"timestamp": "2026-02-09T19:21:30.629Z",
"answer": 0
},
{... | 0 | [
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "ONE_PHI_2",
"status": "ok"
},
{
"lemma": "V1",
"status": ... | {
"lo": 2.52,
"mid": 6.26,
"hi": 10
} | ||
0ee51e_l | algebra_poly_eval_v1_1125832087_1749 | Let $n = 2$. Define $y$ to be the number of nonnegative integers $j$ such that $$
j \ge \sum_{k=0}^{3} (-1)^k \binom{3}{k}, \quad j \le 18496, \quad \text{and} \quad \binom{18496}{j} \equiv 1 \pmod{n}.$$
Compute $$7y^4 + 10y^3 + 7y^2 - 6y + 8.$$ | 8 | COMB | null | COMPUTE | sympy | BINOMIAL_ALTERNATING | [
"BINOMIAL_ALTERNATING",
"V8"
] | efe7d7 | algebra_poly_eval_v1 | null | 6 | 0 | [
"BINOMIAL_ALTERNATING",
"V8"
] | 2 | 0.004 | 2026-02-08T03:54:38.220621Z | {
"verified": false,
"answer": 34200,
"timestamp": "2026-02-08T03:54:38.224336Z"
} | f0e1fd | 0ee51e | legacy_text | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 226,
"completion_tokens": 2775
},
"timestamp": "2026-02-10T16:08:36.119Z",
"answer": 34200
},
{
"... | 1 | [
{
"lemma": "BINOMIAL_ALTERNATING",
"status": "ok"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
... | {
"lo": -2.46,
"mid": 0.47,
"hi": 3.59
} | |
ee14fb | geo_count_lattice_triangle_v1_2051736721_2845 | Let $A$ be the area of the triangle with vertices at $(0,0)$, $(144,196)$, and $(3,121)$, multiplied by $2$. Let $B$ be the sum of the greatest common divisors of the absolute differences of the coordinates of each pair of vertices, specifically:
- $\gcd(|144 - 0|, |196 - 0|)$,
- $\gcd(|3 - 144|, |121 - 196|)$,
- $\gc... | 8,415 | graphs = [
Graph(
let={
"_m": Const(196),
"_n": Const(3),
"area_2x": Abs(arg=Sum(Mul(Const(value=144), Const(value=121)), Mul(Ref(name='_n'), Sub(left=Const(value=0), right=Ref(name='_m'))))),
"boundary": Sum(GCD(a=Abs(arg=Const(value=144)), b=Abs(arg=Const(va... | ALG | NT | COUNT | sympy | LIN_FORM | [
"LIN_FORM/L3C"
] | cf7f86 | geo_count_lattice_triangle_v1 | null | 5 | 0 | [
"L3C",
"LIN_FORM"
] | 2 | 0.01 | 2026-02-08T16:56:11.657981Z | {
"verified": true,
"answer": 8415,
"timestamp": "2026-02-08T16:56:11.668479Z"
} | 5aa6cf | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 211,
"completion_tokens": 535
},
"timestamp": "2026-02-16T08:42:00.493Z",
"answer": 8485
},
{
"id": 11,... | 1 | [
{
"lemma": "L3C",
"status": "ok_later"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
}
] | {
"lo": -8.26,
"mid": -5.01,
"hi": -1.76
} | ||
e0cff6 | modular_sum_quadratic_residues_v1_784195855_7787 | Let $m = 324$. Consider the set of all positive integers $p$ for which there exists a positive integer $q$ such that $pq = 24$, $\gcd(p, q) = 1$, and $p < q$. Let $n$ be the number of such integers $p$. Let $p_{\text{max}}$ be the largest prime number $n$ such that $n \leq m$ and $n \geq n$. Compute $\frac{p_{\text{max... | 25,043 | graphs = [
Graph(
let={
"_m": Const(324),
"_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=24)), Eq(left=GCD(a=Var(name='p'), b=Var(name=... | NT | null | SUM | sympy | COPRIME_PAIRS | [
"COPRIME_PAIRS/MAX_PRIME_BELOW"
] | 2248fc | modular_sum_quadratic_residues_v1 | null | 4 | 0 | [
"COPRIME_PAIRS",
"MAX_PRIME_BELOW"
] | 2 | 0.003 | 2026-02-08T09:31:32.009511Z | {
"verified": true,
"answer": 25043,
"timestamp": "2026-02-08T09:31:32.012550Z"
} | 1a3f32 | 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": 1428
},
"timestamp": "2026-02-14T04:55:34.150Z",
"answer": 25043
},
... | 1 | [
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok_later"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"... | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
0f3c11 | geo_count_lattice_rect_v1_1918700295_3755 | Let $a = 32$ and $b = 60$. Define a lattice point as a point in the coordinate plane with integer coordinates. Consider the rectangle consisting of all points $(x, y)$ such that $0 \leq x \leq a$ and $0 \leq y \leq b$. Compute the number of lattice points contained in this rectangle. | 2,013 | graphs = [
Graph(
let={
"a": Const(32),
"b": Const(60),
"result": LatticePointsRect(a=Ref(name='a'), b=Ref(name='b')),
},
goal=Ref("result"),
)
] | GEOM | null | COUNT | sympy | [] | geo_count_lattice_rect_v1 | null | 3 | 0 | null | null | 0 | 2026-02-08T08:51:24.443275Z | {
"verified": true,
"answer": 2013,
"timestamp": "2026-02-08T08:51:24.443571Z"
} | 9b5eab | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 187,
"completion_tokens": 289
},
"timestamp": "2026-02-24T10:12:07.998Z",
"answer": 2013
},
{
"id... | 1 | [] | {
"lo": -7.18,
"mid": -5,
"hi": -3.01
} | ||||
1fb96e | modular_mod_compute_v1_1915831931_3634 | Let $m$ be the maximum value of $xy$ over all pairs of positive integers $(x, y)$ such that $x + y = 84$. Compute the remainder when $-19$ is divided by $m$. | 1,745 | graphs = [
Graph(
let={
"_n": Const(84),
"a": Const(-19),
"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")), Ref("_n")))), expr=M... | NT | null | COMPUTE | sympy | B1 | [
"B1"
] | 5b950e | modular_mod_compute_v1 | null | 3 | 0 | [
"B1"
] | 1 | 0.004 | 2026-02-08T17:47:36.033405Z | {
"verified": true,
"answer": 1745,
"timestamp": "2026-02-08T17:47:36.036949Z"
} | 41d5c6 | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 104,
"completion_tokens": 472
},
"timestamp": "2026-02-16T11:38:19.941Z",
"answer": -19
},
{
"id": 11,
... | 1 | [
{
"lemma": "B1",
"status": "ok"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
}
] | {
"lo": -8.26,
"mid": -5.01,
"hi": -1.76
} | ||
905d7d | comb_count_permutations_fixed_v1_809748730_1389 | Let $n$ be the smallest integer greater than or equal to $2$ that divides $41327$. Let $P$ be the set of all ordered pairs of positive integers $(x, y)$ such that $x + y = 16$. Define $m$ to be the maximum value of $xy$ over all pairs $(x, y) \in P$. Let $k$ be the number of positive integers $j$ with $1 \leq j \leq 8$... | 330 | graphs = [
Graph(
let={
"_m": Const(41327),
"_n": Const(2),
"n": MinOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Ref("_n")), Divides(divisor=Var("d"), dividend=Ref("_m"))))),
"k": CountOverSet(set=SolutionsSet(var=Var("j"), condition=And(... | NT | COMB | COUNT | sympy | MIN_PRIME_FACTOR | [
"MIN_PRIME_FACTOR",
"B1/C3"
] | 25efea | comb_count_permutations_fixed_v1 | null | 5 | 0 | [
"B1",
"C3",
"MIN_PRIME_FACTOR"
] | 3 | 0.004 | 2026-02-08T12:23:50.192809Z | {
"verified": true,
"answer": 330,
"timestamp": "2026-02-08T12:23:50.196680Z"
} | ef71e0 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 193,
"completion_tokens": 890
},
"timestamp": "2026-02-15T01:12:11.112Z",
"answer": 330
},
{
... | 1 | [
{
"lemma": "B1",
"status": "ok"
},
{
"lemma": "C3",
"status": "ok_later"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "MIN_PRIME_FACTOR",
"status": "ok"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"l... | {
"lo": -5.49,
"mid": 0.22,
"hi": 6.51
} | ||
7053bb | comb_count_partitions_v1_124444284_5813 | Let $T$ be the set of all integers $t$ such that $5 \leq t \leq 490$ and there exist positive integers $a$ and $b$ with $1 \leq a \leq 110$, $1 \leq b \leq 90$, and $t = 2a + 3b$. Let $n$ be the number of elements in $T$. Now consider all pairs of positive integers $(x, y)$ such that $xy = n$. Compute the minimum possi... | 75,175 | 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=110)), Geq(left=Var(name='b'), right=Const(valu... | COMB | null | COUNT | sympy | LIN_FORM | [
"LIN_FORM/B3"
] | 05313e | comb_count_partitions_v1 | null | 7 | 0 | [
"B3",
"LIN_FORM"
] | 2 | 0.003 | 2026-02-08T06:53:10.189725Z | {
"verified": true,
"answer": 75175,
"timestamp": "2026-02-08T06:53:10.192846Z"
} | 7a9b5a | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 250,
"completion_tokens": 32768
},
"timestamp": "2026-02-24T07:20:22.198Z",
"answer": null
},
{
... | 1 | [
{
"lemma": "B3",
"status": "ok_later"
},
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "V8",
"status": "no... | {
"lo": 3.43,
"mid": 5.73,
"hi": 8.84
} | ||
7ccdcd | nt_sum_gcd_range_mod_v1_1520064083_4117 | Let $S$ be the set of all ordered pairs $(x,y)$ of positive integers such that $x + y = t$, where $t$ is the number of integers $t'$ with $33 \leq t' \leq 450$ that can be expressed as $21a + 12b$ for integers $a$ and $b$ satisfying $1 \leq a \leq 6$ and $1 \leq b \leq 27$. Let $N$ be the maximum value of $xy$ over all... | 1,673 | graphs = [
Graph(
let={
"N": MaxOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(Sum(Var("x"), Var("y")), CountOverSet(set=SolutionsSet(var=Var("t"), condition=Exists(var=Var(name='a')... | NT | null | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM/B1"
] | b32639 | nt_sum_gcd_range_mod_v1 | null | 5 | 0 | [
"B1",
"LIN_FORM"
] | 2 | 0.173 | 2026-02-08T06:05:15.788290Z | {
"verified": true,
"answer": 1673,
"timestamp": "2026-02-08T06:05:15.960984Z"
} | a8359d | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 222,
"completion_tokens": 3910
},
"timestamp": "2026-02-12T19:18:05.907Z",
"answer": 1673
},
{... | 1 | [
{
"lemma": "B1",
"status": "ok_later"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma":... | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
e1a162 | comb_count_surjections_v1_349078426_1609 | Let $T$ be the number of integers $t$ such that $9 \leq t \leq 26$ and there exist positive integers $a$ and $b$ with $1 \leq a \leq 2$, $1 \leq b \leq 7$, and $t = 5a + 2b + 2$. Let $n$ be the number of ordered pairs $(x_1, x_2)$ of positive odd integers such that $x_1 + x_2 = T$. Compute the value of $3! \cdot S(n, 3... | 1,806 | 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=2)), Geq(left=Var(name='b'), right=Const(value=... | COMB | null | COUNT | sympy | LIN_FORM | [
"LIN_FORM/COMB1"
] | 268a62 | comb_count_surjections_v1 | null | 6 | 0 | [
"COMB1",
"LIN_FORM"
] | 2 | 0.004 | 2026-02-08T13:45:53.855362Z | {
"verified": true,
"answer": 1806,
"timestamp": "2026-02-08T13:45:53.859007Z"
} | c32a52 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 280,
"completion_tokens": 1668
},
"timestamp": "2026-02-24T18:57:45.668Z",
"answer": 1806
},
{
"i... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COMB1",
"status": "ok_later"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "V7",
"status": "n... | {
"lo": -3.84,
"mid": -1.67,
"hi": 1.32
} | ||
044730 | nt_min_coprime_above_v1_1978505735_5841 | Let $S_1$ be the set of all positive integers $n$ such that $1 \leq n \leq 74$ and $n \equiv 0 \pmod{74}$. Let $s = \sum S_1$.
Let $S_2$ be the set of all ordered pairs $(x_1, y_1)$ of positive integers such that $x_1 + y_1 = s$. For each such pair, compute $x_1 y_1$, and let $p$ be the maximum value of $x_1 y_1$ over... | 32,029 | graphs = [
Graph(
let={
"_n": Const(52364),
"start": Const(16384),
"upper": Const(16468),
"modulus": MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y'))... | NT | null | EXTREMUM | sympy | SUM_DIVISIBLE | [
"SUM_DIVISIBLE/B1/B3"
] | cf3329 | nt_min_coprime_above_v1 | null | 7 | 0 | [
"B1",
"B3",
"SUM_DIVISIBLE"
] | 3 | 0.012 | 2026-02-08T19:15:10.409812Z | {
"verified": true,
"answer": 32029,
"timestamp": "2026-02-08T19:15:10.422160Z"
} | cee3f6 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 282,
"completion_tokens": 2104
},
"timestamp": "2026-02-18T21:45:31.136Z",
"answer": 32029
},
... | 1 | [
{
"lemma": "B1",
"status": "ok_later"
},
{
"lemma": "B3",
"status": "ok_later"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status"... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
978a77 | nt_lcm_compute_v1_717093673_3099 | Let $a = 1881$ and $b = 1028$. Define $\ell$ to be the least common multiple of $a$ and $b$. Let $s$ be the sum of the digits of $\ell$, and let $d$ be the number of digits in $\ell$. Compute $$\sum_{i=0}^{d-1} \text{digit}_i(\ell) \cdot (i+1)^2 + 30625,$$ where $\text{digit}_i(\ell)$ denotes the $i$-th digit of $\ell$... | 31,207 | graphs = [
Graph(
let={
"a": Const(1881),
"b": Const(1028),
"result": LCM(a=Ref("a"), b=Ref("b")),
"Q": Sum(Summation(var="i", start=Summation(var="k", start=Const(0), end=Const(5), expr=Mul(Pow(Const(-1), Var("k")), Binom(n=Const(5), k=Var("k")))), end=Sub(Nu... | COMB | NT | COMPUTE | sympy | BINOMIAL_ALTERNATING | [
"BINOMIAL_ALTERNATING"
] | c21569 | nt_lcm_compute_v1 | null | 5 | 0 | [
"BINOMIAL_ALTERNATING"
] | 1 | 0.003 | 2026-02-08T17:22:32.095170Z | {
"verified": true,
"answer": 31207,
"timestamp": "2026-02-08T17:22:32.098340Z"
} | f35f4b | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 178,
"completion_tokens": 1246
},
"timestamp": "2026-02-18T01:15:31.709Z",
"answer": 31207
},
... | 1 | [
{
"lemma": "BINOMIAL_ALTERNATING",
"status": "ok"
},
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8",
"status": "... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
ee59c3 | modular_modexp_compute_v1_655260480_395 | Let $ a = 47 $. Let $ e $ be the number of nonnegative integers $ j $ such that $ 0 \le j \le 75164 $ and $ \binom{75164}{j} $ is odd. Let $ m = 11831 $. Compute the remainder when $ a^e $ is divided by $ m $. | 4,711 | graphs = [
Graph(
let={
"a": Const(47),
"e": CountOverSet(set=SolutionsSet(var=Var("j"), condition=And(Geq(Var("j"), Const(0)), Leq(Var("j"), Const(75164)), Eq(Mod(value=Binom(n=Const(75164), k=Var("j")), modulus=Const(2)), Const(1))), domain='nonnegative_integers')),
"m"... | NT | null | COMPUTE | sympy | V8 | [
"V8"
] | 86348e | modular_modexp_compute_v1 | null | 6 | 0 | [
"V8"
] | 1 | 0.002 | 2026-02-08T15:22:07.882137Z | {
"verified": true,
"answer": 4711,
"timestamp": "2026-02-08T15:22:07.884524Z"
} | d053a2 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 119,
"completion_tokens": 5520
},
"timestamp": "2026-02-16T04:47:32.901Z",
"answer": 4711
},
{... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "V8",
"status": "ok"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
cf6fd9 | geo_count_lattice_rect_v1_1218484723_2947 | Let $B_n$ denote the $n$-th Bell number. Let $N$ be the number of lattice points $(x, y)$ with $0 \le x \le 100$ and $0 \le y \le 68$. Compute $B_{N \bmod 11}$. | 203 | graphs = [
Graph(
let={
"a": Const(100),
"b": Const(68),
"result": LatticePointsRect(a=Ref(name='a'), b=Ref(name='b')),
"Q": Bell(Mod(value=Abs(arg=Ref(name='result')), modulus=Const(11))),
},
goal=Ref("Q"),
)
] | GEOM | GEOM | COUNT | sympy | [] | geo_count_lattice_rect_v1 | null | 2 | 0 | null | null | 0.002 | 2026-02-25T04:41:25.239691Z | {
"verified": true,
"answer": 203,
"timestamp": "2026-02-25T04:41:25.241337Z"
} | 634215 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 174,
"completion_tokens": 481
},
"timestamp": "2026-03-29T07:25:09.410Z",
"answer": 203
},
{
"id"... | 1 | [] | {
"lo": -4.26,
"mid": -1.8,
"hi": 1.26
} | ||||
e01ecd | nt_sum_gcd_range_mod_v1_2051736721_5719 | Let $N$ be the maximum value of $xy$ over all pairs of positive integers $(x, y)$ such that $x + y = 72$. Let $k$ be the minimum value of $x_1 + y_1$ over all pairs of positive integers $(x_1, y_1)$ such that $x_1 y_1 = 2916$. Define $s = \sum_{n=1}^{N} \gcd(n, k)$. Let $r$ be the remainder when $s$ is divided by 11437... | 13,784 | graphs = [
Graph(
let={
"_n": Const(2916),
"N": MaxOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(Sum(Var("x"), Var("y")), Const(72)))), expr=Mul(Var("x"), Var("y")))),
... | NT | null | COMPUTE | sympy | B3 | [
"B3",
"B1"
] | 655d51 | nt_sum_gcd_range_mod_v1 | null | 6 | 0 | [
"B1",
"B3"
] | 2 | 0.062 | 2026-02-08T18:44:32.123146Z | {
"verified": true,
"answer": 13784,
"timestamp": "2026-02-08T18:44:32.185505Z"
} | 1ebb69 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 215,
"completion_tokens": 2455
},
"timestamp": "2026-02-18T19:21:20.065Z",
"answer": 13784
},
... | 1 | [
{
"lemma": "B1",
"status": "ok"
},
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemm... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
74f3f1 | antilemma_sum_factor_cartesian_v1_153355830_299 | Let $S$ be the set of all ordered pairs $(x,y)$ of positive integers such that $xy = 121$. For each pair $(x,y)$ in $S$, let $s = x + y$. Let $T$ be the set of all such values $s$. Define $d_{\text{min}}$ as the minimum value of $\sum_{d \mid \gcd(15, s)} \mu(d)$ over all $s \in T$, where $\mu$ denotes the M\"obius fun... | 61,758 | graphs = [
Graph(
let={
"_n": Const(80748),
"x": SumOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("i"), Var("j")]), condition=SumOverDivisors(n=GCD(a=Const(value=15), b=MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var(name='x'), Var(name='y')]), co... | NT | null | COMPUTE | sympy | B3 | [
"B3/MOBIUS_COPRIME/SUM_FACTOR_CARTESIAN",
"SUM_FACTOR_CARTESIAN"
] | 0283f3 | antilemma_sum_factor_cartesian_v1 | null | 7 | 0 | [
"B3",
"MOBIUS_COPRIME",
"SUM_FACTOR_CARTESIAN"
] | 3 | 0.002 | 2026-02-08T03:00:36.293006Z | {
"verified": true,
"answer": 61758,
"timestamp": "2026-02-08T03:00:36.294537Z"
} | 186144 | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 297,
"completion_tokens": 524
},
"timestamp": "2026-02-17T17:28:59.191Z",
"answer": null
}
] | 0 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "MOBIUS_COPRIME",
"status"... | {
"lo": -6.48,
"mid": 1.54,
"hi": 9.56
} | ||
2cf380 | nt_sum_divisors_range_v1_153355830_552 | Let $S$ be the set of all positive integers $n$ such that $1 \leq n \leq 10000$. For each $n \in S$, let $d(n)$ denote the number of positive divisors of $n$.
Compute the sum
$$
\sum_{n=1}^{10000} d(n).
$$ | 93,668 | graphs = [
Graph(
let={
"upper": CountOverSet(set=CartesianProduct(left=IntegerRange(start=Const(1), end=Const(100)), right=IntegerRange(start=Const(1), end=Const(100)))),
"result": SumOverSet(set=MapOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Va... | NT | null | SUM | sympy | LTE_SUM | [
"COUNT_CARTESIAN"
] | 409d7d | nt_sum_divisors_range_v1 | null | 5 | 0 | [
"COUNT_CARTESIAN",
"LTE_SUM"
] | 2 | 1.122 | 2026-02-08T03:09:43.027566Z | {
"verified": true,
"answer": 93668,
"timestamp": "2026-02-08T03:09:44.149167Z"
} | c17e24 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 184,
"completion_tokens": 3711
},
"timestamp": "2026-02-10T15:14:17.234Z",
"answer": 93668
},
{
... | 1 | [
{
"lemma": "COUNT_CARTESIAN",
"status": "ok"
},
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "... | {
"lo": -3.42,
"mid": 1.86,
"hi": 7.55
} | ||
7bda8d | comb_count_permutations_fixed_v1_1439011603_494 | Let $n$ be the number of positive integers $p$ for which there exists a positive integer $q$ such that $pq = 147000$, $\gcd(p, q) = 1$, and $p < q$. Define $k = 0$. Compute $\binom{n}{k} \cdot !\left(n - k\right)$, where $!m$ denotes the number of derangements of $m$ elements. | 14,833 | graphs = [
Graph(
let={
"n": CountOverSet(set=SolutionsSet(var=Var("p"), condition=And(IsPositive(arg=Var(name='p')), Exists(var=Var(name='q'), condition=And(Eq(left=Mul(Var(name='p'), Var(name='q')), right=Const(value=147000)), Eq(left=GCD(a=Var(name='p'), b=Var(name='q')), right=Const(value=1)... | NT | COMB | COUNT | sympy | COPRIME_PAIRS | [
"COPRIME_PAIRS"
] | 2bb3aa | comb_count_permutations_fixed_v1 | null | 3 | 0 | [
"COPRIME_PAIRS"
] | 1 | 0.002 | 2026-02-08T15:31:19.877759Z | {
"verified": true,
"answer": 14833,
"timestamp": "2026-02-08T15:31:19.879971Z"
} | 33c4d1 | 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": 2382
},
"timestamp": "2026-02-16T07:53:48.061Z",
"answer": 14833
},
... | 1 | [
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
},
{
"lemma": "VAL_SUM_EQ",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
3ee1c5 | sequence_lucas_compute_v1_124444284_2400 | Let $n$ be the smallest divisor of $10051$ that is at least $2$. Compute the $n$-th Lucas number, where the Lucas sequence is defined by $L_1 = 1$, $L_2 = 3$, and $L_k = L_{k-1} + L_{k-2}$ for $k \geq 3$. | 9,349 | 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(10051))))),
"result": Lucas(arg=Ref(name='n')),
},
goal=Ref("result"),
)
] | NT | null | COMPUTE | sympy | MIN_PRIME_FACTOR | [
"MIN_PRIME_FACTOR"
] | bc3776 | sequence_lucas_compute_v1 | null | 3 | 0 | [
"MIN_PRIME_FACTOR"
] | 1 | 0.001 | 2026-02-08T04:38:24.506573Z | {
"verified": true,
"answer": 9349,
"timestamp": "2026-02-08T04:38:24.507425Z"
} | 55ba80 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 190,
"completion_tokens": 843
},
"timestamp": "2026-02-11T21:41:03.728Z",
"answer": 9349
},
{
"i... | 1 | [
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "MIN_PRIME_FACTOR",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
... | {
"lo": -3.42,
"mid": 1.86,
"hi": 7.55
} | ||
4e6c5b | algebra_vieta_sum_v1_1742523217_4061 | Let $R$ be the product of all real solutions $x$ to the equation $x^2 - 81 = 0$. Compute $\sum_{n=1}^{|R|} \tau(n)$, where $\tau(n)$ denotes the number of positive divisors of $n$. | 373 | graphs = [
Graph(
let={
"result": ProductOverSet(set=SolutionsSet(var=Var(name='x'), condition=Eq(left=Sum(Pow(base=Var(name='x'), exp=Const(value=2)), Const(value=-81)), right=Const(value=0)))),
"Q": Summation(var="n", start=Const(1), end=Abs(arg=Ref(name='result')), expr=NumDivisor... | NT | null | COMPUTE | sympy | K2 | [
"K2"
] | 6897ab | algebra_vieta_sum_v1 | null | 3 | 0 | [
"K2"
] | 1 | 0.021 | 2026-02-08T06:12:48.601485Z | {
"verified": true,
"answer": 373,
"timestamp": "2026-02-08T06:12:48.622962Z"
} | e282f8 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 105,
"completion_tokens": 1678
},
"timestamp": "2026-02-13T06:37:34.306Z",
"answer": 373
},
{
... | 1 | [
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "K2",
"status": "ok"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
... | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
4b9f90 | geo_count_lattice_rect_v1_397696148_2004 | Let $a = 89$ and $b = 21$. Define $L$ to be the number of lattice points in the rectangle $[0, a] \times [0, b]$, including the boundary. Compute the remainder when $44121 \cdot L$ is divided by $83011$. | 32,008 | graphs = [
Graph(
let={
"a": Const(89),
"b": Const(21),
"result": LatticePointsRect(a=Ref(name='a'), b=Ref(name='b')),
"Q": Mod(value=Mul(Const(44121), Ref("result")), modulus=Const(83011)),
},
goal=Ref("Q"),
)
] | GEOM | null | COUNT | sympy | [] | geo_count_lattice_rect_v1 | null | 2 | 0 | null | null | 0.002 | 2026-02-08T12:53:49.002037Z | {
"verified": true,
"answer": 32008,
"timestamp": "2026-02-08T12:53:49.004338Z"
} | 674eb5 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 175,
"completion_tokens": 1053
},
"timestamp": "2026-02-24T16:34:26.191Z",
"answer": 32008
},
{
"... | 1 | [] | {
"lo": -2.35,
"mid": 1.22,
"hi": 4.84
} | ||||
482f17 | diophantine_fbi2_min_v1_1520064083_4023 | Let $k = 77$, $a = 3$, $b = 6$, and $\text{upper} = 87$. Define $d$ to be an integer such that $4 \leq d \leq \text{upper}$, $d$ divides $k$, and $\frac{k}{d} \geq 7$. Find the minimum such $d$. Let $m$ be this minimum value. Compute the smallest positive integer $Q$ such that the $Q$-th Fibonacci number is divisible b... | 12 | graphs = [
Graph(
let={
"k": Const(77),
"a": Const(3),
"b": Const(6),
"upper": Const(87),
"result": MinOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Const(4)), Leq(Var("d"), Ref("upper")), Divides(divisor=Var("d"), dividend=Ref... | NT | null | EXTREMUM | sympy | C2 | [
"C2"
] | 9685eb | diophantine_fbi2_min_v1 | null | 4 | 0 | [
"C2"
] | 1 | 0.077 | 2026-02-08T06:01:43.508078Z | {
"verified": true,
"answer": 12,
"timestamp": "2026-02-08T06:01:43.585183Z"
} | 3ad7d8 | 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": 907
},
"timestamp": "2026-02-12T18:06:34.492Z",
"answer": 12
},
{
... | 1 | [
{
"lemma": "C2",
"status": "ok"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "VAL_SUM_EQ",
"status": "no"
... | {
"lo": -7.01,
"mid": -4.68,
"hi": -2.15
} | ||
58d339 | nt_max_prime_below_v1_1439011603_2 | Let $s$ be the number of positive integers $p$ for which there exists a positive integer $q$ such that $p \cdot q = 12$, $\gcd(p, q) = 1$, and $p < q$. Let $T$ be the set of all prime numbers $n$ satisfying $s \leq n \leq 54289$. Determine the largest element of $T$. | 54,287 | graphs = [
Graph(
let={
"upper": Const(54289),
"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 | 1.304 | 2026-02-08T15:07:20.763792Z | {
"verified": true,
"answer": 54287,
"timestamp": "2026-02-08T15:07:22.067843Z"
} | e656b0 | 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": 2328
},
"timestamp": "2026-02-16T01:13:01.934Z",
"answer": 54287
},
... | 1 | [
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
272b8c | sequence_count_fib_divisible_v1_1520064083_4912 | Let $S$ be the set of all positive integers $p$ such that there exists a positive integer $q$ with $pq = 63547955521050$, $\gcd(p, q) = 1$, and $p < q$. Let $u$ be the number of positive integers $k$ such that $1 \leq k \leq 119680$ and $|S|$ divides $k$. Compute the remainder when $44121$ multiplied by the number of p... | 49,997 | graphs = [
Graph(
let={
"_n": Const(44121),
"upper": CountOverSet(set=SolutionsSet(var=Var("k"), condition=And(Geq(Var("k"), Const(1)), Leq(Var("k"), Const(119680)), Divides(divisor=CountOverSet(set=SolutionsSet(var=Var("p"), condition=And(IsPositive(arg=Var(name='p')), Exists(var=Va... | NT | null | COUNT | sympy | COPRIME_PAIRS | [
"COPRIME_PAIRS/C2"
] | 7a1379 | sequence_count_fib_divisible_v1 | null | 7 | 0 | [
"C2",
"COPRIME_PAIRS"
] | 2 | 0.041 | 2026-02-08T06:30:51.497547Z | {
"verified": true,
"answer": 49997,
"timestamp": "2026-02-08T06:30:51.538760Z"
} | a49773 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 193,
"completion_tokens": 5807
},
"timestamp": "2026-02-13T01:01:03.646Z",
"answer": 49997
},
... | 1 | [
{
"lemma": "C2",
"status": "ok_later"
},
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
... | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
6a19cf | nt_count_divisors_in_range_v1_1874849503_776 | Let $t$ be a positive integer such that $7 \le t \le 160$. Consider the set of all such $t$ for which there exist positive integers $a$ and $b$ with $1 \le a \le 8$, $1 \le b \le 34$, and $t = 3a + 4b$. Let $b$ be the number of such integers $t$.
Let $n = 2520$. Determine the number of positive divisors $d$ of $n$ suc... | 35 | graphs = [
Graph(
let={
"n": Const(2520),
"a": Const(1),
"b": CountOverSet(set=SolutionsSet(var=Var("t"), condition=Exists(var=Var(name='a'), condition=Exists(var=Var(name='b'), condition=And(Geq(left=Var(name='a'), right=Const(value=1)), Leq(left=Var(name='a'), right=Con... | NT | null | COUNT | sympy | COUNT_CARTESIAN | [
"LIN_FORM"
] | 7b2633 | nt_count_divisors_in_range_v1 | null | 5 | 0 | [
"COUNT_CARTESIAN",
"LIN_FORM"
] | 2 | 0.129 | 2026-02-08T13:18:21.963053Z | {
"verified": true,
"answer": 35,
"timestamp": "2026-02-08T13:18:22.091966Z"
} | ac29d6 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 232,
"completion_tokens": 4402
},
"timestamp": "2026-02-11T07:42:04.912Z",
"answer": 35
},
{
"id... | 1 | [
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "V7",
"stat... | {
"lo": -5.48,
"mid": 0.74,
"hi": 7.52
} | ||
cc621e | nt_min_coprime_above_v1_1353956133_468 | Let $S$ be the set of all ordered pairs of positive integers $(x, y)$ such that $xy = 334084$. Define $s$ to be the minimum value of $x + y$ over all such pairs. Let $n$ be the smallest integer greater than $s$ and at most $1291$ such that $\gcd(n, 125) = 1$. Compute the value of
$$
\sum_{i=0}^{d-1} d_i (i+1)^2 + 5,
$$... | 57 | graphs = [
Graph(
let={
"start": 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(334084)))), expr=Sum(Var("x"), Var("y")))),
"upper": Con... | NT | null | EXTREMUM | sympy | B3 | [
"B3"
] | 0cd20d | nt_min_coprime_above_v1 | null | 4 | 0 | [
"B3"
] | 1 | 0.051 | 2026-02-08T11:27:58.770660Z | {
"verified": true,
"answer": 57,
"timestamp": "2026-02-08T11:27:58.821242Z"
} | d48bee | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 203,
"completion_tokens": 926
},
"timestamp": "2026-02-14T14:47:48.646Z",
"answer": 57
},
{
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "VAL_SUM_EQ",
"status": "no"
}
] | {
"lo": -6.96,
"mid": -4.56,
"hi": -1.46
} | ||
2df429 | diophantine_fbi2_count_v1_1520064083_3990 | Let $k = 840$. Determine the number of positive integers $d$ such that $5 \leq d \leq 107$, $d$ divides $k$, and $3 \leq \frac{k}{d} \leq 105$. | 18 | graphs = [
Graph(
let={
"k": Const(840),
"result": CountOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Const(5)), Leq(Var("d"), Const(107)), Divides(divisor=Var("d"), dividend=Ref("k")), Geq(Div(Ref("k"), Var("d")), Const(3)), Leq(Div(Ref("k"), Var("d")), Const(10... | NT | null | COUNT | sympy | LIN_FORM | [
"COPRIME_PAIRS"
] | 2bb3aa | diophantine_fbi2_count_v1 | null | 4 | 0 | [
"COPRIME_PAIRS",
"LIN_FORM"
] | 2 | 0.053 | 2026-02-08T06:00:23.859546Z | {
"verified": true,
"answer": 18,
"timestamp": "2026-02-08T06:00:23.912437Z"
} | f4d808 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 98,
"completion_tokens": 1616
},
"timestamp": "2026-02-12T18:03:51.588Z",
"answer": 18
},
{
... | 1 | [
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
}
] | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
8f26a5 | sequence_fibonacci_compute_v1_655260480_5097 | Let $n$ be the number of integers $t$ such that $21 \leq t \leq 48$ and there exist positive integers $a$ and $b$ with $1 \leq a \leq 7$, $1 \leq b \leq 4$, and $t = 2a + 5b + 14$. Compute the $n$-th Fibonacci number, where $F_1 = 1$, $F_2 = 1$, and $F_k = F_{k-1} + F_{k-2}$ for $k \geq 3$. | 46,368 | 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=7)), Geq(left=Var(name='b'), right=Const(value=1... | NT | null | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | sequence_fibonacci_compute_v1 | null | 4 | 0 | [
"LIN_FORM"
] | 1 | 0.002 | 2026-02-08T18:16:19.159032Z | {
"verified": true,
"answer": 46368,
"timestamp": "2026-02-08T18:16:19.161441Z"
} | 41872b | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 171,
"completion_tokens": 1835
},
"timestamp": "2026-02-18T15:43:36.204Z",
"answer": 46368
},
... | 1 | [
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "LTE_DIFF",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
80e69f | nt_min_phi_inverse_v1_655260480_3189 | Let $n = 59418$. Consider the set of all ordered pairs $(x,y)$ of positive integers such that $xy = 400$. Let $S$ be the set of all values $x + y$ for such pairs. Define $u$ to be the minimum value in $S$. Let $k = 8$. Now consider the set of all positive integers $n$ such that $1 \leq n \leq u$ and $\phi(n) = k$, wher... | 2,985 | graphs = [
Graph(
let={
"_n": Const(59418),
"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(400)))), expr=Sum(Var("x"), Var("y")... | NT | null | EXTREMUM | sympy | B3 | [
"B3"
] | 0cd20d | nt_min_phi_inverse_v1 | null | 6 | 0 | [
"B3"
] | 1 | 0.012 | 2026-02-08T17:14:41.723360Z | {
"verified": true,
"answer": 2985,
"timestamp": "2026-02-08T17:14:41.735779Z"
} | b3b033 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 183,
"completion_tokens": 1048
},
"timestamp": "2026-02-17T22:40:35.611Z",
"answer": 2985
},
{... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
},
{
"lemma": "VAL_SUM_EQ",
"status": ... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
2b52ce | nt_count_intersection_v1_124444284_554 | Let $N$ be the number of positive integers $t$ such that $14 \leq t \leq 20020$ and there exist positive integers $a$ and $b$ with $1 \leq a \leq 3400$, $1 \leq b \leq 642$, and $t = 4a + 10b$. Let $a = 5$ and $b = 14$. Define $S$ as the set of all positive integers $n$ such that $1 \leq n \leq N$, $a$ divides $n$, and... | 27,829 | 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=3400)), Geq(left=Var(name='b'), right=Const(valu... | NT | null | COUNT | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | nt_count_intersection_v1 | null | 5 | 0 | [
"LIN_FORM"
] | 1 | 1.331 | 2026-02-08T03:21:21.991085Z | {
"verified": true,
"answer": 27829,
"timestamp": "2026-02-08T03:21:23.322572Z"
} | 4b5cc4 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 290,
"completion_tokens": 3366
},
"timestamp": "2026-02-09T03:18:49.515Z",
"answer": 27829
},
{
... | 1 | [
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "V3",
"status": "no"
}
] | {
"lo": -3.42,
"mid": 1.86,
"hi": 7.55
} | ||
38169c | diophantine_fbi2_min_v1_1431428450_582 | Let $m = 9$. For each positive integer $k$ from $1$ to $9$, compute $\varphi(k) \cdot \left\lfloor \frac{9}{k} \right\rfloor$, where $\varphi$ is Euler's totient function. Let $S$ be the sum of these values. Let $u$ be the largest prime number $n$ such that $2 \leq n \leq S$. Let $d$ be the smallest divisor of $33$ tha... | 11 | graphs = [
Graph(
let={
"_m": Const(9),
"_n": Const(5),
"k": Const(33),
"upper": MaxOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(2)), Leq(Var("n"), Summation(var="k", start=Const(1), end=Const(9), expr=Mul(EulerPhi(n=Var("k")), Floo... | NT | null | EXTREMUM | sympy | K2 | [
"K2/MAX_PRIME_BELOW"
] | f058da | diophantine_fbi2_min_v1 | null | 5 | 0 | [
"K2",
"MAX_PRIME_BELOW"
] | 2 | 0.01 | 2026-02-08T13:33:01.280892Z | {
"verified": true,
"answer": 11,
"timestamp": "2026-02-08T13:33:01.290466Z"
} | fa43ba | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 179,
"completion_tokens": 1351
},
"timestamp": "2026-02-15T18:05:13.547Z",
"answer": 11
},
{
... | 1 | [
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K2",
"status": "ok"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok_later"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "V3",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
},
... | {
"lo": -8.26,
"mid": -5.01,
"hi": -1.76
} | ||
533c8c | nt_count_coprime_v1_1439011603_370 | Let $S$ be the set of all ordered pairs $(x, y)$ of positive integers such that $xy = 576$. Let $T$ be the set of all values $x + y$ for $(x, y) \in S$. Define $k$ to be the minimum element of $T$. Compute the number of positive integers $n$ such that $1 \leq n \leq 13689$ and $\gcd(n, k) = 1$. | 4,563 | graphs = [
Graph(
let={
"upper": Const(13689),
"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(576)))), expr=Sum(Var("x"), Var("y"))... | NT | null | COUNT | sympy | B3 | [
"B3"
] | 0cd20d | nt_count_coprime_v1 | null | 4 | 0 | [
"B3"
] | 1 | 1.091 | 2026-02-08T15:25:46.209372Z | {
"verified": true,
"answer": 4563,
"timestamp": "2026-02-08T15:25:47.300862Z"
} | 046079 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 145,
"completion_tokens": 1323
},
"timestamp": "2026-02-16T06:29:31.484Z",
"answer": 4563
},
{... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
679325 | antilemma_sum_equals_v1_1918700295_3233 | Let $n$ be the number of integers $t$ with $7 \leq t \leq 85$ for which there exist positive integers $a$ and $b$, with $1 \leq a \leq 19$ and $1 \leq b \leq 7$, such that $t = 3a + 4b$. Let $x$ be the number of ordered pairs $(i, j)$ of integers with $1 \leq i \leq 72$ and $1 \leq j \leq 73$ such that $i + j = n$. Fin... | 72 | 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=19)), Geq(left=Var(name='b'), right=Const(value... | COMB | GEOM | COMPUTE | sympy | COUNT_SUM_EQUALS | [
"LIN_FORM/COUNT_SUM_EQUALS",
"COUNT_SUM_EQUALS"
] | ada383 | antilemma_sum_equals_v1 | null | 5 | 0 | [
"COUNT_SUM_EQUALS",
"LIN_FORM"
] | 2 | 0.038 | 2026-02-08T08:27:49.528558Z | {
"verified": true,
"answer": 72,
"timestamp": "2026-02-08T08:27:49.566401Z"
} | 948620 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 1,
"correct": {
"strict": false,
"boxed": false,
"relaxed": true
},
"usage": {
"prompt_tokens": 246,
"completion_tokens": 32768
},
"timestamp": "2026-02-24T09:37:57.716Z",
"answer": null
},
{
... | 1 | [
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "ok"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8",
"st... | {
"lo": -2.35,
"mid": 1.22,
"hi": 4.84
} | ||
4b85c4 | modular_count_residue_v1_1439011603_751 | Let $$
r = \sum_{k=1}^{3} \varphi(k) \left\lfloor \frac{3}{k} \right\rfloor.
$$
Let $n$ be a positive integer such that $1 \leq n \leq 54289$ and $n \equiv r \pmod{11}$.
Determine the number of such integers $n$. | 4,935 | graphs = [
Graph(
let={
"_n": Const(3),
"upper": Const(54289),
"m": Const(11),
"r": Summation(var="k", start=Const(1), end=Const(3), expr=Mul(EulerPhi(n=Var("k")), Floor(Div(Ref("_n"), Var("k"))))),
"result": CountOverSet(set=SolutionsSet(var=Var("... | NT | null | COUNT | sympy | K2 | [
"K2"
] | 6897ab | modular_count_residue_v1 | null | 4 | 0 | [
"K2"
] | 1 | 5.832 | 2026-02-08T15:41:30.223052Z | {
"verified": true,
"answer": 4935,
"timestamp": "2026-02-08T15:41:36.055276Z"
} | 20ff8f | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 1,
"correct": {
"strict": false,
"boxed": false,
"relaxed": true
},
"usage": {
"prompt_tokens": 145,
"completion_tokens": 643
},
"timestamp": "2026-02-16T06:14:30.294Z",
"answer": 4936
},
{
"id": 11,
... | 1 | [
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "K2",
"status": "ok"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
}
] | {
"lo": -8.26,
"mid": -5.01,
"hi": -1.76
} | ||
52e132 | alg_poly4_sum_v1_1419126231_33 | Let $k = \left|\{ (a_1, b_1) : 1 \le a_1 \le b_1 \le 15,\ 2a_1^2 + 2b_1^2 - 4a_1b_1 = 242 \}\right|$, and let $m = \left|\{ t : 10 \le t \le 453,\ \exists\, 1 \le a \le 144,\ 1 \le b \le 3\ \text{such that}\ t = 3a + 7b \}\right|$. Find the remainder when $$\sum_{a=1}^{181} \sum_{b=1}^{181} \left( 32a^4 + 162b^k + m a^... | 13,100 | graphs = [
Graph(
let={
"_m": Const(242),
"_n": Const(2),
"result": Mod(value=SumOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("a"), Var("b")]), condition=And(Geq(Var("a"), Const(1)), Leq(Var("a"), Const(181)), Geq(Var("b"), Const(1)), Leq(Var("b"), Cons... | ALG | null | COMPUTE | sympy | QF_PSD_ORBIT | [
"QF_PSD_ORBIT",
"LIN_FORM"
] | 7e2c84 | alg_poly4_sum_v1 | null | 6 | 0 | [
"LIN_FORM",
"QF_PSD_ORBIT"
] | 2 | 0.075 | 2026-02-25T09:33:37.298166Z | {
"verified": true,
"answer": 13100,
"timestamp": "2026-02-25T09:33:37.373566Z"
} | d6417e | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 297,
"completion_tokens": 9621
},
"timestamp": "2026-03-30T06:36:06.576Z",
"answer": 72857
},
{
... | 1 | [
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "QF_PSD_ORBIT",
"status": "ok"
}
] | {
"lo": 1.53,
"mid": 4.7,
"hi": 7.23
} | ||
c79748 | nt_count_divisible_and_v1_48377204_2568 | Let $d_1 = \sum_{k=1}^{4} \phi(k) \left\lfloor \frac{4}{k} \right\rfloor$ and $d_2 = 15$. Define $N$ to be the number of positive integers $n$ such that $1 \leq n \leq 49380$, $n \equiv 0 \pmod{d_1}$, and $n \equiv 0 \pmod{d_2}$. Let $Q = 30876 + \sum_{i=0}^{d-1} d_i (i+1)^2$, where $d$ is the number of digits in $N$ a... | 30,968 | graphs = [
Graph(
let={
"_n": Const(2),
"upper": Const(49380),
"d1": Summation(var="k", start=Const(1), end=Const(4), expr=Mul(EulerPhi(n=Var("k")), Floor(Div(Const(4), Var("k"))))),
"d2": Const(15),
"result": CountOverSet(set=SolutionsSet(var=Var(... | NT | null | COUNT | sympy | K2 | [
"K2"
] | 6897ab | nt_count_divisible_and_v1 | null | 6 | 0 | [
"K2"
] | 1 | 1.71 | 2026-02-08T16:49:24.664490Z | {
"verified": true,
"answer": 30968,
"timestamp": "2026-02-08T16:49:26.374363Z"
} | 52070e | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 219,
"completion_tokens": 983
},
"timestamp": "2026-02-17T14:27:56.088Z",
"answer": 30968
},
{... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K2",
"status": "ok"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} |
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