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 |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
e448d0 | nt_count_coprime_v1_655260480_833 | Let $k$ be the minimum value of $x + y$ over all ordered pairs $(x, y)$ of positive integers such that $xy = 25$. Let $r$ be the number of positive integers $n$ with $1 \leq n \leq 20164$ such that $\gcd(n, k) = 1$. Compute $r + 2^{r \bmod 16} \bmod 99051$. | 8,070 | graphs = [
Graph(
let={
"_n": Const(99051),
"upper": Const(20164),
"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(25)))... | NT | null | COUNT | sympy | B3 | [
"B3"
] | 0cd20d | nt_count_coprime_v1 | null | 4 | 0 | [
"B3"
] | 1 | 2.649 | 2026-02-08T15:38:52.601086Z | {
"verified": true,
"answer": 8070,
"timestamp": "2026-02-08T15:38:55.250042Z"
} | 5a0c51 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 139,
"completion_tokens": 917
},
"timestamp": "2026-02-16T10:30:42.986Z",
"answer": 8070
},
{
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "V3",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
44daa2 | comb_count_partitions_v1_397696148_2552 | Let $m = 2$. Let $S$ be the set of all positive integers $n$ such that $1 \leq n \leq \min\left\{ x + y \mid x, y \text{ are positive integers with } xy = 487204 \right\}$, $m$ divides $n$, and $\gcd(n, 21) = 1$. Let $T$ be the set of all ordered pairs $(x, y)$ of positive integers such that $xy = |S|$. Define $n$ to b... | 37,338 | graphs = [
Graph(
let={
"_m": Const(2),
"_n": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(... | NT | COMB | COUNT | sympy | B3 | [
"B3/C5/B3"
] | 9b28a0 | comb_count_partitions_v1 | null | 6 | 0 | [
"B3",
"C5"
] | 2 | 0.003 | 2026-02-08T13:24:49.787475Z | {
"verified": true,
"answer": 37338,
"timestamp": "2026-02-08T13:24:49.790540Z"
} | 599aba | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 190,
"completion_tokens": 1721
},
"timestamp": "2026-02-15T15:22:48.340Z",
"answer": 37338
},
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "C5",
"status": "ok_later"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
... | {
"lo": -5.49,
"mid": 0.22,
"hi": 6.51
} | ||
ae29dc | algebra_poly_eval_v1_50713871_76 | Let $m = 2$. Let $n$ be the number of positive integers $p$ for which there exists a positive integer $q$ such that $p \cdot q = 24$, $\gcd(p, q) = 1$, and $p < q$. Let $z$ be the number of integers $t$ with $7 \leq t \leq 32$ for which there exist integers $a$ and $b$ such that $1 \leq a \leq 11$, $1 \leq b \leq 2$, a... | 5,040 | graphs = [
Graph(
let={
"_m": Const(2),
"_n": CountOverSet(set=SolutionsSet(var=Var("p"), condition=And(IsPositive(arg=Var(name='p')), Exists(var=Var(name='q'), condition=And(Eq(left=Mul(Var(name='p'), Var(name='q')), right=Const(value=24)), Eq(left=GCD(a=Var(name='p'), b=Var(name='q... | NT | null | COMPUTE | sympy | COPRIME_PAIRS | [
"COPRIME_PAIRS/LIN_FORM"
] | a1eac8 | algebra_poly_eval_v1 | null | 6 | 0 | [
"COPRIME_PAIRS",
"LIN_FORM"
] | 2 | 0.002 | 2026-02-08T02:44:23.806684Z | {
"verified": true,
"answer": 5040,
"timestamp": "2026-02-08T02:44:23.809164Z"
} | 217a64 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 289,
"completion_tokens": 1502
},
"timestamp": "2026-02-08T19:47:32.373Z",
"answer": 5040
},
{
"i... | 1 | [
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok_later"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},... | {
"lo": -2.74,
"mid": -0.62,
"hi": 1.6
} | ||
7fe341 | sequence_count_fib_divisible_v1_784195855_7271 | Let $S$ be the set of all ordered pairs $(x, y)$ of positive integers such that $xy = 134689$. Let $u$ be the minimum value of $x + y$ over all such pairs. Let $d = 5$. Determine the number of positive integers $n$ such that $1 \leq n \leq u$ and $d$ divides the $n$th Fibonacci number. Compute this number. | 146 | graphs = [
Graph(
let={
"upper": MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(Mul(Var("x"), Var("y")), Const(134689)))), expr=Sum(Var("x"), Var("y")))),
"d": Const(5... | NT | null | COUNT | sympy | B3 | [
"B3"
] | 0cd20d | sequence_count_fib_divisible_v1 | null | 5 | 0 | [
"B3"
] | 1 | 0.17 | 2026-02-08T09:10:34.705766Z | {
"verified": true,
"answer": 146,
"timestamp": "2026-02-08T09:10:34.875912Z"
} | 5daeac | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 138,
"completion_tokens": 938
},
"timestamp": "2026-02-14T01:21:21.973Z",
"answer": 146
},
{
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "V1",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
}
] | {
"lo": -3.51,
"mid": 1.33,
"hi": 6.56
} | ||
51d4fd | alg_sym_quad_system_v1_1218484723_7606 | Let
\[
T = \left|\{t : \text{there exist integers } a, b \text{ with } 1 \le a \le 1165,\ 1 \le b \le 1933,\ t = 5a + 2b,\ 7 \le t \le 9691\}\right|
\]
be the number of integers $t$ representable in this way. Consider all ordered triples $(a,b,c)$ of positive integers such that
\[
a^{2} + b^{2} + c^{2} = ab + bc + ca \... | 543 | graphs = [
Graph(
let={
"_m": Const(40),
"_n": Const(6),
"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))), Sum... | ALG | null | COMPUTE | sympy | QF_PSD_COUNT_LEQ | [
"QF_PSD_COUNT_LEQ",
"LIN_FORM"
] | 74f7c5 | alg_sym_quad_system_v1 | null | 7 | 0 | [
"LIN_FORM",
"QF_PSD_COUNT_LEQ"
] | 2 | 0.019 | 2026-02-25T09:02:36.478115Z | {
"verified": true,
"answer": 543,
"timestamp": "2026-02-25T09:02:36.497241Z"
} | fefc38 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 411,
"completion_tokens": 17196
},
"timestamp": "2026-03-30T05:29:28.402Z",
"answer": 822
},
{
... | 1 | [
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "QF_PSD_COUNT_LEQ",
"status": "ok"
}
] | {
"lo": 3.81,
"mid": 6.33,
"hi": 9.49
} | ||
d074a5 | diophantine_fbi2_count_v1_1520064083_718 | Let $k = 480$, $a = 5$, and $b = 2$. Compute the number of positive integers $d$ such that $6 \le d \le 185$, $d$ divides $k$, and the quotient $k/d$ is an integer satisfying $3 \le k/d \le 182$. | 17 | graphs = [
Graph(
let={
"k": Const(480),
"a": Const(5),
"b": Const(2),
"upper": Const(180),
"result": CountOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Const(6)), Leq(Var("d"), Const(185)), Divides(divisor=Var("d"), dividend=R... | NT | null | COUNT | sympy | COPRIME_PAIRS | [
"LIN_FORM"
] | 7b2633 | diophantine_fbi2_count_v1 | null | 3 | 0 | [
"COPRIME_PAIRS",
"LIN_FORM"
] | 2 | 0.11 | 2026-02-08T03:34:13.793277Z | {
"verified": true,
"answer": 17,
"timestamp": "2026-02-08T03:34:13.903606Z"
} | 5d8183 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 180,
"completion_tokens": 1665
},
"timestamp": "2026-02-10T14:58:42.285Z",
"answer": 17
},
{
"id"... | 1 | [
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "V1",
"status": "no"
},
{
"lemma": "V3",
"status": "no"
},
{
"lemma": "VAL_SUM_EQ",
"status": "no"
}
] | {
"lo": -3.46,
"mid": 1.03,
"hi": 5.49
} | ||
2ca7f8_l | comb_sum_binomial_mod_v1_124444284_391 | Let $n = 315$. Let $S$ be the set of all ordered pairs $(x_1, x_2)$ of positive odd integers such that $x_1 + x_2 = 626$. Let $m$ be the number of elements in $S$. Compute the remainder when
$$
\sum_{k=18}^{m} \binom{315}{k}
$$
is divided by $10331$. | 0 | ALG | COMB | COMPUTE | sympy | COMB1 | [
"COMB1"
] | 567f58 | comb_sum_binomial_mod_v1 | null | 5 | 0 | [
"COMB1"
] | 1 | 0.039 | 2026-02-08T03:14:43.373758Z | {
"verified": false,
"answer": 4600,
"timestamp": "2026-02-08T03:14:43.413189Z"
} | 387db5 | 2ca7f8 | legacy_text | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 201,
"completion_tokens": 32768
},
"timestamp": "2026-02-23T21:56:08.865Z",
"answer": null
},
{
... | 1 | [
{
"lemma": "COMB1",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
}
] | {
"lo": 3.43,
"mid": 5.73,
"hi": 8.84
} | |
336a7d_l | nt_num_divisors_compute_v1_784195855_61 | Let $n = 33856$. Define $d$ to be the number of positive divisors of $n$. Let $s$ be the sum
$$
\sum_{i = a}^{b} \left( \text{digit}_i(d) \cdot (i+1)^2 \right),
$$
where $a = \sum_{k=0}^{7} (-1)^k \binom{7}{k}$, $b = \text{number of digits of } d - 1$, and $\text{digit}_i(d)$ denotes the $i$-th decimal digit of $d$ (... | 2,033 | COMB | NT | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM",
"BINOMIAL_ALTERNATING"
] | 7d9d78 | nt_num_divisors_compute_v1 | digits_weighted_mod | 5 | 0 | [
"BINOMIAL_ALTERNATING",
"LIN_FORM"
] | 2 | 0.003 | 2026-02-08T02:56:34.308898Z | {
"verified": false,
"answer": 2032,
"timestamp": "2026-02-08T02:56:34.311640Z"
} | aad38b | 336a7d | legacy_text | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 335,
"completion_tokens": 32768
},
"timestamp": "2026-02-23T19:47:03.327Z",
"answer": null
},
{
... | 1 | [
{
"lemma": "BINOMIAL_ALTERNATING",
"status": "ok"
},
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "V7",
"s... | {
"lo": 3.04,
"mid": 4.76,
"hi": 6.54
} | |
01f949 | diophantine_fbi2_count_v1_677425708_408 | Let $k = 480$. Consider the set of all positive integers $d$ such that $5 \leq d \leq 68$, $d$ divides $k$, and $6 \leq \frac{k}{d} \leq 69$. Let $r$ be the number of elements in this set. Let $g = \gcd(17, 19)$, and define $s = \sum_{d \mid g} \mu(d)$, where $\mu$ denotes the M\"obius function. Compute $$\sum_{n = s}^... | 35 | graphs = [
Graph(
let={
"k": Const(480),
"a": Const(4),
"b": Const(5),
"upper": Const(64),
"result": CountOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Const(5)), Leq(Var("d"), Const(68)), Divides(divisor=Var("d"), dividend=Ref... | NT | null | COUNT | sympy | MOBIUS_COPRIME | [
"MOBIUS_COPRIME"
] | ac54ac | diophantine_fbi2_count_v1 | null | 5 | 0 | [
"MOBIUS_COPRIME"
] | 1 | 0.007 | 2026-02-08T03:31:39.036797Z | {
"verified": true,
"answer": 35,
"timestamp": "2026-02-08T03:31:39.043680Z"
} | cc247c | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 265,
"completion_tokens": 2135
},
"timestamp": "2026-02-08T20:33:54.932Z",
"answer": 35
},
{
"id"... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "MOBIUS_COPRIME",
"status": "ok"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "V1",
"status": "no"
}
] | {
"lo": -6.51,
"mid": -0.31,
"hi": 5.43
} | ||
fb7e40 | antilemma_k3_v1_809748730_1570 | Let $n = 59553$. Define $x$ to be the sum of $\phi(d)$ over all positive divisors $d$ of $n$, where $\phi$ denotes Euler's totient function. Compute $x$. | 59,553 | graphs = [
Graph(
let={
"_n": Const(59553),
"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 | 2 | 0 | [
"K3"
] | 1 | 0 | 2026-02-08T12:33:09.009054Z | {
"verified": true,
"answer": 59553,
"timestamp": "2026-02-08T12:33:09.009404Z"
} | 2d902b | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 1,
"correct": {
"strict": false,
"boxed": false,
"relaxed": true
},
"usage": {
"prompt_tokens": 109,
"completion_tokens": 1882
},
"timestamp": "2026-02-16T03:59:02.715Z",
"answer": null
},
{
"id": 11,... | 1 | [
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "K3",
"status": "ok"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "V8_SUM",
"status"... | {
"lo": -6.96,
"mid": -4.56,
"hi": -1.46
} | ||
44bcfb | geo_count_lattice_rect_v1_1742523217_2851 | Compute the number of lattice points in the rectangle $[0, 128] \times [0, 89]$, including the boundary. | 11,610 | graphs = [
Graph(
let={
"a": Const(128),
"b": Const(89),
"result": LatticePointsRect(a=Ref(name='a'), b=Ref(name='b')),
},
goal=Ref("result"),
)
] | GEOM | null | COUNT | sympy | [] | geo_count_lattice_rect_v1 | null | 2 | 0 | null | null | 0.001 | 2026-02-08T05:24:46.406361Z | {
"verified": true,
"answer": 11610,
"timestamp": "2026-02-08T05:24:46.407181Z"
} | c968f6 | 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": 276
},
"timestamp": "2026-02-24T03:32:27.824Z",
"answer": 11610
},
{
"i... | 1 | [] | {
"lo": -9.23,
"mid": -6.18,
"hi": -4.06
} | ||||
32b5b5 | comb_binomial_compute_v1_784195855_7299 | Let $ n $ be the number of integers $ t $ such that $ 6 \leq t \leq 20 $ and $ t = 2a + 3b + 1 $ for some integers $ a $ and $ b $ with $ 1 \leq a \leq 5 $ and $ 1 \leq b \leq 3 $. Let $ k $ be the largest prime number such that $ 2 \leq k \leq 6 $. Compute the remainder when $ 75903 \cdot \binom{n}{k} $ is divided by ... | 23,249 | graphs = [
Graph(
let={
"_n": Const(52564),
"n": CountOverSet(set=SolutionsSet(var=Var("t"), condition=Exists(var=Var(name='a'), condition=Exists(var=Var(name='b'), condition=And(Geq(left=Var(name='a'), right=Const(value=1)), Leq(left=Var(name='a'), right=Const(value=5)), Geq(left=Va... | NT | null | COMPUTE | sympy | LTE_DIFF | [
"MAX_PRIME_BELOW",
"LIN_FORM"
] | d530e2 | comb_binomial_compute_v1 | null | 4 | 0 | [
"LIN_FORM",
"LTE_DIFF",
"MAX_PRIME_BELOW"
] | 3 | 0.01 | 2026-02-08T09:11:45.822813Z | {
"verified": true,
"answer": 23249,
"timestamp": "2026-02-08T09:11:45.832931Z"
} | df40c9 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 168,
"completion_tokens": 2062
},
"timestamp": "2026-02-14T01:23:10.761Z",
"answer": 23249
},
... | 1 | [
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"s... | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
ba545b | modular_modexp_compute_v1_1520064083_6657 | Let $m = 18$. Let $P$ be the set of all prime numbers $n$ such that $2 \leq n \leq m$. Let $a$ be the largest prime number $n$ such that $2 \leq n \leq \max(P)$ and $n$ is prime.
Let $S$ be the set of all ordered pairs $(x, y)$ of positive integers such that $x \cdot y = 1234321$. Let $e$ be the minimum value of $x + ... | 12,321 | graphs = [
Graph(
let={
"_m": Const(18),
"_n": Const(2),
"a": MaxOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Ref("_n")), Leq(Var("n"), MaxOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(2)), Leq(Var("n"), Ref("_m")), IsPrime... | NT | null | COMPUTE | sympy | MAX_PRIME_BELOW | [
"MAX_PRIME_BELOW/MAX_PRIME_BELOW",
"B3"
] | ca513e | modular_modexp_compute_v1 | null | 6 | 0 | [
"B3",
"MAX_PRIME_BELOW"
] | 2 | 0.002 | 2026-02-08T08:15:30.374915Z | {
"verified": true,
"answer": 12321,
"timestamp": "2026-02-08T08:15:30.377400Z"
} | a2d7b1 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 194,
"completion_tokens": 2984
},
"timestamp": "2026-02-13T16:51:05.306Z",
"answer": 12321
},
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok"
},
{
"lemma": "V1",
"status": "no"
},
{
... | {
"lo": -3.51,
"mid": 1.33,
"hi": 6.56
} | ||
ecfc65 | lin_form_endings_v1_397696148_2723 | Let $a = 105$ and $b = 45$. Compute $\left\lfloor \frac{45}{\gcd(a,b)} \right\rfloor$, multiply the result by $10440$, and then take the remainder when divided by $55895$. Find the value of this remainder. | 31,320 | graphs = [
Graph(
let={
"a_coeff": Const(105),
"b_coeff": Const(45),
"_inner_result": Floor(Div(Const(45), GCD(a=Ref("a_coeff"), b=Ref("b_coeff")))),
"_scale_k": Const(10440),
"_scaled": Mul(Ref("_scale_k"), Ref("_inner_result")),
"_mod... | COMB | NT | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | lin_form_endings_v1 | null | 2 | null | [
"LIN_FORM"
] | 1 | 0.001 | 2026-02-08T13:32:20.443021Z | {
"verified": true,
"answer": 31320,
"timestamp": "2026-02-08T13:32:20.443589Z"
} | 63f1a9 | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 131,
"completion_tokens": 330
},
"timestamp": "2026-02-16T04:48:50.475Z",
"answer": 31320
},
{
"id": 11,
... | 2 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
}
] | {
"lo": -10,
"mid": -7.27,
"hi": -4.54
} | ||
6d6d27 | nt_num_divisors_compute_v1_1520064083_8460 | Let $S$ be the set of all positive integers $p$ such that there exists a positive integer $q$ with $p < q$, $pq = 72$, and $\gcd(p, q) = 1$. Let $n$ be the smallest divisor of $19343$ that is at least $|S|$. Compute the number of positive divisors of $n$. | 2 | graphs = [
Graph(
let={
"_n": Const(19343),
"n": MinOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), CountOverSet(set=SolutionsSet(var=Var("p"), condition=And(IsPositive(arg=Var(name='p')), Exists(var=Var(name='q'), condition=And(Eq(left=Mul(Var(name='p'), Var(name=... | NT | null | COMPUTE | sympy | V1 | [
"COPRIME_PAIRS/MIN_PRIME_FACTOR"
] | 52cee2 | nt_num_divisors_compute_v1 | null | 5 | 0 | [
"COPRIME_PAIRS",
"MIN_PRIME_FACTOR",
"V1"
] | 3 | 0.012 | 2026-02-08T10:11:34.705730Z | {
"verified": true,
"answer": 2,
"timestamp": "2026-02-08T10:11:34.717569Z"
} | 2b4fc8 | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 143,
"completion_tokens": 805
},
"timestamp": "2026-02-15T20:51:16.980Z",
"answer": 2
},
{
"id": 11,
"... | 2 | [
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MIN_PRIME_FACTOR",
"status": "ok_later"
},
{
"lemma": "MOD_FACTORIAL",
... | {
"lo": -9.12,
"mid": -6.02,
"hi": -3.62
} | ||
de6ab2 | nt_num_divisors_compute_v1_1080341949_464 | Let $n = 10$. Define $r$ to be the number of positive divisors of $n$. Compute $r + \phi(|r| + 1) + \tau(|r| + 1)$, where $\phi$ denotes Euler's totient function and $\tau(m)$ denotes the number of positive divisors of $m$. | 10 | graphs = [
Graph(
let={
"n": Const(10),
"result": NumDivisors(n=Ref("n")),
"Q": Sum(Ref("result"), EulerPhi(n=Sum(Abs(arg=Ref(name='result')), Const(1))), NumDivisors(n=Sum(Abs(arg=Ref(name='result')), Const(1)))),
},
goal=Ref("Q"),
)
] | NT | null | COMPUTE | sympy | MAX_PRIME_BELOW | [
"ONE_PHI_1"
] | f6b5a5 | nt_num_divisors_compute_v1 | null | 2 | 0 | [
"MAX_PRIME_BELOW",
"ONE_PHI_1"
] | 2 | 0.017 | 2026-02-08T13:31:16.681294Z | {
"verified": true,
"answer": 10,
"timestamp": "2026-02-08T13:31:16.697916Z"
} | 498b52 | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 1,
"correct": {
"strict": false,
"boxed": false,
"relaxed": true
},
"usage": {
"prompt_tokens": 131,
"completion_tokens": 233
},
"timestamp": "2026-02-16T04:49:47.591Z",
"answer": 8
},
{
"id": 11,
... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "ONE_PHI_1",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"sta... | {
"lo": -8.26,
"mid": -5.01,
"hi": -1.76
} | ||
b5189d | comb_count_permutations_fixed_v1_1218484723_5608 | Let $D_n$ denote the number of derangements of $n$ elements, and let $k = 0$. Define
\[
n = \sum_{k_1=0}^{\left|\left\{ a : a \ge 0,\, a \le 29790,\, \bigl( a^{5} + a^{4} + a^{3} + 3a^{2} + 4a \bmod 29791 \bigr)^{5} + \bigl( a^{5} + a^{4} + a^{3} + 3a^{2} + 4a \bmod 29791 \bigr)^{4}
+ \bigl( a^{5} + a^{4} + a^{3} + 3a... | 1,854 | graphs = [
Graph(
let={
"_c": Const(2),
"_m": Const(4),
"_n": Const(2),
"n": Summation(var="k1", start=Const(0), end=CountOverSet(set=SolutionsSet(var=Var("a"), condition=And(Geq(Var("a"), Const(0)), Leq(Var("a"), Const(29790)), Eq(Mod(value=Sum(Pow(Mod(value=... | COMB | NT | COUNT | sympy | LIN_FORM | [
"K2/POLY_ORBIT_HENSEL/SUM_GEOM"
] | b686ff | comb_count_permutations_fixed_v1 | null | 7 | 0 | [
"K2",
"LIN_FORM",
"POLY_ORBIT_HENSEL",
"SUM_GEOM"
] | 4 | 2.35 | 2026-02-25T07:07:42.724336Z | {
"verified": true,
"answer": 1854,
"timestamp": "2026-02-25T07:07:45.074787Z"
} | 709f20 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 509,
"completion_tokens": 9170
},
"timestamp": "2026-03-29T21:55:52.167Z",
"answer": 0
},
{
"i... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "K2",
"status": "ok"
},
{
"lemma": "POLY_ORBIT_HENSEL",
"status": "ok_later"
},
{
"lemma": "SUM_GEOM",
"status": "ok_later"
},
{
"lemma": "V7",
"status... | {
"lo": 3.81,
"mid": 6.33,
"hi": 9.49
} | ||
e887e7 | sequence_count_fib_divisible_v1_1874849503_1671 | Let $N$ be the number of positive integers $n$ such that $1 \le n \le 5742$ and $n \equiv \left\lfloor \frac{n}{2} \right\rfloor \pmod{11}$. Let $R$ be the number of positive integers $n$ such that $1 \le n \le N$ and the $n$-th Fibonacci number is divisible by 5. Compute $R$. | 104 | graphs = [
Graph(
let={
"_n": Const(5742),
"upper": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Ref("_n")), Congruent(a=Var(name='n'), b=Floor(arg=Div(left=Var(name='n'), right=Const(value=2))), modulus=Const(value=11))))),
... | NT | null | COUNT | sympy | COUNT_COPRIME_GRID | [
"L3C"
] | 73f8b0 | sequence_count_fib_divisible_v1 | null | 6 | 0 | [
"COUNT_COPRIME_GRID",
"L3C"
] | 2 | 0.103 | 2026-02-08T14:01:53.894574Z | {
"verified": true,
"answer": 104,
"timestamp": "2026-02-08T14:01:53.997617Z"
} | 202977 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 209,
"completion_tokens": 1174
},
"timestamp": "2026-02-10T06:17:09.087Z",
"answer": 104
},
{
"id... | 1 | [
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "L3C",
"status": "ok"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
}
] | {
"lo": -5.49,
"mid": 0.03,
"hi": 6.12
} | ||
b04b84 | nt_max_prime_below_v1_717093673_2554 | Let $m = 88$, and let $d_{\text{max}}$ be the largest positive divisor of $7832$ that is less than or equal to $m$. Let $P$ be the set of all positive integers $p$ for which there exists a positive integer $q$ such that $pq = 54$, $\gcd(p, q) = 1$, and $p < q$. Let $t$ be the number of elements in $P$. Let $n_{\text{ma... | 33,320 | graphs = [
Graph(
let={
"_m": Const(88),
"_n": MaxOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Const(1)), Leq(Var("d"), Ref("_m")), Divides(divisor=Var("d"), dividend=Const(7832))))),
"upper": Const(65536),
"result": MaxOverSet(set=Soluti... | NT | null | EXTREMUM | sympy | MAX_DIVISOR | [
"MAX_DIVISOR/COPRIME_PAIRS"
] | d8f78a | nt_max_prime_below_v1 | negation_mod | 3 | 0 | [
"COPRIME_PAIRS",
"MAX_DIVISOR"
] | 2 | 5.105 | 2026-02-08T16:56:18.646553Z | {
"verified": true,
"answer": 33320,
"timestamp": "2026-02-08T16:56:23.751978Z"
} | 7a3613 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 198,
"completion_tokens": 2364
},
"timestamp": "2026-02-17T17:00:46.435Z",
"answer": 33320
},
... | 1 | [
{
"lemma": "COPRIME_PAIRS",
"status": "ok_later"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "MAX_DIVISOR",
"status": "ok"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "V3",
"status": "no"
},
{... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
07be96 | comb_factorial_compute_v1_784195855_6593 | Let $m$ be the number of positive integers $p$ for which there exists a positive integer $q$ such that $p \cdot q = 108$, $\gcd(p, q) = 1$, and $p < q$. Let $n$ be the number of integers $t$ with $7 \leq t \leq 20$ such that $t = 2a + 5b$ for some integers $a$ and $b$ satisfying $1 \leq a \leq 5$ and $1 \leq b \leq 2$.... | 5,040 | graphs = [
Graph(
let={
"_m": CountOverSet(set=SolutionsSet(var=Var("p"), condition=And(IsPositive(arg=Var(name='p')), Exists(var=Var(name='q'), condition=And(Eq(left=Mul(Var(name='p'), Var(name='q')), right=Const(value=108)), Eq(left=GCD(a=Var(name='p'), b=Var(name='q')), right=Const(value=1)),... | NT | null | COMPUTE | sympy | COPRIME_PAIRS | [
"COPRIME_PAIRS/LIN_FORM/MAX_PRIME_BELOW"
] | 56a8ee | comb_factorial_compute_v1 | null | 5 | 0 | [
"COPRIME_PAIRS",
"LIN_FORM",
"MAX_PRIME_BELOW"
] | 3 | 0.002 | 2026-02-08T08:44:48.717380Z | {
"verified": true,
"answer": 5040,
"timestamp": "2026-02-08T08:44:48.719840Z"
} | e4de48 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 194,
"completion_tokens": 1492
},
"timestamp": "2026-02-13T21:03:45.793Z",
"answer": 5040
},
{... | 1 | [
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok_later... | {
"lo": -7.01,
"mid": -4.68,
"hi": -2.15
} | ||
bacc41 | sequence_fibonacci_compute_v1_1915831931_2855 | Let $n$ be the number of ordered pairs $(i,j)$ of positive integers such that $1 \leq i \leq 3$, $1 \leq j \leq 10$, and $\gcd(i,j) = 1$. Let $F_n$ denote the $n$th Fibonacci number, where $F_1 = F_2 = 1$ and $F_k = F_{k-1} + F_{k-2}$ for $k \geq 3$. Compute the remainder when $61067 \cdot F_n$ is divided by $84088$. | 17,781 | graphs = [
Graph(
let={
"_n": Const(61067),
"n": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("i"), Var("j")]), condition=Eq(GCD(a=Var("i"), b=Var("j")), Const(1)), domain=CartesianProduct(left=IntegerRange(start=Const(1), end=Const(3)), right=IntegerRange(start=Const(1), en... | NT | null | COMPUTE | sympy | COUNT_COPRIME_GRID | [
"COUNT_COPRIME_GRID"
] | 20ec03 | sequence_fibonacci_compute_v1 | null | 3 | 0 | [
"COUNT_COPRIME_GRID"
] | 1 | 0.002 | 2026-02-08T17:10:48.486423Z | {
"verified": true,
"answer": 17781,
"timestamp": "2026-02-08T17:10:48.488127Z"
} | 2a4b74 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 168,
"completion_tokens": 2077
},
"timestamp": "2026-02-17T20:27:29.431Z",
"answer": 17781
},
... | 1 | [
{
"lemma": "COUNT_COPRIME_GRID",
"status": "ok"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "V7",... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
023408 | nt_count_divisible_and_v1_655260480_3451 | Let $d_1$ be the number of positive integers $p$ for which there exists a positive integer $q$ such that $pq = 60$, $\gcd(p, q) = 1$, and $p < q$. Let $d_2 = 6$. Determine the number of positive integers $n$ such that $1 \le n \le 16644$, $n$ is divisible by $d_1$, and $n$ is divisible by $d_2$. | 1,387 | graphs = [
Graph(
let={
"upper": Const(16644),
"d1": 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=60)), Eq(left=GCD(a=Var(name='p'), b=Var(... | NT | null | COUNT | sympy | COPRIME_PAIRS | [
"COPRIME_PAIRS"
] | 2bb3aa | nt_count_divisible_and_v1 | null | 3 | 0 | [
"COPRIME_PAIRS"
] | 1 | 1.152 | 2026-02-08T17:23:18.604021Z | {
"verified": true,
"answer": 1387,
"timestamp": "2026-02-08T17:23:19.755624Z"
} | 37b93d | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 150,
"completion_tokens": 2124
},
"timestamp": "2026-02-18T00:56:51.611Z",
"answer": 1387
},
{... | 1 | [
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "V1",
"status": "no"
},
{
"lemma": "VAL_SUM_EQ",
"status": "no"
}... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
0d637c | alg_qf_psd_count_leq_v1_601307018_300 | Let $k = \left|\{ (a_1, b_1) : 1 \leq a_1, b_1 \leq 35,\; 5a_1^2 + 10a_1b_1 + 5b_1^2 = 4500 \}\right|$. Find the number of ordered pairs $(a, b)$ of positive integers with $1 \le a, b \le 59$ such that $$25b^2 - 46ab + k a^2 \leq 40016.$$ | 2,937 | graphs = [
Graph(
let={
"_n": Const(2),
"result": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("a"), Var("b")]), condition=And(Geq(Var("a"), Const(1)), Leq(Var("a"), Const(59)), Geq(Var("b"), Const(1)), Leq(Var("b"), Const(59)), Leq(Sum(Mul(Const(25), Pow(Var("b"), Const(2))... | ALG | null | COUNT | sympy | QF_PSD_COUNT | [
"QF_PSD_COUNT"
] | 09ce67 | alg_qf_psd_count_leq_v1 | null | 5 | 0 | [
"QF_PSD_COUNT"
] | 1 | 0.019 | 2026-03-10T00:50:35.021926Z | {
"verified": true,
"answer": 2937,
"timestamp": "2026-03-10T00:50:35.040886Z"
} | 883624 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 230,
"completion_tokens": 8476
},
"timestamp": "2026-03-28T22:45:45.416Z",
"answer": 3269
},
{
... | 0 | [
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "QF_PSD_COUNT",
"status": "ok"
}
] | {
"lo": 5.22,
"mid": 7.83,
"hi": 10
} | ||
81ad30 | modular_mod_compute_v1_2051736721_2124 | Compute the remainder when $84681$ is divided by $11025$. | 7,506 | graphs = [
Graph(
let={
"a": Const(84681),
"m": Const(11025),
"result": Mod(value=Ref("a"), modulus=Ref("m")),
},
goal=Ref("result"),
)
] | NT | null | COMPUTE | sympy | MAX_PRIME_BELOW | [
"MAX_PRIME_BELOW"
] | dc3ad3 | modular_mod_compute_v1 | null | 2 | 0 | [
"MAX_PRIME_BELOW"
] | 1 | 0.008 | 2026-02-08T16:29:37.166563Z | {
"verified": true,
"answer": 7506,
"timestamp": "2026-02-08T16:29:37.174877Z"
} | c7b2da | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 76,
"completion_tokens": 472
},
"timestamp": "2026-02-16T07:28:02.318Z",
"answer": 169
},
{
"id": 11,
... | 1 | [
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "V1",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
}
] | {
"lo": -8.26,
"mid": -5.01,
"hi": -1.76
} | ||
d07b55 | modular_count_residue_v1_458359167_4638 | Let $m = 15$ and let $r$ be the largest prime number not exceeding $5$. Compute the number of positive integers $n \leq 80000$ such that $n \equiv r \pmod{m}$. Let this count be $C$. Find the remainder when $81057 \cdot C$ is divided by $78313$. | 70,278 | graphs = [
Graph(
let={
"_n": Const(5),
"upper": Const(80000),
"m": Const(15),
"r": MaxOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(2)), Leq(Var("n"), MaxOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(2)), ... | NT | null | COUNT | sympy | MAX_PRIME_BELOW | [
"MAX_PRIME_BELOW/MAX_PRIME_BELOW"
] | 15be89 | modular_count_residue_v1 | null | 4 | 0 | [
"MAX_PRIME_BELOW"
] | 1 | 2.799 | 2026-02-08T11:57:10.743098Z | {
"verified": true,
"answer": 70278,
"timestamp": "2026-02-08T11:57:13.542298Z"
} | 1430c4 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 120,
"completion_tokens": 858
},
"timestamp": "2026-02-14T21:18:37.118Z",
"answer": 70278
},
{... | 1 | [
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok"
},
{
"lemma": "V3",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
}
] | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
f9a1e6 | comb_bell_compute_v1_2051736721_5722 | Let $e = \sum_{k=0}^{9} (-1)^k \binom{9}{k}$. Define $a = 3 + e$ and $b = 5$, and let $n_1 = a + b$. Let $t = \sum_{k_1=0}^{n_1} (-1)^{k_1} \binom{n_1}{k_1}$. Define $n = 8 + t$. Compute the $n$-th Bell number, which counts the number of partitions of a set of size $n$. Find the value of this Bell number. | 4,140 | graphs = [
Graph(
let={
"n2": Const(9),
"e": Summation(var="k", start=Const(0), end=Ref("n2"), expr=Mul(Pow(Const(-1), Var("k")), Binom(n=Ref("n2"), k=Var("k")))),
"a": Sum(Const(3), Ref("e")),
"b": Const(5),
"n1": Sum(Ref("a"), Ref("b")),
... | COMB | null | COMPUTE | sympy | BINOMIAL_ALTERNATING | [
"BINOMIAL_ALTERNATING"
] | c21569 | comb_bell_compute_v1 | null | 3 | 2 | [
"BINOMIAL_ALTERNATING"
] | 1 | 0.002 | 2026-02-08T18:44:33.249229Z | {
"verified": true,
"answer": 4140,
"timestamp": "2026-02-08T18:44:33.251512Z"
} | ac819e | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 172,
"completion_tokens": 584
},
"timestamp": "2026-02-18T19:20:45.881Z",
"answer": 4140
},
{
... | 1 | [
{
"lemma": "BINOMIAL_ALTERNATING",
"status": "ok"
},
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "V... | {
"lo": -5.39,
"mid": -2.64,
"hi": 0.63
} | ||
d60201 | nt_sum_gcd_range_mod_v1_1520064083_3075 | Let $m = 17303$ and let $d$ be the smallest divisor of $m$ that is at least $2$. Let $N = \sum_{k=1}^{104} k$ and let $k = 120$. Define $S = \sum_{n=1}^{N} \gcd(n, k)$. Let $r$ be the remainder when $S$ is divided by $11471$. Compute the Bell number of $|r| \bmod d$. | 203 | graphs = [
Graph(
let={
"_m": Const(17303),
"_n": MinOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Const(2)), Divides(divisor=Var("d"), dividend=Ref("_m"))))),
"N": Summation(var="k", start=Const(1), end=Const(104), expr=Var("k")),
"k": Co... | NT | COMB | COMPUTE | sympy | LIOUVILLE_MINUS_ONE | [
"MIN_PRIME_FACTOR/SUM_ARITHMETIC"
] | d04c64 | nt_sum_gcd_range_mod_v1 | bell_mod | 7 | 0 | [
"LIOUVILLE_MINUS_ONE",
"MIN_PRIME_FACTOR",
"SUM_ARITHMETIC"
] | 3 | 0.779 | 2026-02-08T05:27:05.152617Z | {
"verified": true,
"answer": 203,
"timestamp": "2026-02-08T05:27:05.931966Z"
} | a5671f | 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": 1765
},
"timestamp": "2026-02-12T08:43:31.024Z",
"answer": 203
},
{
... | 1 | [
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "MIN_PRIME_FACTOR",
"status": "ok"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemm... | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
f47d0c | comb_count_surjections_v1_1353956133_308 | Let $n = 6$ and $k = 3$. The number of ways to partition a set of $n$ labeled elements into $k$ nonempty unlabeled subsets is given by the Stirling number of the second kind, $S(n,k)$. Multiplying by $k!$ gives the number of surjective functions from a set of $n$ elements to a set of $k$ elements. Let this value be $R$... | 300 | graphs = [
Graph(
let={
"n": Const(6),
"k": Const(3),
"result": Mul(Factorial(Ref("k")), Stirling2(n=Ref(name='n'), k=Ref(name='k'))),
"_c": CountOverSet(set=CartesianProduct(left=IntegerRange(start=Const(1), end=Const(28)), right=IntegerRange(start=Const(1), ... | COMB | null | COUNT | sympy | COUNT_CARTESIAN | [
"COUNT_CARTESIAN"
] | 009729 | comb_count_surjections_v1 | negation_mod | 4 | 0 | [
"COUNT_CARTESIAN"
] | 1 | 0.002 | 2026-02-08T11:23:55.074998Z | {
"verified": true,
"answer": 300,
"timestamp": "2026-02-08T11:23:55.077100Z"
} | 8a0075 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 256,
"completion_tokens": 3113
},
"timestamp": "2026-02-24T13:40:28.948Z",
"answer": 300
},
{
"id... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "ok"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
},
{
"lemma": "V8_SUM",
"status"... | {
"lo": -5.97,
"mid": -3.97,
"hi": -1.93
} | ||
fadb7c | comb_binomial_compute_v1_1440796553_1468 | Let $n_2$ be the number of integers $t$ such that $7 \le t \le 22$ and there exist positive integers $a$, $b$ with $1 \le a \le 2$, $1 \le b \le 6$, and $t = 5a + 2b$. Let $s = \sum_{k=0}^{n_2} (-1)^k \binom{n_2}{k}$. Let $n_1$ be the number of ordered pairs $(a, b)$ such that $1 \le a \le 3$ and $1 \le b \le 4$. Let $... | 12,870 | graphs = [
Graph(
let={
"n2": CountOverSet(set=SolutionsSet(var=Var("t"), condition=Exists(var=Var(name='a'), condition=Exists(var=Var(name='b'), condition=And(Geq(left=Var(name='a'), right=Const(value=1)), Leq(left=Var(name='a'), right=Const(value=2)), Geq(left=Var(name='b'), right=Const(value=... | COMB | null | COMPUTE | sympy | COUNT_CARTESIAN | [
"COUNT_CARTESIAN/BINOMIAL_ALTERNATING",
"LIN_FORM/BINOMIAL_ALTERNATING"
] | 30bb38 | comb_binomial_compute_v1 | null | 6 | 2 | [
"BINOMIAL_ALTERNATING",
"COUNT_CARTESIAN",
"LIN_FORM"
] | 3 | 0.004 | 2026-02-08T14:01:38.475666Z | {
"verified": true,
"answer": 12870,
"timestamp": "2026-02-08T14:01:38.479359Z"
} | b3bf7d | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 308,
"completion_tokens": 1044
},
"timestamp": "2026-02-24T19:33:35.704Z",
"answer": 12870
},
{
"... | 1 | [
{
"lemma": "BINOMIAL_ALTERNATING",
"status": "ok_later"
},
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "ok"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemm... | {
"lo": -8.52,
"mid": -5.43,
"hi": -3.2
} | ||
7c5622 | nt_min_phi_inverse_v1_1978505735_5298 | Let $m = 15$. Define $s$ to be the minimum value of $x + y$ over all ordered pairs $(x, y)$ of positive integers such that $xy = 17161$. Let $u$ be the number of positive integers $n$ such that $1 \le n \le s$, $n$ is even, and $\gcd(n, m) = 1$. Given that $k = 16$, determine the value of the smallest positive integer ... | 17 | graphs = [
Graph(
let={
"_m": Const(15),
"_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(17161)))), expr=Sum(Var("x"), Var("y")))),... | NT | null | EXTREMUM | sympy | COUNT_FIB_DIVISIBLE | [
"B3/C5"
] | cde3b3 | nt_min_phi_inverse_v1 | null | 5 | 0 | [
"B3",
"C5",
"COUNT_FIB_DIVISIBLE"
] | 3 | 0.031 | 2026-02-08T18:53:14.168716Z | {
"verified": true,
"answer": 17,
"timestamp": "2026-02-08T18:53:14.199654Z"
} | e5ca22 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 175,
"completion_tokens": 2000
},
"timestamp": "2026-02-18T20:26:10.505Z",
"answer": 17
},
{
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "C5",
"status": "ok_later"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
15cb0f | geo_count_lattice_triangle_v1_717093673_3632 | Consider the triangle with vertices at $(0,0)$, $(200,121)$, and $(66,121)$. The area of this triangle is $\frac{1}{2} \cdot \text{base} \cdot \text{height}$, but we compute twice the area as an integer. Let
\[
\text{area}_{2x} = \left| 2 \cdot \left( 200 \cdot 121 + 66 \cdot (0 - 121) \right) \right|.
\]
Let the numbe... | 8,035 | graphs = [
Graph(
let={
"_n": Const(121),
"area_2x": Abs(arg=Sum(Mul(Const(value=200), Const(value=121)), Mul(Const(value=66), Sub(left=Const(value=0), right=Const(value=121))))),
"boundary": Sum(GCD(a=Abs(arg=Const(value=200)), b=Abs(arg=Ref(name='_n'))), GCD(a=Abs(arg=S... | ALG | NT | COUNT | sympy | C5 | [
"C5"
] | 1d9668 | geo_count_lattice_triangle_v1 | null | 4 | 0 | [
"C5"
] | 1 | 0.01 | 2026-02-08T17:43:56.642962Z | {
"verified": true,
"answer": 8035,
"timestamp": "2026-02-08T17:43:56.653118Z"
} | ae67f4 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 268,
"completion_tokens": 1735
},
"timestamp": "2026-02-18T07:14:07.352Z",
"answer": 8035
},
{... | 1 | [
{
"lemma": "C5",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
0092f9 | alg_poly3_sum_v1_601307018_1798 | Compute the remainder when $$\sum_{\substack{1 \leq a \leq 47 \\ 1 \leq b \leq 47 \\ 1 \leq c \leq 47}} \left( -69a^3 - 180a^2b - 63a^2c + 54ab^2 + 252abc + 108b^2c - 54b^3 - 234bc^2 - 153ac^2 + c^3 \cdot \left|\left\{ v : 5 \leq v \leq 980,\ \exists\, 1 \leq a' \leq 14,\ 1 \leq b' \leq 14\ \text{s.t.}\ 4a'^2 - 4a'b' +... | 77,509 | graphs = [
Graph(
let={
"_n": Const(47),
"result": Mod(value=SumOverSet(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"), Ref("_n")), Geq(Var("c")... | ALG | null | COMPUTE | sympy | QF_PSD_DISTINCT | [
"QF_PSD_DISTINCT"
] | a8f9cb | alg_poly3_sum_v1 | null | 5 | 0 | [
"QF_PSD_DISTINCT"
] | 1 | 0.375 | 2026-03-10T02:32:36.046620Z | {
"verified": true,
"answer": 77509,
"timestamp": "2026-03-10T02:32:36.421292Z"
} | 1a3b33 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 311,
"completion_tokens": 27536
},
"timestamp": "2026-03-29T03:27:32.646Z",
"answer": 77509
},
{
... | 1 | [
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "QF_PSD_DISTINCT",
"status": "ok"
}
] | {
"lo": 3.99,
"mid": 6.11,
"hi": 9.15
} | ||
52e3cd | modular_count_residue_v1_655260480_4960 | Let $m$ be the number of integers $j$ with $0 \le j \le 131$ such that $\binom{131}{j}$ is odd. Let $\text{result}$ be the number of positive integers $n$ with $1 \le n \le 40320$ such that $n \equiv 0 \pmod{m}$. Compute $68121 - \text{result}$. | 63,081 | graphs = [
Graph(
let={
"_n": Const(131),
"upper": Const(40320),
"m": CountOverSet(set=SolutionsSet(var=Var("j"), condition=And(Geq(Var("j"), Const(0)), Leq(Var("j"), Ref("_n")), Eq(Mod(value=Binom(n=Const(131), k=Var("j")), modulus=Const(2)), Const(1))), domain='nonnegat... | ALG | COMB | COUNT | sympy | V8 | [
"V8"
] | 86348e | modular_count_residue_v1 | null | 6 | 0 | [
"V8"
] | 1 | 1.258 | 2026-02-08T18:13:38.289800Z | {
"verified": true,
"answer": 63081,
"timestamp": "2026-02-08T18:13:39.548066Z"
} | 4493f7 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 132,
"completion_tokens": 1486
},
"timestamp": "2026-02-18T15:27:10.420Z",
"answer": 63081
},
... | 1 | [
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "V8",
"status": "ok"
},
{
"lemma": "V8_SUM",
"status": "no"
}
] | {
"lo": -3.12,
"mid": 1.47,
"hi": 6.57
} | ||
e368b8 | modular_count_residue_v1_1520064083_1283 | Compute the number of integers $n$ such that $1 \le n \le 85264$ and $n \equiv 0 \pmod{3}$. | 28,421 | graphs = [
Graph(
let={
"upper": Const(85264),
"m": Const(3),
"r": Const(0),
"result": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), EulerPhi(n=Const(2))), Leq(Var("n"), Ref("upper")), Eq(Mod(value=Var("n"), modulus=Ref("m")), Ref("r"... | NT | null | COUNT | sympy | ONE_PHI_2 | [
"ONE_PHI_2"
] | e19278 | modular_count_residue_v1 | null | 2 | 0 | [
"ONE_PHI_2"
] | 1 | 6.004 | 2026-02-08T03:53:59.057162Z | {
"verified": true,
"answer": 28421,
"timestamp": "2026-02-08T03:54:05.060718Z"
} | 9725b2 | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 130,
"completion_tokens": 438
},
"timestamp": "2026-02-18T06:52:34.949Z",
"answer": 28421
}
] | 2 | [
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "ONE_PHI_2",
"status": "ok"
},
{
"lemma": "V3",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
}
] | {
"lo": -10,
"mid": -6.47,
"hi": -2.95
} | ||
9a2b15 | nt_lcm_compute_v1_865884756_3227 | Let $a = 1628$ and $b = 1251$. Let $m = \operatorname{lcm}(a, b)$. Let $T$ be the set of all ordered pairs $(x, y)$ of positive integers such that $xy = 2209$. Let $s$ be the minimum value of $x + y$ over all pairs $(x, y) \in T$. Let $U$ be the set of all ordered pairs $(x, y)$ of positive integers such that $x + y = ... | 58,462 | graphs = [
Graph(
let={
"_n": Const(2209),
"a": Const(1628),
"b": Const(1251),
"result": LCM(a=Ref("a"), b=Ref("b")),
"_c": MaxOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='... | NT | null | COMPUTE | sympy | B3 | [
"B3/B1"
] | 6cdf3d | nt_lcm_compute_v1 | negation_mod | 5 | 0 | [
"B1",
"B3"
] | 2 | 0.004 | 2026-02-08T17:14:46.031954Z | {
"verified": true,
"answer": 58462,
"timestamp": "2026-02-08T17:14:46.036261Z"
} | 63f1fd | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 198,
"completion_tokens": 1348
},
"timestamp": "2026-02-17T22:12:50.566Z",
"answer": 58462
},
... | 1 | [
{
"lemma": "B1",
"status": "ok_later"
},
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "MOD... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
c7c6f6 | antilemma_sum_equals_v1_1978505735_3741 | Let $A$ be the set of all integers $t$ such that $16 \leq t \leq 34$ and there exist positive integers $a$ and $b$ with $1 \leq a \leq 3$, $1 \leq b \leq 7$, and $t = 3a + 2b + 11$. Let $m$ be the number of elements in $A$. Determine the number of ordered pairs $(i, j)$ of positive integers such that $i + j = m$ and $1... | 12 | 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=3)), Geq(left=Var(name='b'), right=Const(value=... | COMB | GEOM | COMPUTE | sympy | COUNT_CARTESIAN | [
"LIN_FORM/COUNT_SUM_EQUALS",
"COUNT_SUM_EQUALS"
] | ada383 | antilemma_sum_equals_v1 | null | 3 | 0 | [
"COUNT_CARTESIAN",
"COUNT_SUM_EQUALS",
"LIN_FORM"
] | 3 | 0.091 | 2026-02-08T17:49:38.564084Z | {
"verified": true,
"answer": 12,
"timestamp": "2026-02-08T17:49:38.654828Z"
} | d6f0b2 | 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": 1721
},
"timestamp": "2026-02-18T08:27:58.195Z",
"answer": 12
},
{
... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "ok"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "V8",
"status... | {
"lo": -4.1,
"mid": -1.76,
"hi": 1.32
} | ||
089fd3 | geo_count_lattice_rect_v1_655260480_5485 | Let $a = 225$ and $b = 115$. Compute the number of lattice points $(x, y)$ such that $0 \leq x \leq a$ and $0 \leq y \leq b$. Multiply this count by $77617$, and find the remainder when the product is divided by $65068$. | 776 | graphs = [
Graph(
let={
"a": Const(225),
"b": Const(115),
"result": LatticePointsRect(a=Ref(name='a'), b=Ref(name='b')),
"Q": Mod(value=Mul(Const(77617), Ref("result")), modulus=Const(65068)),
},
goal=Ref("Q"),
)
] | GEOM | null | COUNT | sympy | [] | geo_count_lattice_rect_v1 | null | 3 | 0 | null | null | 0.001 | 2026-02-08T18:29:53.508760Z | {
"verified": true,
"answer": 776,
"timestamp": "2026-02-08T18:29:53.509635Z"
} | f504ae | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 115,
"completion_tokens": 2336
},
"timestamp": "2026-02-18T17:26:01.316Z",
"answer": 776
},
{
... | 1 | [] | {
"lo": -3.12,
"mid": 1.47,
"hi": 6.57
} | ||||
c8b186 | comb_sum_binomial_row_v1_1470522791_614 | Let $S$ be the set of all positive integers $p$ for which there exists a positive integer $q$ such that $pq = 18$, $\gcd(p, q) = 1$, and $p < q$. Let $A = |S|$. Define $R = A^{15}$. Compute the remainder when $48259 \cdot R$ is divided by $62715$. | 54,902 | graphs = [
Graph(
let={
"_n": Const(48259),
"n": Const(15),
"result": Pow(CountOverSet(set=SolutionsSet(var=Var("p"), condition=And(IsPositive(arg=Var(name='p')), Exists(var=Var(name='q'), condition=And(Eq(left=Mul(Var(name='p'), Var(name='q')), right=Const(value=18)), Eq... | NT | null | SUM | sympy | COPRIME_PAIRS | [
"COPRIME_PAIRS"
] | 2bb3aa | comb_sum_binomial_row_v1 | null | 3 | 0 | [
"COPRIME_PAIRS"
] | 1 | 0.001 | 2026-02-08T13:08:27.586297Z | {
"verified": true,
"answer": 54902,
"timestamp": "2026-02-08T13:08:27.587765Z"
} | d4dcb7 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 129,
"completion_tokens": 1828
},
"timestamp": "2026-02-15T09:57:30.937Z",
"answer": 54902
},
... | 1 | [
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
... | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
625aa3 | diophantine_fbi2_min_v1_784195855_3726 | Let $k = 12$, $a = 5$, and $b = \phi(1)$. Define $\text{upper} = 22$. Let $d$ be an integer such that $6 \leq d \leq 22$, $d$ divides $k$, and $\frac{k}{d} \geq 2$. Determine the minimum possible value of such $d$, and denote this value by $r$. Compute the sum $$\sum_{n=1}^{|r|} \tau(n),$$ where $\tau(n)$ denotes the n... | 14 | graphs = [
Graph(
let={
"k": Const(12),
"a": Const(5),
"b": EulerPhi(n=Const(1)),
"upper": Const(22),
"result": MinOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Const(6)), Leq(Var("d"), Ref("upper")), Divides(divisor=Var("d"), ... | NT | null | EXTREMUM | sympy | MAX_PRIME_BELOW | [
"ONE_PHI_1"
] | f6b5a5 | diophantine_fbi2_min_v1 | null | 3 | 0 | [
"MAX_PRIME_BELOW",
"ONE_PHI_1"
] | 2 | 0.021 | 2026-02-08T06:35:41.654957Z | {
"verified": true,
"answer": 14,
"timestamp": "2026-02-08T06:35:41.675501Z"
} | df75ac | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 223,
"completion_tokens": 674
},
"timestamp": "2026-02-19T11:45:48.696Z",
"answer": 14
}
] | 2 | [
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "ONE_PHI_1",
"stat... | {
"lo": -10,
"mid": -6.47,
"hi": -2.95
} | ||
636a1a | algebra_poly_eval_v1_1978505735_8162 | Let $d$ be the smallest divisor of $77$ that is at least $2$. Compute $d \cdot 10^2 - 6 \cdot 10 - 6$. | 634 | graphs = [
Graph(
let={
"_n": Const(2),
"n": Const(10),
"result": Sum(Mul(MinOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Const(2)), Divides(divisor=Var("d"), dividend=Const(77))))), Pow(Ref("n"), Ref("_n"))), Mul(Const(-6), Ref("n")), Const(-6)),
... | NT | null | COMPUTE | sympy | MIN_PRIME_FACTOR | [
"MIN_PRIME_FACTOR"
] | bc3776 | algebra_poly_eval_v1 | null | 3 | 0 | [
"MIN_PRIME_FACTOR"
] | 1 | 0.004 | 2026-02-08T20:41:53.247253Z | {
"verified": true,
"answer": 634,
"timestamp": "2026-02-08T20:41:53.250786Z"
} | 623e5d | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 98,
"completion_tokens": 235
},
"timestamp": "2026-02-16T18:52:47.834Z",
"answer": 634
},
{
"id": 11,
... | 2 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "MIN_PRIME_FACTOR",
"status": "ok"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "VAL_SUM_EQ",
"status":... | {
"lo": -10,
"mid": -7.27,
"hi": -4.54
} | ||
16383d | comb_count_partitions_v1_124444284_7409 | Let $n_2 = 0$. Define $m = \sum_{k=0}^{n_2} (-1)^k \binom{n_2}{k}$. Let $u = 3$ and $n_1 = u + 1$. Define $s = \sum_{k=0}^{n_1} (-1)^k \binom{n_1}{k}$. Let $n = 40m + s$. Let $p(n)$ denote the number of integer partitions of $n$. Compute the remainder when $44121 \cdot p(n)$ is divided by $54968$. | 53,906 | graphs = [
Graph(
let={
"n2": Const(0),
"m": 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(3),
"n1": Sum(Ref("u"), Const(1)),
"s": Summation(var="k", start=Const(0)... | COMB | null | COUNT | sympy | BINOMIAL_ALTERNATING | [
"BINOMIAL_ALTERNATING"
] | c21569 | comb_count_partitions_v1 | null | 4 | 2 | [
"BINOMIAL_ALTERNATING"
] | 1 | 0.001 | 2026-02-08T09:06:40.353658Z | {
"verified": true,
"answer": 53906,
"timestamp": "2026-02-08T09:06:40.354699Z"
} | 0858cc | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 242,
"completion_tokens": 32768
},
"timestamp": "2026-02-24T10:33:48.929Z",
"answer": null
},
{
... | 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": "V8",
"status": "no"
},
{
"lemma": "... | {
"lo": 1.15,
"mid": 4.18,
"hi": 6.61
} | ||
3a0d08 | nt_sum_divisors_compute_v1_784195855_3892 | Let $n = 55696$. Compute the sum of the positive divisors of $n$, and denote this sum by $\sigma(n)$. Let $A$ be the sum
$$
\sum_{i=0}^{d-1} \left( \text{digit}_i(\sigma(n)) \cdot (i+1)^2 \right),
$$
where $d$ is the number of decimal digits of $\sigma(n)$ and $\text{digit}_i(m)$ denotes the $i$-th digit (starting from... | 1,497 | graphs = [
Graph(
let={
"_n": Const(49),
"n": Const(55696),
"result": SumDivisors(n=Ref("n")),
"_c": Summation(var="k", start=Const(1), end=Const(49), expr=Mul(EulerPhi(n=Var("k")), Floor(Div(Ref("_n"), Var("k"))))),
"Q": Sum(Summation(var="i", sta... | NT | null | COMPUTE | sympy | K2 | [
"K2"
] | b365d9 | nt_sum_divisors_compute_v1 | digits_weighted_mod | 5 | 0 | [
"K2"
] | 1 | 0.003 | 2026-02-08T06:41:21.646959Z | {
"verified": true,
"answer": 1497,
"timestamp": "2026-02-08T06:41:21.649623Z"
} | ec1bce | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 224,
"completion_tokens": 1231
},
"timestamp": "2026-02-13T03:07:10.305Z",
"answer": 1497
},
{... | 1 | [
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K2",
"status": "ok"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
... | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
67cf22 | algebra_quadratic_discriminant_v1_677425708_3051 | Let $a = -7$, $b = 4$, and $c = 5$. Compute $b^2 - 4ac$. | 156 | graphs = [
Graph(
let={
"a": Const(-7),
"b": Const(4),
"c": Const(5),
"result": Sub(Pow(Ref("b"), Const(2)), Mul(Const(4), Ref("a"), Ref("c"))),
},
goal=Ref("result"),
)
] | NT | null | COMPUTE | sympy | B3 | [
"COPRIME_PAIRS"
] | 2bb3aa | algebra_quadratic_discriminant_v1 | null | 2 | 0 | [
"B3",
"COPRIME_PAIRS"
] | 2 | 0.03 | 2026-02-08T05:27:15.054168Z | {
"verified": true,
"answer": 156,
"timestamp": "2026-02-08T05:27:15.083810Z"
} | 3dc03a | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 85,
"completion_tokens": 170
},
"timestamp": "2026-02-11T22:48:55.779Z",
"answer": 156
},
{
"id": 11,
... | 2 | [
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "V1",
"status": "no"
}
] | {
"lo": -10,
"mid": -7.73,
"hi": -5.46
} | ||
1294b5 | v7_endings_v1_1116507919_118 | Let $k$ be the smallest positive integer such that $1 \leq k \leq 137$ and $2^5$ divides $\binom{137}{k}$. Compute the remainder when $19041 \cdot k$ is divided by $77830$. | 34,750 | graphs = [
Graph(
let={
"_inner_result": MinOverSet(set=SolutionsSet(var=Var("k"), condition=And(Geq(Var("k"), Const(1)), Leq(Var("k"), Const(137)), Geq(MaxKDivides(target=Binom(n=Const(137), k=Var("k")), base=Const(2)), Const(5))))),
"_scale_k": Const(19041),
"_scaled": ... | NT | null | COMPUTE | sympy | V7 | [
"V7"
] | 0672d4 | v7_endings_v1 | null | 7 | null | [
"V7"
] | 1 | 0.001 | 2026-02-08T02:26:19.971876Z | {
"verified": true,
"answer": 34750,
"timestamp": "2026-02-08T02:26:19.973063Z"
} | b7324b | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 172,
"completion_tokens": 2129
},
"timestamp": "2026-02-08T19:05:00.440Z",
"answer": 34850
},
{
... | 1 | [
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "V7",
"stat... | {
"lo": 1.07,
"mid": 4.17,
"hi": 6.6
} | ||
b7f1a6 | algebra_poly_eval_v1_784195855_2267 | Let $z = 23$ and define $r = 6z^2 - 9z + m$, where $m$ is the largest prime number satisfying $2 \leq m \leq 9$. Let $k$ be the largest integer such that $2^k \leq 1384355567388$. Compute the remainder when $k - r$ is divided by $85042$. | 82,108 | graphs = [
Graph(
let={
"_m": Const(2),
"_n": Const(2),
"z": Const(23),
"result": Sum(Mul(Const(6), Pow(Ref("z"), Ref("_n"))), Mul(Const(-9), Ref("z")), MaxOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(2)), Leq(Var("n"), Const(9)), I... | NT | null | COMPUTE | sympy | MAX_VAL | [
"MAX_VAL",
"MAX_PRIME_BELOW"
] | b61fe9 | algebra_poly_eval_v1 | negation_mod | 3 | 0 | [
"MAX_PRIME_BELOW",
"MAX_VAL"
] | 2 | 0.002 | 2026-02-08T05:37:44.163074Z | {
"verified": true,
"answer": 82108,
"timestamp": "2026-02-08T05:37:44.165394Z"
} | 615750 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 129,
"completion_tokens": 776
},
"timestamp": "2026-02-12T12:04:11.737Z",
"answer": 82108
},
{... | 1 | [
{
"lemma": "K16",
"status": "same_pattern_wrong"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok"
},
{
"lemma": "MAX_VAL",
"status": "ok"
},
{
"lemma": "MOD_SUB",
"statu... | {
"lo": -5.55,
"mid": -3.01,
"hi": 0.32
} | ||
1448c2 | nt_sum_divisors_mod_v1_898971024_415 | Let $n$ be the sum of all real solutions to the equation $x^2 - 240x - 21700 = 0$. Let $\sigma$ be the sum of all positive divisors of $n$. Compute the remainder when $\sigma$ is divided by $10139$. | 744 | graphs = [
Graph(
let={
"n": SumOverSet(set=SolutionsSet(var=Var("x"), condition=Eq(Sum(Pow(Var("x"), Const(2)), Mul(Const(-240), Var("x")), Const(-21700)), Const(0)))),
"M": Const(10139),
"sigma": SumDivisors(n=Ref("n")),
"result": Mod(value=Ref("sigma"), mod... | NT | null | COMPUTE | sympy | VIETA_SUM | [
"VIETA_SUM"
] | b33a7a | nt_sum_divisors_mod_v1 | null | 4 | 0 | [
"VIETA_SUM"
] | 1 | 0.003 | 2026-02-08T15:27:01.071352Z | {
"verified": true,
"answer": 744,
"timestamp": "2026-02-08T15:27:01.074103Z"
} | 830830 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 106,
"completion_tokens": 543
},
"timestamp": "2026-02-16T06:10:34.421Z",
"answer": 744
},
{
... | 1 | [
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "VIETA_SUM",
"status... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
287308 | sequence_lucas_compute_v1_677425708_996 | Let $c = 93627$ and $n_0 = 97661$. Let $A$ be the set of all positive integers $n \leq 1200$ such that $30$ divides the $n$-th Fibonacci number. Let $k$ be the number of elements in $A$. Let $n$ be the largest prime number not exceeding $k$. Define $L_n$ to be the $n$-th Lucas number. Compute the remainder when $c \cdo... | 80,941 | graphs = [
Graph(
let={
"_n": Const(97661),
"n": MaxOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(2)), Leq(Var("n"), CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Const(1200)), Divides(divisor=Const(30), di... | NT | null | COMPUTE | sympy | COUNT_FIB_DIVISIBLE | [
"COUNT_FIB_DIVISIBLE/MAX_PRIME_BELOW"
] | c3fe6d | sequence_lucas_compute_v1 | null | 7 | 0 | [
"COUNT_FIB_DIVISIBLE",
"MAX_PRIME_BELOW"
] | 2 | 0.002 | 2026-02-08T03:56:44.783377Z | {
"verified": true,
"answer": 80941,
"timestamp": "2026-02-08T03:56:44.785538Z"
} | 1fdfc2 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 230,
"completion_tokens": 3991
},
"timestamp": "2026-02-09T14:40:59.492Z",
"answer": 80941
},
{
"... | 1 | [
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "ok"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok_later"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
},
{
"lemma": "V7",
"status": "no"... | {
"lo": -3.53,
"mid": 1.02,
"hi": 5.49
} | ||
82c387 | antilemma_k2_v1_898971024_1150 | Let $m = 149$ and define $n = \sum_{d \mid m} \phi(d)$, where $\phi$ denotes Euler's totient function. Compute $\sum_{k=1}^{n} \phi(k) \left\lfloor \frac{149}{k} \right\rfloor$. | 11,175 | graphs = [
Graph(
let={
"_m": Const(149),
"_n": SumOverDivisors(n=Ref(name='_m'), var='d', expr=EulerPhi(n=Var(name='d'))),
"x": Summation(var="k", start=Const(1), end=Ref("_n"), expr=Mul(EulerPhi(n=Var("k")), Floor(Div(Const(149), Var("k"))))),
},
goal=Re... | NT | COMB | COMPUTE | sympy | K13 | [
"K3/K2",
"K2"
] | c7f244 | antilemma_k2_v1 | null | 5 | 0 | [
"K13",
"K2",
"K3"
] | 3 | 0.003 | 2026-02-08T15:58:42.082083Z | {
"verified": true,
"answer": 11175,
"timestamp": "2026-02-08T15:58:42.085108Z"
} | 7642f1 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 111,
"completion_tokens": 751
},
"timestamp": "2026-02-16T17:35:15.655Z",
"answer": 11175
},
{... | 1 | [
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K2",
"status": "ok"
},
{
"lemma": "K3",
"status": "ok"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "MOD_F... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
95a5b6 | modular_count_residue_v1_124444284_740 | Let $A = \gcd(13, 17)$. Compute the sum $\sum_{d \mid A} \mu(d)$, where $\mu$ is the M\"obius function, and denote this sum by $L$. Let $U = 35344$ and $m = 15$. Determine the number of integers $n$ such that $L \leq n \leq U$ and $n \equiv 5 \pmod{15}$. | 2,356 | graphs = [
Graph(
let={
"upper": Const(35344),
"m": Const(15),
"r": Const(5),
"result": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), SumOverDivisors(n=GCD(a=Const(value=13), b=Const(value=17)), var='d', expr=MoebiusMu(n=Var(name='d')... | NT | null | COUNT | sympy | MOBIUS_COPRIME | [
"MOBIUS_COPRIME"
] | ac54ac | modular_count_residue_v1 | null | 4 | 0 | [
"MOBIUS_COPRIME"
] | 1 | 1.179 | 2026-02-08T03:29:18.557501Z | {
"verified": true,
"answer": 2356,
"timestamp": "2026-02-08T03:29:19.736776Z"
} | 9c3929 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 211,
"completion_tokens": 605
},
"timestamp": "2026-02-09T21:19:41.099Z",
"answer": 2353
},
{
... | 1 | [
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "MOBIUS_COPRIME",
"status": "ok"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "VAL_SUM_EQ",
"status": "no"
}
] | {
"lo": -6.51,
"mid": -0.31,
"hi": 5.43
} | ||
196a6e | lin_form_endings_v1_717093673_265 | Let $a = 105$ and $b = 30$. Compute $\gcd(a, b)$, and denote this value by $d$. Let $k = 525$. Define $s = \left\lfloor \frac{k}{\gcd(k, d)} \right\rfloor$. Multiply $s$ by $7395$, and let the result be $t$. Find the remainder when $t$ is divided by $78236$. | 24,117 | graphs = [
Graph(
let={
"a_coeff": Const(105),
"b_coeff": Const(30),
"k_val": Const(525),
"step": GCD(a=Ref("a_coeff"), b=Ref("b_coeff")),
"_inner_result": Floor(Div(Ref("k_val"), GCD(a=Ref("k_val"), b=Ref("step")))),
"_scale_k": Const(... | COMB | NT | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | lin_form_endings_v1 | null | 4 | null | [
"LIN_FORM"
] | 1 | 0.001 | 2026-02-08T15:16:17.416058Z | {
"verified": true,
"answer": 24117,
"timestamp": "2026-02-08T15:16:17.417217Z"
} | 1af2f9 | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 163,
"completion_tokens": 503
},
"timestamp": "2026-02-16T05:26:09.450Z",
"answer": 10941
},
{
"id": 11... | 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": -8.26,
"mid": -5.01,
"hi": -1.76
} | ||
44e856 | nt_min_coprime_above_v1_1918700295_2421 | Let $T$ be the set of all integers $t$ such that $23 \leq t \leq 40$ and $t = 5a + 2b + 16$ for some integers $a \in \{1, 2\}$ and $b \in \{1, 2, \dots, 7\}$. Let $m$ be the number of elements in $T$. Find the smallest integer $n$ such that $21316 < n \leq 21340$ and $\gcd(n, m) = \varphi(1)$. Enter this value of $n$ a... | 21,317 | graphs = [
Graph(
let={
"start": Const(21316),
"upper": Const(21340),
"modulus": 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(n... | NT | null | EXTREMUM | sympy | LIN_FORM | [
"LIN_FORM",
"ONE_PHI_1"
] | e67fb6 | nt_min_coprime_above_v1 | null | 5 | 0 | [
"LIN_FORM",
"ONE_PHI_1"
] | 2 | 0.006 | 2026-02-08T07:52:51.923435Z | {
"verified": true,
"answer": 21317,
"timestamp": "2026-02-08T07:52:51.929912Z"
} | a95fa3 | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 232,
"completion_tokens": 736
},
"timestamp": "2026-02-20T07:08:18.403Z",
"answer": 21317
}
] | 2 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "ONE_PHI_1",
"status": "ok"
},
{
"lemma": "V8_SUM",
"status": "no"
}... | {
"lo": -10,
"mid": -6.47,
"hi": -2.95
} | ||
cd963a | antilemma_sum_primes_v1_784195855_2634 | Let $p$ and $q$ be positive integers such that $pq = 54$, $\gcd(p, q) = 1$, and $p < q$. Let $m$ be the number of such pairs $(p, q)$. Let $S$ be the set of all prime numbers $n$ such that $m \leq n \leq 3$. Compute the sum of all elements in $S$. | 5 | graphs = [
Graph(
let={
"_n": Const(3),
"x": SumOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), CountOverSet(set=SolutionsSet(var=Var("p"), condition=And(IsPositive(arg=Var(name='p')), Exists(var=Var(name='q'), condition=And(Eq(left=Mul(Var(name='p'), Var(name='q')... | NT | null | COMPUTE | sympy | C3 | [
"COPRIME_PAIRS/SUM_PRIMES",
"SUM_PRIMES"
] | 020700 | antilemma_sum_primes_v1 | null | 5 | 0 | [
"C3",
"COPRIME_PAIRS",
"SUM_PRIMES"
] | 3 | 0.011 | 2026-02-08T05:54:46.059251Z | {
"verified": true,
"answer": 5,
"timestamp": "2026-02-08T05:54:46.070612Z"
} | e37ccd | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 183,
"completion_tokens": 215
},
"timestamp": "2026-02-18T20:59:51.058Z",
"answer": 5
}
] | 2 | [
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "SUM_PRIMES",
"status":... | {
"lo": -10,
"mid": -6.47,
"hi": -2.95
} | ||
69bdef | comb_binomial_compute_v1_1742523217_3241 | Let $m = 10$ and $n = 63010$. Define $a$ to be the number of nonnegative integers $j \leq 11280$ such that $\binom{11280}{j}$ is odd. Let $S$ be the set of prime numbers $d$ such that $d \geq 2$ and $d$ divides 6. Define $k$ to be the largest prime number $n$ such that $n \leq m$ and $n \geq \min(S)$. Compute the remai... | 33,510 | graphs = [
Graph(
let={
"_m": Const(10),
"_n": Const(63010),
"n": CountOverSet(set=SolutionsSet(var=Var("j"), condition=And(Geq(Var("j"), Const(0)), Leq(Var("j"), Const(11280)), Eq(Mod(value=Binom(n=Const(11280), k=Var("j")), modulus=Const(2)), Const(1))), domain='nonnega... | NT | null | COMPUTE | sympy | MIN_PRIME_FACTOR | [
"MIN_PRIME_FACTOR/MAX_PRIME_BELOW",
"V8"
] | 633099 | comb_binomial_compute_v1 | null | 6 | 0 | [
"MAX_PRIME_BELOW",
"MIN_PRIME_FACTOR",
"V8"
] | 3 | 0.005 | 2026-02-08T05:44:47.538215Z | {
"verified": true,
"answer": 33510,
"timestamp": "2026-02-08T05:44:47.542917Z"
} | 3581c2 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 177,
"completion_tokens": 2159
},
"timestamp": "2026-02-12T13:33:39.010Z",
"answer": 33510
},
... | 1 | [
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok_later"
},
{
"lemma": "MIN_PRIME_FACTOR",
"status": "ok"
},
{
"lemma":... | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
158ec5 | modular_count_residue_v1_677425708_3491 | Let $r$ be the minimum value of $x + y$ over all ordered pairs $(x, y)$ of positive integers such that $xy = 4$. Let $m = 10$ and $U = 58081$. Let $N$ be the number of positive integers $n \leq U$ such that $n \equiv r \pmod{m}$. Compute the smallest positive integer $k$ such that the $k$-th Fibonacci number is divisib... | 840 | graphs = [
Graph(
let={
"_n": Const(4),
"upper": Const(58081),
"m": Const(10),
"r": 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")... | NT | null | COUNT | sympy | B3 | [
"B3"
] | 0cd20d | modular_count_residue_v1 | null | 6 | 0 | [
"B3"
] | 1 | 4.2 | 2026-02-08T05:45:13.219498Z | {
"verified": true,
"answer": 840,
"timestamp": "2026-02-08T05:45:17.419662Z"
} | 7e44bf | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 150,
"completion_tokens": 1756
},
"timestamp": "2026-02-12T14:06:20.543Z",
"answer": 840
},
{
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
}
] | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
34c169 | comb_count_derangements_v1_168721529_1041 | Let $n = 8$. Let $d_n$ denote the number of derangements of $n$ objects. Let $S$ be the set of all positive integers $n$ such that $1 \leq n \leq 11$ and $n \equiv 0 \pmod{11}$. Let $s$ be the sum of all elements in $S$. Compute the Bell number $B_k$, where $k = d_n \bmod s$. | 52 | graphs = [
Graph(
let={
"n": Const(8),
"result": Subfactorial(arg=Ref(name='n')),
"Q": Bell(Mod(value=Abs(arg=Ref(name='result')), modulus=SumOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Const(11)), Eq(Mod(value=Var("n"), mod... | COMB | null | COUNT | sympy | SUM_DIVISIBLE | [
"SUM_DIVISIBLE"
] | 0fae4f | comb_count_derangements_v1 | bell_mod | 3 | 0 | [
"SUM_DIVISIBLE"
] | 1 | 0.004 | 2026-02-08T13:26:00.756070Z | {
"verified": true,
"answer": 52,
"timestamp": "2026-02-08T13:26:00.760146Z"
} | b60df4 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 214,
"completion_tokens": 1171
},
"timestamp": "2026-02-09T12:51:39.605Z",
"answer": 52
},
{
"id"... | 1 | [
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "SUM_DIVISIBLE",
"status": "ok"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8_SUM",... | {
"lo": -2.77,
"mid": -0.49,
"hi": 2.44
} | ||
175e27 | nt_count_divisible_and_v1_151522320_1692 | Let $d_1$ be the number of integers $t$ with $15 \leq t \leq 42$ for which there exist positive integers $a \leq 4$ and $b \leq 2$ such that
$$
t = 6a + 9b.
$$
Let $d_2 = 12$. Define $N$ to be the number of positive integers $n \leq 52368$ that are divisible by both $d_1$ and $d_2$. Compute the remainder when $74169 \c... | 52,486 | graphs = [
Graph(
let={
"_n": Const(53642),
"upper": Const(52368),
"d1": CountOverSet(set=SolutionsSet(var=Var("t"), condition=Exists(var=Var(name='a'), condition=Exists(var=Var(name='b'), condition=And(Geq(left=Var(name='a'), right=Const(value=1)), Leq(left=Var(name='a')... | NT | null | COUNT | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | nt_count_divisible_and_v1 | null | 4 | 0 | [
"LIN_FORM"
] | 1 | 3.572 | 2026-02-08T04:11:53.506408Z | {
"verified": true,
"answer": 52486,
"timestamp": "2026-02-08T04:11:57.078612Z"
} | 247147 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 241,
"completion_tokens": 1672
},
"timestamp": "2026-02-10T15:38:47.356Z",
"answer": 52486
},
{
... | 1 | [
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "VAL_SUM_EQ",
"status": "no"
}
] | {
"lo": -3.42,
"mid": 1.86,
"hi": 7.55
} | ||
f8fce7 | nt_sum_divisors_compute_v1_865884756_1581 | Let $n = 21317$. Compute the sum of all positive divisors of $n$. | 21,318 | graphs = [
Graph(
let={
"n": Const(21317),
"result": SumDivisors(n=Ref("n")),
},
goal=Ref("result"),
)
] | NT | null | COMPUTE | sympy | MAX_DIVISOR | [
"MAX_DIVISOR/DIVISOR_PARITY/EULER_TOTIENT_SUM"
] | 064c83 | nt_sum_divisors_compute_v1 | null | 2 | 0 | [
"DIVISOR_PARITY",
"EULER_TOTIENT_SUM",
"MAX_DIVISOR"
] | 3 | 0.005 | 2026-02-08T16:09:42.378733Z | {
"verified": true,
"answer": 21318,
"timestamp": "2026-02-08T16:09:42.383496Z"
} | 17a4ce | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 78,
"completion_tokens": 484
},
"timestamp": "2026-02-16T06:57:36.701Z",
"answer": 21318
},
{
"id": 11,
... | 2 | [
{
"lemma": "DIVISOR_PARITY",
"status": "ok_later"
},
{
"lemma": "EULER_TOTIENT_SUM",
"status": "ok_later"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "MAX_DIVISO... | {
"lo": -10,
"mid": -7.27,
"hi": -4.54
} | ||
1d7fb3 | nt_sum_divisors_mod_v1_677425708_227 | Let $n = 45360$ and $M = 10477$. Define $\sigma$ to be the sum of all positive divisors of $n$. Let $\text{result} = \sigma \bmod M$. Define $Q = \text{result} + \phi(|\text{result}| + \phi(1)) + \tau(|\text{result}| + 1)$, where $\phi$ is Euler's totient function and $\tau(k)$ denotes the number of positive divisors o... | 2,719 | graphs = [
Graph(
let={
"n": Const(45360),
"M": Const(10477),
"sigma": SumDivisors(n=Ref("n")),
"result": Mod(value=Ref("sigma"), modulus=Ref("M")),
"Q": Sum(Ref("result"), EulerPhi(n=Sum(Abs(arg=Ref(name='result')), EulerPhi(n=Const(1)))), NumDivi... | NT | null | COMPUTE | sympy | ONE_PHI_1 | [
"ONE_PHI_1"
] | f6b5a5 | nt_sum_divisors_mod_v1 | null | 4 | 0 | [
"ONE_PHI_1"
] | 1 | 0.002 | 2026-02-08T03:09:48.466922Z | {
"verified": true,
"answer": 2719,
"timestamp": "2026-02-08T03:09:48.469148Z"
} | 77fa9a | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 232,
"completion_tokens": 1606
},
"timestamp": "2026-02-08T20:25:11.496Z",
"answer": 2563
},
{
... | 1 | [
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "ONE_PHI_1",
"status": "ok"
},
{
"lemma": "V3",
"status": "no"
}
] | {
"lo": 1.06,
"mid": 4.17,
"hi": 6.6
} | ||
24cbc2 | comb_count_partitions_v1_655260480_6036 | Let $n$ be the number of integers $t$ with $8 \leq t \leq 49$ for which there exist positive integers $a$ and $b$ such that $1 \leq a \leq 14$, $1 \leq b \leq 6$, and $t = 2a + 3b + 3$. Compute the number of integer partitions of $n$. | 37,338 | 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=14)), Geq(left=Var(name='b'), right=Const(value=... | COMB | null | COUNT | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | comb_count_partitions_v1 | null | 6 | 0 | [
"LIN_FORM"
] | 1 | 0.002 | 2026-02-08T18:47:28.470869Z | {
"verified": true,
"answer": 37338,
"timestamp": "2026-02-08T18:47:28.472385Z"
} | a9ac66 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 130,
"completion_tokens": 4784
},
"timestamp": "2026-02-18T19:32:33.523Z",
"answer": 37338
},
... | 1 | [
{
"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": "V7",
"statu... | {
"lo": -3.12,
"mid": 1.47,
"hi": 6.57
} | ||
d51f0a | nt_count_phi_equals_v1_124444284_2273 | Let $ N $ be the number of ordered pairs $ (x_1, x_2) $ of positive odd integers such that $ x_1 + x_2 = 2592 $. Let $ k = 162 $. Define $ R $ to be the number of positive integers $ n \leq N $ such that $ \phi(n) = k $. Compute the remainder when $ 44121 \cdot R $ is divided by $ 96361 $. | 80,123 | graphs = [
Graph(
let={
"_n": Const(96361),
"upper": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x1"), Var("x2")]), condition=And(IsPositive(arg=Var(name='x1')), IsPositive(arg=Var(name='x2')), IsOdd(arg=Var(name='x1')), IsOdd(arg=Var(name='x2')), Eq(Sum(Var("x1"), Var("x2... | NT | null | COUNT | sympy | COMB1 | [
"COMB1"
] | 567f58 | nt_count_phi_equals_v1 | null | 7 | 0 | [
"COMB1"
] | 1 | 0.091 | 2026-02-08T04:34:04.893495Z | {
"verified": true,
"answer": 80123,
"timestamp": "2026-02-08T04:34:04.984346Z"
} | 658e91 | 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": 4730
},
"timestamp": "2026-02-10T17:14:29.779Z",
"answer": 80123
},
{
... | 1 | [
{
"lemma": "COMB1",
"status": "ok"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "V3",
"status": "no"
},
{
"lemma": "VAL_SUM_EQ",
"statu... | {
"lo": -3.42,
"mid": 1.86,
"hi": 7.55
} | ||
56a6b2 | nt_sum_totient_over_divisors_v1_349078426_69 | Let $ n $ be the number of integers $ t $ such that $ 22 \leq t \leq 18040 $ and there exist positive integers $ a \leq 908 $ and $ b \leq 666 $ satisfying $ t = 14a + 8b $. Compute $ \sum_{d \mid n} \phi(d) $, where $ \phi $ denotes Euler's totient function. | 8,992 | 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=908)), Geq(left=Var(name='b'), right=Const(value... | NT | null | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | nt_sum_totient_over_divisors_v1 | null | 5 | 0 | [
"LIN_FORM"
] | 1 | 0.003 | 2026-02-08T12:48:31.406705Z | {
"verified": true,
"answer": 8992,
"timestamp": "2026-02-08T12:48:31.410181Z"
} | 6894c2 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 132,
"completion_tokens": 4811
},
"timestamp": "2026-02-15T05:25:47.753Z",
"answer": 8992
},
{... | 1 | [
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "V3",
"status": "no"
}
] | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
7edcb3 | sequence_count_fib_divisible_v1_784195855_2529 | Let $\phi(n)$ denote the number of positive integers at most $n$ that are relatively prime to $n$. Define $u = \phi(2315)$ with respect to modulus 6, meaning $u$ is the number of positive integers $n \leq 2315$ such that $\gcd(n, 6) = 1$. Let $d = 15$. Compute the number of positive integers $n \leq u$ such that $d$ di... | 38 | graphs = [
Graph(
let={
"_n": Const(6),
"upper": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Const(2315)), Eq(GCD(a=Var("n"), b=Ref("_n")), Const(1))))),
"d": Const(15),
"result": CountOverSet(set=SolutionsS... | NT | null | COUNT | sympy | C4 | [
"C4"
] | 08d162 | sequence_count_fib_divisible_v1 | null | 6 | 0 | [
"C4"
] | 1 | 0.066 | 2026-02-08T05:50:43.138266Z | {
"verified": true,
"answer": 38,
"timestamp": "2026-02-08T05:50:43.204383Z"
} | 6536ee | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 152,
"completion_tokens": 1184
},
"timestamp": "2026-02-12T14:49:12.929Z",
"answer": 38
},
{
... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "C4",
"status": "ok"
},
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
}
] | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
7a2eb3 | modular_count_residue_v1_1915831931_2634 | Let $S$ be the set of all positive integers $n$ such that $1 \leq n \leq 58081$ and $n \equiv 2 \pmod{7}$. Let $c$ be the largest prime number $n_1$ such that $2 \leq n_1 \leq 7010$. Define
$$
r_1 = |S| \bmod 199, \quad r_2 = |S| \bmod 499.
$$
Compute the remainder when $r_1 + c \cdot r_2$ is divided by $69385$. | 47,518 | graphs = [
Graph(
let={
"upper": Const(58081),
"m": Const(7),
"r": 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("m")), Ref("r"))))),
... | NT | null | COUNT | sympy | MAX_PRIME_BELOW | [
"MAX_PRIME_BELOW"
] | 08a653 | modular_count_residue_v1 | two_moduli | 4 | 0 | [
"MAX_PRIME_BELOW"
] | 1 | 2.972 | 2026-02-08T17:00:42.430865Z | {
"verified": true,
"answer": 47518,
"timestamp": "2026-02-08T17:00:45.402544Z"
} | e6876c | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 171,
"completion_tokens": 2437
},
"timestamp": "2026-02-17T17:16:08.263Z",
"answer": 47518
},
... | 1 | [
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
}... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
572af1 | geo_count_lattice_rect_v1_1080341949_528 | Let $a = 50$ and $b = 183$. Define $R$ to be the number of lattice points in the rectangle $[0, a] \times [0, b]$, including the boundary. Let $c = 41$. Find the remainder when $c - R$ is divided by $76477$. | 67,134 | graphs = [
Graph(
let={
"a": Const(50),
"b": Const(183),
"result": LatticePointsRect(a=Ref(name='a'), b=Ref(name='b')),
"_c": Const(41),
"Q": Mod(value=Sub(Ref("_c"), Ref("result")), modulus=Const(76477)),
},
goal=Ref("Q"),
)
] | GEOM | null | COUNT | sympy | [] | geo_count_lattice_rect_v1 | null | 5 | 0 | null | null | 0.002 | 2026-02-08T13:34:01.751761Z | {
"verified": true,
"answer": 67134,
"timestamp": "2026-02-08T13:34:01.753530Z"
} | 1e214d | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 179,
"completion_tokens": 626
},
"timestamp": "2026-02-24T18:35:57.278Z",
"answer": 67134
},
{
"i... | 1 | [] | {
"lo": -7.18,
"mid": -5,
"hi": -3.01
} | ||||
8f3973 | nt_gcd_compute_v1_677425708_3182 | Let $a = 41928$ and $b = 78615$. Let $g = \gcd(a, b)$. Let $S$ be the set of all ordered pairs $(x, y)$ of positive integers such that $x + y = 82$. Let $P$ be the set of all values of $xy$ as $(x, y)$ ranges over $S$. Let $M$ be the maximum element of $P$. Compute the remainder when $M - g$ is divided by 62574. | 59,014 | graphs = [
Graph(
let={
"_n": Const(62574),
"a": Const(41928),
"b": Const(78615),
"result": GCD(a=Ref("a"), b=Ref("b")),
"Q": Mod(value=Sub(MaxOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositiv... | NT | null | COMPUTE | sympy | B1 | [
"B1"
] | d2b6e1 | nt_gcd_compute_v1 | negation_mod | 4 | 0 | [
"B1"
] | 1 | 0.002 | 2026-02-08T05:31:32.568577Z | {
"verified": true,
"answer": 59014,
"timestamp": "2026-02-08T05:31:32.570268Z"
} | 45a146 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 155,
"completion_tokens": 824
},
"timestamp": "2026-02-12T09:58:33.491Z",
"answer": 59014
},
{... | 1 | [
{
"lemma": "B1",
"status": "ok"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "V3",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
}
] | {
"lo": -5.55,
"mid": -3.01,
"hi": 0.32
} | ||
7a19a9 | modular_inverse_v1_1431428450_960 | Let $T$ be the set of all integers $t$ such that there exist positive integers $a$ and $b$ with $1 \leq a \leq 463$, $1 \leq b \leq 40$, $t = 4a + 14b + 12$, and $30 \leq t \leq 2424$. Let $m$ be the number of elements in $T$. Find the smallest positive integer $x$ such that $1 \leq x \leq m$ and $706x \equiv 1 \pmod{1... | 779 | graphs = [
Graph(
let={
"a": Const(706),
"m": Const(1193),
"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'), rig... | NT | null | EXTREMUM | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | modular_inverse_v1 | null | 6 | 0 | [
"LIN_FORM"
] | 1 | 0.081 | 2026-02-08T13:48:40.882192Z | {
"verified": true,
"answer": 779,
"timestamp": "2026-02-08T13:48:40.963076Z"
} | 4e91d1 | 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": 3716
},
"timestamp": "2026-02-15T20:37:23.097Z",
"answer": 779
},
{
... | 1 | [
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
}
] | {
"lo": -5.49,
"mid": 0.22,
"hi": 6.51
} | ||
041063 | alg_poly_orbit_count_v1_1218484723_40 | For a non-negative integer $a$, define the sequence:
\[
N = (2a^4 - 2a^3 - 5a^2 - 2a + 1) \bmod 61,\quad M = (2N^4 - 2N^3 - 5N^2 - 2N + 1) \bmod 61,
\]
\[
R = (2M^4 - 2M^3 - 5M^2 - 2M + 1) \bmod 61,\quad S = (2R^4 - 2R^3 - 5R^2 - 2R + 1) \bmod 61,
\]
\[
T = (2S^4 - 2S^3 - 5S^2 - 2S + 1) \bmod 61.
\]
Let $Q$ be the numb... | 9,160 | graphs = [
Graph(
let={
"p1": Mod(value=Sum(Mul(Const(2), Pow(Var("a"), Const(4))), Mul(Const(-2), Pow(Var("a"), Const(3))), Mul(Const(-5), Pow(Var("a"), Const(2))), Mul(Const(-2), Var("a")), Const(1)), modulus=Const(61)),
"p2": Mod(value=Sum(Mul(Const(2), Pow(Ref("p1"), Const(4))), ... | ALG | null | COUNT | sympy | POLY_ORBIT_COUNT | [
"POLY_ORBIT_COUNT"
] | 4ad965 | alg_poly_orbit_count_v1 | null | 6 | null | [
"POLY_ORBIT_COUNT"
] | 1 | 0.113 | 2026-02-25T01:44:35.135876Z | {
"verified": true,
"answer": 9160,
"timestamp": "2026-02-25T01:44:35.248619Z"
} | 844979 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 362,
"completion_tokens": 32768
},
"timestamp": "2026-03-10T08:17:19.477Z",
"answer": null
},
{
... | 1 | [
{
"lemma": "POLY_ORBIT_COUNT",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
}
] | {
"lo": 3.86,
"mid": 5.72,
"hi": 7.83
} | ||
cf28f9 | antilemma_k3_v1_153355830_2643 | Compute $$\sum_{d \mid 45588} \phi(d),$$ where $\phi(d)$ denotes Euler's totient function. Let $x$ be the value of this sum. Find the remainder when $289 - x$ is divided by $59227$. | 13,928 | graphs = [
Graph(
let={
"x": SumOverDivisors(n=Const(value=45588), var='d', expr=EulerPhi(n=Var(name='d'))),
"_c": Const(289),
"Q": Mod(value=Sub(Ref("_c"), Ref("x")), modulus=Const(59227)),
},
goal=Ref("Q"),
)
] | NT | COMB | COMPUTE | sympy | K13 | [
"K3"
] | 54c41e | antilemma_k3_v1 | null | 4 | 0 | [
"K13",
"K3"
] | 2 | 0.002 | 2026-02-08T07:15:14.997507Z | {
"verified": true,
"answer": 13928,
"timestamp": "2026-02-08T07:15:14.999540Z"
} | a016bb | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 101,
"completion_tokens": 382
},
"timestamp": "2026-02-13T09:20:14.270Z",
"answer": 13928
},
{... | 1 | [
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "K3",
"status": "ok"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
}
] | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
15e65e | antilemma_cartesian_v1_655260480_2496 | Let $x$ be the number of ordered pairs $(a, b)$ such that $1 \leq a \leq 26$ and $1 \leq b \leq 38$. Let $S$ be the set of all integers $t$ for which there exist integers $a$ and $b$ satisfying $1 \leq a \leq 4$, $1 \leq b \leq 3$, $5 \leq t \leq 17$, and $t = 2a + 3b$. Compute the Bell number of $|x| \bmod |S|$, where... | 21,147 | graphs = [
Graph(
let={
"x": CountOverSet(set=CartesianProduct(left=IntegerRange(start=Const(1), end=Const(26)), right=IntegerRange(start=Const(1), end=Const(38)))),
"Q": Bell(Mod(value=Abs(arg=Ref(name='x')), modulus=CountOverSet(set=SolutionsSet(var=Var("t"), condition=Exists(var=V... | COMB | GEOM | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM",
"COUNT_CARTESIAN"
] | 6e491f | antilemma_cartesian_v1 | bell_mod | 3 | 0 | [
"COUNT_CARTESIAN",
"LIN_FORM"
] | 2 | 0.004 | 2026-02-08T16:47:37.622968Z | {
"verified": true,
"answer": 21147,
"timestamp": "2026-02-08T16:47:37.626604Z"
} | 95c737 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 199,
"completion_tokens": 1161
},
"timestamp": "2026-02-17T11:24:41.189Z",
"answer": 21147
},
... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "ok"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "V7",
"sta... | {
"lo": -2.38,
"mid": 1.74,
"hi": 6.59
} | ||
9f39de | comb_sum_binomial_row_v1_865884756_1353 | Let $n = 11$. Let $r$ be the number of positive integers $p$ for which there exists a positive integer $q$ such that $pq = 18$, $\gcd(p, q) = 1$, and $p < q$. Let $m = r^{11}$. Find the smallest positive integer $k$ such that the $k$-th Fibonacci number is divisible by $m + 2$. Determine the value of $k$. | 300 | graphs = [
Graph(
let={
"n": Const(11),
"result": Pow(CountOverSet(set=SolutionsSet(var=Var("p"), condition=And(IsPositive(arg=Var(name='p')), Exists(var=Var(name='q'), condition=And(Eq(left=Mul(Var(name='p'), Var(name='q')), right=Const(value=18)), Eq(left=GCD(a=Var(name='p'), b=Var... | NT | null | SUM | sympy | COPRIME_PAIRS | [
"COPRIME_PAIRS"
] | 2bb3aa | comb_sum_binomial_row_v1 | null | 4 | 0 | [
"COPRIME_PAIRS"
] | 1 | 0.002 | 2026-02-08T15:58:32.756475Z | {
"verified": true,
"answer": 300,
"timestamp": "2026-02-08T15:58:32.758796Z"
} | d25a8e | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 142,
"completion_tokens": 1742
},
"timestamp": "2026-02-16T17:56:52.578Z",
"answer": 300
},
{
... | 1 | [
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "V1",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
493748 | comb_bell_compute_v1_1978505735_1754 | Let $m = 14$. Define $n$ to be the number of ordered pairs $(i, j)$ of integers such that $1 \le i \le 12$, $1 \le j \le 12$, and $i + j = m$. Let
$$
v = \sum_{k_1=0}^{5} (-1)^{k_1} \binom{5}{k_1}
$$
and
$$
c = \sum_{k=0}^{0} (-1)^k \binom{0}{k}.
$$
Define $n'$ to be the number of ordered pairs $(i_1, j_1)$ of integers... | 17,157 | graphs = [
Graph(
let={
"_m": Const(14),
"_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(12)), right=IntegerRange(start=Const(1), end=Co... | COMB | null | COMPUTE | sympy | COUNT_SUM_EQUALS | [
"COUNT_SUM_EQUALS/COUNT_SUM_EQUALS/BINOMIAL_ALTERNATING"
] | 8f93ab | comb_bell_compute_v1 | null | 5 | 2 | [
"BINOMIAL_ALTERNATING",
"COUNT_SUM_EQUALS"
] | 2 | 0.028 | 2026-02-08T16:23:27.014429Z | {
"verified": true,
"answer": 17157,
"timestamp": "2026-02-08T16:23:27.042892Z"
} | 313d7f | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 344,
"completion_tokens": 2419
},
"timestamp": "2026-02-24T20:50:34.808Z",
"answer": 17157
},
{
... | 1 | [
{
"lemma": "BINOMIAL_ALTERNATING",
"status": "ok_later"
},
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "ok"
},
{
"lem... | {
"lo": 1.98,
"mid": 5.23,
"hi": 8.52
} | ||
bfa440 | algebra_poly_eval_v1_717093673_1553 | Let $n_0 = 2$. Let $t$ be the largest prime number $n$ such that $2 \le n \le 15$. Compute the value of $t^3 - 7t^2 + 2t + 2$. | 1,042 | graphs = [
Graph(
let={
"_n": Const(2),
"t": MaxOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Ref("_n")), Leq(Var("n"), Const(15)), IsPrime(Var("n"))))),
"result": Sum(Pow(Ref("t"), Const(3)), Mul(Const(-7), Pow(Ref("t"), Const(2))), Mul(Const(2), Ref... | NT | null | COMPUTE | sympy | MAX_PRIME_BELOW | [
"MAX_PRIME_BELOW"
] | dc3ad3 | algebra_poly_eval_v1 | null | 3 | 0 | [
"MAX_PRIME_BELOW"
] | 1 | 0.003 | 2026-02-08T16:10:15.043674Z | {
"verified": true,
"answer": 1042,
"timestamp": "2026-02-08T16:10:15.046370Z"
} | cd13d6 | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 111,
"completion_tokens": 261
},
"timestamp": "2026-02-16T06:58:47.934Z",
"answer": 1016
},
{
"id": 11,... | 1 | [
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "VAL_SUM_EQ",
"s... | {
"lo": -8.26,
"mid": -5.01,
"hi": -1.76
} | ||
2decf4 | antilemma_sum_equals_v1_1526740231_493 | Let $m = 94$. Define $n$ to be the number of ordered pairs $(x_1, x_2)$ of positive odd integers such that $x_1 + x_2 = m$. Compute the number of ordered pairs $(i, j)$ with $1 \le i \le 45$ and $1 \le j \le 46$ such that $i + j = n$. | 45 | graphs = [
Graph(
let={
"_m": Const(94),
"_n": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x1"), Var("x2")]), condition=And(IsPositive(arg=Var(name='x1')), IsPositive(arg=Var(name='x2')), IsOdd(arg=Var(name='x1')), IsOdd(arg=Var(name='x2')), Eq(Sum(Var("x1"), Var("x2")), R... | COMB | GEOM | COMPUTE | sympy | COUNT_CARTESIAN | [
"COMB1/COUNT_SUM_EQUALS",
"COUNT_SUM_EQUALS"
] | 3e1adf | antilemma_sum_equals_v1 | null | 4 | 0 | [
"COMB1",
"COUNT_CARTESIAN",
"COUNT_SUM_EQUALS"
] | 3 | 0.016 | 2026-02-08T11:34:06.682554Z | {
"verified": true,
"answer": 45,
"timestamp": "2026-02-08T11:34:06.698142Z"
} | 67257e | 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": 1812
},
"timestamp": "2026-02-24T14:18:48.958Z",
"answer": 45
},
{
"id"... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COMB1",
"status": "ok"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS... | {
"lo": -9.23,
"mid": -6.18,
"hi": -4.06
} | ||
5e9d3b | comb_sum_binomial_row_v1_1353956133_265 | Let $n$ be the number of nonnegative integers $j$ such that $0 \leq j \leq 802$ and $\binom{802}{j}$ is odd. Compute the remainder when $55481 \cdot 2^n$ is divided by $71870$. | 27,646 | graphs = [
Graph(
let={
"_n": Const(2),
"n": CountOverSet(set=SolutionsSet(var=Var("j"), condition=And(Geq(Var("j"), Const(0)), Leq(Var("j"), Const(802)), Eq(Mod(value=Binom(n=Const(802), k=Var("j")), modulus=Const(2)), Const(1))), domain='nonnegative_integers')),
"result... | ALG | COMB | SUM | sympy | V8 | [
"V8"
] | 86348e | comb_sum_binomial_row_v1 | null | 6 | 0 | [
"V8"
] | 1 | 0.002 | 2026-02-08T11:22:30.472633Z | {
"verified": true,
"answer": 27646,
"timestamp": "2026-02-08T11:22:30.474173Z"
} | 34aaec | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 172,
"completion_tokens": 6627
},
"timestamp": "2026-02-24T13:40:52.002Z",
"answer": 27646
},
{
"... | 1 | [
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "V8",
"status": "ok"
}
] | {
"lo": -2.35,
"mid": 1.22,
"hi": 4.84
} | ||
eacf72 | alg_poly3_sum_v1_1218484723_1389 | Let $A = \left|\{ (a_1, b_1) : 1 \leq a_1, b_1 \leq 25,\ 2b_1^2 + 13a_1^2 - 2a_1b_1 \leq 692 \}\right|$ and $B = \left|\{ (a_2, b_2) : 1 \leq a_2, b_2 \leq 25,\ 41a_2^2 - 12a_2b_2 + 20b_2^2 \leq 12473 \}\right|$. Compute the remainder when $$\sum_{\substack{1 \leq a \leq 110 \\ 1 \leq b \leq A}} \left( 250a^3 + 195a b^... | 3,806 | graphs = [
Graph(
let={
"_m": Const(3),
"_n": Const(2),
"result": Mod(value=SumOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("a"), Var("b")]), condition=And(Geq(Var("a"), Const(1)), Leq(Var("a"), Const(110)), Geq(Var("b"), Const(1)), Leq(Var("b"), CountO... | ALG | null | COMPUTE | sympy | MIN_PRIME_FACTOR | [
"QF_PSD_COUNT_LEQ"
] | 009d0f | alg_poly3_sum_v1 | null | 5 | 0 | [
"MIN_PRIME_FACTOR",
"QF_PSD_COUNT_LEQ"
] | 2 | 0.192 | 2026-02-25T03:07:44.982899Z | {
"verified": true,
"answer": 3806,
"timestamp": "2026-02-25T03:07:45.174628Z"
} | 3ef1e2 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 322,
"completion_tokens": 17194
},
"timestamp": "2026-03-10T06:46:47.166Z",
"answer": 6869
},
{
... | 1 | [
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "QF_PSD_COUNT_LEQ",
"status": "ok"
}
] | {
"lo": 3.14,
"mid": 5.37,
"hi": 7.61
} | ||
6ead9b | modular_count_residue_v1_151522320_469 | Let $m$ be the minimum value of $x + y$ over all ordered pairs of positive integers $(x, y)$ such that $xy = 81$. Let $r$ be the smallest divisor of $2146981$ that is at least $2$. Determine the value of the number of positive integers $n$ such that $1 \leq n \leq 81225$ and $n \equiv r \pmod{m}$. | 4,512 | graphs = [
Graph(
let={
"_n": Const(2),
"upper": Const(81225),
"m": MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(Mul(Var("x"), Var("y")), Const(81)))), e... | NT | null | COUNT | sympy | MIN_PRIME_FACTOR | [
"MIN_PRIME_FACTOR",
"B3"
] | 6c6c26 | modular_count_residue_v1 | null | 5 | 0 | [
"B3",
"MIN_PRIME_FACTOR"
] | 2 | 2.967 | 2026-02-08T03:20:52.959241Z | {
"verified": true,
"answer": 4512,
"timestamp": "2026-02-08T03:20:55.926338Z"
} | f2bcc6 | 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": 1217
},
"timestamp": "2026-02-10T13:58:42.472Z",
"answer": 4512
},
{
"i... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "MIN_PRIME_FACTOR",
"status": "ok"
},
{
... | {
"lo": -3.46,
"mid": 1.03,
"hi": 5.49
} | ||
7c7446 | diophantine_fbi2_min_v1_1978505735_6760 | Let $k$ be the sum of all real solutions $x$ to the equation $x^2 - 77x + 76 = 0$. Let $d$ be the smallest integer such that $4 \leq d \leq 87$, $d$ divides $k$, and $\frac{k}{d} \geq 5$. Determine the value of $d$. | 7 | graphs = [
Graph(
let={
"k": SumOverSet(set=SolutionsSet(var=Var("x"), condition=Eq(Sum(Pow(Var("x"), Const(2)), Mul(Const(-77), Var("x")), Const(76)), Const(0)))),
"upper": Const(87),
"result": MinOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Const(4... | NT | null | EXTREMUM | sympy | MIN_PRIME_FACTOR | [
"VIETA_SUM"
] | b33a7a | diophantine_fbi2_min_v1 | null | 4 | 0 | [
"MIN_PRIME_FACTOR",
"VIETA_SUM"
] | 2 | 0.026 | 2026-02-08T19:47:01.181314Z | {
"verified": true,
"answer": 7,
"timestamp": "2026-02-08T19:47:01.207249Z"
} | 6b1fe2 | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 1,
"correct": {
"strict": false,
"boxed": false,
"relaxed": true
},
"usage": {
"prompt_tokens": 138,
"completion_tokens": 387
},
"timestamp": "2026-02-16T18:45:44.574Z",
"answer": 11
},
{
"id": 11,
... | 1 | [
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "V3",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
},
{
"lemma": "VIETA_SUM",
"status": "ok"... | {
"lo": -8.26,
"mid": -5.01,
"hi": -1.76
} | ||
71a5c2 | geo_visible_lattice_v1_1918700295_2159 | Let $ n = 89 $. Define $ L $ 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 $. Compute the remainder when $ 51173 \cdot L $ is divided by 68188. | 37,823 | graphs = [
Graph(
let={
"n": Const(89),
"result": VisibleLatticePoints(n=Ref(name='n')),
"Q": Mod(value=Mul(Const(51173), Ref("result")), modulus=Const(68188)),
},
goal=Ref("Q"),
)
] | GEOM | null | COUNT | sympy | [] | geo_visible_lattice_v1 | null | 3 | 0 | null | null | 0.357 | 2026-02-08T07:43:53.366927Z | {
"verified": true,
"answer": 37823,
"timestamp": "2026-02-08T07:43:53.723852Z"
} | b637b0 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 187,
"completion_tokens": 16551
},
"timestamp": "2026-02-24T08:24:32.768Z",
"answer": 37823
},
{
... | 1 | [] | {
"lo": 1.15,
"mid": 4.18,
"hi": 6.61
} | ||||
aa8c2c | geo_count_lattice_triangle_v1_1820931509_168 | Let the points $A = (111, 70)$, $B = (50, 120)$, and $C = (0, 0)$ define triangle $ABC$. The area of triangle $ABC$ is half the absolute value of $111 \cdot 120 + 50 \cdot (-70)$. Let $b$ be the number of lattice points on the boundary of triangle $ABC$, which is given by the sum of the greatest common divisors of the ... | 13,366 | graphs = [
Graph(
let={
"area_2x": Abs(arg=Sum(Mul(Const(value=111), Const(value=120)), Mul(Const(value=50), Sub(left=Const(value=0), right=Const(value=70))))),
"boundary": Sum(GCD(a=Abs(arg=Const(value=111)), b=Abs(arg=Const(value=70))), GCD(a=Abs(arg=Sub(left=Const(value=50), right... | ALG | NT | COUNT | sympy | [] | geo_count_lattice_triangle_v1 | null | 5 | 0 | null | null | 0.005 | 2026-02-08T11:23:49.690606Z | {
"verified": true,
"answer": 13366,
"timestamp": "2026-02-08T11:23:49.695822Z"
} | f00b7e | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 191,
"completion_tokens": 2249
},
"timestamp": "2026-02-14T13:10:31.072Z",
"answer": 13366
},
... | 1 | [] | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||||
cc7a44 | nt_num_divisors_compute_v1_865884756_2780 | Let $n = 78400$. Compute the number of positive divisors of $n$. | 63 | graphs = [
Graph(
let={
"n": Const(78400),
"result": NumDivisors(n=Ref("n")),
},
goal=Ref("result"),
)
] | NT | null | COMPUTE | sympy | MIN_PRIME_FACTOR | [
"MIN_PRIME_FACTOR/K2"
] | 352a97 | nt_num_divisors_compute_v1 | null | 2 | 0 | [
"K2",
"MIN_PRIME_FACTOR"
] | 2 | 0.024 | 2026-02-08T16:55:58.043260Z | {
"verified": true,
"answer": 63,
"timestamp": "2026-02-08T16:55:58.067124Z"
} | 11cb40 | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 77,
"completion_tokens": 265
},
"timestamp": "2026-02-16T08:40:12.431Z",
"answer": 84
},
{
"id": 11,
... | 1 | [
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K2",
"status": "ok_later"
},
{
"lemma": "MIN_PRIME_FACTOR",
"status": "ok"
},
{
"lemma": "V3",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
},
{
"l... | {
"lo": -8.26,
"mid": -5.01,
"hi": -1.76
} | ||
1bbdc8 | diophantine_fbi2_min_v1_548369836_307 | Let $m = 2$, $n = 13$, and $k = 81$. Define
$$
\text{upper} = \sum_{k=\phi(2)}^{13} \phi(k) \left\lfloor \frac{\nu_m(7^{2048} - 5^{2048})}{k} \right\rfloor,
$$
where $\phi(k)$ is Euler's totient function and $\nu_m(N)$ denotes the largest integer $e$ such that $m^e$ divides $N$. Let $S$ be the set of all integers $d$ s... | 9 | graphs = [
Graph(
let={
"_m": Const(2),
"_n": Const(13),
"k": Const(81),
"upper": Summation(var="k", start=EulerPhi(n=Const(2)), end=Ref("_n"), expr=Mul(EulerPhi(n=Var("k")), Floor(Div(MaxKDivides(target=Sub(Pow(Const(7), Const(2048)), Pow(Const(5), Const(2048... | NT | null | EXTREMUM | sympy | K2 | [
"LTE_DIFF_P2/K2",
"ONE_PHI_2"
] | a7753d | diophantine_fbi2_min_v1 | null | 7 | 0 | [
"K2",
"LTE_DIFF_P2",
"ONE_PHI_2"
] | 3 | 0.044 | 2026-02-08T02:51:42.132017Z | {
"verified": true,
"answer": 9,
"timestamp": "2026-02-08T02:51:42.175946Z"
} | 625331 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 287,
"completion_tokens": 909
},
"timestamp": "2026-02-08T20:17:51.715Z",
"answer": 9
},
{
"id": ... | 2 | [
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "K2",
"status": "ok_later"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "ok"
},
{
"lemm... | {
"lo": -10,
"mid": -6.5,
"hi": -3.01
} | ||
762580 | lin_form_endings_v1_1125832087_1941 | Let $a = 60$ and $b = 48$. Define $\ell$ to be the least common multiple of $a$ and $b$. Let $s = \ell + a + b$. Compute the remainder when $19465 \cdot s$ is divided by $61306$. | 30,160 | graphs = [
Graph(
let={
"a_coeff": Const(60),
"b_coeff": Const(48),
"k_val": Const(1),
"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 | 3 | null | [
"LIN_FORM"
] | 1 | 0.002 | 2026-02-08T04:15:13.771610Z | {
"verified": true,
"answer": 30160,
"timestamp": "2026-02-08T04:15:13.773203Z"
} | b28362 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 172,
"completion_tokens": 744
},
"timestamp": "2026-02-10T15:56:13.122Z",
"answer": 30160
},
{
"... | 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_SUM",
... | {
"lo": -3.42,
"mid": 1.86,
"hi": 7.55
} | ||
9823e3 | nt_count_coprime_v1_1742523217_1249 | Let $k$ be the number of positive integers $p$ for which there exists a positive integer $q$ such that $pq = 6$, $\gcd(p, q) = 1$, and $p < q$. Let $S$ be the set of all integers $n$ with $1 \leq n \leq 61504$ such that $\gcd(n, k) = 1$. Compute the number of elements in $S$. | 30,752 | graphs = [
Graph(
let={
"upper": Const(61504),
"k": CountOverSet(set=SolutionsSet(var=Var("p"), condition=And(IsPositive(arg=Var(name='p')), Exists(var=Var(name='q'), condition=And(Eq(left=Mul(Var(name='p'), Var(name='q')), right=Const(value=6)), Eq(left=GCD(a=Var(name='p'), b=Var(na... | NT | null | COUNT | sympy | COPRIME_PAIRS | [
"COPRIME_PAIRS",
"ONE_PHI_1"
] | 81fa00 | nt_count_coprime_v1 | null | 3 | 0 | [
"COPRIME_PAIRS",
"ONE_PHI_1"
] | 2 | 5.447 | 2026-02-08T03:35:00.056875Z | {
"verified": true,
"answer": 30752,
"timestamp": "2026-02-08T03:35:05.503511Z"
} | add073 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 207,
"completion_tokens": 554
},
"timestamp": "2026-02-10T05:38:48.249Z",
"answer": 30752
},
{
"i... | 1 | [
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "ONE_PHI_1",
"status": "ok"
},
{
... | {
"lo": -6.5,
"mid": -0.2,
"hi": 6.11
} | ||
682260 | algebra_poly_eval_v1_238844314_113 | Let $t = 13$. Define $r$ to be the value of
$$
\frac{4t^3 + \sum_{k=1}^{2} \varphi(k) \left\lfloor \frac{2}{k} \right\rfloor \cdot t^2 - 3t + 7}{59}.
$$
Compute the remainder when $25535 \cdot r$ is divided by $66621$. | 11,735 | graphs = [
Graph(
let={
"_n": Const(2),
"t": Const(13),
"result": Div(Sum(Mul(Const(4), Pow(Ref("t"), Const(3))), Mul(Summation(var="k", start=Const(1), end=Const(2), expr=Mul(EulerPhi(n=Var("k")), Floor(Div(Const(2), Var("k"))))), Pow(Ref("t"), Ref("_n"))), Mul(Const(-3)... | NT | null | COMPUTE | sympy | K2 | [
"K2"
] | 6897ab | algebra_poly_eval_v1 | null | 4 | 0 | [
"K2"
] | 1 | 0.003 | 2026-02-08T13:07:42.267762Z | {
"verified": true,
"answer": 11735,
"timestamp": "2026-02-08T13:07:42.270348Z"
} | db8b74 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 134,
"completion_tokens": 875
},
"timestamp": "2026-02-15T10:07:43.367Z",
"answer": 11735
},
{... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K2",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
}
] | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
691b4a | diophantine_product_count_v1_655260480_2621 | Let $k = 120$. Let $T$ be the set of all integers $t$ such that $20 \leq t \leq 96$ and there exist positive integers $a$, $b$ with $1 \leq a \leq 5$, $1 \leq b \leq 15$, and $t = 5a + 4b + 11$. Let $u = |T|$. Now consider the set of all positive integers $x$ such that $1 \leq x \leq u$, $x$ divides $k$, and $\frac{k}{... | 14 | graphs = [
Graph(
let={
"k": Const(120),
"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=5)), Geq(left=V... | NT | null | COUNT | sympy | L3B | [
"LIN_FORM"
] | 7b2633 | diophantine_product_count_v1 | null | 5 | 0 | [
"L3B",
"LIN_FORM"
] | 2 | 0.054 | 2026-02-08T16:52:14.023582Z | {
"verified": true,
"answer": 14,
"timestamp": "2026-02-08T16:52:14.077759Z"
} | 183a1e | 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": 3050
},
"timestamp": "2026-02-17T13:29:24.126Z",
"answer": 14
},
{
... | 1 | [
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "V3",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
4ab582 | algebra_poly_eval_v1_677425708_1151 | Let $m = 3$ and $n = 3$. Compute
$$
\left( \sum_{k=1}^{3} \phi(k) \left\lfloor \frac{3}{k} \right\rfloor \right) \cdot 10^4 - 2 \cdot 10^{\sum_{k=1}^{2} \phi(k) \left\lfloor \frac{2}{k} \right\rfloor} + 4 \cdot 10^2 + 2 \cdot 10 + 4.
$$ | 58,424 | graphs = [
Graph(
let={
"_m": Const(3),
"_n": Const(3),
"a": Const(10),
"result": Sum(Mul(Summation(var="k", start=Const(1), end=Ref("_m"), expr=Mul(EulerPhi(n=Var("k")), Floor(Div(Ref("_n"), Var("k"))))), Pow(Ref("a"), Const(4))), Mul(Const(-2), Pow(Ref("a"),... | NT | null | COMPUTE | sympy | K2 | [
"K2"
] | 6897ab | algebra_poly_eval_v1 | null | 4 | 0 | [
"K2"
] | 1 | 0.004 | 2026-02-08T04:01:18.531473Z | {
"verified": true,
"answer": 58424,
"timestamp": "2026-02-08T04:01:18.535130Z"
} | 36b2fb | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 234,
"completion_tokens": 816
},
"timestamp": "2026-02-09T16:17:48.898Z",
"answer": 58424
},
{
"i... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K2",
"status": "ok"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "V1",
"status": "no"
},
{
"lemma": "V3",
"status": "no"
}
] | {
"lo": -7.01,
"mid": -4.68,
"hi": -2.15
} | ||
e77501 | nt_max_prime_below_v1_1742523217_1039 | Let $P$ be the set of all positive integers $p$ for which there exists a positive integer $q$ such that $p \cdot q = 72$, $\gcd(p, q) = 1$, and $p < q$. Let $c = |P|$. Let $T$ be the set of all prime numbers $n$ such that $c \leq n \leq 80089$. Let $\text{result}$ be the largest element of $T$. Compute the remainder wh... | 9,479 | graphs = [
Graph(
let={
"upper": Const(80089),
"result": MaxOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), CountOverSet(set=SolutionsSet(var=Var("p"), condition=And(IsPositive(arg=Var(name='p')), Exists(var=Var(name='q'), condition=And(Eq(left=Mul(Var(name='p'), V... | NT | null | EXTREMUM | sympy | COPRIME_PAIRS | [
"COPRIME_PAIRS"
] | 2bb3aa | nt_max_prime_below_v1 | null | 4 | 0 | [
"COPRIME_PAIRS"
] | 1 | 1.862 | 2026-02-08T03:23:49.198779Z | {
"verified": true,
"answer": 9479,
"timestamp": "2026-02-08T03:23:51.061130Z"
} | 0eb766 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 238,
"completion_tokens": 6049
},
"timestamp": "2026-02-09T10:12:02.238Z",
"answer": 9479
},
{
"... | 1 | [
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
}
] | {
"lo": -3.42,
"mid": 1.86,
"hi": 7.55
} | ||
9b3e4e | comb_sum_binomial_row_v1_168721529_1560 | Let $m = 2$ and $n = 58399$. Define $a = 15$ and $R = 2^a$. Let $S$ be the set of all ordered pairs $(x, y)$ of positive integers such that $xy = 169$. Let $T$ be the set of all values $x + y$ where $(x, y) \in S$. Let $u$ be the minimum value in $T$. Let $P$ be the set of all prime numbers $k$ such that $m \leq k \leq... | 25,654 | graphs = [
Graph(
let={
"_m": Const(2),
"_n": Const(58399),
"n": Const(15),
"result": Pow(Const(2), Ref("n")),
"Q": Mod(value=Sub(MaxOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Ref("_m")), Leq(Var("n"), MinOverSet(set=MapOver... | NT | null | SUM | sympy | B3 | [
"B3/MAX_PRIME_BELOW"
] | 511ec9 | comb_sum_binomial_row_v1 | negation_mod | 4 | 0 | [
"B3",
"MAX_PRIME_BELOW"
] | 2 | 0.002 | 2026-02-08T13:46:57.540401Z | {
"verified": true,
"answer": 25654,
"timestamp": "2026-02-08T13:46:57.542418Z"
} | e4a0cc | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 267,
"completion_tokens": 603
},
"timestamp": "2026-02-09T18:53:54.668Z",
"answer": 25654
},
{
"i... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok_later"
},
{
"lemma": "MOD_FACTORIAL",
... | {
"lo": -8.26,
"mid": -5.01,
"hi": -1.76
} | ||
7b16a0 | comb_sum_binomial_row_v1_1978505735_6186 | Let $d$ be the smallest divisor of $634933$ that is at least $2$. Compute the remainder when $34655 \cdot 2^d$ is divided by $99813$. | 25,588 | graphs = [
Graph(
let={
"_n": Const(2),
"n": MinOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Const(2)), Divides(divisor=Var("d"), dividend=Const(634933))))),
"result": Pow(Ref("_n"), Ref("n")),
"Q": Mod(value=Mul(Const(34655), Ref("result... | NT | null | SUM | sympy | MIN_PRIME_FACTOR | [
"MIN_PRIME_FACTOR"
] | bc3776 | comb_sum_binomial_row_v1 | null | 3 | 0 | [
"MIN_PRIME_FACTOR"
] | 1 | 0.002 | 2026-02-08T19:27:55.746343Z | {
"verified": true,
"answer": 25588,
"timestamp": "2026-02-08T19:27:55.748044Z"
} | 5a562d | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 88,
"completion_tokens": 1093
},
"timestamp": "2026-02-18T22:30:50.911Z",
"answer": 25588
},
{... | 1 | [
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "MIN_PRIME_FACTOR",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "V3",
"status": "no"
},
{
"lemma": "V8",
"statu... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
f93c24 | modular_mod_compute_v1_865884756_5840 | Let $S$ be the set of all ordered pairs $(x, y)$ of positive integers such that $xy = 2458624$. For each pair $(x, y)$, compute $x + y$, and let $m$ be the minimum value among these sums. Compute the remainder when $(-76729) \mod m$ is multiplied by $44121$, and then divided by $89107$. | 34,702 | graphs = [
Graph(
let={
"_n": Const(44121),
"a": Const(-76729),
"m": MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(Mul(Var("x"), Var("y")), Const(2458624)... | NT | null | COMPUTE | sympy | B3 | [
"B3"
] | 0cd20d | modular_mod_compute_v1 | null | 5 | 0 | [
"B3"
] | 1 | 0.001 | 2026-02-08T18:48:08.324298Z | {
"verified": true,
"answer": 34702,
"timestamp": "2026-02-08T18:48:08.325410Z"
} | 722d67 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 131,
"completion_tokens": 2858
},
"timestamp": "2026-02-18T19:44:02.617Z",
"answer": 34702
},
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "V3",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
73115b | comb_count_derangements_v1_1915831931_4143 | Let $S$ be the set of all ordered pairs $(x,y)$ of positive integers such that $xy = 16$. For each such pair, define $s = x + y$. Let $n$ be the minimum value of $s$ over all such pairs. Define $r = !n$, the subfactorial of $n$. Compute the remainder when $37325 \cdot r$ is divided by $95592$. | 68,453 | 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(16)))), expr=Sum(Var("x"), Var("y")))),
"result": Subfactori... | COMB | null | COUNT | sympy | B3 | [
"B3"
] | 0cd20d | comb_count_derangements_v1 | null | 3 | 0 | [
"B3"
] | 1 | 0.002 | 2026-02-08T18:07:43.616328Z | {
"verified": true,
"answer": 68453,
"timestamp": "2026-02-08T18:07:43.618443Z"
} | fcf329 | 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": 1953
},
"timestamp": "2026-02-18T14:32:13.168Z",
"answer": 68453
},
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8_SUM",
"status"... | {
"lo": -3.12,
"mid": 1.47,
"hi": 6.57
} | ||
782333 | diophantine_fbi2_count_v1_971394319_1384 | Let $ S $ be the set of all divisors $ d $ of $ 60 $ such that $ 6 \leq d \leq 60 $, $ \frac{60}{d} \geq 5 $, and $ \frac{60}{d} \leq \min(T) $, where $ T $ is the set of all integers $ d \geq 2 $ that divide $ 764215259 $. Let $ A $ be the number of elements in $ S $. Let $ R $ be the set of all ordered pairs $ (x, y)... | 4,480 | graphs = [
Graph(
let={
"_m": Const(60),
"_n": Const(6),
"k": Const(60),
"result": CountOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Ref("_n")), Leq(Var("d"), Ref("_m")), Divides(divisor=Var("d"), dividend=Ref("k")), Geq(Div(Ref("k"), Var... | NT | null | COUNT | sympy | B3 | [
"B3",
"MIN_PRIME_FACTOR"
] | f123d1 | diophantine_fbi2_count_v1 | quadratic_mod | 4 | 0 | [
"B3",
"MIN_PRIME_FACTOR"
] | 2 | 0.009 | 2026-02-08T13:39:46.473786Z | {
"verified": true,
"answer": 4480,
"timestamp": "2026-02-08T13:39:46.483225Z"
} | 236004 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 218,
"completion_tokens": 3216
},
"timestamp": "2026-02-15T18:58:15.249Z",
"answer": 4480
},
{... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "MIN_PRIME_FACTOR",
"status": "ok... | {
"lo": -5.49,
"mid": 0.22,
"hi": 6.51
} | ||
2fe3b2 | modular_mod_compute_v1_677425708_2400 | Let $n = 3844$. Let $m$ be the number of positive integers $j$ such that $1 \leq j \leq n$ and $j^5 \leq 839299365868340224$. Compute the remainder when $-73441$ is divided by $m$. | 3,439 | graphs = [
Graph(
let={
"_n": Const(3844),
"a": Const(-73441),
"m": CountOverSet(set=SolutionsSet(var=Var("j"), condition=And(Geq(Var("j"), Const(1)), Leq(Var("j"), Ref("_n")), Leq(Pow(Var("j"), Const(5)), Const(839299365868340224))), domain='positive_integers')),
... | NT | null | COMPUTE | sympy | C3 | [
"C3"
] | 8a214c | modular_mod_compute_v1 | null | 3 | 0 | [
"C3"
] | 1 | 0.001 | 2026-02-08T05:01:54.843361Z | {
"verified": true,
"answer": 3439,
"timestamp": "2026-02-08T05:01:54.844341Z"
} | 6f4ce5 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 175,
"completion_tokens": 6160
},
"timestamp": "2026-02-11T22:46:08.740Z",
"answer": 3439
},
{
"i... | 1 | [
{
"lemma": "C3",
"status": "ok"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "V1",
"status": "no"
},
{
"lemma": "V3",
"status": "no"
}
] | {
"lo": -3.45,
"mid": 1.15,
"hi": 6.18
} | ||
31db8b | sequence_fibonacci_compute_v1_677425708_3229 | Let $m$ be the number of integers $t$ with $7 \leq t \leq 35$ for which there exist integers $a$ and $b$ such that $1 \leq a \leq 5$, $1 \leq b \leq 5$, and $t = 4a + 3b$. Let $n$ be the number of positive integers $j$ such that $1 \leq j \leq m$ and $j^k \leq 279841$, where $k$ is the number of positive integers $p$ s... | 28,657 | graphs = [
Graph(
let={
"_n": CountOverSet(set=SolutionsSet(var=Var("t"), condition=Exists(var=Var(name='a'), condition=Exists(var=Var(name='b'), condition=And(Geq(left=Var(name='a'), right=Const(value=1)), Leq(left=Var(name='a'), right=Const(value=5)), Geq(left=Var(name='b'), right=Const(value=... | NT | null | COMPUTE | sympy | COPRIME_PAIRS | [
"COPRIME_PAIRS/C3",
"LIN_FORM/C3"
] | 66bfb5 | sequence_fibonacci_compute_v1 | null | 7 | 0 | [
"C3",
"COPRIME_PAIRS",
"LIN_FORM"
] | 3 | 0.003 | 2026-02-08T05:32:29.110301Z | {
"verified": true,
"answer": 28657,
"timestamp": "2026-02-08T05:32:29.113779Z"
} | 1f357e | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 203,
"completion_tokens": 2751
},
"timestamp": "2026-02-12T11:30:44.363Z",
"answer": 28657
},
... | 1 | [
{
"lemma": "C3",
"status": "ok_later"
},
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status":... | {
"lo": -3.51,
"mid": 1.33,
"hi": 6.56
} | ||
478d69 | comb_sum_binomial_row_v1_153355830_1325 | Let $n_2 = 7 + \binom{14}{0}$ and $n_1 = \binom{14}{0} - 1$. Define
$$
s = \sum_{k=0}^{n_2} (-1)^k \binom{n_2}{k}
\quad\text{and}\quad
w = \sum_{k=0}^{n_1} (-1)^k \binom{n_1}{k}.
$$
Let $n$ be the number of elements in the Cartesian product of the sets $\{1, 2\}$ and $\{1, 2, 3, 4, 5\}$. Define $\text{result} = (2w)^n$... | 44,789 | graphs = [
Graph(
let={
"_n": Const(87641),
"u": Const(7),
"n2": Sum(Ref("u"), Binom(n=Const(14), k=Const(0))),
"s": Summation(var="k", start=Const(0), end=Ref("n2"), expr=Mul(Pow(Const(-1), Var("k")), Binom(n=Ref("n2"), k=Var("k")))),
"n1": Sub(Bi... | COMB | null | SUM | sympy | BINOMIAL_ALTERNATING | [
"BINOMIAL_ALTERNATING",
"COUNT_CARTESIAN",
"ZERO_BINOM_0",
"ONE_BINOM_0"
] | 2a48d5 | comb_sum_binomial_row_v1 | null | 3 | 2 | [
"BINOMIAL_ALTERNATING",
"COUNT_CARTESIAN",
"ONE_BINOM_0",
"ZERO_BINOM_0"
] | 4 | 0.004 | 2026-02-08T06:19:07.593723Z | {
"verified": true,
"answer": 44789,
"timestamp": "2026-02-08T06:19:07.597461Z"
} | 71429b | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 305,
"completion_tokens": 1577
},
"timestamp": "2026-02-24T06:00:09.028Z",
"answer": 44789
},
{
"... | 1 | [
{
"lemma": "BINOMIAL_ALTERNATING",
"status": "ok"
},
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "ok"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "O... | {
"lo": -2.46,
"mid": 0.47,
"hi": 3.59
} | ||
d7c962 | comb_binomial_compute_v1_1520064083_1605 | Let $m$ be the number of nonnegative integers $j$ at most $265$ for which $\binom{265}{j}$ is odd. Let $n$ be the largest positive divisor of $221$ that is at most $m + 5$. Compute $24649 - \binom{n}{7}$. | 22,933 | graphs = [
Graph(
let={
"_m": Const(5),
"_n": Sum(CountOverSet(set=SolutionsSet(var=Var("j"), condition=And(Geq(Var("j"), Const(0)), Leq(Var("j"), Const(265)), Eq(Mod(value=Binom(n=Const(265), k=Var("j")), modulus=Const(2)), Const(1))), domain='nonnegative_integers')), Ref("_m")),
... | NT | null | COMPUTE | sympy | V8 | [
"V8/MAX_DIVISOR"
] | 0dd13c | comb_binomial_compute_v1 | null | 6 | 0 | [
"MAX_DIVISOR",
"V8"
] | 2 | 0.004 | 2026-02-08T04:08:11.064337Z | {
"verified": true,
"answer": 22933,
"timestamp": "2026-02-08T04:08:11.068501Z"
} | 86d41e | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 179,
"completion_tokens": 896
},
"timestamp": "2026-02-10T15:26:23.160Z",
"answer": 22933
},
{
"... | 1 | [
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "MAX_DIVISOR",
"status": "ok_later"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "V1",
"status": "no"
},
{
"lemma": "V8",
"status": "ok"
},
{
"l... | {
"lo": -5.55,
"mid": -3.01,
"hi": 0.33
} | ||
4f1a7b | modular_sum_quadratic_residues_v1_153355830_1582 | Let $p$ be the largest prime number not exceeding $582$. Compute $\frac{p(p-1)}{4}$. Determine the value of this quantity. | 83,088 | graphs = [
Graph(
let={
"_n": Const(2),
"p": MaxOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Ref("_n")), Leq(Var("n"), Const(582)), IsPrime(Var("n"))))),
"result": Div(Mul(Ref("p"), Sub(Ref("p"), Const(1))), Const(4)),
},
goal=Ref("re... | NT | null | SUM | sympy | MAX_PRIME_BELOW | [
"MAX_PRIME_BELOW"
] | dc3ad3 | modular_sum_quadratic_residues_v1 | null | 3 | 0 | [
"MAX_PRIME_BELOW"
] | 1 | 0.003 | 2026-02-08T06:30:02.694816Z | {
"verified": true,
"answer": 83088,
"timestamp": "2026-02-08T06:30:02.697826Z"
} | 94026b | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 78,
"completion_tokens": 955
},
"timestamp": "2026-02-13T00:51:06.398Z",
"answer": 83088
},
{
... | 1 | [
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok"
},
{
"lemma": "V5",
"status": "no"
}
] | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
41bc49 | diophantine_fbi2_min_v1_124444284_1481 | Let $k = 16$ and let $d$ be an integer such that $2 \leq d \leq 26$, $d$ divides $k$, and $\frac{k}{d} \geq 7$. Determine the value of the smallest such $d$. | 2 | graphs = [
Graph(
let={
"k": Const(16),
"a": Const(1),
"b": Const(6),
"upper": Const(26),
"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... | NT | null | EXTREMUM | sympy | LIN_FORM | [
"MOBIUS_COPRIME"
] | ac54ac | diophantine_fbi2_min_v1 | null | 2 | 0 | [
"LIN_FORM",
"MOBIUS_COPRIME"
] | 2 | 0.094 | 2026-02-08T03:56:04.233319Z | {
"verified": true,
"answer": 2,
"timestamp": "2026-02-08T03:56:04.327187Z"
} | fdb333 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 169,
"completion_tokens": 460
},
"timestamp": "2026-02-10T16:16:32.307Z",
"answer": 2
},
{
"id": ... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "MOBIUS_COPRIME",
"status": "ok"
},
{
"lemma": "V7",
"status": "no... | {
"lo": -7.01,
"mid": -4.68,
"hi": -2.15
} | ||
5bd987 | modular_min_modexp_v1_798873815_459 | Let $n$ be a positive integer. Define $a = 13$ and $m = 887$. Let $b$ be the number of positive integers $n \le 3505$ such that $5$ divides $n$ and $\gcd(n, 12) = 1$. Let $S$ be the set of all integers $x$ satisfying $\sum_{d\mid\gcd(3,5)} \mu(d) \le x \le 443$ and $a^x \equiv b \pmod{m}$. Compute the minimum value of ... | 262 | graphs = [
Graph(
let={
"_n": Const(3505),
"a": Const(13),
"b": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Ref("_n")), Divides(divisor=Const(5), dividend=Var("n")), Eq(GCD(a=Var("n"), b=Const(12)), Const(1))))),
... | NT | null | EXTREMUM | sympy | MOBIUS_COPRIME | [
"MOBIUS_COPRIME",
"C5"
] | 070692 | modular_min_modexp_v1 | null | 7 | 0 | [
"C5",
"MOBIUS_COPRIME"
] | 2 | 0.02 | 2026-02-08T02:38:50.670483Z | {
"verified": true,
"answer": 262,
"timestamp": "2026-02-08T02:38:50.690740Z"
} | ff1f58 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 241,
"completion_tokens": 5012
},
"timestamp": "2026-02-09T17:22:18.876Z",
"answer": 262
},
{
"i... | 1 | [
{
"lemma": "C5",
"status": "ok"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "MOBIUS_COPRIME",
"status": "ok"
},
{
"lemma": "V1",
"status": "no"
},
{
"lemm... | {
"lo": -4.56,
"mid": 1.23,
"hi": 7.53
} | ||
59b823 | algebra_quadratic_discriminant_v1_1915831931_1619 | Let $a = 3$, $b = 2$, and $n = 11$. Let $c$ be the largest prime number $p$ such that $2 \le p \le n$. Let $T$ be the set of all prime numbers $q$ such that $2 \le q \le 7$. Compute the absolute value of $b^2 - a \cdot c \cdot |T|$. | 128 | graphs = [
Graph(
let={
"_n": Const(11),
"a": Const(3),
"b": Const(2),
"c": MaxOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(2)), Leq(Var("n"), Ref("_n")), IsPrime(Var("n"))))),
"result": Sub(Pow(Ref("b"), Const(2)), Mul(... | NT | null | COMPUTE | sympy | K3 | [
"MAX_PRIME_BELOW",
"COUNT_PRIMES"
] | 0c6ade | algebra_quadratic_discriminant_v1 | null | 2 | 0 | [
"COUNT_PRIMES",
"K3",
"MAX_PRIME_BELOW"
] | 3 | 0.016 | 2026-02-08T16:18:50.913595Z | {
"verified": true,
"answer": 128,
"timestamp": "2026-02-08T16:18:50.929122Z"
} | 808e72 | 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": 370
},
"timestamp": "2026-02-17T01:57:50.757Z",
"answer": 128
},
{
... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_PRIMES",
"status": "ok"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} |
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