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 |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
5ffbad | modular_count_residue_v1_2051736721_4061 | Let $m$ be the number of ordered pairs $(a, b)$ of integers with $1 \leq a \leq 5$ and $1 \leq b \leq 5$. Let $n = 14741$ and let $r = 9$. Compute the number of positive integers $k$ such that $1 \leq k \leq 88804$ and $k \equiv r \pmod{m}$. Let this count be $C$. Find the remainder when $n \cdot C$ is divided by $9451... | 91,025 | graphs = [
Graph(
let={
"_n": Const(14741),
"upper": Const(88804),
"m": CountOverSet(set=CartesianProduct(left=IntegerRange(start=Const(1), end=Const(5)), right=IntegerRange(start=Const(1), end=Const(5)))),
"r": Const(9),
"result": CountOverSet(set... | NT | null | COUNT | sympy | COUNT_CARTESIAN | [
"COUNT_CARTESIAN"
] | 409d7d | modular_count_residue_v1 | null | 3 | 0 | [
"COUNT_CARTESIAN"
] | 1 | 2.917 | 2026-02-08T17:41:34.008365Z | {
"verified": true,
"answer": 91025,
"timestamp": "2026-02-08T17:41:36.925718Z"
} | 1c4138 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 159,
"completion_tokens": 1260
},
"timestamp": "2026-02-18T06:03:59.171Z",
"answer": 91025
},
... | 1 | [
{
"lemma": "COUNT_CARTESIAN",
"status": "ok"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "V1",
"status": "n... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
f6b8d8 | diophantine_fbi2_min_v1_1520064083_3273 | For each integer $k$ from 1 to 5, compute $\varphi(k)$, the number of positive integers less than or equal to $k$ that are relatively prime to $k$. Let
$$
K = \sum_{k=1}^{5} \varphi(k) \left\lfloor \frac{5}{k} \right\rfloor.
$$
Let $D$ be the set of all integers $d$ such that $2 \leq d \leq 25$, $d$ divides $K$, and $\... | 3 | graphs = [
Graph(
let={
"k": Summation(var="k", start=Const(1), end=Const(5), expr=Mul(EulerPhi(n=Var("k")), Floor(Div(Const(5), Var("k"))))),
"upper": Const(25),
"result": MinOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Const(2)), Leq(Var("d"), Ref(... | NT | null | EXTREMUM | sympy | SUM_ARITHMETIC | [
"K2"
] | 6897ab | diophantine_fbi2_min_v1 | null | 6 | 0 | [
"K2",
"SUM_ARITHMETIC"
] | 2 | 0.095 | 2026-02-08T05:33:30.772755Z | {
"verified": true,
"answer": 3,
"timestamp": "2026-02-08T05:33:30.867651Z"
} | 6e1d78 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 173,
"completion_tokens": 957
},
"timestamp": "2026-02-12T10:20:48.515Z",
"answer": 3
},
{
... | 1 | [
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "K2",
"status": "ok"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "V3",
"status": "no"
}
] | {
"lo": -9.14,
"mid": -6.05,
"hi": -3.73
} | ||
335e64 | modular_mod_compute_v1_458359167_610 | Let $a = -15120$. Define $m$ to be the number of integers $t$ such that $8 \leq t \leq 4915$ and there exist positive integers $a'$ and $b'$ with $1 \leq a' \leq 572$, $1 \leq b' \leq 685$, and $t = 5a' + 3b'$. Let $\text{result}$ be the remainder when $a$ is divided by $m$. Compute $\text{result}$. | 4,480 | graphs = [
Graph(
let={
"a": Const(-15120),
"m": CountOverSet(set=SolutionsSet(var=Var("t"), condition=Exists(var=Var(name='a'), condition=Exists(var=Var(name='b'), condition=And(Geq(left=Var(name='a'), right=Const(value=1)), Leq(left=Var(name='a'), right=Const(value=572)), Geq(left=... | NT | null | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | modular_mod_compute_v1 | null | 6 | 0 | [
"LIN_FORM"
] | 1 | 0.002 | 2026-02-08T03:26:18.600415Z | {
"verified": true,
"answer": 4480,
"timestamp": "2026-02-08T03:26:18.602642Z"
} | 3a99e1 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 225,
"completion_tokens": 2076
},
"timestamp": "2026-02-10T13:29:51.558Z",
"answer": 4496
},
{
... | 1 | [
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
}... | {
"lo": 1.96,
"mid": 5.23,
"hi": 8.52
} | ||
a6d534 | comb_count_partitions_v1_784195855_6016 | Let $n$ be the number of integers $t$ such that $14 \leq t \leq 104$ and there exist positive integers $a$ and $b$ with $1 \leq a \leq 16$, $1 \leq b \leq 4$, and $t = 4a + 10b$. Let $p(n)$ denote the number of integer partitions of $n$. Compute the remainder when $44121 \cdot p(n)$ is divided by $57130$. | 46,604 | graphs = [
Graph(
let={
"_n": Const(57130),
"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=16)), Geq(left=V... | COMB | null | COUNT | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | comb_count_partitions_v1 | null | 6 | 0 | [
"LIN_FORM"
] | 1 | 0.003 | 2026-02-08T08:15:17.556757Z | {
"verified": true,
"answer": 46604,
"timestamp": "2026-02-08T08:15:17.559339Z"
} | ca0024 | 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": 7136
},
"timestamp": "2026-02-24T09:15:49.604Z",
"answer": 46604
},
{
"... | 1 | [
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
}
... | {
"lo": -2.35,
"mid": 1.22,
"hi": 4.84
} | ||
a11c56 | geo_count_lattice_rect_v1_458359167_1957 | Let $a = 50$ and $b = 155$. Compute the number of lattice points $(x, y)$ such that $0 \le x \le a$ and $0 \le y \le b$. Find the value of this number. | 7,956 | graphs = [
Graph(
let={
"a": Const(50),
"b": Const(155),
"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 | 0.003 | 2026-02-08T04:56:52.883869Z | {
"verified": true,
"answer": 7956,
"timestamp": "2026-02-08T04:56:52.887286Z"
} | 7b9812 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 163,
"completion_tokens": 287
},
"timestamp": "2026-02-24T02:22:11.516Z",
"answer": 7956
},
{
"id... | 1 | [] | {
"lo": -7.18,
"mid": -4.99,
"hi": -3
} | ||||
f84832 | alg_poly4_sum_v1_601307018_7362 | Let $S = \left|\{ t : \text{there exist integers } a, b \text{ with } 1 \leq a \leq 216, 1 \leq b \leq 4 \text{ such that } t = 12a + 21b + 8,\ 41 \leq t \leq 2684 \right\}|$. Compute the remainder when $$\sum_{\substack{1 \leq a \leq 223 \\ 1 \leq b \leq 223}} \left(81a^4 + 432a^3b + 257b^4 + S a^2b^2 + 768ab^3\right)... | 44,680 | graphs = [
Graph(
let={
"_n": Const(81),
"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(223)), Geq(Var("b"), Const(1)), Leq(Var("b"), Const(223)))), expr=Sum(Mul(Ref("... | ALG | null | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | alg_poly4_sum_v1 | null | 4 | 0 | [
"LIN_FORM"
] | 1 | 0.46 | 2026-03-10T07:56:04.455311Z | {
"verified": true,
"answer": 44680,
"timestamp": "2026-03-10T07:56:04.915116Z"
} | 490c30 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 273,
"completion_tokens": 7811
},
"timestamp": "2026-04-19T06:30:18.902Z",
"answer": 44680
},
{
... | 1 | [
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
}
] | {
"lo": -5.34,
"mid": 1.1,
"hi": 7.53
} | ||
8e9cf2 | comb_count_partitions_v1_1742523217_4521 | Let $n$ be the number of integers $t$ such that $9 \leq t \leq 52$ and $t = 2a + 7b$ for some integers $a$ and $b$ satisfying $1 \leq a \leq 19$ and $1 \leq b \leq 2$. Compute the number of integer partitions of $n$. | 26,015 | 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 | null | COUNT | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | comb_count_partitions_v1 | null | 4 | 0 | [
"LIN_FORM"
] | 1 | 0.002 | 2026-02-08T08:53:36.411769Z | {
"verified": true,
"answer": 26015,
"timestamp": "2026-02-08T08:53:36.414085Z"
} | 1d0e56 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 194,
"completion_tokens": 1155
},
"timestamp": "2026-02-24T10:10:09.642Z",
"answer": 26015
},
{
"... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
}
] | {
"lo": 1.15,
"mid": 4.18,
"hi": 6.61
} | ||
63b28e | comb_factorial_compute_v1_397696148_1470 | Let $d$ be a divisor of $143143$ that is at least $2$. Let $n$ be the smallest such $d$. Compute the remainder when $18186 \cdot n!$ is divided by $87007$. | 39,069 | graphs = [
Graph(
let={
"_n": Const(87007),
"n": MinOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Const(2)), Divides(divisor=Var("d"), dividend=Const(143143))))),
"result": Factorial(Ref("n")),
"Q": Mod(value=Mul(Const(18186), Ref("result"... | NT | null | COMPUTE | sympy | MIN_PRIME_FACTOR | [
"MIN_PRIME_FACTOR"
] | bc3776 | comb_factorial_compute_v1 | null | 6 | 0 | [
"MIN_PRIME_FACTOR"
] | 1 | 0.002 | 2026-02-08T12:34:09.198734Z | {
"verified": true,
"answer": 39069,
"timestamp": "2026-02-08T12:34:09.200332Z"
} | d3c153 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 96,
"completion_tokens": 1656
},
"timestamp": "2026-02-15T01:55:24.019Z",
"answer": 39069
},
{... | 1 | [
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "MIN_PRIME_FACTOR",
"status": "ok"
},
{
"lemma": "V5",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
}
] | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
f97aa2 | antilemma_product_of_sums_v1_548369836_250 | For each pair $(k, j)$ with $1 \leq k \leq 8$ and $1 \leq j \leq 4$, include $k$ in a multiset. Let $A$ be the sum of all elements in this multiset. Let $B = \sum_{k=1}^{17} k$. Define $x = A \cdot B$. Now, let $d_i$ denote the $i$-th decimal digit of $|x|$ (starting from the units digit as $i=0$), and let $t$ be the n... | 60,612 | graphs = [
Graph(
let={
"x": Mul(SumOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("k"), Var("_j")]), condition=Const(1), domain=CartesianProduct(left=IntegerRange(start=Const(1), end=Const(8)), right=IntegerRange(start=Const(1), end=Const(4)))), expr=Var("k"))), Summation(var="... | NT | null | COMPUTE | sympy | PRODUCT_OF_SUMS | [
"PRODUCT_OF_SUMS"
] | f2b2b0 | antilemma_product_of_sums_v1 | null | 5 | 0 | [
"PRODUCT_OF_SUMS"
] | 1 | 0.001 | 2026-02-08T02:49:42.124800Z | {
"verified": true,
"answer": 60612,
"timestamp": "2026-02-08T02:49:42.125866Z"
} | 93a256 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 273,
"completion_tokens": 901
},
"timestamp": "2026-02-08T20:17:02.160Z",
"answer": 60612
},
{
"i... | 1 | [
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "PRODUCT_OF_SUMS",
"status": "ok"
},
{
"lemma": "V7",
"status": "no"
}
] | {
"lo": -6.69,
"mid": -2.4,
"hi": 1.73
} | ||
d881b0 | nt_sum_over_divisible_v1_48377204_1813 | Let $\text{result}$ be the sum of all positive integers $n$ such that $1 \leq n \leq 7626$ and $n$ is divisible by $82$. Let $d_{\text{min}}$ be the smallest integer $d \geq 2$ that divides $40811711$. Compute the remainder when
$$
\left( \text{result} \bmod 293 \right) + 3001 \cdot \left( \text{result} \bmod d_{\text... | 3,394 | graphs = [
Graph(
let={
"_n": Const(94980),
"upper": Const(7626),
"divisor": Const(82),
"result": SumOverSet(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")), Cons... | NT | null | SUM | sympy | MIN_PRIME_FACTOR | [
"MIN_PRIME_FACTOR"
] | cffc20 | nt_sum_over_divisible_v1 | two_moduli | 4 | 0 | [
"MIN_PRIME_FACTOR"
] | 1 | 0.487 | 2026-02-08T16:26:24.001431Z | {
"verified": true,
"answer": 3394,
"timestamp": "2026-02-08T16:26:24.488697Z"
} | 356b97 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 167,
"completion_tokens": 6218
},
"timestamp": "2026-02-17T03:00:07.650Z",
"answer": 3394
},
{... | 1 | [
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MIN_PRIME_FACTOR",
"status": "ok"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "V8_SUM",
"stat... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
0cbdfe | geo_visible_lattice_v1_1125832087_2236 | Let $n = 81$. A visible lattice point is a point $(x,y)$ in the first quadrant with integer coordinates such that $1 \leq x, y \leq n$ and $\gcd(x,y) = 1$. Let $A$ be the number of visible lattice points. Compute $27720 - A$. | 23,681 | graphs = [
Graph(
let={
"n": Const(81),
"result": VisibleLatticePoints(n=Ref(name='n')),
"_c": Const(27720),
"Q": Sub(Ref("_c"), Ref("result")),
},
goal=Ref("Q"),
)
] | GEOM | null | COUNT | sympy | [] | geo_visible_lattice_v1 | null | 5 | 0 | null | null | 0.14 | 2026-02-08T04:25:34.322687Z | {
"verified": true,
"answer": 23681,
"timestamp": "2026-02-08T04:25:34.462760Z"
} | 48ddb2 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 180,
"completion_tokens": 32768
},
"timestamp": "2026-02-24T00:49:46.941Z",
"answer": null
},
{
... | 1 | [] | {
"lo": 1.97,
"mid": 4.36,
"hi": 6.69
} | ||||
93be0f | comb_catalan_compute_v1_655260480_4941 | Let $n = 11$ and let $\text{result}$ be the $n$-th Catalan number. Compute the remainder when $\text{result} + \phi(|\text{result}| + 0!) + \tau(|\text{result}| + \binom{7}{7})$ is divided by $91469$, where $\phi$ denotes Euler's totient function and $\tau$ denotes the number of positive divisors. | 26,105 | graphs = [
Graph(
let={
"n": Const(11),
"result": Catalan(Ref("n")),
"Q": Mod(value=Sum(Ref("result"), EulerPhi(n=Sum(Abs(arg=Ref(name='result')), Factorial(Const(0)))), NumDivisors(n=Sum(Abs(arg=Ref(name='result')), Binom(n=Const(7), k=Const(7))))), modulus=Const(91469))... | COMB | NT | COMPUTE | sympy | ONE_FACTORIAL_0 | [
"ONE_FACTORIAL_0",
"ONE_BINOM_N"
] | 7463f0 | comb_catalan_compute_v1 | null | 3 | 0 | [
"ONE_BINOM_N",
"ONE_FACTORIAL_0"
] | 2 | 0.002 | 2026-02-08T18:13:34.001866Z | {
"verified": true,
"answer": 26105,
"timestamp": "2026-02-08T18:13:34.004018Z"
} | 525f5b | 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": 4022
},
"timestamp": "2026-02-18T15:26:21.779Z",
"answer": 26105
},
... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "ONE_BINOM_N",
"status": "ok"
},
{
"lemma": "ONE_FACTORIAL... | {
"lo": -3.12,
"mid": 1.47,
"hi": 6.57
} | ||
afc203 | alg_qf_psd_min_v1_601307018_5647 | Let $Q$ be the minimum value of
\[
14076ab + 4554a^2 + 4554c^2 + d \cdot ac + 2484bc + 12006b^2
\]
over all ordered triples $(a, b, c)$ of positive integers with $1 \le a, b, c \le 47$, where $d$ is the largest positive divisor of $17193420$ such that $d^2 \le 17193420$. Find $Q$. | 41,814 | graphs = [
Graph(
let={
"_n": Const(4554),
"result": MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("a"), Var("b"), Var("c")]), condition=And(Geq(Var("a"), Const(1)), Leq(Var("a"), Const(47)), Geq(Var("b"), Const(1)), Leq(Var("b"), Const(47)), Geq(Var("c"), Const(... | NT | null | COMPUTE | sympy | B3_CLOSEST | [
"B3_CLOSEST"
] | 25e610 | alg_qf_psd_min_v1 | null | 6 | 0 | [
"B3_CLOSEST"
] | 1 | 1.132 | 2026-03-10T06:14:10.888208Z | {
"verified": true,
"answer": 41814,
"timestamp": "2026-03-10T06:14:12.020165Z"
} | 13ef39 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 221,
"completion_tokens": 2585
},
"timestamp": "2026-04-19T02:37:45.095Z",
"answer": 41814
},
{
... | 1 | [
{
"lemma": "B3_CLOSEST",
"status": "ok"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
}
] | {
"lo": -5.35,
"mid": 0.52,
"hi": 5.84
} | ||
781f20 | comb_sum_binomial_mod_v1_1440796553_295 | Let $S$ be the set of all integers $t$ such that $8 \leq t \leq 345$ and $t = 3a + 5b$ for some integers $a$ and $b$ with $1 \leq a \leq 50$ and $1 \leq b \leq 39$. Let $k$ be the number of elements in $S$. Compute the remainder when $\sum_{i=120}^{k} \binom{384}{i}$ is divided by 11287. Let $r$ be this remainder. Find... | 203 | graphs = [
Graph(
let={
"_n": Const(11),
"sum": Summation(var="k", start=Const(120), end=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=... | COMB | null | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | comb_sum_binomial_mod_v1 | null | 4 | 0 | [
"LIN_FORM"
] | 1 | 0.026 | 2026-02-08T11:43:24.988650Z | {
"verified": true,
"answer": 203,
"timestamp": "2026-02-08T11:43:25.014593Z"
} | c40579 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 1,
"correct": {
"strict": false,
"boxed": false,
"relaxed": true
},
"usage": {
"prompt_tokens": 254,
"completion_tokens": 32768
},
"timestamp": "2026-02-24T14:34:12.119Z",
"answer": null
},
{
... | 0 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "V8",
"statu... | {
"lo": 3.25,
"mid": 5.68,
"hi": 8.81
} | ||
b81d51 | geo_count_lattice_rect_v1_458359167_5391 | Let $ a = 99 $ and $ b = 27 $. Define $ L $ to be the number of lattice points $ (x, y) $ such that $ 0 \leq x \leq a $ and $ 0 \leq y \leq b $. Let $ c = 1521 $. Compute the remainder when $ c - L $ is divided by $ 76862 $. | 75,583 | graphs = [
Graph(
let={
"a": Const(99),
"b": Const(27),
"result": LatticePointsRect(a=Ref(name='a'), b=Ref(name='b')),
"_c": Const(1521),
"Q": Mod(value=Sub(Ref("_c"), Ref("result")), modulus=Const(76862)),
},
goal=Ref("Q"),
)
] | GEOM | null | COUNT | sympy | [] | geo_count_lattice_rect_v1 | null | 3 | 0 | null | null | 0.001 | 2026-02-08T12:27:21.103270Z | {
"verified": true,
"answer": 75583,
"timestamp": "2026-02-08T12:27:21.103791Z"
} | b97ca0 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 195,
"completion_tokens": 605
},
"timestamp": "2026-02-24T15:39:48.932Z",
"answer": 75583
},
{
"i... | 1 | [] | {
"lo": -7.18,
"mid": -5,
"hi": -3.01
} | ||||
773c2c | sequence_lucas_compute_v1_2051736721_3334 | Let $n$ be the number of positive integers $j$ such that $1 \le j \le 20$ and $j^2 \le 400$. 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 $k \ge 3$. | 15,127 | graphs = [
Graph(
let={
"_n": Const(20),
"n": CountOverSet(set=SolutionsSet(var=Var("j"), condition=And(Geq(Var("j"), Const(1)), Leq(Var("j"), Ref("_n")), Leq(Pow(Var("j"), Const(2)), Const(400))), domain='positive_integers')),
"result": Lucas(arg=Ref(name='n')),
... | NT | null | COMPUTE | sympy | C3 | [
"C3"
] | 8a214c | sequence_lucas_compute_v1 | null | 2 | 0 | [
"C3"
] | 1 | 0.002 | 2026-02-08T17:15:16.626365Z | {
"verified": true,
"answer": 15127,
"timestamp": "2026-02-08T17:15:16.628713Z"
} | 0606d1 | 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": 594
},
"timestamp": "2026-02-17T22:28:47.121Z",
"answer": 15127
},
{... | 1 | [
{
"lemma": "C3",
"status": "ok"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
0fa118 | algebra_quadratic_discriminant_v1_1439011603_572 | Let $M$ be the number of integers $n_1$ with $1 \le n_1 \le 19847$ such that
$$n_1 \equiv \left\lfloor \frac{n_1}{2} \right\rfloor \pmod{3}.$$
Let $D$ be the set of all integers $d$ with $2 \le d \le M$ such that $d$ divides $M$, and let $L$ be the minimum element of $D$ (assume $D$ is nonempty). Let $b$ be the sum of ... | 23 | graphs = [
Graph(
let={
"_m": Const(19847),
"_n": Const(2),
"a": Const(3),
"b": SumOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Ref("_n")), Leq(Var("n"), MinOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Const(2)), Div... | NT | null | COMPUTE | sympy | COPRIME_PAIRS | [
"L3C/MIN_PRIME_FACTOR/SUM_PRIMES",
"COPRIME_PAIRS"
] | 9da625 | algebra_quadratic_discriminant_v1 | null | 7 | 0 | [
"COPRIME_PAIRS",
"L3C",
"MIN_PRIME_FACTOR",
"SUM_PRIMES"
] | 4 | 0.05 | 2026-02-08T15:35:29.269639Z | {
"verified": true,
"answer": 23,
"timestamp": "2026-02-08T15:35:29.319172Z"
} | 39ce04 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 274,
"completion_tokens": 1954
},
"timestamp": "2026-02-16T10:10:06.335Z",
"answer": 23
},
{
... | 1 | [
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "L3C",
"status": "ok"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "MIN_PRIME_FACTOR",
... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
395da6 | algebra_poly_eval_v1_397696148_632 | Let $m = 2$ and $n = 7$. Let $d_0$ be the smallest integer $d \geq m$ that divides 6125. Let $P$ be the set of all positive integers $p$ for which there exists an integer $q$ such that $pq = 6750$, $\gcd(p, q) = 1$, and $p < q$. Let $k$ be the number of elements in $P$. Compute the value of the expression
\[
7d_0^k - d... | 4,063 | graphs = [
Graph(
let={
"_m": Const(2),
"_n": Const(7),
"t": MinOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Ref("_m")), Divides(divisor=Var("d"), dividend=Const(6125))))),
"result": Sum(Mul(Ref("_n"), Pow(Ref("t"), CountOverSet(set=Solut... | NT | null | COMPUTE | sympy | MIN_PRIME_FACTOR | [
"MIN_PRIME_FACTOR",
"COPRIME_PAIRS"
] | a3b634 | algebra_poly_eval_v1 | null | 4 | 0 | [
"COPRIME_PAIRS",
"MIN_PRIME_FACTOR"
] | 2 | 0.007 | 2026-02-08T11:38:03.536136Z | {
"verified": true,
"answer": 4063,
"timestamp": "2026-02-08T11:38:03.543583Z"
} | 9aa958 | 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": 2731
},
"timestamp": "2026-02-14T16:31:15.729Z",
"answer": 4063
},
{... | 1 | [
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "MIN_PRIME_FACTOR",
"status... | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
7e03ea | nt_sum_totient_over_divisors_v1_655260480_5742 | Let $d=73$ and $m=55381$. Consider all ordered pairs $(x,y)$ of positive integers such that $xy=1369$. Let $S$ be the set of all values of $x+y$ as $(x,y)$ ranges over these ordered pairs, and let $T$ be the minimum of $S$.
Let $n_1$ be a prime integer satisfying $2\le n_1\le T$, and let $N$ be the maximum possible va... | 46,364 | graphs = [
Graph(
let={
"_d": Const(73),
"_m": Const(55381),
"_n": MaxOverSet(set=SolutionsSet(var=Var("n1"), condition=And(Geq(Var("n1"), Const(2)), Leq(Var("n1"), MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositi... | NT | null | COMPUTE | sympy | B3 | [
"B3/MAX_PRIME_BELOW/K2"
] | 7202db | nt_sum_totient_over_divisors_v1 | affine_mod | 5 | 0 | [
"B3",
"K2",
"MAX_PRIME_BELOW"
] | 3 | 0.004 | 2026-02-08T18:38:43.775363Z | {
"verified": true,
"answer": 46364,
"timestamp": "2026-02-08T18:38:43.779381Z"
} | 05223b | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 269,
"completion_tokens": 2562
},
"timestamp": "2026-02-18T18:16:45.372Z",
"answer": 46364
},
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "K2",
"status": "ok_later"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
4e8d79 | geo_visible_lattice_v1_124444284_58 | Let $ n = 64 $. Define $ r $ to be the number of ordered pairs $ (x, y) $ of positive integers such that $ 1 \leq x, y \leq n $ and $ \gcd(x, y) = 1 $. Let $ Q $ be the remainder when $ 24377r $ is divided by $ 73322 $. Compute $ Q $. | 35,149 | graphs = [
Graph(
let={
"n": Const(64),
"result": VisibleLatticePoints(n=Ref(name='n')),
"_c": Const(24377),
"Q": Mod(value=Mul(Ref("_c"), Ref("result")), modulus=Const(73322)),
},
goal=Ref("Q"),
)
] | GEOM | null | COUNT | sympy | [] | geo_visible_lattice_v1 | null | 4 | 0 | null | null | 0.106 | 2026-02-08T02:56:30.174507Z | {
"verified": true,
"answer": 35149,
"timestamp": "2026-02-08T02:56:30.280841Z"
} | 1370a0 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 197,
"completion_tokens": 5013
},
"timestamp": "2026-02-09T13:30:53.046Z",
"answer": 35149
},
{
"... | 1 | [] | {
"lo": -0.05,
"mid": 2.89,
"hi": 5.27
} | ||||
a63894 | modular_mod_compute_v1_1470522791_1837 | Let $m$ be the sum of all real solutions $x$ to the equation $x^2 - 3600x - 362404 = 0$. Compute the remainder when $-29929$ is divided by $m$. | 2,471 | graphs = [
Graph(
let={
"_n": Const(2),
"a": Const(-29929),
"m": SumOverSet(set=SolutionsSet(var=Var("x"), condition=Eq(Sum(Pow(Var("x"), Ref("_n")), Mul(Const(-3600), Var("x")), Const(-362404)), Const(0)))),
"result": Mod(value=Ref("a"), modulus=Ref("m")),
... | NT | null | COMPUTE | sympy | VIETA_SUM | [
"VIETA_SUM"
] | b33a7a | modular_mod_compute_v1 | null | 4 | 0 | [
"VIETA_SUM"
] | 1 | 0.005 | 2026-02-08T14:00:32.553872Z | {
"verified": true,
"answer": 2471,
"timestamp": "2026-02-08T14:00:32.558480Z"
} | c7ba27 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 95,
"completion_tokens": 591
},
"timestamp": "2026-02-15T23:44:32.109Z",
"answer": 2471
},
{
... | 1 | [
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "V1",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
},
{
"lemma": "VIETA_SUM",
"status": "ok"
... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
0b562b_n | alg_qf_psd_min_v1_1218484723_4511 | A drone's flight efficiency is modeled by the expression $46155a^2 + 36924ab + Sb^2$, where $a$ and $b$ are positive integers between 1 and 240 representing tuning parameters, and $S$ is the sum of the roots of the quadratic equation $x^2 - 9231x + 413370 = 0$. What is the minimum possible efficiency value? | 92,310 | ALG | null | COMPUTE | sympy | VIETA_SUM | [
"VIETA_SUM"
] | b33a7a | alg_qf_psd_min_v1 | null | 5 | null | [
"VIETA_SUM"
] | 1 | 0.091 | 2026-02-25T06:11:07.111332Z | null | 1798e8 | 0b562b | narrative | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 196,
"completion_tokens": 985
},
"timestamp": "2026-03-30T21:46:19.898Z",
"answer": 92310
},
{
"i... | 2 | [
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "VIETA_SUM",
"status": "ok"
}
] | {
"lo": -10,
"mid": -5.89,
"hi": -1.79
} | |
90910e | sequence_count_fib_divisible_v1_784195855_10349 | Let $S$ be the set of all ordered pairs $(x, y)$ of positive integers such that $xy = 83521$. Define $T$ to be the set of all values $x + y$ where $(x, y) \in S$. Let $u$ be the minimum element of $T$. Let $A$ be the set of all positive integers $p$ for which there exists a positive integer $q$ such that $pq = 36$, $\g... | 115 | graphs = [
Graph(
let={
"_n": Const(83521),
"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")), Ref("_n")))), expr=Sum(Var("x"), Var("y"))... | NT | null | COUNT | sympy | COPRIME_PAIRS | [
"COPRIME_PAIRS/MAX_PRIME_BELOW",
"B3"
] | fdc414 | sequence_count_fib_divisible_v1 | null | 7 | 0 | [
"B3",
"COPRIME_PAIRS",
"MAX_PRIME_BELOW"
] | 3 | 0.037 | 2026-02-08T17:35:06.461882Z | {
"verified": true,
"answer": 115,
"timestamp": "2026-02-08T17:35:06.498498Z"
} | bd955c | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 228,
"completion_tokens": 1740
},
"timestamp": "2026-02-18T07:41:15.535Z",
"answer": 115
},
{
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
223df5 | algebra_quadratic_discriminant_v1_1742523217_2242 | Let $a = -2$, $b = -8$, and $c = 7$. Compute the discriminant $D = b^2 - 4ac$. Let $\sigma$ be the sum of all positive divisors of 36. Define $\alpha = 1$ if $D > 0$, and $0$ otherwise. Define $\beta = 1$ if $D = \sum_{d \mid 36} \mu(d)$, where $\mu$ is the M\"obius function, and $0$ otherwise. Compute $2\alpha + \beta... | 2 | graphs = [
Graph(
let={
"a": Const(-2),
"b": Const(-8),
"c": Const(7),
"D": Sub(Pow(Ref("b"), Const(2)), Mul(Const(4), Ref("a"), Ref("c"))),
"result": Sum(Mul(Const(2), Iverson(condition=Gt(Ref("D"), Const(0)))), Iverson(condition=Eq(Ref("D"), SumO... | NT | null | COMPUTE | sympy | MOBIUS_SUM | [
"MOBIUS_SUM"
] | 518e32 | algebra_quadratic_discriminant_v1 | null | 4 | 0 | [
"MOBIUS_SUM"
] | 1 | 0.002 | 2026-02-08T04:37:29.878670Z | {
"verified": true,
"answer": 2,
"timestamp": "2026-02-08T04:37:29.880534Z"
} | 0de046 | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 219,
"completion_tokens": 495
},
"timestamp": "2026-02-18T12:48:05.642Z",
"answer": 2
}
] | 2 | [
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "MOBIUS_SUM",
"status": "ok"
},
{
"lemma": "V1",
"status": "no"
},
{
"lemma": "V3",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
}
] | {
"lo": -10,
"mid": -6.47,
"hi": -2.95
} | ||
1869b9 | antilemma_k2_v1_349078426_1432 | Let $x = \sum_{k=1}^{271} \phi(k) \left\lfloor \frac{271}{k} \right\rfloor$, where $\phi$ denotes Euler's totient function. Compute the remainder when $43892 \cdot x$ is divided by 88319. | 32,748 | graphs = [
Graph(
let={
"x": Summation(var="k", start=Const(1), end=Const(271), expr=Mul(EulerPhi(n=Var("k")), Floor(Div(Const(271), Var("k"))))),
"_c": Const(43892),
"Q": Mod(value=Mul(Ref("_c"), Ref("x")), modulus=Const(88319)),
},
goal=Ref("Q"),
)
] | NT | COMB | COMPUTE | sympy | K2 | [
"K2"
] | 6897ab | antilemma_k2_v1 | null | 6 | 0 | [
"K2"
] | 1 | 0.002 | 2026-02-08T13:38:41.929602Z | {
"verified": true,
"answer": 32748,
"timestamp": "2026-02-08T13:38:41.931883Z"
} | d9487f | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 108,
"completion_tokens": 6956
},
"timestamp": "2026-02-15T19:11:39.946Z",
"answer": 32748
},
... | 1 | [
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "K2",
"status": "ok"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "V1",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
}
] | {
"lo": -5.49,
"mid": 0.22,
"hi": 6.51
} | ||
bb1b38 | algebra_quadratic_discriminant_v1_784195855_9062 | Let $n$ be the number of positive integers $p$ such that there exists a positive integer $q > p$ with $p \cdot q = 5400$ and $\gcd(p, q) = 1$. Let $m$ be the number of positive integers $p$ such that there exists a positive integer $q > p$ with $p \cdot q = 24$ and $\gcd(p, q) = 1$. Compute
$$
(-40)^m - (-2) \cdot (-20... | 0 | 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=5400)), Eq(left=GCD(a=Var(name='p'), b=Var(name='q')), right=Const(value=1))... | NT | null | COMPUTE | sympy | COPRIME_PAIRS | [
"COPRIME_PAIRS/COPRIME_PAIRS"
] | 3bbd71 | algebra_quadratic_discriminant_v1 | null | 5 | 0 | [
"COPRIME_PAIRS"
] | 1 | 0.003 | 2026-02-08T16:30:48.347647Z | {
"verified": true,
"answer": 0,
"timestamp": "2026-02-08T16:30:48.350164Z"
} | fd0169 | 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": 1817
},
"timestamp": "2026-02-17T05:33:16.607Z",
"answer": 0
},
{
... | 1 | [
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
154dd1 | comb_count_surjections_v1_809748730_1408 | Let $S$ be the set of all ordered pairs $(i, j)$ of integers with $1 \le i \le 5$ and $1 \le j \le 5$ such that $i + j = 6$. Let $N$ be the number of elements in $S$. Let $T$ be the set of all integers $t$ such that $5 \le t \le 12$ and there exist integers $a$ and $b$ with $1 \le a \le 3$, $1 \le b \le 2$, and $t = 2a... | 540 | graphs = [
Graph(
let={
"_m": Const(6),
"_n": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("i"), Var("j")]), condition=Eq(Sum(Var("i"), Var("j")), Ref("_m")), domain=CartesianProduct(left=IntegerRange(start=Const(1), end=Const(5)), right=IntegerRange(start=Const(1), end=Cons... | COMB | null | COUNT | sympy | COUNT_SUM_EQUALS | [
"COUNT_SUM_EQUALS/COMB1",
"LIN_FORM"
] | 99e2c9 | comb_count_surjections_v1 | null | 6 | 0 | [
"COMB1",
"COUNT_SUM_EQUALS",
"LIN_FORM"
] | 3 | 0.027 | 2026-02-08T12:24:57.320105Z | {
"verified": true,
"answer": 540,
"timestamp": "2026-02-08T12:24:57.347177Z"
} | 78994d | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 343,
"completion_tokens": 1227
},
"timestamp": "2026-02-24T15:42:24.243Z",
"answer": 540
},
{
"id... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COMB1",
"status": "ok_later"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "ok"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "V7",
"status": "no"... | {
"lo": -3.84,
"mid": -1.67,
"hi": 1.32
} | ||
efd543 | nt_min_coprime_above_v1_677425708_2823 | Let $ S $ be the set of all positive divisors $ d $ of $ 239021 $ such that $ 1 \leq d \leq 479 $. Let $ m $ be the largest prime number $ n $ satisfying $ 2 \leq n \leq \max(S) $. Find the smallest integer $ r $ such that $ 24310 < r \leq 24799 $ and $ \gcd(r, m) = 1 $. Compute $ 58564 - r $. | 34,253 | graphs = [
Graph(
let={
"start": Const(24310),
"upper": Const(24799),
"modulus": MaxOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(2)), Leq(Var("n"), MaxOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Const(1)), Leq(Var("d"), C... | NT | null | EXTREMUM | sympy | MAX_DIVISOR | [
"MAX_DIVISOR/MAX_PRIME_BELOW"
] | 495f8b | nt_min_coprime_above_v1 | null | 5 | 0 | [
"MAX_DIVISOR",
"MAX_PRIME_BELOW"
] | 2 | 0.042 | 2026-02-08T05:17:46.439040Z | {
"verified": true,
"answer": 34253,
"timestamp": "2026-02-08T05:17:46.481064Z"
} | aeb405 | 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": 2571
},
"timestamp": "2026-02-12T06:31:13.484Z",
"answer": 34253
},
... | 1 | [
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "MAX_DIVISOR",
"status": "ok"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok_later"
},
{
"lemma": "MOD_MUL",
"status": "no"
... | {
"lo": -5.55,
"mid": -3.01,
"hi": 0.32
} | ||
3889b8 | comb_sum_binomial_row_v1_1520064083_7899 | Let $n$ be the largest prime number satisfying $2 \leq n \leq 12$. Define $r = 2^n$. Let $Q$ be the remainder when $44121 \cdot r$ is divided by $52546$. Find the value of $Q$. | 33,234 | graphs = [
Graph(
let={
"_n": Const(2),
"n": MaxOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Ref("_n")), Leq(Var("n"), Const(12)), IsPrime(Var("n"))))),
"result": Pow(Const(2), Ref("n")),
"Q": Mod(value=Mul(Const(44121), Ref("result")), m... | NT | null | SUM | sympy | MAX_PRIME_BELOW | [
"MAX_PRIME_BELOW"
] | dc3ad3 | comb_sum_binomial_row_v1 | null | 3 | 0 | [
"MAX_PRIME_BELOW"
] | 1 | 0.001 | 2026-02-08T09:21:36.949685Z | {
"verified": true,
"answer": 33234,
"timestamp": "2026-02-08T09:21:36.950523Z"
} | 370cd9 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 104,
"completion_tokens": 1084
},
"timestamp": "2026-02-14T03:53:53.558Z",
"answer": 33234
},
... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "VAL_SUM_EQ",
"status": "no"... | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
bf512a | diophantine_product_count_v1_717093673_1365 | Let $T$ be the set of integers $t$ such that $14 \leq t \leq 194$ and $t = 4a + 10b$ for some integers $a, b$ with $1 \leq a \leq 41$ and $1 \leq b \leq 3$. Let $k = 180$ and $u = |T|$. Let $R$ be the set of positive integers $x$ such that $1 \leq x \leq u$, $x$ divides $k$, and $\frac{k}{x} \leq u$. Let $r = |R|$. Def... | 38,288 | graphs = [
Graph(
let={
"_n": Const(21904),
"k": Const(180),
"upper": CountOverSet(set=SolutionsSet(var=Var("t"), condition=Exists(var=Var(name='a'), condition=Exists(var=Var(name='b'), condition=And(Geq(left=Var(name='a'), right=Const(value=1)), Leq(left=Var(name='a'), r... | NT | null | COUNT | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | diophantine_product_count_v1 | null | 6 | 0 | [
"LIN_FORM"
] | 1 | 0.062 | 2026-02-08T16:01:53.977711Z | {
"verified": true,
"answer": 38288,
"timestamp": "2026-02-08T16:01:54.039299Z"
} | 6aea39 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 200,
"completion_tokens": 2068
},
"timestamp": "2026-02-16T19:00:49.853Z",
"answer": 38288
},
... | 1 | [
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "LTE_DIFF",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
30be87 | geo_count_lattice_rect_v1_1470522791_65 | Compute the number of lattice points in the rectangle $[0, 512] \times [0, 126]$, including the boundary. | 65,151 | graphs = [
Graph(
let={
"a": Const(512),
"b": Const(126),
"result": LatticePointsRect(a=Ref(name='a'), b=Ref(name='b')),
},
goal=Ref("result"),
)
] | GEOM | null | COUNT | sympy | [] | geo_count_lattice_rect_v1 | null | 3 | 0 | null | null | 0.001 | 2026-02-08T12:48:41.433669Z | {
"verified": true,
"answer": 65151,
"timestamp": "2026-02-08T12:48:41.434209Z"
} | 38c22d | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 139,
"completion_tokens": 200
},
"timestamp": "2026-02-24T16:19:46.359Z",
"answer": 65151
},
{
"i... | 1 | [] | {
"lo": -5.97,
"mid": -3.97,
"hi": -1.93
} | ||||
031253 | modular_count_residue_v1_1918700295_2583 | Let $m = 13$. Let $r$ be the number of nonnegative integers $j$ such that $0 \leq j \leq 16464$ and $\binom{16464}{j}$ is odd. Determine the value of the number of positive integers $n$ such that $1 \leq n \leq 81796$ and $n \equiv r \pmod{m}$. | 6,292 | graphs = [
Graph(
let={
"upper": Const(81796),
"m": Const(13),
"r": CountOverSet(set=SolutionsSet(var=Var("j"), condition=And(Geq(Var("j"), Const(0)), Leq(Var("j"), Const(16464)), Eq(Mod(value=Binom(n=Const(16464), k=Var("j")), modulus=Const(2)), Const(1))), domain='nonne... | ALG | COMB | COUNT | sympy | V8 | [
"V8"
] | 86348e | modular_count_residue_v1 | null | 6 | 0 | [
"V8"
] | 1 | 2.697 | 2026-02-08T08:00:11.368740Z | {
"verified": true,
"answer": 6292,
"timestamp": "2026-02-08T08:00:14.065424Z"
} | 2c8542 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 200,
"completion_tokens": 907
},
"timestamp": "2026-02-24T08:51:04.644Z",
"answer": 6292
},
{
"id... | 1 | [
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "V8",
"status": "ok"
}
] | {
"lo": -4.92,
"mid": -2.91,
"hi": -0.68
} | ||
c3f6b0 | comb_count_partitions_v1_151522320_1519 | Define $f = \sum_{k=0}^{0} (-1)^k \binom{0}{k}$ and $c = \sum_{k=0}^{0} (-1)^k \binom{0}{k}$. Let $n = 43 \cdot f$ and let $p(n)$ denote the number of integer partitions of $n$. Compute $p(n)$. | 63,261 | graphs = [
Graph(
let={
"n2": Const(0),
"c": Summation(var="k", start=Const(0), end=Ref("n2"), expr=Mul(Pow(Const(-1), Var("k")), Binom(n=Ref("n2"), k=Var("k")))),
"n1": Const(0),
"f": Summation(var="k", start=Const(0), end=Ref("n1"), expr=Mul(Pow(Const(-1), V... | COMB | null | COUNT | sympy | BINOMIAL_ALTERNATING | [
"BINOMIAL_ALTERNATING"
] | c21569 | comb_count_partitions_v1 | null | 4 | 2 | [
"BINOMIAL_ALTERNATING"
] | 1 | 0.001 | 2026-02-08T04:04:37.210385Z | {
"verified": true,
"answer": 63261,
"timestamp": "2026-02-08T04:04:37.211271Z"
} | e02486 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 194,
"completion_tokens": 1142
},
"timestamp": "2026-02-23T23:20:00.728Z",
"answer": 63261
},
{
"... | 1 | [
{
"lemma": "BINOMIAL_ALTERNATING",
"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": "... | {
"lo": 1.97,
"mid": 4.36,
"hi": 6.69
} | ||
dcc25c | comb_binomial_compute_v1_1080341949_461 | Let $n = 12$ and let $k$ be the largest integer such that $2^k \leq 79$. Let $r = \binom{n}{k}$. Find the remainder when $44121 \cdot r$ is divided by $75800$. | 63,204 | graphs = [
Graph(
let={
"_n": Const(44121),
"n": Const(12),
"k": MaxOverSet(set=SolutionsSet(var=Var("k"), condition=Leq(Pow(Const(2), Var("k")), Const(79)))),
"result": Binom(n=Ref("n"), k=Ref("k")),
"Q": Mod(value=Mul(Ref("_n"), Ref("result")), m... | ALG | COMB | COMPUTE | sympy | MAX_VAL | [
"MAX_VAL"
] | 1da621 | comb_binomial_compute_v1 | null | 3 | 0 | [
"MAX_VAL"
] | 1 | 0.001 | 2026-02-08T13:31:13.829160Z | {
"verified": true,
"answer": 63204,
"timestamp": "2026-02-08T13:31:13.830440Z"
} | 12e40a | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 170,
"completion_tokens": 1309
},
"timestamp": "2026-02-24T18:34:18.263Z",
"answer": 63204
},
{
"... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "K16",
"status": "same_pattern_wrong"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "ok"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
},
{
... | {
"lo": -2.35,
"mid": 1.22,
"hi": 4.84
} | ||
c698a4 | comb_count_derangements_v1_898971024_3099 | Let $n$ be the number of nonnegative integers $j$ such that $0 \le j \le 16464$ and $\binom{16464}{j}$ is odd. Let $D_n$ denote the number of derangements of $n$ elements. Determine the value of $k$, the smallest positive integer such that the $k$-th Fibonacci number is divisible by $D_n + 2$. | 1,320 | graphs = [
Graph(
let={
"_n": Const(16464),
"n": CountOverSet(set=SolutionsSet(var=Var("j"), condition=And(Geq(Var("j"), Const(0)), Leq(Var("j"), Const(16464)), Eq(Mod(value=Binom(n=Ref("_n"), k=Var("j")), modulus=Const(2)), Const(1))), domain='nonnegative_integers')),
"r... | NT | COMB | COUNT | sympy | V8 | [
"V8"
] | 86348e | comb_count_derangements_v1 | null | 7 | 0 | [
"V8"
] | 1 | 0.002 | 2026-02-08T17:08:58.217884Z | {
"verified": true,
"answer": 1320,
"timestamp": "2026-02-08T17:08:58.219889Z"
} | ea4048 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 133,
"completion_tokens": 2934
},
"timestamp": "2026-02-17T19:31:15.385Z",
"answer": 1320
},
{... | 1 | [
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "V8",
"status": "ok"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
f65e63 | nt_sum_gcd_range_mod_v1_1125832087_139 | Let $D$ be the set of all ordered pairs $(x, y)$ of positive integers such that $xy = 1382976$. Let $s$ be the minimum value of $x + y$ over all such pairs. Let $k$ be the number of positive integers $n$ such that $1 \leq n \leq s$ and $n \equiv \left\lfloor \frac{n}{2} \right\rfloor \pmod{7}$. Let $S = \sum_{n=1}^{101... | 9,371 | graphs = [
Graph(
let={
"_n": MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(Mul(Var("x"), Var("y")), Const(1382976)))), expr=Sum(Var("x"), Var("y")))),
"N": Const(101... | NT | null | COMPUTE | sympy | B3 | [
"B3/L3C"
] | 345f3b | nt_sum_gcd_range_mod_v1 | null | 7 | 0 | [
"B3",
"L3C"
] | 2 | 0.056 | 2026-02-08T02:53:00.850645Z | {
"verified": true,
"answer": 9371,
"timestamp": "2026-02-08T02:53:00.906418Z"
} | d6bfbe | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 250,
"completion_tokens": 5308
},
"timestamp": "2026-02-23T18:28:49.749Z",
"answer": 9371
},
{
"i... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "L3C",
"status": "ok_later"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
},
{
"lemma": ... | {
"lo": 2.17,
"mid": 4.01,
"hi": 5.72
} | ||
157cbd | comb_count_permutations_fixed_v1_1918700295_4083 | Let $n = 9$. Let $p_0$ be the number of positive integers $p$ for which there exists a positive integer $q$ such that $pq = 216$, $\gcd(p, q) = 1$, and $p < q$. Let $k$ be the smallest positive divisor of $29645$ that is at least $p_0$. Let $r = \binom{9}{k} \cdot !(9 - k)$, where $!m$ denotes the number of derangement... | 27,038 | graphs = [
Graph(
let={
"_n": Const(84184),
"n": Const(9),
"k": MinOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), CountOverSet(set=SolutionsSet(var=Var("p"), condition=And(IsPositive(arg=Var(name='p')), Exists(var=Var(name='q'), condition=And(Eq(left=M... | NT | COMB | COUNT | sympy | COPRIME_PAIRS | [
"COPRIME_PAIRS/MIN_PRIME_FACTOR"
] | 52cee2 | comb_count_permutations_fixed_v1 | null | 6 | 0 | [
"COPRIME_PAIRS",
"MIN_PRIME_FACTOR"
] | 2 | 0.003 | 2026-02-08T09:08:03.252445Z | {
"verified": true,
"answer": 27038,
"timestamp": "2026-02-08T09:08:03.255529Z"
} | fd3a37 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 180,
"completion_tokens": 1686
},
"timestamp": "2026-02-14T00:40:44.281Z",
"answer": 27038
},
... | 1 | [
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "MIN_PRIME_FACTOR",
"status": "ok_later"
},
{
"lemma": "... | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
70f6dc | antilemma_sum_equals_v1_1520064083_805 | Let $n$ be the number of ordered pairs $(i, j)$ such that $1 \le i \le 4$ and $1 \le j \le 11$. Let $S$ be the set of all ordered pairs $(i, j)$ of positive integers such that $1 \le i \le 42$, $1 \le j \le 42$, and $i + j = n$. Compute the number of elements in $S$. | 41 | graphs = [
Graph(
let={
"_n": CountOverSet(set=CartesianProduct(left=IntegerRange(start=Const(1), end=Const(4)), right=IntegerRange(start=Const(1), end=Const(11)))),
"x": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("i"), Var("j")]), condition=Eq(Sum(Var("i"), Var("j")), Ref... | COMB | GEOM | COMPUTE | sympy | COMB1 | [
"COUNT_CARTESIAN/COUNT_SUM_EQUALS",
"COUNT_SUM_EQUALS"
] | 8bee9e | antilemma_sum_equals_v1 | null | 3 | 0 | [
"COMB1",
"COUNT_CARTESIAN",
"COUNT_SUM_EQUALS"
] | 3 | 0.271 | 2026-02-08T03:36:07.705200Z | {
"verified": true,
"answer": 41,
"timestamp": "2026-02-08T03:36:07.975738Z"
} | aa7e0c | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 206,
"completion_tokens": 725
},
"timestamp": "2026-02-10T15:06:29.622Z",
"answer": 41
},
{
"id":... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "ok"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "ok"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8",
"status": "no... | {
"lo": -4.92,
"mid": -2.9,
"hi": -0.7
} | ||
cf5bd2 | comb_count_derangements_v1_1218484723_3993 | Let $n = \sum_{k=0}^{2} 2^k$. Compute $18145 - D_n$, where $D_n$ denotes the number of derangements of $n$ elements. | 16,291 | graphs = [
Graph(
let={
"_n": Const(2),
"n": Summation(var="k", start=Const(0), end=Ref("_n"), expr=Pow(Const(2), Var("k"))),
"result": Subfactorial(arg=Ref(name='n')),
"_c": Const(18145),
"Q": Sub(Ref("_c"), Ref("result")),
},
goal... | COMB | null | COUNT | sympy | SUM_GEOM | [
"SUM_GEOM"
] | 04214c | comb_count_derangements_v1 | null | 3 | 0 | [
"SUM_GEOM"
] | 1 | 0.001 | 2026-02-25T05:35:53.390341Z | {
"verified": true,
"answer": 16291,
"timestamp": "2026-02-25T05:35:53.391178Z"
} | 7b7a06 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 153,
"completion_tokens": 1080
},
"timestamp": "2026-03-29T13:16:13.113Z",
"answer": 16291
},
{
"... | 1 | [
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "SUM_GEOM",
"status": "ok"
},
{
"lemma": ... | {
"lo": -4.26,
"mid": -1.8,
"hi": 1.26
} | ||
ce82a6 | geo_count_lattice_triangle_v1_1218484723_912 | Let $R = \left|180 \cdot 100 - 81 \cdot 289\right|$. Let $A$ be the minimum value of $x + y$ over all pairs of positive integers $(x, y)$ such that $xy = 8100$. Let $T$ be the number of integers $t$ in the range $[39, 651]$ that can be expressed as $t = 14a + 8b + 17$ for some integers $a, b$ with $1 \leq a \leq 15$, $... | 2,700 | graphs = [
Graph(
let={
"_m": Const(100),
"_n": Const(100),
"area_2x": Abs(arg=Sum(Mul(Const(value=180), Const(value=100)), Mul(Const(value=81), Sub(left=Const(value=0), right=Const(value=289))))),
"boundary": Sum(GCD(a=Abs(arg=MinOverSet(set=MapOverSet(set=So... | GEOM | NT | COUNT | sympy | LIN_FORM | [
"LIN_FORM",
"B3"
] | 688dbe | geo_count_lattice_triangle_v1 | null | 4 | 0 | [
"B3",
"LIN_FORM"
] | 2 | 0.011 | 2026-02-25T02:37:31.859467Z | {
"verified": true,
"answer": 2700,
"timestamp": "2026-02-25T02:37:31.870359Z"
} | 9f3654 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 296,
"completion_tokens": 32768
},
"timestamp": "2026-03-10T02:53:19.498Z",
"answer": null
},
{
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "LIN_FORM",
"status": "ok"
}
] | {
"lo": -0.93,
"mid": 2.04,
"hi": 4.6
} | ||
704c34 | nt_count_intersection_v1_1439011603_1210 | Let $N$ be the maximum value of $xy$ over all ordered pairs $(x,y)$ of positive integers such that $x + y = 200$. Let $a = 9$ and $b = 20$. Determine the value of $Q$, where $Q$ is the remainder when $89679$ multiplied by the number of positive integers $n$ at most $N$ that are divisible by $a$ and relatively prime to ... | 41,615 | graphs = [
Graph(
let={
"_n": Const(57860),
"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(200)))), expr=Mul(Var("x"), Var("y")))),... | NT | null | COUNT | sympy | B1 | [
"B1"
] | 5b950e | nt_count_intersection_v1 | null | 5 | 0 | [
"B1"
] | 1 | 0.346 | 2026-02-08T15:58:45.460041Z | {
"verified": true,
"answer": 41615,
"timestamp": "2026-02-08T15:58:45.806526Z"
} | 45f248 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 149,
"completion_tokens": 1236
},
"timestamp": "2026-02-16T18:32:10.507Z",
"answer": 41615
},
... | 1 | [
{
"lemma": "B1",
"status": "ok"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
9f6a1d | diophantine_fbi2_count_v1_1978505735_3539 | Let $n = 132$ and $k = 180$. Define $D$ to be the set of all integers $d$ such that $2 \le d \le n$, $d$ divides $k$, and $2 \le \frac{k}{d} \le 132$. Let $r$ be the number of elements in $D$. Let $c$ be the largest prime number at most $2007$. Compute the value of $r \bmod 293 + c \cdot (r \bmod 337)$. | 32,064 | graphs = [
Graph(
let={
"_n": Const(132),
"k": Const(180),
"result": CountOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Const(2)), Leq(Var("d"), Ref("_n")), Divides(divisor=Var("d"), dividend=Ref("k")), Geq(Div(Ref("k"), Var("d")), Const(2)), Leq(Div(... | NT | null | COUNT | sympy | MAX_PRIME_BELOW | [
"MAX_PRIME_BELOW"
] | 08a653 | diophantine_fbi2_count_v1 | two_moduli | 4 | 0 | [
"MAX_PRIME_BELOW"
] | 1 | 0.016 | 2026-02-08T17:42:44.723300Z | {
"verified": true,
"answer": 32064,
"timestamp": "2026-02-08T17:42:44.739524Z"
} | c72c8b | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 160,
"completion_tokens": 1804
},
"timestamp": "2026-02-18T07:21:56.146Z",
"answer": 32064
},
... | 1 | [
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "V3",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
e37701 | antilemma_k3_v1_124444284_3218 | Let $n = 35693$ and define
\[
x = \sum_{d \mid n} \phi(d),
\]
where $\phi$ denotes Euler's totient function. Let $c = 33124$, and let $Q$ be the remainder when $c - x$ is divided by $86401$.
Find the value of $Q$. | 83,832 | graphs = [
Graph(
let={
"_n": Const(35693),
"x": SumOverDivisors(n=Ref(name='_n'), var='d', expr=EulerPhi(n=Var(name='d'))),
"_c": Const(33124),
"Q": Mod(value=Sub(Ref("_c"), Ref("x")), modulus=Const(86401)),
},
goal=Ref("Q"),
)
] | NT | COMB | COMPUTE | sympy | K3 | [
"K3"
] | 54c41e | antilemma_k3_v1 | null | 4 | 0 | [
"K3"
] | 1 | 0.001 | 2026-02-08T05:17:27.180872Z | {
"verified": true,
"answer": 83832,
"timestamp": "2026-02-08T05:17:27.181871Z"
} | 98c5de | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 122,
"completion_tokens": 411
},
"timestamp": "2026-02-12T05:54:19.726Z",
"answer": 83832
},
{... | 1 | [
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "K3",
"status": "ok"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "V3",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
}
] | {
"lo": -3.51,
"mid": 1.33,
"hi": 6.56
} | ||
a43fea | comb_count_surjections_v1_677425708_1037 | Let $n$ be the number of integers $t$ with $5 \leq t \leq 12$ such that there exist integers $a$ and $b$ satisfying $1 \leq a \leq 2$, $1 \leq b \leq 3$, and $t = 3a + 2b$. Let $k$ be the number of ordered triples $(x_1, x_2, x_3)$ of positive odd integers such that $x_1 + x_2 + x_3 = 5$. Let $\text{result} = k! \cdot ... | 30,085 | graphs = [
Graph(
let={
"_n": Const(30625),
"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=Va... | COMB | null | COUNT | sympy | LIN_FORM | [
"LIN_FORM",
"COMB1"
] | 3d1461 | comb_count_surjections_v1 | null | 7 | 0 | [
"COMB1",
"LIN_FORM"
] | 2 | 0.005 | 2026-02-08T03:57:30.661775Z | {
"verified": true,
"answer": 30085,
"timestamp": "2026-02-08T03:57:30.666503Z"
} | a2f001 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 279,
"completion_tokens": 1151
},
"timestamp": "2026-02-09T15:02:52.021Z",
"answer": 30085
},
{
"... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COMB1",
"status": "ok"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "V7",
"status": "no"
},
... | {
"lo": -3.83,
"mid": -1.68,
"hi": 1.09
} | ||
db0dbd | algebra_quadratic_discriminant_v1_865884756_6318 | Let $a = 1$, $b = -2$, and $c = -35$. Define $S$ to be the set of all positive integers $p$ for which there exists a positive integer $q$ such that $pq = 6$, $\gcd(p, q) = 1$, and $p < q$. Let $n$ be the number of elements in $S$. Compute the value of $(-2)^n - 4ac$. Then, let $Q$ be the remainder when $73148$ times th... | 45,881 | graphs = [
Graph(
let={
"_n": Const(58589),
"a": Const(1),
"b": Const(-2),
"c": Const(-35),
"result": Sub(Pow(Ref("b"), CountOverSet(set=SolutionsSet(var=Var("p"), condition=And(IsPositive(arg=Var(name='p')), Exists(var=Var(name='q'), condition=And... | NT | null | COMPUTE | sympy | COPRIME_PAIRS | [
"COPRIME_PAIRS"
] | 2bb3aa | algebra_quadratic_discriminant_v1 | null | 3 | 0 | [
"COPRIME_PAIRS"
] | 1 | 0.016 | 2026-02-08T19:08:45.610168Z | {
"verified": true,
"answer": 45881,
"timestamp": "2026-02-08T19:08:45.626162Z"
} | 9fe22f | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 174,
"completion_tokens": 1456
},
"timestamp": "2026-02-18T21:24:16.638Z",
"answer": 45881
},
... | 1 | [
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
ea2369 | sequence_lucas_compute_v1_124444284_5015 | Let $N = 19$. Let $n$ be the number of positive integers $j$ such that $1 \le j \le N$ and $j^3 \le 6859$. Compute the $n$-th Lucas number. | 9,349 | graphs = [
Graph(
let={
"_n": Const(19),
"n": CountOverSet(set=SolutionsSet(var=Var("j"), condition=And(Geq(Var("j"), Const(1)), Leq(Var("j"), Ref("_n")), Leq(Pow(Var("j"), Const(3)), Const(6859))), domain='positive_integers')),
"result": Lucas(arg=Ref(name='n')),
... | NT | null | COMPUTE | sympy | C3 | [
"C3"
] | 8a214c | sequence_lucas_compute_v1 | null | 3 | 0 | [
"C3"
] | 1 | 0.001 | 2026-02-08T06:20:46.060044Z | {
"verified": true,
"answer": 9349,
"timestamp": "2026-02-08T06:20:46.060741Z"
} | 207d17 | 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": 737
},
"timestamp": "2026-02-12T23:12:29.603Z",
"answer": 9349
},
{
... | 1 | [
{
"lemma": "C3",
"status": "ok"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "V1",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
}
] | {
"lo": -5.55,
"mid": -3.01,
"hi": 0.32
} | ||
77ee21 | nt_sum_gcd_range_mod_v1_971394319_753 | Let $j$ be a positive integer. Define $N$ as the number of such $j$ satisfying $j^4 \leq 256000000000000$ and $1 \leq j \leq S$, where $S$ is the number of positive integers $n \leq 24000$ for which $8$ divides the $n$-th Fibonacci number. Let $k$ be the number of ordered pairs $(a, b)$ where $a$ and $b$ are integers w... | 2,480 | graphs = [
Graph(
let={
"_n": Const(24000),
"N": CountOverSet(set=SolutionsSet(var=Var("j"), condition=And(Geq(Var("j"), Const(1)), Leq(Var("j"), CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Ref("_n")), Divides(divisor=Const(8), div... | NT | null | COMPUTE | sympy | COUNT_FIB_DIVISIBLE | [
"COUNT_FIB_DIVISIBLE/C3",
"COUNT_CARTESIAN"
] | a2d892 | nt_sum_gcd_range_mod_v1 | null | 7 | 0 | [
"C3",
"COUNT_CARTESIAN",
"COUNT_FIB_DIVISIBLE"
] | 3 | 0.207 | 2026-02-08T13:17:18.464457Z | {
"verified": true,
"answer": 2480,
"timestamp": "2026-02-08T13:17:18.671499Z"
} | 633d11 | 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": 2445
},
"timestamp": "2026-02-15T12:49:32.123Z",
"answer": 2480
},
{... | 1 | [
{
"lemma": "C3",
"status": "ok_later"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "ok"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "ok"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"statu... | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
bbffb9 | nt_sum_totient_over_divisors_v1_784195855_9598 | Let $n = 65062$. Define $\text{result} = \sum_{d \mid n} \phi(d)$, where $\phi$ denotes Euler's totient function. Let $S$ be the set of all ordered pairs $(x, y)$ of positive integers such that $x + y = 66$. Define $c$ to be the maximum value of $xy$ over all such pairs. Compute the remainder when $\text{result}^2 + 10... | 64,088 | graphs = [
Graph(
let={
"_n": Const(10),
"n": Const(65062),
"result": SumOverDivisors(n=Ref(name='n'), var='d', expr=EulerPhi(n=Var(name='d'))),
"_c": MaxOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive... | NT | null | COMPUTE | sympy | B1 | [
"B1"
] | bf138c | nt_sum_totient_over_divisors_v1 | quadratic_mod | 4 | 0 | [
"B1"
] | 1 | 0.002 | 2026-02-08T16:54:18.860969Z | {
"verified": true,
"answer": 64088,
"timestamp": "2026-02-08T16:54:18.862710Z"
} | bbbf28 | 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": 6979
},
"timestamp": "2026-02-17T15:37:41.631Z",
"answer": 64088
},
... | 1 | [
{
"lemma": "B1",
"status": "ok"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
167c81 | modular_modexp_compute_v1_601307018_8253 | Let $a$ be the largest prime number $n$ with $2 \le n \le 41$. Let $e$ be the minimum value of $|x - y|$ over all ordered pairs $(x, y)$ of positive integers such that $xy = 3015966$. Compute $a^e \bmod 36864$. | 32,873 | graphs = [
Graph(
let={
"_m": Const(41),
"_n": Const(2),
"a": MaxOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Ref("_n")), Leq(Var("n"), Ref("_m")), IsPrime(Var("n"))))),
"e": MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[... | NT | null | COMPUTE | sympy | MAX_PRIME_BELOW | [
"MAX_PRIME_BELOW",
"B3_DIFF"
] | 7ffb58 | modular_modexp_compute_v1 | null | 5 | 0 | [
"B3_DIFF",
"MAX_PRIME_BELOW"
] | 2 | 0.007 | 2026-03-10T08:45:25.692379Z | {
"verified": true,
"answer": 32873,
"timestamp": "2026-03-10T08:45:25.699127Z"
} | 47db9f | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 183,
"completion_tokens": 9164
},
"timestamp": "2026-04-19T08:41:08.075Z",
"answer": 32873
},
{
... | 1 | [
{
"lemma": "B3_DIFF",
"status": "ok"
},
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "... | {
"lo": -5.34,
"mid": 1.1,
"hi": 7.53
} | ||
490f16 | antilemma_v8_lucas_548369836_117 | Let $x$ be the number of integers $j$ such that $0 \leq j \leq 98303$ and $\binom{98303}{j}$ is odd. Compute the remainder when $44121 \cdot x$ is divided by $93839$. | 52,749 | graphs = [
Graph(
let={
"x": CountOverSet(set=SolutionsSet(var=Var("j"), condition=And(Geq(Var("j"), SumOverDivisors(n=Const(value=19), var='d', expr=MoebiusMu(n=Var(name='d')))), Leq(Var("j"), Const(98303)), Eq(Mod(value=Binom(n=Const(98303), k=Var("j")), modulus=Const(2)), Const(1))), domain='... | NT | null | COMPUTE | sympy | MOBIUS_SUM | [
"MOBIUS_SUM",
"V8"
] | 39d31c | antilemma_v8_lucas | null | 5 | 0 | [
"MOBIUS_SUM",
"V8"
] | 2 | 0.001 | 2026-02-08T02:46:10.756229Z | {
"verified": true,
"answer": 52749,
"timestamp": "2026-02-08T02:46:10.757251Z"
} | 6a4704 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 173,
"completion_tokens": 3591
},
"timestamp": "2026-02-08T19:53:38.076Z",
"answer": 52749
},
{
"... | 1 | [
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "MOBIUS_SUM",
... | {
"lo": -1.89,
"mid": 1.79,
"hi": 4.93
} | ||
0b6953 | antilemma_k3_v1_2051736721_2733 | Let $n = 92551$. Compute the sum of $\phi(d)$ over all positive divisors $d$ of $n$, where $\phi$ denotes Euler's totient function. | 92,551 | graphs = [
Graph(
let={
"_n": Const(92551),
"x": SumOverDivisors(n=Ref(name='_n'), var='d', expr=EulerPhi(n=Var(name='d'))),
},
goal=Ref("x"),
)
] | NT | COMB | COMPUTE | sympy | K3 | [
"K3"
] | 54c41e | antilemma_k3_v1 | null | 3 | 0 | [
"K3"
] | 1 | 0.001 | 2026-02-08T16:52:19.261683Z | {
"verified": true,
"answer": 92551,
"timestamp": "2026-02-08T16:52:19.262206Z"
} | 727441 | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 1,
"correct": {
"strict": false,
"boxed": false,
"relaxed": true
},
"usage": {
"prompt_tokens": 0,
"completion_tokens": 0
},
"timestamp": "2026-02-16T08:05:45.848Z",
"answer": null
},
{
"id": 11,
... | 1 | [
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K3",
"status": "ok"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"
}
] | {
"lo": -8.26,
"mid": -5.01,
"hi": -1.76
} | ||
60a849 | comb_binomial_compute_v1_1218484723_2008 | Find the minimum value $n$ of the expression $16a^4 - 64a^3b + 96a^2b^2 - 64ab^3 + 32b^4$ over all ordered pairs of positive integers $(a, b)$ with $1 \leq a, b \leq 5$. Then compute $\binom{n}{8}$. | 12,870 | graphs = [
Graph(
let={
"_n": Const(5),
"n": MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("a"), Var("b")]), condition=And(Geq(Var("a"), Const(1)), Leq(Var("a"), Ref("_n")), Geq(Var("b"), Const(1)), Leq(Var("b"), Const(5)))), expr=Sum(Mul(Const(-64), Var("a"), Po... | COMB | null | COMPUTE | sympy | POLY4_MIN | [
"POLY4_MIN"
] | 82de3b | comb_binomial_compute_v1 | null | 6 | 0 | [
"POLY4_MIN"
] | 1 | 0.003 | 2026-02-25T03:42:49.775554Z | {
"verified": true,
"answer": 12870,
"timestamp": "2026-02-25T03:42:49.778483Z"
} | a4147c | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 192,
"completion_tokens": 951
},
"timestamp": "2026-03-29T02:29:16.187Z",
"answer": 12870
},
{
"i... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "POLY4_MIN",
"status": "ok"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
}
] | {
"lo": -4.26,
"mid": -1.81,
"hi": 1.23
} | ||
cf5a3a | nt_count_gcd_equals_v1_1820931509_515 | Let $k$ be the minimum value of $x + y$ over all ordered pairs $(x, y)$ of positive integers such that $xy = 5929$. Let $d = 7$. Compute the number of positive integers $n$ such that $1 \le n \le 13225$ and $\gcd(n, k) = d$. | 859 | graphs = [
Graph(
let={
"upper": Const(13225),
"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(5929)))), expr=Sum(Var("x"), Var("y")... | NT | null | COUNT | sympy | B3 | [
"B3"
] | 0cd20d | nt_count_gcd_equals_v1 | null | 5 | 0 | [
"B3"
] | 1 | 1.052 | 2026-02-08T11:40:40.206577Z | {
"verified": true,
"answer": 859,
"timestamp": "2026-02-08T11:40:41.258109Z"
} | 158052 | 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": 1296
},
"timestamp": "2026-02-14T17:57:53.284Z",
"answer": 859
},
{
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
},
{
"lemma": "VAL_SUM_EQ",
"status": "no"
}
] | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
78f3ce | lin_form_endings_v1_2051736721_1504 | Let $a = 25$, $b = 10$, and $k = 3$. Compute the least common multiple of $a$ and $b$, denoted $\text{lcm}(a, b)$. Let $s = 3 \cdot \text{lcm}(a, b) + a + b$. Now compute $13502 \cdot s$, and let $x$ be the remainder when this value is divided by $55937$. Find the value of $x$. | 36,642 | graphs = [
Graph(
let={
"a_coeff": Const(25),
"b_coeff": Const(10),
"k_val": Const(3),
"lcm_node": LCM(a=Ref("a_coeff"), b=Ref("b_coeff")),
"_inner_result": Sum(Mul(Ref("k_val"), Ref("lcm_node")), Ref("a_coeff"), Ref("b_coeff")),
"_scal... | COMB | NT | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | lin_form_endings_v1 | null | 2 | null | [
"LIN_FORM"
] | 1 | 0.001 | 2026-02-08T16:04:22.593487Z | {
"verified": true,
"answer": 36642,
"timestamp": "2026-02-08T16:04:22.594289Z"
} | 2d3ea9 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 146,
"completion_tokens": 659
},
"timestamp": "2026-02-16T20:43:39.900Z",
"answer": 36642
},
{... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "V8",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
60babd | comb_sum_binomial_row_v1_1218484723_101 | Let $M$ be the number of prime integers $n_1$ in the range $2 \leq n_1 \leq 14419$. Let $n$ be the number of non-negative integers $v \leq M$ for which there exist integers $a, b$ with $1 \leq a, b \leq 14$ such that $10a^2 + 10b^2 - 20ab = v$. Compute $2^n$. | 16,384 | graphs = [
Graph(
let={
"_m": Const(2),
"_n": CountOverSet(set=SolutionsSet(var=Var("n1"), condition=And(Geq(Var("n1"), Ref("_m")), Leq(Var("n1"), Const(14419)), IsPrime(Var("n1"))))),
"n": CountOverSet(set=SolutionsSet(var=Var("v"), condition=And(Geq(Var("v"), Const(0)),... | COMB | NT | SUM | sympy | COUNT_PRIMES | [
"COUNT_PRIMES/QF_PSD_DISTINCT"
] | fff0c5 | comb_sum_binomial_row_v1 | null | 4 | 0 | [
"COUNT_PRIMES",
"QF_PSD_DISTINCT"
] | 2 | 0.007 | 2026-02-25T01:49:42.052533Z | {
"verified": true,
"answer": 16384,
"timestamp": "2026-02-25T01:49:42.059418Z"
} | d1248e | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 1,
"correct": {
"strict": false,
"boxed": false,
"relaxed": true
},
"usage": {
"prompt_tokens": 212,
"completion_tokens": 32768
},
"timestamp": "2026-03-10T08:21:50.213Z",
"answer": null
},
{
... | 1 | [
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_PRIMES",
"status": "ok"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "QF_PSD_DISTINCT",
"status": "ok_later"
},
{
"lemma": "V1",
"status":... | {
"lo": -0.93,
"mid": 2.04,
"hi": 4.6
} | ||
99e03b | sequence_lucas_compute_v1_1125832087_124 | Let $L_n$ denote the $n$th Lucas number, where $L_1 = 1$, $L_2 = 3$, and $L_n = L_{n-1} + L_{n-2}$ for $n \geq 3$. Let $r = L_{19}$. Let $c$ be the number of integers $t$ such that $10 \leq t \leq 660$ and there exist positive integers $a$ and $b$ with $1 \leq a \leq 72$, $1 \leq b \leq 62$, and $t = 4a + 6b$. Compute ... | 30,096 | graphs = [
Graph(
let={
"n": Const(19),
"result": Lucas(arg=Ref(name='n')),
"_c": 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(... | NT | null | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM"
] | 2ba0ea | sequence_lucas_compute_v1 | quadratic_mod | 5 | 0 | [
"LIN_FORM"
] | 1 | 0.001 | 2026-02-08T02:52:25.510368Z | {
"verified": true,
"answer": 30096,
"timestamp": "2026-02-08T02:52:25.511675Z"
} | 45c2f0 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 274,
"completion_tokens": 32768
},
"timestamp": "2026-02-23T18:30:16.853Z",
"answer": 30096
},
{
... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "V1",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "VAL_SUM_EQ",
"status": "no"
}
] | {
"lo": 1.66,
"mid": 3.8,
"hi": 5.62
} | ||
81aed1 | geo_count_lattice_rect_v1_124444284_9846 | Let $a = 111$ and $b = 275$. Let $R$ be the number of lattice points $(x, y)$ such that $0 \leq x \leq a$ and $0 \leq y \leq b$. Compute the remainder when $22150 \cdot R$ is divided by $52793$. | 28,383 | graphs = [
Graph(
let={
"a": Const(111),
"b": Const(275),
"result": LatticePointsRect(a=Ref(name='a'), b=Ref(name='b')),
"_c": Const(22150),
"Q": Mod(value=Mul(Ref("_c"), Ref("result")), modulus=Const(52793)),
},
goal=Ref("Q"),
... | GEOM | null | COUNT | sympy | [] | geo_count_lattice_rect_v1 | null | 4 | 0 | null | null | 0.002 | 2026-02-08T12:42:15.323847Z | {
"verified": true,
"answer": 28383,
"timestamp": "2026-02-08T12:42:15.325844Z"
} | 109a2d | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 183,
"completion_tokens": 14111
},
"timestamp": "2026-02-24T16:13:57.526Z",
"answer": 28383
},
{
... | 1 | [] | {
"lo": -2.35,
"mid": 1.22,
"hi": 4.84
} | ||||
064265 | modular_modexp_compute_v1_655260480_3404 | Let $a = 3$. Let $e$ be the number of positive integers $k$ such that $k \leq 336200$ and $50$ divides $k$. Let $m = 44444$. Define $r$ to be the remainder when $a^e$ is divided by $m$. Let $c = 37941$ and let $Q$ be the remainder when $c \cdot r$ is divided by $98776$. Compute $Q$. | 11,165 | graphs = [
Graph(
let={
"_n": Const(98776),
"a": Const(3),
"e": CountOverSet(set=SolutionsSet(var=Var("k"), condition=And(Geq(Var("k"), Const(1)), Leq(Var("k"), Const(336200)), Divides(divisor=Const(50), dividend=Var("k"))), domain='positive_integers')),
"m": ... | NT | null | COMPUTE | sympy | C2 | [
"C2"
] | 9685eb | modular_modexp_compute_v1 | null | 3 | 0 | [
"C2"
] | 1 | 0.003 | 2026-02-08T17:22:21.705313Z | {
"verified": true,
"answer": 11165,
"timestamp": "2026-02-08T17:22:21.707975Z"
} | 6679a1 | 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": 2029
},
"timestamp": "2026-02-18T00:54:06.550Z",
"answer": 11165
},
... | 1 | [
{
"lemma": "C2",
"status": "ok"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "V3",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
c23c53 | comb_count_partitions_v1_1125832087_2397 | Let $T$ be the set of all integers $t$ such that $15 \leq t \leq 1101$ and $t = 6a + 9b$ for some integers $a$ and $b$ with $1 \leq a \leq 20$ and $1 \leq b \leq 109$. Let $P$ be the number of elements in $T$. Define $S$ as the set of all ordered pairs $(x, y)$ of positive integers such that $xy = P$. Let $n$ be the mi... | 51,336 | graphs = [
Graph(
let={
"_n": Const(64807),
"n": MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(Mul(Var("x"), Var("y")), CountOverSet(set=SolutionsSet(var=Var("t"), co... | COMB | null | COUNT | sympy | LIN_FORM | [
"LIN_FORM/B3"
] | 05313e | comb_count_partitions_v1 | null | 7 | 0 | [
"B3",
"LIN_FORM"
] | 2 | 0.009 | 2026-02-08T04:34:57.448337Z | {
"verified": true,
"answer": 51336,
"timestamp": "2026-02-08T04:34:57.456886Z"
} | 15360c | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 277,
"completion_tokens": 2222
},
"timestamp": "2026-02-11T09:29:12.937Z",
"answer": 2176
},
{
... | 1 | [
{
"lemma": "B3",
"status": "ok_later"
},
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "V7",
"status": "no"... | {
"lo": 3.43,
"mid": 5.73,
"hi": 8.84
} | ||
ef449a | nt_count_intersection_v1_48377204_431 | Let $S$ be the set of all ordered pairs $(x, y)$ of positive integers such that $xy = 6250000$. Let $N$ be the minimum value of $x + y$ as $(x, y)$ ranges over $S$. Let $T$ be the set of all integers $t$ such that $8 \leq t \leq 35$ and there exist positive integers $a$, $b$ with $1 \leq a \leq 5$, $1 \leq b \leq 4$, a... | 666 | graphs = [
Graph(
let={
"N": MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(Mul(Var("x"), Var("y")), Const(6250000)))), expr=Sum(Var("x"), Var("y")))),
"a": Const(3),
... | NT | null | COUNT | sympy | LIN_FORM | [
"LIN_FORM",
"B3"
] | 688dbe | nt_count_intersection_v1 | null | 6 | 0 | [
"B3",
"LIN_FORM"
] | 2 | 0.604 | 2026-02-08T15:26:22.129219Z | {
"verified": true,
"answer": 666,
"timestamp": "2026-02-08T15:26:22.732801Z"
} | 03c634 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 216,
"completion_tokens": 1860
},
"timestamp": "2026-02-16T07:26:35.274Z",
"answer": 666
},
{
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": ... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
642447 | nt_min_phi_inverse_v1_971394319_278 | Let $u$ be the number of integers $t$ such that $7 \leq t \leq 20$ and there exist positive integers $a$ and $b$ with $1 \leq a \leq 2$, $1 \leq b \leq 5$, and $t = 5a + 2b$. Determine the value of the smallest positive integer $n$ such that $1 \leq n \leq u$ and $\phi(n) = 2$. | 3 | graphs = [
Graph(
let={
"upper": CountOverSet(set=SolutionsSet(var=Var("t"), condition=Exists(var=Var(name='a'), condition=Exists(var=Var(name='b'), condition=And(Geq(left=Var(name='a'), right=Const(value=1)), Leq(left=Var(name='a'), right=Const(value=2)), Geq(left=Var(name='b'), right=Const(val... | NT | null | EXTREMUM | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | nt_min_phi_inverse_v1 | null | 5 | 0 | [
"LIN_FORM"
] | 1 | 0.004 | 2026-02-08T12:56:17.817991Z | {
"verified": true,
"answer": 3,
"timestamp": "2026-02-08T12:56:17.822096Z"
} | 382a5e | 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": 1898
},
"timestamp": "2026-02-15T08:06:42.822Z",
"answer": 3
},
{
... | 1 | [
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "MAX_VAL",
"... | {
"lo": -6.96,
"mid": -4.56,
"hi": -1.46
} | ||
e2020a | comb_catalan_compute_v1_1439011603_459 | Let $ u_1 $ be the number of ordered pairs $ (i, j) $ of integers such that $ 1 \leq i \leq 9 $, $ 1 \leq j \leq 9 $, and $ i + j = 9 $. Let $ n_2 = u_1 + 1 $. Define
$$
t = \sum_{k=0}^{n_2} (-1)^k \binom{n_2}{k}.
$$
Let $ u $ be the number of ordered pairs $ (i_1, j_1) $ of integers such that $ 1 \leq i_1 \leq 4 $, $ ... | 58,786 | graphs = [
Graph(
let={
"_n": Const(9),
"u1": 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(9)), right=IntegerRange(start=Const(1), end=Cons... | COMB | null | COMPUTE | sympy | COUNT_SUM_EQUALS | [
"COUNT_SUM_EQUALS/BINOMIAL_ALTERNATING"
] | ab0fe8 | comb_catalan_compute_v1 | null | 4 | 2 | [
"BINOMIAL_ALTERNATING",
"COUNT_SUM_EQUALS"
] | 2 | 0.024 | 2026-02-08T15:30:16.925930Z | {
"verified": true,
"answer": 58786,
"timestamp": "2026-02-08T15:30:16.950310Z"
} | 4ac0ea | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 356,
"completion_tokens": 8165
},
"timestamp": "2026-02-24T21:10:36.530Z",
"answer": 58786
},
{
"... | 1 | [
{
"lemma": "BINOMIAL_ALTERNATING",
"status": "ok_later"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "ok"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma"... | {
"lo": -8,
"mid": -4.75,
"hi": -2.29
} | ||
b86ada | nt_sum_gcd_range_mod_v1_1520064083_9218 | Let $S$ be the set of all ordered pairs $(x, y)$ of positive integers such that $xy = 12250000$. Define $N$ to be the minimum value of $x + y$ as $(x, y)$ ranges over $S$. Let $k$ be the sum of all solutions $x$ to the equation $x^2 - 288x - 17289 = 0$. Define $\sigma = \sum_{n=1}^{N} \gcd(n, k)$. Find the remainder wh... | 6,225 | graphs = [
Graph(
let={
"N": MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(Mul(Var("x"), Var("y")), Const(12250000)))), expr=Sum(Var("x"), Var("y")))),
"k": SumOverSe... | NT | null | COMPUTE | sympy | VIETA_SUM | [
"VIETA_SUM",
"B3"
] | 018050 | nt_sum_gcd_range_mod_v1 | null | 7 | 0 | [
"B3",
"VIETA_SUM"
] | 2 | 0.46 | 2026-02-08T10:36:57.299406Z | {
"verified": true,
"answer": 6225,
"timestamp": "2026-02-08T10:36:57.759865Z"
} | 90a87a | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 167,
"completion_tokens": 2747
},
"timestamp": "2026-02-14T07:53:31.304Z",
"answer": 6225
},
{... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "V1",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
},
{
"lemma": "VIETA_SUM",
... | {
"lo": -5.49,
"mid": 0.22,
"hi": 6.51
} | ||
2e85c9 | comb_count_derangements_v1_124444284_1445 | Let $t = \sum_{k=0}^{6} (-1)^k \binom{6}{k}$. Define $a = 2 + t$ and $b = 1$, and let $n_1 = a + b$. Let $c = \sum_{k=0}^{n_1} (-1)^k \binom{n_1}{k}$. Define $n = 7 + c$. Compute the subfactorial $!n$, which is the number of derangements of $n$ elements. | 1,854 | graphs = [
Graph(
let={
"a1": Const(1),
"b1": Const(5),
"n2": Sum(Ref("a1"), Ref("b1")),
"t": Summation(var="k", start=Sub(Binom(n=Const(12), k=Const(0)), Const(1)), end=Ref("n2"), expr=Mul(Pow(Const(-1), Var("k")), Binom(n=Ref("n2"), k=Var("k")))),
... | COMB | null | COUNT | sympy | BINOMIAL_ALTERNATING | [
"BINOMIAL_ALTERNATING",
"ZERO_BINOM_0"
] | 38a409 | comb_count_derangements_v1 | null | 5 | 2 | [
"BINOMIAL_ALTERNATING",
"ZERO_BINOM_0"
] | 2 | 0.002 | 2026-02-08T03:52:46.133736Z | {
"verified": true,
"answer": 1854,
"timestamp": "2026-02-08T03:52:46.135949Z"
} | edf7af | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 224,
"completion_tokens": 867
},
"timestamp": "2026-02-10T16:15:10.204Z",
"answer": 1854
},
{
"id... | 1 | [
{
"lemma": "BINOMIAL_ALTERNATING",
"status": "ok"
},
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
},
{
"lemma": "V8_SUM",
"status... | {
"lo": -5.97,
"mid": -3.96,
"hi": -1.93
} | ||
f91c91 | modular_sum_quadratic_residues_v1_865884756_2304 | Let $n = 4$ and $p = 569$. Consider the set of all ordered pairs $(x,y)$ of positive integers such that $xy = n$. For each such pair, compute $x + y$, and let $S$ be the set of all such sums. Let $m$ be the minimum value in $S$. Compute $\frac{p(p-1)}{m}$. | 80,798 | graphs = [
Graph(
let={
"_n": Const(4),
"p": Const(569),
"result": Div(Mul(Ref("p"), Sub(Ref("p"), Const(1))), 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 | MIN_PRIME_FACTOR | [
"B3"
] | 0cd20d | modular_sum_quadratic_residues_v1 | null | 3 | 0 | [
"B3",
"MIN_PRIME_FACTOR"
] | 2 | 0.004 | 2026-02-08T16:41:09.786616Z | {
"verified": true,
"answer": 80798,
"timestamp": "2026-02-08T16:41:09.790293Z"
} | ad772d | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 128,
"completion_tokens": 563
},
"timestamp": "2026-02-17T09:51:12.805Z",
"answer": 80798
},
{... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
d43a74 | geo_count_lattice_rect_v1_1520064083_2431 | Compute the number of lattice points $(x, y)$ such that $0 \leq x \leq 196$ and $0 \leq y \leq 208$. Determine the value of this count. | 41,173 | graphs = [
Graph(
let={
"a": Const(196),
"b": Const(208),
"result": LatticePointsRect(a=Ref(name='a'), b=Ref(name='b')),
},
goal=Ref("result"),
)
] | GEOM | null | COUNT | sympy | [] | geo_count_lattice_rect_v1 | null | 3 | 0 | null | null | 0.001 | 2026-02-08T04:44:09.213143Z | {
"verified": true,
"answer": 41173,
"timestamp": "2026-02-08T04:44:09.213813Z"
} | 6c1a05 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 155,
"completion_tokens": 329
},
"timestamp": "2026-02-24T01:35:22.004Z",
"answer": 41173
},
{
"i... | 1 | [] | {
"lo": -5.97,
"mid": -3.96,
"hi": -1.93
} | ||||
f976d4 | antilemma_k3_v1_153355830_1254 | Let $n = 20434$. Define $x = \sum_{d \mid n} \phi(d)$, where the sum is taken over all positive divisors $d$ of $n$, and $\phi(d)$ denotes Euler's totient function. Compute $x$. | 20,434 | graphs = [
Graph(
let={
"_n": Const(20434),
"x": SumOverDivisors(n=Ref(name='_n'), var='d', expr=EulerPhi(n=Var(name='d'))),
},
goal=Ref("x"),
)
] | NT | COMB | COMPUTE | sympy | K3 | [
"K3"
] | 54c41e | antilemma_k3_v1 | null | 3 | 0 | [
"K3"
] | 1 | 0.001 | 2026-02-08T06:13:08.823821Z | {
"verified": true,
"answer": 20434,
"timestamp": "2026-02-08T06:13:08.824396Z"
} | 51a866 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 102,
"completion_tokens": 388
},
"timestamp": "2026-02-12T21:43:30.049Z",
"answer": 20434
},
{... | 1 | [
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "K3",
"status": "ok"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
}
] | {
"lo": -5.55,
"mid": -3.01,
"hi": 0.32
} | ||
bdbcde | nt_sum_divisors_mod_v1_153355830_1571 | Let $x$ and $y$ be positive integers such that $xy = 16402500$. Define $n_1$ to be the minimum value of $x + y$ over all such pairs. Now let $x$ and $y$ be positive integers such that $xy = n_1$, and define $n$ to be the minimum value of $x + y$ over all such pairs. Let $\sigma$ denote the sum of all positive divisors ... | 546 | graphs = [
Graph(
let={
"_n": MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(Mul(Var("x"), Var("y")), Const(16402500)))), expr=Sum(Var("x"), Var("y")))),
"n": MinOverS... | NT | null | COMPUTE | sympy | B3 | [
"B3/B3"
] | 8ffef9 | nt_sum_divisors_mod_v1 | null | 7 | 0 | [
"B3"
] | 1 | 0.002 | 2026-02-08T06:29:51.037877Z | {
"verified": true,
"answer": 546,
"timestamp": "2026-02-08T06:29:51.040357Z"
} | fda796 | 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": 1042
},
"timestamp": "2026-02-13T00:52:56.850Z",
"answer": 546
},
{
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "VAL_SUM_EQ",
"status": "no"
... | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
deb0e9 | nt_count_gcd_equals_v1_1248542787_877 | Let $d$ be the largest prime number $n$ such that $2 \leq n \leq 27$. Let $R$ be the number of positive integers $n$ such that $1 \leq n \leq 34596$ and $\gcd(n, 184) = d$. Compute $5^R \bmod 99991$, add $10201$ to the result, and then find the remainder when this sum is divided by $60366$. | 46,120 | graphs = [
Graph(
let={
"_n": Const(2),
"upper": Const(34596),
"k": Const(184),
"d": MaxOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Ref("_n")), Leq(Var("n"), Const(27)), IsPrime(Var("n"))))),
"result": CountOverSet(set=Soluti... | NT | null | COUNT | sympy | MAX_PRIME_BELOW | [
"MAX_PRIME_BELOW"
] | dc3ad3 | nt_count_gcd_equals_v1 | null | 4 | 0 | [
"MAX_PRIME_BELOW"
] | 1 | 4.679 | 2026-02-08T03:28:10.538733Z | {
"verified": true,
"answer": 46120,
"timestamp": "2026-02-08T03:28:15.217681Z"
} | 6fabaf | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 212,
"completion_tokens": 11477
},
"timestamp": "2026-02-23T20:03:40.372Z",
"answer": 46120
},
{
... | 1 | [
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "V1",
"status": "no"
},
{
"lemma": "V3",
"status": "no"
}
] | {
"lo": -3.42,
"mid": 1.86,
"hi": 7.55
} | ||
e1f1fd | nt_num_divisors_compute_v1_1742523217_1228 | Compute the number of positive divisors of 99. | 6 | graphs = [
Graph(
let={
"n": Const(99),
"result": NumDivisors(n=Ref("n")),
},
goal=Ref("result"),
)
] | NT | null | COMPUTE | sympy | COPRIME_PAIRS | [
"COPRIME_PAIRS"
] | 2bb3aa | nt_num_divisors_compute_v1 | null | 2 | 0 | [
"COPRIME_PAIRS"
] | 1 | 0.007 | 2026-02-08T03:34:21.286140Z | {
"verified": true,
"answer": 6,
"timestamp": "2026-02-08T03:34:21.293101Z"
} | 8997e9 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 121,
"completion_tokens": 69
},
"timestamp": "2026-02-10T05:18:11.530Z",
"answer": 6
},
{
"id": 2... | 2 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"st... | {
"lo": -10,
"mid": -7.73,
"hi": -5.46
} | ||
e5692c | diophantine_fbi2_min_v1_865884756_562 | Let $k$ be the number of nonnegative integers $j$ at most $5272$ for which $\binom{5272}{j}$ is odd. Determine the smallest integer $d$ at least $4$ and at most $42$ such that $d$ divides $k$ and $\frac{k}{d} \geq 3$. Compute the value of $d$. | 4 | graphs = [
Graph(
let={
"_m": Const(5272),
"_n": Const(3),
"k": CountOverSet(set=SolutionsSet(var=Var("j"), condition=And(Geq(Var("j"), Const(0)), Leq(Var("j"), Const(5272)), Eq(Mod(value=Binom(n=Ref("_m"), k=Var("j")), modulus=Const(2)), Const(1))), domain='nonnegative_i... | NT | null | EXTREMUM | sympy | C3 | [
"COMB1",
"V8"
] | 6cf807 | diophantine_fbi2_min_v1 | null | 6 | 0 | [
"C3",
"COMB1",
"V8"
] | 3 | 0.06 | 2026-02-08T15:30:52.379367Z | {
"verified": true,
"answer": 4,
"timestamp": "2026-02-08T15:30:52.438881Z"
} | b204fa | 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": 1292
},
"timestamp": "2026-02-16T07:37:34.023Z",
"answer": 4
},
{
... | 1 | [
{
"lemma": "COMB1",
"status": "ok"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
5748c8 | nt_count_gcd_equals_v1_717093673_2901 | Let $P$ be the maximum value of $x_1 y_1$ over all ordered pairs $(x_1, y_1)$ of positive integers such that $x_1 + y_1 = 54$. Let $k$ be the minimum value of $x + y$ over all ordered pairs $(x, y)$ of positive integers such that $xy = P$. Let $d$ be the number of integers $t$ such that $7 \le t \le 66$ and $t = 3a + 4... | 824 | graphs = [
Graph(
let={
"upper": Const(44521),
"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")), MaxOverSet(set=MapOverSet(set=SolutionsSet(... | NT | null | COUNT | sympy | B1 | [
"B1/B3",
"LIN_FORM"
] | a93fcd | nt_count_gcd_equals_v1 | null | 6 | 0 | [
"B1",
"B3",
"LIN_FORM"
] | 3 | 3.594 | 2026-02-08T17:15:45.309022Z | {
"verified": true,
"answer": 824,
"timestamp": "2026-02-08T17:15:48.902931Z"
} | 6cd7f2 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 225,
"completion_tokens": 2726
},
"timestamp": "2026-02-17T23:06:20.746Z",
"answer": 824
},
{
... | 1 | [
{
"lemma": "B1",
"status": "ok"
},
{
"lemma": "B3",
"status": "ok_later"
},
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "MOD_... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
0b1d31 | nt_gcd_compute_v1_677425708_609 | Let $a = 267608$ and $b = 501765$. Define $d$ to be the greatest common divisor of $a$ and $b$. Let $S$ be the set of all prime numbers $n$ such that $2 \leq n \leq 1009$. Compute the value of
$$
\left( d \bmod 293 \right) + \left( \max(S) \cdot (d \bmod 337) \right).
$$ | 88,841 | graphs = [
Graph(
let={
"_n": Const(293),
"a": Const(267608),
"b": Const(501765),
"result": GCD(a=Ref("a"), b=Ref("b")),
"Q": Sum(Mod(value=Ref("result"), modulus=Ref("_n")), Mul(MaxOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"),... | NT | null | COMPUTE | sympy | MAX_PRIME_BELOW | [
"MAX_PRIME_BELOW"
] | 08a653 | nt_gcd_compute_v1 | two_moduli | 3 | 0 | [
"MAX_PRIME_BELOW"
] | 1 | 0.003 | 2026-02-08T03:36:38.968085Z | {
"verified": true,
"answer": 88841,
"timestamp": "2026-02-08T03:36:38.970602Z"
} | 36b179 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 219,
"completion_tokens": 2310
},
"timestamp": "2026-02-08T20:50:43.867Z",
"answer": 88841
},
{
"... | 1 | [
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok"
},
{
"lemma": "V1",
"status": "no"
},
{
"lemma": "V5",
"status":... | {
"lo": -3.46,
"mid": 1.03,
"hi": 5.49
} | ||
b6ce8e | modular_sum_quadratic_residues_v1_458359167_1581 | Let $n = 842$. Define $p$ to be the number of ordered pairs $(x_1, x_2)$ of positive odd integers such that $x_1 + x_2 = n$. Let $\text{result} = \frac{p(p - 1)}{4}$. Compute the remainder when $47095 \cdot \text{result}$ is divided by $74148$. | 55,227 | graphs = [
Graph(
let={
"_n": Const(842),
"p": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x1"), Var("x2")]), condition=And(IsPositive(arg=Var(name='x1')), IsPositive(arg=Var(name='x2')), IsOdd(arg=Var(name='x1')), IsOdd(arg=Var(name='x2')), Eq(Sum(Var("x1"), Var("x2")), R... | NT | null | SUM | sympy | COMB1 | [
"COMB1"
] | 567f58 | modular_sum_quadratic_residues_v1 | null | 4 | 0 | [
"COMB1"
] | 1 | 0.001 | 2026-02-08T04:45:57.261010Z | {
"verified": true,
"answer": 55227,
"timestamp": "2026-02-08T04:45:57.262226Z"
} | a54bb7 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 196,
"completion_tokens": 2321
},
"timestamp": "2026-02-11T21:52:45.528Z",
"answer": 55227
},
{
... | 1 | [
{
"lemma": "COMB1",
"status": "ok"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "V8",
"... | {
"lo": -3.42,
"mid": 1.86,
"hi": 7.55
} | ||
e02463 | geo_count_lattice_rect_v1_1918700295_3164 | Compute the number of lattice points $(x,y)$ such that $0 \leq x \leq 17$ and $0 \leq y \leq 55$. | 1,008 | graphs = [
Graph(
let={
"a": Const(17),
"b": Const(55),
"result": LatticePointsRect(a=Ref(name='a'), b=Ref(name='b')),
},
goal=Ref("result"),
)
] | GEOM | null | COUNT | sympy | [] | geo_count_lattice_rect_v1 | null | 3 | 0 | null | null | 0.002 | 2026-02-08T08:26:42.208376Z | {
"verified": true,
"answer": 1008,
"timestamp": "2026-02-08T08:26:42.210592Z"
} | 9ed495 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 147,
"completion_tokens": 216
},
"timestamp": "2026-02-24T09:31:19.085Z",
"answer": 1008
},
{
"id... | 2 | [] | {
"lo": -10,
"mid": -7.79,
"hi": -5.57
} | ||||
d06058 | comb_bell_compute_v1_1742523217_5336 | Let $a$ be the number of ordered pairs $(i, j)$ of integers such that $1 \leq i \leq 6$, $1 \leq j \leq 6$, and $i + j = 8$. Let $n_2 = a + 1$. Define
$$
s = \sum_{k=0}^{n_2} (-1)^k \binom{n_2}{k}.
$$
Let $n_1 = 0$ and
$$
f = \sum_{k=0}^{n_1} (-1)^k \binom{n_1}{k}.
$$
Let $n = (9 + s) \cdot f$. Determine the value of t... | 21,147 | graphs = [
Graph(
let={
"_n": Const(9),
"a": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("i"), Var("j")]), condition=Eq(Sum(Var("i"), Var("j")), Const(8)), domain=CartesianProduct(left=IntegerRange(start=Const(1), end=Const(6)), right=IntegerRange(start=Const(1), end=Const(... | COMB | null | COMPUTE | sympy | COUNT_SUM_EQUALS | [
"COUNT_SUM_EQUALS/BINOMIAL_ALTERNATING"
] | ab0fe8 | comb_bell_compute_v1 | null | 2 | 2 | [
"BINOMIAL_ALTERNATING",
"COUNT_SUM_EQUALS"
] | 2 | 0.016 | 2026-02-08T10:55:49.764697Z | {
"verified": true,
"answer": 21147,
"timestamp": "2026-02-08T10:55:49.780654Z"
} | afcbd5 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 273,
"completion_tokens": 886
},
"timestamp": "2026-02-24T12:34:55.173Z",
"answer": 21147
},
{
"i... | 1 | [
{
"lemma": "BINOMIAL_ALTERNATING",
"status": "ok_later"
},
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "ok"
},
{
"lemma"... | {
"lo": -3.84,
"mid": -1.67,
"hi": 1.32
} | ||
538318 | alg_sym_quad_system_v1_1218484723_5639 | Consider all ordered triples $(a, b, c)$ of positive integers satisfying
\[
a^{2} + b^{2} + c^{2} = ab + bc + ca,\qquad 6a + 2b + 7c = 4725,
\]
with $a \ge 1$, $b \ge 1$, and $c \ge 1$. Let
\[
X = \sum_{(a,b,c)} \bigl(a^{5} + b^{5} + c^{5}\bigr),
\]
where the sum runs over all such triples $(a,b,c)$.
Now consider all ... | 1,025 | graphs = [
Graph(
let={
"_m": Const(17),
"_n": Const(34),
"result": Mod(value=SumOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("a"), Var("b"), Var("c")]), condition=And(Eq(Sum(Pow(Var("a"), Const(2)), Pow(Var("b"), Const(2)), Pow(Var("c"), Const(2))), Su... | ALG | null | COMPUTE | sympy | QF_PSD_MIN | [
"QF_PSD_MIN/QF_PSD_COUNT_LEQ"
] | c40f8b | alg_sym_quad_system_v1 | null | 7 | 0 | [
"QF_PSD_COUNT_LEQ",
"QF_PSD_MIN"
] | 2 | 0.019 | 2026-02-25T07:10:27.008189Z | {
"verified": true,
"answer": 1025,
"timestamp": "2026-02-25T07:10:27.027112Z"
} | 735bcc | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 447,
"completion_tokens": 17828
},
"timestamp": "2026-03-29T22:06:35.094Z",
"answer": 1025
},
{
"... | 1 | [
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "QF_PSD_COUNT_LEQ",
"status": "ok_later"
},
{
"lemma": "QF_PSD_MIN",
"status": "ok"
}
] | {
"lo": -3.33,
"mid": 1.03,
"hi": 5.26
} | ||
384188 | geo_count_lattice_rect_v1_865884756_2581 | Compute the number of lattice points $(x, y)$ such that $0 \leq x \leq 66$ and $0 \leq y \leq 60$. | 4,087 | graphs = [
Graph(
let={
"a": Const(66),
"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 | 4 | 0 | null | null | 0 | 2026-02-08T16:50:10.144557Z | {
"verified": true,
"answer": 4087,
"timestamp": "2026-02-08T16:50:10.145002Z"
} | d80144 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 81,
"completion_tokens": 494
},
"timestamp": "2026-02-24T21:58:53.096Z",
"answer": 4087
},
{
... | 1 | [] | {
"lo": -8.52,
"mid": -5.43,
"hi": -3.2
} | ||||
606574 | nt_count_intersection_v1_124444284_9829 | Let $N$ be the number of integers $n$ with $1 \leq n \leq 25000$ such that $n \equiv \left\lfloor \frac{n}{2} \right\rfloor \pmod{5}$. Let $b$ be the number of integers $t$ with $7 \leq t \leq 22$ for which there exist integers $a$ and $b$ such that $1 \leq a \leq 2$, $1 \leq b \leq 6$, and $t = 5a + 2b$. Determine the... | 333 | graphs = [
Graph(
let={
"N": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Const(25000)), Congruent(a=Var(name='n'), b=Floor(arg=Div(left=Var(name='n'), right=Const(value=2))), modulus=Const(value=5))))),
"a": Const(5),
"... | NT | null | COUNT | sympy | LIN_FORM | [
"LIN_FORM",
"L3C"
] | ecf77f | nt_count_intersection_v1 | null | 5 | 0 | [
"L3C",
"LIN_FORM"
] | 2 | 0.2 | 2026-02-08T12:41:59.099637Z | {
"verified": true,
"answer": 333,
"timestamp": "2026-02-08T12:41:59.300020Z"
} | 3ab973 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 204,
"completion_tokens": 1720
},
"timestamp": "2026-02-15T04:09:55.111Z",
"answer": 333
},
{
... | 1 | [
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "L3C",
"status": "ok"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma... | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
79798c | diophantine_product_count_v1_48377204_1197 | Let $n = 84637$. Let $j$ be a positive integer satisfying $1 \le j \le 60$ and $j^4 \le 12960000$. Let $k$ be the number of such integers $j$. Let $\text{upper} = 51$. Let $S$ be the set of all positive integers $x$ such that $1 \le x \le \text{upper}$, $x$ divides $k$, and $\frac{k}{x} \le \text{upper}$. Let $\text{re... | 1,669 | graphs = [
Graph(
let={
"_n": Const(84637),
"k": CountOverSet(set=SolutionsSet(var=Var("j"), condition=And(Geq(Var("j"), Const(1)), Leq(Var("j"), Const(60)), Leq(Pow(Var("j"), Const(4)), Const(12960000))), domain='positive_integers')),
"upper": Const(51),
"res... | NT | null | COUNT | sympy | C3 | [
"C3"
] | 8a214c | diophantine_product_count_v1 | null | 5 | 0 | [
"C3"
] | 1 | 0.009 | 2026-02-08T15:56:01.292759Z | {
"verified": true,
"answer": 1669,
"timestamp": "2026-02-08T15:56:01.302140Z"
} | 004663 | 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": 1203
},
"timestamp": "2026-02-16T18:20:15.976Z",
"answer": 1669
},
{... | 1 | [
{
"lemma": "C3",
"status": "ok"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"stat... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
c551c3 | comb_sum_binomial_row_v1_971394319_1604 | Let $c = \sum_{k=0}^{0} (-1)^k \binom{0}{k}$, $u = 5$, and $n_1 = u + c$. Let $e = \sum_{k=0}^{n_1} (-1)^k \binom{n_1}{k}$ and $n = 13 + e$. Define $\text{result} = 2^n$ and let $Q$ be the remainder when $19669 \cdot \text{result}$ is divided by $94440$. Find the value of $Q$. | 13,808 | graphs = [
Graph(
let={
"n2": Const(0),
"c": Summation(var="k", start=Const(0), end=Ref("n2"), expr=Mul(Pow(Const(-1), Var("k")), Binom(n=Ref("n2"), k=Var("k")))),
"u": Const(5),
"n1": Sum(Ref("u"), Ref("c")),
"e": Summation(var="k", start=Const(0)... | COMB | null | SUM | sympy | BINOMIAL_ALTERNATING | [
"BINOMIAL_ALTERNATING"
] | c21569 | comb_sum_binomial_row_v1 | null | 4 | 2 | [
"BINOMIAL_ALTERNATING"
] | 1 | 0.002 | 2026-02-08T13:46:49.964541Z | {
"verified": true,
"answer": 13808,
"timestamp": "2026-02-08T13:46:49.966605Z"
} | 4cc716 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 236,
"completion_tokens": 2297
},
"timestamp": "2026-02-24T19:10:23.345Z",
"answer": 13808
},
{
"... | 1 | [
{
"lemma": "BINOMIAL_ALTERNATING",
"status": "ok"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
... | {
"lo": -2.37,
"mid": 1.22,
"hi": 4.84
} | ||
13a17a | nt_count_digit_sum_v1_784195855_1696 | Let $T$ be the set of all integers $t$ such that $17 \leq t \leq 10023$ and there exist positive integers $a \leq 1437$, $b \leq 943$ satisfying $t = 5a + 3b + 9$. Let $m$ be the number of elements in $T$. Let $S$ be the set of all positive integers $n \leq m$ such that the sum of the decimal digits of $n$ is $13$. Com... | 47,712 | graphs = [
Graph(
let={
"upper": CountOverSet(set=SolutionsSet(var=Var("t"), condition=Exists(var=Var(name='a'), condition=Exists(var=Var(name='b'), condition=And(Geq(left=Var(name='a'), right=Const(value=1)), Leq(left=Var(name='a'), right=Const(value=1437)), Geq(left=Var(name='b'), right=Const(... | NT | null | COUNT | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | nt_count_digit_sum_v1 | null | 6 | 0 | [
"LIN_FORM"
] | 1 | 0.362 | 2026-02-08T05:13:52.502898Z | {
"verified": true,
"answer": 47712,
"timestamp": "2026-02-08T05:13:52.864649Z"
} | cde52f | 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": 5189
},
"timestamp": "2026-02-12T06:10:03.294Z",
"answer": 47712
},
... | 1 | [
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "LTE_SUM",
"status": ... | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
acd7e9 | geo_count_lattice_rect_v1_153355830_1445 | Compute the number of lattice points $(x, y)$ such that $0 \leq x \leq 128$ and $0 \leq y \leq 97$. | 12,642 | graphs = [
Graph(
let={
"a": Const(128),
"b": Const(97),
"result": LatticePointsRect(a=Ref(name='a'), b=Ref(name='b')),
},
goal=Ref("result"),
)
] | GEOM | null | COUNT | sympy | [] | geo_count_lattice_rect_v1 | null | 4 | 0 | null | null | 0.003 | 2026-02-08T06:24:33.988401Z | {
"verified": true,
"answer": 12642,
"timestamp": "2026-02-08T06:24:33.991730Z"
} | f486ab | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 148,
"completion_tokens": 120
},
"timestamp": "2026-02-24T06:12:52.019Z",
"answer": 12642
},
{
"i... | 1 | [] | {
"lo": -7.18,
"mid": -5,
"hi": -3.01
} | ||||
ec26a1 | nt_count_divisible_v1_1820931509_865 | Let $n = 22500$ and $u = 54756$. Define $R$ as the number of even positive integers $n'$ such that $1 \leq n' \leq u$. Let $C$ be the minimum value of $x + y$ over all ordered pairs $(x, y)$ of positive integers satisfying $xy = n$. Compute the remainder when $C - R$ is divided by $70313$. | 43,235 | graphs = [
Graph(
let={
"_n": Const(22500),
"upper": Const(54756),
"divisor": Const(2),
"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")), Co... | NT | null | COUNT | sympy | B3 | [
"B3"
] | fc629c | nt_count_divisible_v1 | negation_mod | 5 | 0 | [
"B3"
] | 1 | 3.717 | 2026-02-08T11:57:23.382561Z | {
"verified": true,
"answer": 43235,
"timestamp": "2026-02-08T11:57:27.099692Z"
} | 0e3790 | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 156,
"completion_tokens": 560
},
"timestamp": "2026-02-16T03:28:05.881Z",
"answer": 42935
},
{
"id": 11... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "V1",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
}
] | {
"lo": -6.96,
"mid": -4.56,
"hi": -1.46
} | ||
df548c | algebra_quadratic_discriminant_v1_458359167_200 | Let $d$ be a positive integer such that $d \geq 2$ and $d$ divides $13013$. Let $m$ be the smallest such $d$.
Let $n$ be a positive integer such that $1 \leq n \leq m$, and let $C$ be the number of such $n$ for which the sum of the decimal digits of $n$ is odd.
Compute the value of $(-2)^2 - 1 \cdot (-15) \cdot C$. | 64 | graphs = [
Graph(
let={
"_n": Const(2),
"a": Const(1),
"b": Const(-2),
"c": Const(-15),
"result": Sub(Pow(Ref("b"), Ref("_n")), Mul(CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), MinOverSet(set=Solu... | NT | null | COMPUTE | sympy | B3 | [
"MIN_PRIME_FACTOR/L3B"
] | 27deec | algebra_quadratic_discriminant_v1 | null | 5 | 0 | [
"B3",
"L3B",
"MIN_PRIME_FACTOR"
] | 3 | 0.022 | 2026-02-08T03:04:04.995836Z | {
"verified": true,
"answer": 64,
"timestamp": "2026-02-08T03:04:05.017756Z"
} | 0ee335 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 221,
"completion_tokens": 863
},
"timestamp": "2026-02-10T12:32:32.483Z",
"answer": 64
},
{
"id":... | 1 | [
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "L3B",
"status": "ok_later"
},
{
"lemma": "MIN_PRIME_FACTOR",
"status": "ok"
},
{
"lemma": "MOD_ADD",
"status": "no"
}... | {
"lo": -7.01,
"mid": -4.68,
"hi": -2.15
} | ||
786aa3 | diophantine_fbi2_count_v1_48377204_1681 | Let $k = 360$ and $n = 199$. Consider the set of all ordered pairs $(x,y)$ of positive integers such that $xy = 10000$. Let $S$ be the set of all values of $x + y$ as $(x,y)$ ranges over these pairs. Let $m$ be the minimum value in $S$. Let $T$ be the set of all prime integers $p$ such that $2 \leq p \leq m$. Let $M$ b... | 56,826 | graphs = [
Graph(
let={
"_n": Const(199),
"k": Const(360),
"result": CountOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Const(4)), Leq(Var("d"), MaxOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(2)), Leq(Var("n"), MinOverSet(... | NT | null | COUNT | sympy | B3 | [
"B3/MAX_PRIME_BELOW"
] | f253c0 | diophantine_fbi2_count_v1 | null | 7 | 0 | [
"B3",
"MAX_PRIME_BELOW"
] | 2 | 0.022 | 2026-02-08T16:18:18.648783Z | {
"verified": true,
"answer": 56826,
"timestamp": "2026-02-08T16:18:18.670578Z"
} | 65d178 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 255,
"completion_tokens": 1470
},
"timestamp": "2026-02-17T00:56:24.587Z",
"answer": 56826
},
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok_later"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "V3",
"status": "no"... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
5497c5 | nt_count_coprime_v1_1520064083_2438 | Let $c$ be the minimum value of $x + y$ over all pairs of positive integers $(x, y)$ such that $xy = 100$. Let $m$ be the number of ordered pairs $(i, j)$ with $1 \le i \le 27$ and $1 \le j \le 37$. Let $n$ be the number of positive integers at most $m$ that are relatively prime to $c$. Let $k$ be the minimum value of ... | 23,233 | graphs = [
Graph(
let={
"_d": Const(100),
"_c": MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(Mul(Var("x"), Var("y")), Ref("_d")))), expr=Sum(Var("x"), Var("y")))),
... | NT | null | COUNT | sympy | B3 | [
"B3/COUNT_CARTESIAN/C4/B3"
] | a0f8f8 | nt_count_coprime_v1 | null | 7 | 0 | [
"B3",
"C4",
"COUNT_CARTESIAN"
] | 3 | 4.45 | 2026-02-08T04:44:17.493040Z | {
"verified": true,
"answer": 23233,
"timestamp": "2026-02-08T04:44:21.943180Z"
} | 71a3ec | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 254,
"completion_tokens": 1441
},
"timestamp": "2026-02-11T21:50:34.436Z",
"answer": 23233
},
{
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "C4",
"status": "ok_later"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "ok_later"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K14",
"status": "no... | {
"lo": -3.42,
"mid": 1.86,
"hi": 7.55
} | ||
3f2da3 | nt_count_digit_sum_v1_1470522791_1271 | Let $T$ be the set of all integers $t$ such that $14 \leq t \leq 20018$ and there exist positive integers $a$, $b$ with $1 \leq a \leq 1801$, $1 \leq b \leq 502$, satisfying $t = 10a + 4b$. Define $\text{upper}$ to be the number of elements in $T$.
Let $S$ be the set of all positive integers $n$ such that $1 \leq n \l... | 660 | graphs = [
Graph(
let={
"upper": CountOverSet(set=SolutionsSet(var=Var("t"), condition=Exists(var=Var(name='a'), condition=Exists(var=Var(name='b'), condition=And(Geq(left=Var(name='a'), right=Const(value=1)), Leq(left=Var(name='a'), right=Const(value=1801)), Geq(left=Var(name='b'), right=Const(... | NT | null | COUNT | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | nt_count_digit_sum_v1 | null | 4 | 0 | [
"LIN_FORM"
] | 1 | 0.493 | 2026-02-08T13:32:54.696915Z | {
"verified": true,
"answer": 660,
"timestamp": "2026-02-08T13:32:55.190125Z"
} | 0e5ad8 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 187,
"completion_tokens": 6177
},
"timestamp": "2026-02-15T17:09:10.231Z",
"answer": 660
},
{
... | 1 | [
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no... | {
"lo": -5.49,
"mid": 0.22,
"hi": 6.51
} | ||
9c9a16 | antilemma_k3_v1_1520064083_4477 | Let $n = 14830$. Define $x$ to be the sum of $\phi(d)$ over all positive divisors $d$ of $n$, where $\phi$ denotes Euler's totient function. Let $c = 10609$. Compute the remainder when $c \cdot x$ is divided by $58039$. | 45,780 | graphs = [
Graph(
let={
"_n": Const(14830),
"x": SumOverDivisors(n=Ref(name='_n'), var='d', expr=EulerPhi(n=Var(name='d'))),
"_c": Const(10609),
"Q": Mod(value=Mul(Ref("_c"), Ref("x")), modulus=Const(58039)),
},
goal=Ref("Q"),
)
] | NT | COMB | COMPUTE | sympy | K3 | [
"K3"
] | 54c41e | antilemma_k3_v1 | null | 4 | 0 | [
"K3"
] | 1 | 0 | 2026-02-08T06:17:44.515796Z | {
"verified": true,
"answer": 45780,
"timestamp": "2026-02-08T06:17:44.516248Z"
} | f83c11 | 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": 1414
},
"timestamp": "2026-02-12T22:13:43.143Z",
"answer": 45780
},
... | 1 | [
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K3",
"status": "ok"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "V1",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
}
] | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
09f151 | geo_count_lattice_rect_v1_601307018_2863 | Let $b = \sum_{k=0}^{\sum_{d=1}^{3} \varphi(d) \cdot \lfloor \frac{3}{d} \rfloor} 2^k$. Find the number of lattice points $(x,y)$ with $0 \le x \le 49$ and $0 \le y \le b$. | 6,400 | graphs = [
Graph(
let={
"_n": Const(2),
"a": Const(49),
"b": Summation(var="k", start=Sub(Const(81), Const(81)), end=Summation(var="k1", start=Const(1), end=Const(3), expr=Mul(EulerPhi(n=Var("k1")), Floor(Div(Const(3), Var("k1"))))), expr=Pow(Ref("_n"), Var("k"))),
... | GEOM | GEOM | COUNT | sympy | K2 | [
"K2/SUM_GEOM",
"IDENTITY_SUB_SELF"
] | 6c10f9 | geo_count_lattice_rect_v1 | null | 4 | 0 | [
"IDENTITY_SUB_SELF",
"K2",
"SUM_GEOM"
] | 3 | 0.002 | 2026-03-10T03:28:58.092027Z | {
"verified": true,
"answer": 6400,
"timestamp": "2026-03-10T03:28:58.094380Z"
} | 1449bb | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 188,
"completion_tokens": 946
},
"timestamp": "2026-03-29T06:43:38.533Z",
"answer": 6400
},
{
"id... | 2 | [
{
"lemma": "IDENTITY_SUB_SELF",
"status": "ok"
},
{
"lemma": "K2",
"status": "ok"
},
{
"lemma": "SUM_GEOM",
"status": "ok_later"
}
] | {
"lo": -10,
"mid": -6.41,
"hi": -2.82
} | ||
ea350a | diophantine_fbi2_min_v1_349078426_1106 | Let $k = 60$ and let $\text{upper} = 70$. Consider the set of all integers $d$ such that $d \geq 2$, $d \leq 70$, $d$ divides $60$, and $\frac{60}{d} \geq \min\left\{ d' \mid d' \geq 2 \text{ and } d' \text{ divides } 385 \right\}$. Compute the minimum value of $d$ in this set. | 2 | graphs = [
Graph(
let={
"k": Const(60),
"upper": Const(70),
"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=So... | NT | null | EXTREMUM | sympy | B3 | [
"MIN_PRIME_FACTOR"
] | bc3776 | diophantine_fbi2_min_v1 | null | 5 | 0 | [
"B3",
"MIN_PRIME_FACTOR"
] | 2 | 0.019 | 2026-02-08T13:24:43.253015Z | {
"verified": true,
"answer": 2,
"timestamp": "2026-02-08T13:24:43.271987Z"
} | 88a568 | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 170,
"completion_tokens": 672
},
"timestamp": "2026-02-16T04:36:42.164Z",
"answer": 2
},
{
"id": 11,
"... | 2 | [
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"le... | {
"lo": -10,
"mid": -7.27,
"hi": -4.54
} | ||
f9202b | diophantine_sum_product_min_v1_397696148_674 | Let $n = 10$ and $S = 11$. Let $P$ be the sum $\sum_{k=1}^{4} k$. Consider the set of all integers $x$ such that $1 \leq x \leq n$ and $x(S - x) = P$. Compute the minimum value of $x$ in this set. | 1 | graphs = [
Graph(
let={
"_n": Const(10),
"S": Const(11),
"P": Summation(var="k", start=Const(1), end=Const(4), expr=Var("k")),
"result": MinOverSet(set=SolutionsSet(var=Var("x"), condition=And(Geq(Var("x"), Const(1)), Leq(Var("x"), Ref("_n")), Eq(Mul(Var("x"),... | NT | null | EXTREMUM | sympy | B3 | [
"SUM_ARITHMETIC"
] | eb34f0 | diophantine_sum_product_min_v1 | null | 3 | 0 | [
"B3",
"SUM_ARITHMETIC"
] | 2 | 0.244 | 2026-02-08T11:40:45.301043Z | {
"verified": true,
"answer": 1,
"timestamp": "2026-02-08T11:40:45.544772Z"
} | 90a6f3 | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 133,
"completion_tokens": 621
},
"timestamp": "2026-02-16T03:09:48.777Z",
"answer": 1
},
{
"id": 11,
"... | 2 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "SUM_ARITHMETIC",
"status": "ok"
}
] | {
"lo": -10,
"mid": -7.71,
"hi": -5.43
} | ||
ff0014 | comb_count_derangements_v1_458359167_556 | Let $n$ be the number of integers $t$ with $10 \leq t \leq 28$ that can be written in the form $4a + 6b$ for positive integers $a \leq 4$ and $b \leq 2$. Compute the subfactorial of $n$, denoted $!n$, which is the number of derangements of $n$ elements. | 14,833 | 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_derangements_v1 | null | 5 | 0 | [
"LIN_FORM"
] | 1 | 0.001 | 2026-02-08T03:24:54.212855Z | {
"verified": true,
"answer": 14833,
"timestamp": "2026-02-08T03:24:54.213670Z"
} | e9ce24 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 198,
"completion_tokens": 1272
},
"timestamp": "2026-02-10T14:20:00.062Z",
"answer": 14833
},
{
"... | 1 | [
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8",
"st... | {
"lo": -5.97,
"mid": -3.96,
"hi": -1.93
} | ||
97a084 | comb_catalan_compute_v1_1918700295_3543 | Let $T$ be the set of all integers $t$ such that $10 \le t \le 34$ and $t = 6a + 4b$ for some positive integers $a$, $b$ with $1 \le a \le 3$ and $1 \le b \le 4$. Let $n$ be the number of elements in $T$. Let $C_n$ denote the $n$th Catalan number. Compute the remainder when $42776 \cdot C_n$ is divided by $78079$. | 17,662 | graphs = [
Graph(
let={
"_n": Const(78079),
"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_catalan_compute_v1 | null | 4 | 0 | [
"LIN_FORM"
] | 1 | 0.002 | 2026-02-08T08:41:59.665510Z | {
"verified": true,
"answer": 17662,
"timestamp": "2026-02-08T08:41:59.667355Z"
} | 32bf20 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 227,
"completion_tokens": 2343
},
"timestamp": "2026-02-24T09:55:42.720Z",
"answer": 17662
},
{
"... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "V8",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
... | {
"lo": -2.35,
"mid": 1.22,
"hi": 4.84
} | ||
14c9cd | diophantine_sum_product_min_v1_153355830_32 | Let $S$ be the largest integer $k$ such that $11^k$ divides $1254!$. Let $P = 3115$. Determine the value of $x$, where $x$ is the smallest positive integer between $1$ and $123$ inclusive such that $x(S - x) = P$. Find the remainder when $81929x$ is divided by $84777$. | 69,874 | graphs = [
Graph(
let={
"_n": Const(1254),
"S": MaxKDivides(target=Factorial(Ref("_n")), base=Const(11)),
"P": Const(3115),
"result": MinOverSet(set=SolutionsSet(var=Var("x"), condition=And(Geq(Var("x"), Const(1)), Leq(Var("x"), Const(123)), Eq(Mul(Var("x"), S... | NT | null | EXTREMUM | sympy | V1 | [
"V1"
] | dae96f | diophantine_sum_product_min_v1 | null | 7 | 0 | [
"V1"
] | 1 | 0.007 | 2026-02-08T02:51:18.486193Z | {
"verified": true,
"answer": 69874,
"timestamp": "2026-02-08T02:51:18.493440Z"
} | ab1bd9 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 198,
"completion_tokens": 1010
},
"timestamp": "2026-02-08T22:09:20.710Z",
"answer": 69874
},
{
... | 1 | [
{
"lemma": "K5",
"status": "same_pattern_wrong"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "V1",
"status": "ok"
},
{
"lemma": "V3",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V... | {
"lo": -6.49,
"mid": 0.51,
"hi": 7.52
} | ||
72ef05 | modular_count_residue_v1_238844314_996 | Let $m$ be the number of integers $t$ such that $7 \leq t \leq 27$ and there exist integers $a$ and $b$ with $1 \leq a \leq 5$, $1 \leq b \leq 3$, and $t = 3a + 4b$. Let $r = 12$. Determine the value of the number of positive integers $n$ such that $1 \leq n \leq 88804$ and $n \equiv r \pmod{m}$. | 5,920 | graphs = [
Graph(
let={
"upper": Const(88804),
"m": CountOverSet(set=SolutionsSet(var=Var("t"), condition=Exists(var=Var(name='a'), condition=Exists(var=Var(name='b'), condition=And(Geq(left=Var(name='a'), right=Const(value=1)), Leq(left=Var(name='a'), right=Const(value=5)), Geq(left... | NT | null | COUNT | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | modular_count_residue_v1 | null | 3 | 0 | [
"LIN_FORM"
] | 1 | 3.384 | 2026-02-08T13:50:47.187596Z | {
"verified": true,
"answer": 5920,
"timestamp": "2026-02-08T13:50:50.572006Z"
} | e34870 | 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": 1389
},
"timestamp": "2026-02-15T21:20:08.489Z",
"answer": 5920
},
{... | 1 | [
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "LTE_DIFF",
"status": "no"
}
] | {
"lo": -5.49,
"mid": 0.22,
"hi": 6.51
} | ||
f3d4bb | nt_count_divisible_and_v1_1520064083_2681 | Let $S$ be the set of positive integers $n \leq 35568$ such that $n$ is divisible by 12 and
$$
n \equiv \sum_{k=0}^{t} (-1)^k \binom{6}{k} \pmod{9},
$$
where $t$ is the number of integers in the interval $[15, 22]$ that can be expressed as $3a + 2b + 10$ for some integers $a, b$ with $1 \leq a \leq 2$ and $1 \leq b \... | 988 | graphs = [
Graph(
let={
"upper": Const(35568),
"d1": Const(9),
"d2": Const(12),
"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("d1")), Summation(var="... | COMB | null | COUNT | sympy | LIN_FORM | [
"LIN_FORM/BINOMIAL_ALTERNATING"
] | bebeab | nt_count_divisible_and_v1 | null | 5 | 0 | [
"BINOMIAL_ALTERNATING",
"LIN_FORM"
] | 2 | 1.375 | 2026-02-08T04:55:06.259334Z | {
"verified": true,
"answer": 988,
"timestamp": "2026-02-08T04:55:07.634398Z"
} | 3feb25 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 255,
"completion_tokens": 2534
},
"timestamp": "2026-02-24T02:29:14.360Z",
"answer": 988
},
{
"id... | 1 | [
{
"lemma": "BINOMIAL_ALTERNATING",
"status": "ok_later"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"... | {
"lo": -5.97,
"mid": -3.96,
"hi": -1.93
} | ||
8bfee3 | nt_min_phi_inverse_v1_151522320_2565 | Let $x$ and $y$ be positive integers such that $x + y = 20$. Define $M$ to be the maximum value of $xy$ over all such pairs. Let $k = 24$. Consider the set of all positive integers $n$ such that $1 \leq n \leq M$ and $\phi(n) = k$, where $\phi$ denotes Euler's totient function. Compute the smallest element of this set. | 35 | graphs = [
Graph(
let={
"upper": MaxOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(Sum(Var("x"), Var("y")), Const(20)))), expr=Mul(Var("x"), Var("y")))),
"k": Const(24),
... | NT | null | EXTREMUM | sympy | B1 | [
"B1"
] | 5b950e | nt_min_phi_inverse_v1 | null | 6 | 0 | [
"B1"
] | 1 | 0.01 | 2026-02-08T04:52:55.114887Z | {
"verified": true,
"answer": 35,
"timestamp": "2026-02-08T04:52:55.124454Z"
} | b0e4bb | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 206,
"completion_tokens": 2758
},
"timestamp": "2026-02-11T22:22:15.467Z",
"answer": 35
},
{
"id... | 1 | [
{
"lemma": "B1",
"status": "ok"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
}
] | {
"lo": -5.55,
"mid": -3.01,
"hi": 0.33
} | ||
2d0539 | v1_endings_v1_168721529_1011 | Let $n = 96518$ and $p = 3$. Let $n!$ denote the factorial of $n$. Define $v_p$ to be the largest integer $k$ such that $p^k$ divides $n!$. Let $s$ be the sum of the decimal digits of $v_p$. Compute $v_p + s$. | 48,275 | graphs = [
Graph(
let={
"n_val": Const(96518),
"p_val": Const(3),
"n_fact": Factorial(Ref("n_val")),
"vp": MaxKDivides(target=Ref("n_fact"), base=Ref("p_val")),
"ds": DigitSum(Ref("vp")),
"total": Sum(Ref("vp"), Ref("ds")),
... | NT | null | COMPUTE | sympy | V1 | [
"V1"
] | dae96f | v1_endings_v1 | null | 4 | null | [
"V1"
] | 1 | 0.001 | 2026-02-08T13:24:15.731342Z | {
"verified": true,
"answer": 48275,
"timestamp": "2026-02-08T13:24:15.732651Z"
} | 9090c6 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 189,
"completion_tokens": 802
},
"timestamp": "2026-02-09T12:10:08.960Z",
"answer": 48254
},
{
... | 1 | [
{
"lemma": "K5",
"status": "same_pattern_wrong"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "V1",
"status": "ok"
},
{
"lemma": "V3",
"status": "no"
},
... | {
"lo": -1.99,
"mid": 2.14,
"hi": 6.33
} | ||
dada0f | alg_sum_powers_v1_1218484723_5345 | Let $S$ be the set of ordered pairs $(a, b)$ of integers with $1 \le a \le 25$, $1 \le b \le 25$, and
$$25b^{2} + 10a^{2} - 18ab \le 7786.$$
Compute the remainder when
$$\sum_{k=1}^{|S|} k^{2}$$
is divided by the size of the set
$$T = \left\{ x : 1 \le x \le \left|\left\{ t : \text{there exist integers } a, b \text{ wi... | 4,516 | graphs = [
Graph(
let={
"_c": Const(4),
"_m": Const(15100),
"_n": Const(15104),
"result": Mod(value=Summation(var="k", start=Const(1), end=CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("a"), Var("b")]), condition=And(Geq(Var("a"), Const(1)), Leq(Var("a... | ALG | null | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM/ABS_INEQ",
"QF_PSD_COUNT_LEQ"
] | 3219f5 | alg_sum_powers_v1 | null | 7 | 0 | [
"ABS_INEQ",
"LIN_FORM",
"QF_PSD_COUNT_LEQ"
] | 3 | 0.028 | 2026-02-25T06:57:03.075072Z | {
"verified": true,
"answer": 4516,
"timestamp": "2026-02-25T06:57:03.102947Z"
} | b8ccfd | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 315,
"completion_tokens": 32768
},
"timestamp": "2026-03-29T20:41:45.560Z",
"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": 1.53,
"mid": 4.7,
"hi": 7.23
} |
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