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 |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
0e52c2 | comb_bell_compute_v1_677425708_2638 | Let $u$ be the number of integers $t$ with $5 \le t \le 14$ for which there exist integers $a$ and $b$ such that $1 \le a \le 4$, $1 \le b \le 2$, and $t = 2a + 3b$. Let $n_1 = u + 1$. Define
$$
e = \sum_{k=0}^{10} (-1)^k \binom{10}{k}
\quad\text{and}\quad
f = \sum_{k=0}^{n_1} (-1)^k \binom{n_1}{k}.
$$
Let $n = 8 + e +... | 4,140 | graphs = [
Graph(
let={
"n2": Const(10),
"e": Summation(var="k", start=Const(0), end=Ref("n2"), expr=Mul(Pow(Const(-1), Var("k")), Binom(n=Ref("n2"), k=Var("k")))),
"u": CountOverSet(set=SolutionsSet(var=Var("t"), condition=Exists(var=Var(name='a'), condition=Exists(var=V... | COMB | null | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM/BINOMIAL_ALTERNATING"
] | bebeab | comb_bell_compute_v1 | null | 6 | 2 | [
"BINOMIAL_ALTERNATING",
"LIN_FORM"
] | 2 | 0.002 | 2026-02-08T05:10:12.619503Z | {
"verified": true,
"answer": 4140,
"timestamp": "2026-02-08T05:10:12.621244Z"
} | fb0cf9 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 276,
"completion_tokens": 834
},
"timestamp": "2026-02-24T02:46:08.987Z",
"answer": 4140
},
{
"id... | 1 | [
{
"lemma": "BINOMIAL_ALTERNATING",
"status": "ok_later"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},... | {
"lo": -5.97,
"mid": -3.96,
"hi": -1.93
} | ||
7e408e | nt_count_with_divisor_count_v1_151522320_1406 | Let $p$ be the largest prime number less than or equal to 6191. Let $N$ be the number of positive integers $n$ such that $1 \leq n \leq p$ and the number of positive divisors of $n$ is exactly 10. Compute the value of $N$. | 100 | graphs = [
Graph(
let={
"_n": Const(2),
"upper": MaxOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Ref("_n")), Leq(Var("n"), Const(6191)), IsPrime(Var("n"))))),
"div_count": Const(10),
"result": CountOverSet(set=SolutionsSet(var=Var("n"), c... | NT | null | COUNT | sympy | MAX_PRIME_BELOW | [
"MAX_PRIME_BELOW"
] | dc3ad3 | nt_count_with_divisor_count_v1 | null | 4 | 0 | [
"MAX_PRIME_BELOW"
] | 1 | 0.513 | 2026-02-08T03:59:16.155762Z | {
"verified": true,
"answer": 100,
"timestamp": "2026-02-08T03:59:16.669203Z"
} | f32bde | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 177,
"completion_tokens": 5187
},
"timestamp": "2026-02-11T16:12:02.769Z",
"answer": 100
},
{
"id... | 1 | [
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
}
] | {
"lo": -3.53,
"mid": 1.02,
"hi": 5.49
} | ||
367b08 | comb_count_permutations_fixed_v1_2051736721_2079 | Let $N = 85245$, $n = 10$, and $k = 7$. Define $T = \binom{n}{k} \cdot !(n - k)$, where $!m$ denotes the number of derangements of $m$ elements. Let $S$ be the set of all nonnegative integers $j$ such that $0 \leq j \leq 85245$ and $\binom{N}{j}$ is odd. Compute $|S| - T$. | 1,808 | graphs = [
Graph(
let={
"_n": Const(85245),
"n": Const(10),
"k": Const(7),
"result": Mul(Binom(n=Ref("n"), k=Ref("k")), Subfactorial(arg=Sub(left=Ref(name='n'), right=Ref(name='k')))),
"Q": Sub(CountOverSet(set=SolutionsSet(var=Var("j"), condition=... | COMB | null | COUNT | sympy | V8 | [
"V8"
] | 04a712 | comb_count_permutations_fixed_v1 | negation_mod | 7 | 0 | [
"V8"
] | 1 | 0.003 | 2026-02-08T16:26:15.857469Z | {
"verified": true,
"answer": 1808,
"timestamp": "2026-02-08T16:26:15.860482Z"
} | 339c29 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 219,
"completion_tokens": 913
},
"timestamp": "2026-02-24T21:07:14.053Z",
"answer": 1808
},
{
"i... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "V8",
"status": "ok"
}
] | {
"lo": -2.4,
"mid": 1.57,
"hi": 5.75
} | ||
577024 | algebra_poly_eval_v1_601307018_8131 | Let $z = 9$. Let $E = \min\{x + y : x > 0, y > 0, xy = 2474329\}$. Let $C = \left|\{ (a_1, b_1) : 1 \le a_1, b_1 \le 35,\, 26a_1^2 - 52a_1b_1 + 26b_1^2 = E \}\right|$. Let $N = \left|\{ (a, b) : 1 \le a, b \le 35,\, 91a^3 - 8b^3 - 96a^2b + C \cdot a b^2 = 40824 \}\right|$. Compute $3 \cdot z^N - 8z^2 + 6z + 4$. | 1,597 | graphs = [
Graph(
let={
"_c": Const(2),
"_m": Const(35),
"_n": Const(2),
"z": Const(9),
"result": Sum(Mul(Const(3), Pow(Ref("z"), CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("a"), Var("b")]), condition=And(Geq(Var("a"), Const(1)), Leq(Var... | ALG | null | COMPUTE | sympy | B3 | [
"B3/QF_PSD_COUNT/POLY3_COUNT"
] | 9d2081 | algebra_poly_eval_v1 | null | 7 | 0 | [
"B3",
"POLY3_COUNT",
"QF_PSD_COUNT"
] | 3 | 0.069 | 2026-03-10T08:36:42.241102Z | {
"verified": true,
"answer": 1597,
"timestamp": "2026-03-10T08:36:42.310239Z"
} | f43a57 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 300,
"completion_tokens": 8192
},
"timestamp": "2026-04-19T08:21:05.512Z",
"answer": 1597
},
{
"... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "POLY3_COUNT",
"status": "ok_later"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "QF_PSD_COUNT",
"status": "ok_later"
}
] | {
"lo": -5.34,
"mid": 1.1,
"hi": 7.53
} | ||
adaf5b | algebra_vieta_sum_v1_898971024_2720 | Let $S$ be the set of all real numbers $x$ satisfying
$$
2x^3 - 24x^2 - 54x + m = 0,
$$
where $m$ is the minimum value of $x_1 + y$ over all ordered pairs $(x_1, y)$ of positive real numbers such that $x_1 y = 236196$. Let $\text{result}$ be the product of all elements of $S$. Compute the remainder when $40942 \cdot \t... | 3,293 | graphs = [
Graph(
let={
"_n": Const(98035),
"result": ProductOverSet(set=SolutionsSet(var=Var(name='x'), condition=Eq(left=Sum(Mul(Const(value=2), Pow(base=Var(name='x'), exp=Const(value=3))), Mul(Const(value=-24), Pow(base=Var(name='x'), exp=Const(value=2))), Mul(Const(value=-54), V... | NT | null | COMPUTE | sympy | B3 | [
"B3"
] | 0cd20d | algebra_vieta_sum_v1 | null | 6 | 0 | [
"B3"
] | 1 | 0.017 | 2026-02-08T16:55:43.189306Z | {
"verified": true,
"answer": 3293,
"timestamp": "2026-02-08T16:55:43.206169Z"
} | d49843 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 165,
"completion_tokens": 1595
},
"timestamp": "2026-02-17T16:01:59.425Z",
"answer": 3293
},
{... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
ac4395 | alg_poly_preperiod_count_v1_601307018_3661 | Let $N = (a^2 + 1) \bmod 67$, $M = (N^2 + 1) \bmod 67$, $R = (M^2 + 1) \bmod 67$, and $S = (R^2 + 1) \bmod 67$. Find the number of non-negative integers $a$ with $0 \le a \le 12193$ such that $S = N$, $M \ne N$, and $R \ne N$. | 1,092 | graphs = [
Graph(
let={
"p1": Mod(value=Sum(Pow(Var("a"), Const(2)), Const(1)), modulus=Const(67)),
"p2": Mod(value=Sum(Pow(Ref("p1"), Const(2)), Const(1)), modulus=Const(67)),
"p3": Mod(value=Sum(Pow(Ref("p2"), Const(2)), Const(1)), modulus=Const(67)),
"p4": ... | ALG | null | COUNT | sympy | POLY_ORBIT_COUNT | [
"POLY_ORBIT_COUNT"
] | 4ad965 | alg_poly_preperiod_count_v1 | null | 6 | null | [
"POLY_ORBIT_COUNT"
] | 1 | 0.02 | 2026-03-10T04:16:39.902944Z | {
"verified": true,
"answer": 1092,
"timestamp": "2026-03-10T04:16:39.923257Z"
} | 27a732 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 222,
"completion_tokens": 6897
},
"timestamp": "2026-03-29T09:32:02.422Z",
"answer": 1092
},
{
"i... | 1 | [
{
"lemma": "POLY_ORBIT_COUNT",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
}
] | {
"lo": 3.34,
"mid": 5.77,
"hi": 8.89
} | ||
577a11 | comb_binomial_compute_v1_153355830_2699 | Let $n = 15$. Define $k$ to be the value of
$$
\sum_{i=1}^{3} \phi(i) \left\lfloor \frac{3}{i} \right\rfloor,
$$
where $\phi$ denotes Euler's totient function. Compute $\binom{n}{k}$. | 5,005 | graphs = [
Graph(
let={
"_n": Const(3),
"n": Const(15),
"k": Summation(var="k", start=Const(1), end=Const(3), expr=Mul(EulerPhi(n=Var("k")), Floor(Div(Ref("_n"), Var("k"))))),
"result": Binom(n=Ref("n"), k=Ref("k")),
},
goal=Ref("result"),
... | NT | null | COMPUTE | sympy | K2 | [
"K2"
] | 6897ab | comb_binomial_compute_v1 | null | 2 | 0 | [
"K2"
] | 1 | 0.001 | 2026-02-08T07:17:36.218358Z | {
"verified": true,
"answer": 5005,
"timestamp": "2026-02-08T07:17:36.219291Z"
} | 04c8b0 | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 132,
"completion_tokens": 432
},
"timestamp": "2026-02-15T18:56:00.392Z",
"answer": 5005
},
{
"id": 11,
... | 2 | [
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "K2",
"status": "ok"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "V3",
"status": "no"
}
] | {
"lo": -10,
"mid": -7.73,
"hi": -5.46
} | ||
e7a77f | sequence_lucas_compute_v1_124444284_5675 | Let $n$ be the number of positive integers $k$ such that $1 \le k \le 528$ and $24$ divides $k$. Let $L_n$ denote the $n$th Lucas number, defined by $L_1 = 1$, $L_2 = 3$, and $L_m = L_{m-1} + L_{m-2}$ for $m \ge 3$. Let $r = |L_n|$, and let $b$ be the remainder when $r$ is divided by $11$. Compute the $b$th Bell number... | 5 | graphs = [
Graph(
let={
"_n": Const(11),
"n": CountOverSet(set=SolutionsSet(var=Var("k"), condition=And(Geq(Var("k"), Const(1)), Leq(Var("k"), Const(528)), Divides(divisor=Const(24), dividend=Var("k"))), domain='positive_integers')),
"result": Lucas(arg=Ref(name='n')),
... | COMB | NT | COMPUTE | sympy | C2 | [
"C2"
] | 9685eb | sequence_lucas_compute_v1 | null | 4 | 0 | [
"C2"
] | 1 | 0.001 | 2026-02-08T06:46:09.641509Z | {
"verified": true,
"answer": 5,
"timestamp": "2026-02-08T06:46:09.642946Z"
} | 57370b | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 188,
"completion_tokens": 809
},
"timestamp": "2026-02-13T04:24:25.900Z",
"answer": 5
},
{
... | 1 | [
{
"lemma": "C2",
"status": "ok"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
}
] | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
f3b33a | alg_sum_ap_v1_1218484723_3012 | Let $T$ be the set of positive integers $t$ for which there exist integers $a, b$ with $1 \leq a \leq 756$, $1 \leq b \leq 443$ such that $t = 4a + 3b$ and $7 \leq t \leq 4353$. Let $m = |T|$. Compute $22222 - \left( \sum_{k=0}^{898} (13k + 29) \bmod m \right)$. | 18,662 | graphs = [
Graph(
let={
"_n": Const(898),
"result": Mod(value=Summation(var="k", start=Const(0), end=Ref("_n"), expr=Sum(Mul(Const(13), Var("k")), Const(29))), modulus=CountOverSet(set=SolutionsSet(var=Var("t"), condition=Exists(var=Var(name='a'), condition=Exists(var=Var(name='b'), ... | ALG | null | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | alg_sum_ap_v1 | null | 3 | 0 | [
"LIN_FORM"
] | 1 | 0.011 | 2026-02-25T04:44:39.374281Z | {
"verified": true,
"answer": 18662,
"timestamp": "2026-02-25T04:44:39.385583Z"
} | 436c91 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 225,
"completion_tokens": 29100
},
"timestamp": "2026-03-29T07:53:46.199Z",
"answer": 18662
},
{
... | 1 | [
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
}
] | {
"lo": 1.55,
"mid": 4.7,
"hi": 7.23
} | ||
17bfe3 | sequence_lucas_compute_v1_238844314_412 | Let $ n = \sum_{k=1}^{6} \phi(k) \left\lfloor \frac{6}{k} \right\rfloor $, where $ \phi(k) $ denotes Euler's totient function. Let $ Q = L_n $, the $ n $-th Lucas number, where the Lucas sequence is defined by $ L_1 = 1 $, $ L_2 = 3 $, and $ L_m = L_{m-1} + L_{m-2} $ for $ m \geq 3 $. Compute $ Q $. | 24,476 | graphs = [
Graph(
let={
"_n": Const(6),
"n": Summation(var="k", start=Const(1), end=Ref("_n"), expr=Mul(EulerPhi(n=Var("k")), Floor(Div(Const(6), Var("k"))))),
"result": Lucas(arg=Ref(name='n')),
"Q": Ref("result"),
},
goal=Ref("Q"),
)
] | NT | null | COMPUTE | sympy | K2 | [
"K2"
] | 6897ab | sequence_lucas_compute_v1 | null | 6 | 0 | [
"K2"
] | 1 | 0.002 | 2026-02-08T13:20:08.805003Z | {
"verified": true,
"answer": 24476,
"timestamp": "2026-02-08T13:20:08.806707Z"
} | 2c4b99 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 166,
"completion_tokens": 1096
},
"timestamp": "2026-02-15T13:04:27.456Z",
"answer": 24476
},
... | 1 | [
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "K2",
"status": "ok"
},
{
"lemma": "V1",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
}
] | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
86551c | algebra_poly_eval_v1_601307018_280 | Let $m = 21$. Let $$N = \frac{32 m^4 + \max \{ d : d \ge 1, d \le 444, d \mid 204684 \} \cdot m^3 - 1123 m^2 - 539m + 336}{6105}.$$ Determine the multiplicative order of $2$ modulo $|N| \cdot 2 + 3$. | 1,460 | graphs = [
Graph(
let={
"m": Const(21),
"result": Div(Sum(Mul(Const(32), Pow(Ref("m"), Const(4))), Mul(MaxOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Const(1)), Leq(Var("d"), Const(444)), Divides(divisor=Var("d"), dividend=Const(204684))))), Pow(Ref("m"), Const... | NT | NT | COMPUTE | sympy | MAX_DIVISOR | [
"MAX_DIVISOR"
] | 51757e | algebra_poly_eval_v1 | null | 5 | 0 | [
"MAX_DIVISOR"
] | 1 | 0.004 | 2026-03-10T00:49:40.549203Z | {
"verified": true,
"answer": 1460,
"timestamp": "2026-03-10T00:49:40.553431Z"
} | 9edb66 | CC BY 4.0 | null | null | [
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MAX_DIVISOR",
"status": "ok"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
}
] | {
"lo": -10,
"mid": 0,
"hi": 10
} | ||
729609 | nt_sum_divisors_compute_v1_1520064083_3166 | Let $n = 41616$ and let $\sigma(n)$ denote the sum of all positive divisors of $n$. Let $c$ be the number of integers $m$ such that $1 \leq m \leq 1452$ and $m \equiv \left\lfloor \frac{m}{2} \right\rfloor \pmod{3}$. Compute the remainder when $\sigma(n)^2 + 15\sigma(n) + c$ is divided by $65987$. | 22,088 | graphs = [
Graph(
let={
"_n": Const(1452),
"n": Const(41616),
"result": SumDivisors(n=Ref("n")),
"Q": Mod(value=Sum(Pow(Ref("result"), Const(2)), Mul(Const(15), Ref("result")), CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), ... | NT | null | COMPUTE | sympy | L3C | [
"L3C"
] | b81e9a | nt_sum_divisors_compute_v1 | quadratic_mod | 5 | 0 | [
"L3C"
] | 1 | 0.001 | 2026-02-08T05:29:49.879153Z | {
"verified": true,
"answer": 22088,
"timestamp": "2026-02-08T05:29:49.880357Z"
} | 80eb89 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 147,
"completion_tokens": 2194
},
"timestamp": "2026-02-12T09:30:18.994Z",
"answer": 22088
},
... | 1 | [
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "L3C",
"status": "ok"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
}
] | {
"lo": -3.51,
"mid": 1.33,
"hi": 6.56
} | ||
7e4491 | nt_num_divisors_compute_v1_898971024_2248 | Let $n = 33489$. Define $r$ to be the number of positive divisors of $n$. Let $S$ be the set of all ordered pairs $(x, y)$ of positive integers such that $x + y = 162$. Let $P$ be the set of all products $xy$ where $(x, y) \in S$. Let $c$ be the maximum value in $P$. Compute $c - r$. | 6,552 | graphs = [
Graph(
let={
"_n": Const(162),
"n": Const(33489),
"result": NumDivisors(n=Ref("n")),
"_c": MaxOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')... | NT | null | COMPUTE | sympy | B1 | [
"B1"
] | d2b6e1 | nt_num_divisors_compute_v1 | negation_mod | 3 | 0 | [
"B1"
] | 1 | 0.003 | 2026-02-08T16:37:24.764415Z | {
"verified": true,
"answer": 6552,
"timestamp": "2026-02-08T16:37:24.767433Z"
} | f3f13b | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 140,
"completion_tokens": 589
},
"timestamp": "2026-02-17T07:51:29.014Z",
"answer": 6552
},
{
... | 1 | [
{
"lemma": "B1",
"status": "ok"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
fddfd0 | nt_count_coprime_and_v1_1125832087_907 | Let $U = 37403$. Determine the number of positive integers $n$ such that $1 \le n \le U$, $\gcd(n,5) = 1$, and $\gcd(n,7) = 1$. Call this number $r$. Let $D$ be the set of positive divisors $d$ of $3440989$ such that $1 \le d \le 1849$. Let $c$ be the maximum element of $D$. Define $Q$ as the sum of $c$ and the sum ove... | 2,057 | graphs = [
Graph(
let={
"upper": Const(37403),
"k1": Const(5),
"k2": Const(7),
"result": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Ref("upper")), Eq(GCD(a=Var("n"), b=Ref("k1")), Const(1)), Eq(GCD(a=Var("n... | NT | null | COUNT | sympy | MAX_DIVISOR | [
"MAX_DIVISOR"
] | 07ce98 | nt_count_coprime_and_v1 | digits_weighted_mod | 5 | 0 | [
"MAX_DIVISOR"
] | 1 | 5.118 | 2026-02-08T03:21:32.737563Z | {
"verified": true,
"answer": 2057,
"timestamp": "2026-02-08T03:21:37.855467Z"
} | 49106b | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 306,
"completion_tokens": 2479
},
"timestamp": "2026-02-10T13:19:59.772Z",
"answer": 2057
},
{
"... | 1 | [
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "MAX_DIVISOR",
"status": "ok"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "VAL_SUM_EQ",
"status": "no"
}
] | {
"lo": -3.42,
"mid": 1.86,
"hi": 7.55
} | ||
31b77f | antilemma_sum_equals_v1_784195855_1551 | Let $\_n$ be the number of ordered pairs $(i,j)$ such that $1 \leq i \leq 8$ and $1 \leq j \leq 11$. Compute the number of ordered pairs $(i,j)$ of positive integers with $1 \leq i, j \leq 88$ such that $i + j = \_n$. | 87 | graphs = [
Graph(
let={
"_n": CountOverSet(set=CartesianProduct(left=IntegerRange(start=Const(1), end=Const(8)), right=IntegerRange(start=Const(1), end=Const(11)))),
"x": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("i"), Var("j")]), condition=Eq(Sum(Var("i"), Var("j")), Ref... | COMB | GEOM | COMPUTE | sympy | COUNT_CARTESIAN | [
"COUNT_CARTESIAN/COUNT_SUM_EQUALS",
"COUNT_SUM_EQUALS"
] | 8bee9e | antilemma_sum_equals_v1 | null | 3 | 0 | [
"COUNT_CARTESIAN",
"COUNT_SUM_EQUALS"
] | 2 | 0.003 | 2026-02-08T05:08:06.807642Z | {
"verified": true,
"answer": 87,
"timestamp": "2026-02-08T05:08:06.811010Z"
} | 37e595 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 191,
"completion_tokens": 440
},
"timestamp": "2026-02-24T02:46:41.761Z",
"answer": 87
},
{
"id":... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "ok"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "ok"
},
{
"lemma": "V7",
... | {
"lo": -3.83,
"mid": -1.68,
"hi": 1.09
} | ||
055b4c | nt_count_primes_v1_1742523217_776 | Let $ S $ be the set of all positive integers $ p $ such that there exists an integer $ q $ with $ p < q $, $ \gcd(p, q) = 1 $, and $ pq = 54 $. Let $ m $ be the number of elements in $ S $. Determine the value of $ m $.
Let $ T $ be the set of all prime numbers $ n $ such that $ m \leq n \leq 50625 $. Compute the num... | 5,191 | graphs = [
Graph(
let={
"upper": Const(50625),
"result": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), CountOverSet(set=SolutionsSet(var=Var("p"), condition=And(IsPositive(arg=Var(name='p')), Exists(var=Var(name='q'), condition=And(Eq(left=Mul(Var(name='p'),... | NT | null | COUNT | sympy | COPRIME_PAIRS | [
"COPRIME_PAIRS"
] | 2bb3aa | nt_count_primes_v1 | null | 4 | 0 | [
"COPRIME_PAIRS"
] | 1 | 1.153 | 2026-02-08T03:14:15.357061Z | {
"verified": true,
"answer": 5191,
"timestamp": "2026-02-08T03:14:16.510539Z"
} | 06b0c0 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 217,
"completion_tokens": 18753
},
"timestamp": "2026-02-23T17:48:15.006Z",
"answer": 5191
},
{
... | 1 | [
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
}... | {
"lo": -3.45,
"mid": 1.18,
"hi": 5.72
} | ||
30fcb7 | comb_count_permutations_fixed_v1_784195855_8538 | Let $n$ be the minimum value of $x + y$ over all ordered pairs of positive integers $(x, y)$ such that $xy = 9$. Compute $25921 - \binom{n}{3} \cdot !(n - 3)$, where $!k$ denotes the number of derangements of $k$ elements. | 25,881 | 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(9)))), expr=Sum(Var("x"), Var("y")))),
"k": Const(3),
... | COMB | null | COUNT | sympy | B3 | [
"B3"
] | 0cd20d | comb_count_permutations_fixed_v1 | null | 4 | 0 | [
"B3"
] | 1 | 0.002 | 2026-02-08T16:08:47.298347Z | {
"verified": true,
"answer": 25881,
"timestamp": "2026-02-08T16:08:47.300185Z"
} | e4b49a | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 184,
"completion_tokens": 439
},
"timestamp": "2026-02-24T20:04:13.533Z",
"answer": 25881
},
{
"... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
}
] | {
"lo": -8,
"mid": -4.75,
"hi": -2.28
} | ||
86be9e | algebra_quadratic_discriminant_v1_717093673_1030 | Let $a = 1$, $b = -5$, and $c = -50$. Define the discriminant $D = b^2 - 4ac$. Let $S = \sum_{k=0}^{5} (-1)^k \binom{5}{k}$. Compute the value of $2 \cdot \mathbf{1}_{D > S} + \mathbf{1}_{D = 0}$, where $\mathbf{1}_{\text{condition}}$ is 1 if the condition is true and 0 otherwise. | 2 | graphs = [
Graph(
let={
"a": Const(1),
"b": Const(-5),
"c": Const(-50),
"D": Sub(Pow(Ref("b"), Const(2)), Mul(Const(4), Ref("a"), Ref("c"))),
"result": Sum(Mul(Const(2), Iverson(condition=Gt(Ref("D"), Summation(var="k", start=Const(0), end=Const(5)... | COMB | null | COMPUTE | sympy | B3 | [
"BINOMIAL_ALTERNATING"
] | c21569 | algebra_quadratic_discriminant_v1 | null | 3 | 0 | [
"B3",
"BINOMIAL_ALTERNATING"
] | 2 | 0.022 | 2026-02-08T15:47:57.980626Z | {
"verified": true,
"answer": 2,
"timestamp": "2026-02-08T15:47:58.002842Z"
} | 7f8e1c | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 226,
"completion_tokens": 384
},
"timestamp": "2026-02-24T18:43:31.735Z",
"answer": 2
},
{
"id":... | 2 | [
{
"lemma": "BINOMIAL_ALTERNATING",
"status": "ok"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
},
{
"lemma": "V8_SUM",
"st... | {
"lo": -10,
"mid": -7.42,
"hi": -4.85
} | ||
154ed4 | comb_count_surjections_v1_2051736721_5574 | Let $s$ be the number of ordered pairs $(x_{11}, x_{21})$ of positive odd integers such that $x_{11} + x_{21} = 20$. Let $n$ be the number of ordered pairs $(x_1, x_2)$ of positive odd integers such that $x_1 + x_2 = s$. Let $k = 2$. Compute the remainder when $58549 \cdot k! \cdot S(n, k)$ is divided by $92016$, where... | 8,166 | graphs = [
Graph(
let={
"_n": Const(92016),
"n": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x1"), Var("x2")]), condition=And(IsPositive(arg=Var(name='x1')), IsPositive(arg=Var(name='x2')), IsOdd(arg=Var(name='x1')), IsOdd(arg=Var(name='x2')), Eq(Sum(Var("x1"), Var("x2")),... | COMB | null | COUNT | sympy | COMB1 | [
"COMB1/COMB1"
] | b2c526 | comb_count_surjections_v1 | null | 5 | 0 | [
"COMB1"
] | 1 | 0.034 | 2026-02-08T18:40:04.441309Z | {
"verified": true,
"answer": 8166,
"timestamp": "2026-02-08T18:40:04.475133Z"
} | 0be2bf | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 170,
"completion_tokens": 1723
},
"timestamp": "2026-02-18T18:35:54.650Z",
"answer": 8166
},
{... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COMB1",
"status": "ok"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "V8",
"statu... | {
"lo": -3.12,
"mid": 1.47,
"hi": 6.57
} | ||
eae78a | modular_sum_quadratic_residues_v1_601307018_10907 | Let $S$ be the set of ordered pairs $(a, b)$ of positive integers with $1 \leq a, b \leq 40$ such that $41a^2 + 20b^2 - 12ab \leq 34697$, and let $T = |S|$. Find the number $p$ of positive integers $x$ with $1 \leq x \leq T$ satisfying $|2x - 1086| \leq 612$, then compute $\frac{p(p - 1)}{4}$. | 93,789 | graphs = [
Graph(
let={
"_n": Const(4),
"p": CountOverSet(set=SolutionsSet(var=Var("x"), condition=And(Geq(Var("x"), Const(1)), Leq(Var("x"), CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("a"), Var("b")]), condition=And(Geq(Var("a"), Const(1)), Leq(Var("a"), Const(40)), Geq(V... | NT | null | SUM | sympy | QF_PSD_COUNT_LEQ | [
"QF_PSD_COUNT_LEQ/ABS_INEQ"
] | ed242b | modular_sum_quadratic_residues_v1 | null | 6 | 0 | [
"ABS_INEQ",
"QF_PSD_COUNT_LEQ"
] | 2 | 0.003 | 2026-03-10T11:22:31.925766Z | {
"verified": true,
"answer": 93789,
"timestamp": "2026-03-10T11:22:31.929014Z"
} | bb595c | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 231,
"completion_tokens": 7548
},
"timestamp": "2026-04-19T15:02:50.815Z",
"answer": 93789
},
{
... | 1 | [
{
"lemma": "ABS_INEQ",
"status": "ok_later"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "QF_PSD_COUNT_LE... | {
"lo": -5.34,
"mid": 1.1,
"hi": 7.53
} | ||
e78d27 | algebra_poly_eval_v1_124444284_4837 | Let $S$ be the set of all ordered pairs $(x,y)$ of positive integers such that $xy = 9216$. Define $T$ to be the set of all values $x + y$ where $(x,y) \in S$. Let $A$ be the minimum element of $T$. Let $B$ be the number of ordered pairs $(x_1, x_2)$ of positive odd integers such that $x_1 + x_2 = 16874$. Compute the v... | 1,780 | graphs = [
Graph(
let={
"_m": Const(2),
"_n": Const(315),
"k": Const(17),
"result": Div(Sum(Mul(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(... | NT | null | COMPUTE | sympy | COMB1 | [
"COMB1",
"B3"
] | 44bb30 | algebra_poly_eval_v1 | null | 6 | 0 | [
"B3",
"COMB1"
] | 2 | 0.008 | 2026-02-08T06:14:56.291829Z | {
"verified": true,
"answer": 1780,
"timestamp": "2026-02-08T06:14:56.299914Z"
} | 746c62 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 195,
"completion_tokens": 1974
},
"timestamp": "2026-02-12T21:37:31.951Z",
"answer": 1780
},
{... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "COMB1",
"status": "ok"
},
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "DS2",
"status"... | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
d4a17b | nt_lcm_compute_v1_124444284_4375 | Let $a$ be the minimum value of $x + y$ over all ordered pairs $(x, y)$ of positive integers such that $xy = 2079364$. Let $b = 2127$, and let $r = \mathrm{lcm}(a, b)$. Compute the remainder when $r + 2^{r \bmod 14} \bmod 74882$ is divided by $74882$. Determine the value of this remainder. | 68,827 | graphs = [
Graph(
let={
"_n": Const(2),
"a": MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(Mul(Var("x"), Var("y")), Const(2079364)))), expr=Sum(Var("x"), Var("y")))),... | NT | null | COMPUTE | sympy | B3 | [
"B3"
] | 0cd20d | nt_lcm_compute_v1 | null | 6 | 0 | [
"B3"
] | 1 | 0.001 | 2026-02-08T05:58:37.501972Z | {
"verified": true,
"answer": 68827,
"timestamp": "2026-02-08T05:58:37.503337Z"
} | 834b4d | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 143,
"completion_tokens": 1628
},
"timestamp": "2026-02-12T18:09:43.019Z",
"answer": 68827
},
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
}
] | {
"lo": -3.51,
"mid": 1.33,
"hi": 6.56
} | ||
a2c43a | geo_count_lattice_rect_v1_1520064083_4693 | Compute the number of lattice points in the rectangle $[0, 80] \times [0, 23]$, including the boundary. Multiply this number by 44121 and find the remainder when the product is divided by 73984. | 23,768 | graphs = [
Graph(
let={
"a": Const(80),
"b": Const(23),
"result": LatticePointsRect(a=Ref(name='a'), b=Ref(name='b')),
"Q": Mod(value=Mul(Const(44121), Ref("result")), modulus=Const(73984)),
},
goal=Ref("Q"),
)
] | GEOM | null | COUNT | sympy | [] | geo_count_lattice_rect_v1 | null | 3 | 0 | null | null | 0.003 | 2026-02-08T06:23:19.413947Z | {
"verified": true,
"answer": 23768,
"timestamp": "2026-02-08T06:23:19.416555Z"
} | 5a6397 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 160,
"completion_tokens": 747
},
"timestamp": "2026-02-24T06:06:16.834Z",
"answer": 24218
},
{
... | 1 | [] | {
"lo": 1.97,
"mid": 4.36,
"hi": 6.69
} | ||||
ed4558 | nt_count_primes_v1_1978505735_1670 | Let $S$ be the set of all positive integers $p$ for which there exists a positive integer $q$ such that $p < q$, $\gcd(p, q) = 1$, and $pq = 108$. Let $L$ be the number of elements in $S$. Compute the number of prime numbers $n$ such that $L \leq n \leq 20164$. | 2,281 | graphs = [
Graph(
let={
"upper": Const(20164),
"result": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), CountOverSet(set=SolutionsSet(var=Var("p"), condition=And(IsPositive(arg=Var(name='p')), Exists(var=Var(name='q'), condition=And(Eq(left=Mul(Var(name='p'),... | NT | null | COUNT | sympy | COPRIME_PAIRS | [
"COPRIME_PAIRS"
] | 2bb3aa | nt_count_primes_v1 | null | 4 | 0 | [
"COPRIME_PAIRS"
] | 1 | 0.708 | 2026-02-08T16:19:45.279432Z | {
"verified": true,
"answer": 2281,
"timestamp": "2026-02-08T16:19:45.987817Z"
} | 76ce69 | 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": 2271
},
"timestamp": "2026-02-17T01:03:35.595Z",
"answer": 2281
},
{... | 1 | [
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "VAL_SUM_EQ",
"status":... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
ff089b | nt_count_divisible_v1_784195855_2406 | Let $A$ be the set of all positive integers $n$ such that $n$ is divisible by $30$, and $n \leq 51984$. Let $u = \sum_{d \mid \gcd(11,13)} \mu(d)$, where $\mu$ is the Möbius function. Define $|A|$ to be the number of elements in $A$. Compute $15876 - |A|$. | 14,144 | graphs = [
Graph(
let={
"upper": Const(51984),
"divisor": Const(30),
"result": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), SumOverDivisors(n=GCD(a=Const(value=11), b=Const(value=13)), var='d', expr=MoebiusMu(n=Var(name='d')))), Leq(Var("n"), Re... | NT | null | COUNT | sympy | MOBIUS_COPRIME | [
"MOBIUS_COPRIME"
] | ac54ac | nt_count_divisible_v1 | null | 3 | 0 | [
"MOBIUS_COPRIME"
] | 1 | 5.877 | 2026-02-08T05:43:39.758098Z | {
"verified": true,
"answer": 14144,
"timestamp": "2026-02-08T05:43:45.635592Z"
} | d23364 | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 196,
"completion_tokens": 322
},
"timestamp": "2026-02-18T19:19:35.180Z",
"answer": 14144
}
] | 2 | [
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "MOBIUS_COPRIME",
"status": "ok"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "VAL_SUM_EQ",
"status": "no"
}
... | {
"lo": -10,
"mid": -6.47,
"hi": -2.95
} | ||
5b2bd6 | sequence_fibonacci_compute_v1_2051736721_1655 | Let $n$ be the minimum value of $x + y$ over all ordered pairs $(x, y)$ of positive integers such that $xy = 144$. Let $F_n$ denote the $n$th Fibonacci number, where $F_1 = 1$, $F_2 = 1$, and $F_k = F_{k-1} + F_{k-2}$ for $k \geq 3$. Compute the remainder when $44121 \cdot F_n$ is divided by $60839$. | 30,314 | graphs = [
Graph(
let={
"_n": Const(144),
"n": MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(Mul(Var("x"), Var("y")), Ref("_n")))), expr=Sum(Var("x"), Var("y")))),
... | NT | null | COMPUTE | sympy | B3 | [
"B3"
] | 0cd20d | sequence_fibonacci_compute_v1 | null | 4 | 0 | [
"B3"
] | 1 | 0.002 | 2026-02-08T16:08:53.696078Z | {
"verified": true,
"answer": 30314,
"timestamp": "2026-02-08T16:08:53.697716Z"
} | 87efbc | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 157,
"completion_tokens": 1846
},
"timestamp": "2026-02-16T21:20:09.291Z",
"answer": 30314
},
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "V8",
"status": "no... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
c10c32 | modular_modexp_compute_v1_1470522791_472 | Let $a = 29$. Define $e = \sum_{k=1}^{15} \phi(k) \left\lfloor \frac{15}{k} \right\rfloor$, where $\phi$ denotes Euler's totient function. Let $m = 16384$ and let $r$ be the remainder when $a^e$ is divided by $m$. Compute the remainder when $50615 \cdot r$ is divided by $85107$. | 32,544 | graphs = [
Graph(
let={
"_n": Const(85107),
"a": Const(29),
"e": Summation(var="k", start=Const(1), end=Const(15), expr=Mul(EulerPhi(n=Var("k")), Floor(Div(Const(15), Var("k"))))),
"m": Const(16384),
"result": ModExp(base=Ref("a"), exp=Ref("e"), mo... | NT | null | COMPUTE | sympy | K2 | [
"K2"
] | 6897ab | modular_modexp_compute_v1 | null | 4 | 0 | [
"K2"
] | 1 | 0.002 | 2026-02-08T13:01:58.450063Z | {
"verified": true,
"answer": 32544,
"timestamp": "2026-02-08T13:01:58.451725Z"
} | 06577f | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 143,
"completion_tokens": 3764
},
"timestamp": "2026-02-15T08:43:03.610Z",
"answer": 32544
},
... | 1 | [
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "K2",
"status": "ok"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "V8",
"status": ... | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
fa1da4 | nt_count_divisible_and_v1_655260480_3094 | Let $u = 291180$. Let $T$ be the set of all integers $t$ for which there exist integers $a$ and $b$ with $1 \le a \le 3$, $1 \le b \le 4$, $10 \le t \le 36$, and $t = 4a + 6b$. Let $d$ be the number of elements in $T$. Let $N$ be the set of all positive integers $n$ such that $1 \le n \le u$, $n$ is divisible by $10$, ... | 4,853 | graphs = [
Graph(
let={
"upper": Const(291180),
"d1": Const(10),
"d2": 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 | 10.291 | 2026-02-08T17:10:52.054668Z | {
"verified": true,
"answer": 4853,
"timestamp": "2026-02-08T17:11:02.345932Z"
} | 226b21 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 189,
"completion_tokens": 1017
},
"timestamp": "2026-02-17T21:04:27.764Z",
"answer": 4853
},
{... | 1 | [
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status":... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
50b979 | geo_count_lattice_triangle_v1_1353956133_655 | Let $A$ be the area of the triangle with vertices at $(169, 100)$, $(256, 200)$, and $(0, 0)$, multiplied by $2$. Let $B$ be the sum of the greatest common divisors of the absolute differences of the coordinates of each pair of vertices, that is,
$$
B = \gcd(|169|, |100|) + \gcd(|256 - 169|, |200 - 100|) + \gcd(|0 - 25... | 2,616 | graphs = [
Graph(
let={
"_n": Const(169),
"area_2x": Abs(arg=Sum(Mul(Ref(name='_n'), Const(value=200)), Mul(Const(value=256), Sub(left=Const(value=0), right=Const(value=100))))),
"boundary": Sum(GCD(a=Abs(arg=Const(value=169)), b=Abs(arg=Const(value=100))), GCD(a=Abs(arg=... | ALG | NT | COUNT | sympy | C4 | [
"C4"
] | 08d162 | geo_count_lattice_triangle_v1 | null | 6 | 0 | [
"C4"
] | 1 | 0.008 | 2026-02-08T11:46:33.111238Z | {
"verified": true,
"answer": 2616,
"timestamp": "2026-02-08T11:46:33.119122Z"
} | 077812 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 193,
"completion_tokens": 1624
},
"timestamp": "2026-02-14T18:55:24.915Z",
"answer": 2616
},
{... | 1 | [
{
"lemma": "C4",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
}
] | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
79d1c0 | comb_catalan_compute_v1_601307018_10823 | Let $n = \sum_{k=1}^{4} \varphi(k) \cdot \left\lfloor \frac{4}{k} \right\rfloor$, and let $M = C_n$ where $C_n$ denotes the $n$-th Catalan number. Find the remainder when $44121M$ is divided by $74161$. | 39,604 | graphs = [
Graph(
let={
"_n": Const(4),
"n": Summation(var="k", start=Const(1), end=Ref("_n"), expr=Mul(EulerPhi(n=Var("k")), Floor(Div(Const(4), Var("k"))))),
"result": Catalan(Ref("n")),
"Q": Mod(value=Mul(Const(44121), Ref("result")), modulus=Const(74161)),... | COMB | NT | COMPUTE | sympy | K2 | [
"K2"
] | 6897ab | comb_catalan_compute_v1 | null | 5 | 0 | [
"K2"
] | 1 | 0.002 | 2026-03-10T11:16:44.764398Z | {
"verified": true,
"answer": 39604,
"timestamp": "2026-03-10T11:16:44.766150Z"
} | d45bfa | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 189,
"completion_tokens": 1337
},
"timestamp": "2026-04-19T14:48:08.857Z",
"answer": 39604
},
{
... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "K2",
"status": "ok"
},
{
"lemma": "V8_SUM",
"statu... | {
"lo": -5.34,
"mid": 1.1,
"hi": 7.53
} | ||
d954e4 | algebra_vieta_sum_v1_1470522791_1166 | Let $S$ be the set of all positive integers $x$ such that $$
x^d - 27x^2 + 242x - 720 = 0,
$$ where $d$ is the smallest divisor of 1575 that is at least 2. Compute the product of all elements in $S$. | 720 | graphs = [
Graph(
let={
"_n": Const(2),
"result": ProductOverSet(set=SolutionsSet(var=Var(name='x'), condition=Eq(left=Sum(Pow(base=Var(name='x'), exp=MinOverSet(set=SolutionsSet(var=Var(name='d'), condition=And(Geq(left=Var(name='d'), right=Ref(name='_n')), Divides(divisor=Var(name=... | NT | null | COMPUTE | sympy | MIN_PRIME_FACTOR | [
"MIN_PRIME_FACTOR"
] | bc3776 | algebra_vieta_sum_v1 | null | 4 | 0 | [
"MIN_PRIME_FACTOR"
] | 1 | 0.01 | 2026-02-08T13:28:59.442329Z | {
"verified": true,
"answer": 720,
"timestamp": "2026-02-08T13:28:59.452393Z"
} | ccd4c7 | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 1,
"correct": {
"strict": false,
"boxed": false,
"relaxed": true
},
"usage": {
"prompt_tokens": 133,
"completion_tokens": 466
},
"timestamp": "2026-02-16T04:36:07.435Z",
"answer": 900
},
{
"id": 11,
... | 1 | [
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MIN_PRIME_FACTOR",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "... | {
"lo": -8.26,
"mid": -5.01,
"hi": -1.76
} | ||
4867a7 | algebra_quadratic_discriminant_v1_1125832087_392 | Let $m = 51$. Let $d_{\text{min}}$ be the smallest integer $d \geq 2$ that divides $6907543$. Define $c$ as the number of positive integers $n \leq 51$ such that the sum of the decimal digits of $n$ is even. Let $a = -1$, $b = 0$, and define $\text{result} = b^2 - 4ac$. Let $Q = (d_{\text{min}} - \text{result}) \mod 67... | 67,684 | graphs = [
Graph(
let={
"_m": Const(51),
"_n": MinOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Const(2)), Divides(divisor=Var("d"), dividend=Const(6907543))))),
"a": Const(-1),
"b": Const(0),
"c": CountOverSet(set=SolutionsSet... | NT | null | COMPUTE | sympy | COMB1 | [
"MIN_PRIME_FACTOR/L3B"
] | b1b960 | algebra_quadratic_discriminant_v1 | negation_mod | 5 | 0 | [
"COMB1",
"L3B",
"MIN_PRIME_FACTOR"
] | 3 | 0.036 | 2026-02-08T03:02:44.318621Z | {
"verified": true,
"answer": 67684,
"timestamp": "2026-02-08T03:02:44.354148Z"
} | 41fe09 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 254,
"completion_tokens": 1918
},
"timestamp": "2026-02-10T12:34:27.802Z",
"answer": 67690
},
{
... | 1 | [
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "L3B",
"status": "ok_later"
},
{
"lemma": "L3b",
"status": "no... | {
"lo": 3.24,
"mid": 5.68,
"hi": 8.81
} | ||
f416e9 | comb_factorial_compute_v1_153355830_3026 | Let $S$ be the set of all real solutions $x$ to the equation $x^2 - 1001x + 13818 = 0$. Let $T$ be the sum of all elements of $S$. Let $n$ be the smallest integer $d \geq 2$ that divides $T$. Compute $n!$. | 5,040 | graphs = [
Graph(
let={
"_m": Const(2),
"_n": Const(2),
"n": MinOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Ref("_n")), Divides(divisor=Var("d"), dividend=SumOverSet(set=SolutionsSet(var=Var("x"), condition=Eq(Sum(Pow(Var("x"), Ref("_m")), Mul(Const... | NT | null | COMPUTE | sympy | VIETA_SUM | [
"VIETA_SUM/MIN_PRIME_FACTOR"
] | b1c8ca | comb_factorial_compute_v1 | null | 6 | 0 | [
"MIN_PRIME_FACTOR",
"VIETA_SUM"
] | 2 | 0.002 | 2026-02-08T07:32:50.275882Z | {
"verified": true,
"answer": 5040,
"timestamp": "2026-02-08T07:32:50.277516Z"
} | 165c80 | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 134,
"completion_tokens": 537
},
"timestamp": "2026-02-15T19:00:48.922Z",
"answer": 5040
},
{
"id": 11,
... | 2 | [
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "MIN_PRIME_FACTOR",
"status": "ok_later"
},
{
"lemma": "MOD_FACTORIAL",
"statu... | {
"lo": -10,
"mid": -7.73,
"hi": -5.46
} | ||
ca7eec | comb_binomial_compute_v1_1470522791_247 | Let $n$ be the smallest divisor of $1356277$ that is at least $2$, and let $k$ be the smallest divisor of $7007$ that is at least $2$. Compute $\binom{n}{k}$. | 1,716 | 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(1356277))))),
"k": MinOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Ref("_n")), Divi... | NT | null | COMPUTE | sympy | MIN_PRIME_FACTOR | [
"MIN_PRIME_FACTOR"
] | bc3776 | comb_binomial_compute_v1 | null | 3 | 0 | [
"MIN_PRIME_FACTOR"
] | 1 | 0.003 | 2026-02-08T12:55:04.741596Z | {
"verified": true,
"answer": 1716,
"timestamp": "2026-02-08T12:55:04.744619Z"
} | 6be2ad | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 96,
"completion_tokens": 878
},
"timestamp": "2026-02-15T07:26:31.146Z",
"answer": 1716
},
{
... | 1 | [
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "MIN_PRIME_FACTOR",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "VAL_SUM_EQ",
"sta... | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
d0a782 | comb_catalan_compute_v1_1520064083_934 | Let $ S $ be the set of all integers $ t $ such that $ 23 \leq t \leq 35 $ and there exist integers $ a $ and $ b $ with $ 1 \leq a \leq 3 $, $ 1 \leq b \leq 4 $, and $ t = 3a + 2b + 18 $. Let $ m $ be the number of elements in $ S $. Let $ P $ be the set of all ordered pairs $ (i, j) $ such that $ 1 \leq i \leq 10 $, ... | 16,796 | 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 | null | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM/COUNT_SUM_EQUALS"
] | 8a3f7a | comb_catalan_compute_v1 | null | 5 | 0 | [
"COUNT_SUM_EQUALS",
"LIN_FORM"
] | 2 | 0.011 | 2026-02-08T03:40:21.398360Z | {
"verified": true,
"answer": 16796,
"timestamp": "2026-02-08T03:40:21.409471Z"
} | ef2aa8 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 282,
"completion_tokens": 1303
},
"timestamp": "2026-02-23T22:40:36.203Z",
"answer": 16796
},
{
"... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "ok_later"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "V7",
... | {
"lo": -3.83,
"mid": -1.68,
"hi": 1.09
} | ||
008691 | comb_sum_binomial_mod_v1_717093673_1028 | Let $n_0 = 80613$. Define $n_1 = 3 + 4$. Let $v = \sum_{k=0}^{n_1} (-1)^k \binom{n_1}{k}$. Let $u = 1$, and define $n = u + 1$. Let $f = \sum_{k_1=0}^{n} (-1)^{k_1} \binom{n}{k_1}$. Let $T$ be the set of all ordered pairs $(x_1, x_2)$ of positive odd integers such that $x_1 + x_2 = 172$. Let $s = |T|$. Compute the rema... | 35,163 | graphs = [
Graph(
let={
"_n": Const(80613),
"a": Const(3),
"b": Const(4),
"n1": Sum(Ref("a"), Ref("b")),
"v": Summation(var="k", start=Const(0), end=Ref("n1"), expr=Mul(Pow(Const(-1), Var("k")), Binom(n=Ref("n1"), k=Var("k")))),
"u": Co... | COMB | null | COMPUTE | sympy | BINOMIAL_ALTERNATING | [
"BINOMIAL_ALTERNATING",
"COMB1"
] | e741ba | comb_sum_binomial_mod_v1 | null | 5 | 2 | [
"BINOMIAL_ALTERNATING",
"COMB1"
] | 2 | 0.021 | 2026-02-08T15:47:57.884330Z | {
"verified": true,
"answer": 35163,
"timestamp": "2026-02-08T15:47:57.904923Z"
} | 919f41 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 315,
"completion_tokens": 3919
},
"timestamp": "2026-02-24T18:43:44.557Z",
"answer": 35163
},
{
... | 1 | [
{
"lemma": "BINOMIAL_ALTERNATING",
"status": "ok"
},
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COMB1",
"status": "ok"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "V8",
"stat... | {
"lo": -2.4,
"mid": 1.57,
"hi": 5.75
} | ||
133a55 | algebra_poly_eval_v1_601307018_6007 | Let $N$ be the largest positive integer $d$ such that $d^2 \le 4096567$ and $d \mid 4096567$. Let $a = 8$ and $R = 5a^4 + 4a^3 - a^2 + a + 9$. Let $M = \max\{d_1 : d_1 \ge 1,\, d_1 \mid 783,\, d_1^2 \le 783\}$. Find the remainder when $R^2 + M \cdot R + N$ is divided by $58749$. | 57,981 | graphs = [
Graph(
let={
"_n": Const(4),
"a": Const(8),
"result": Sum(Mul(Const(5), Pow(Ref("a"), Const(4))), Mul(Ref("_n"), Pow(Ref("a"), Const(3))), Mul(Const(-1), Pow(Ref("a"), Const(2))), Ref("a"), Const(9)),
"_c": MaxOverSet(set=SolutionsSet(var=Var("d"), ... | NT | null | COMPUTE | sympy | POLY_ORBIT_HENSEL | [
"B3_CLOSEST"
] | d8bbcd | algebra_poly_eval_v1 | quadratic_mod | 4 | 0 | [
"B3_CLOSEST",
"POLY_ORBIT_HENSEL"
] | 2 | 14.269 | 2026-03-10T06:35:48.110093Z | {
"verified": true,
"answer": 57981,
"timestamp": "2026-03-10T06:36:02.379565Z"
} | e7be85 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 243,
"completion_tokens": 20244
},
"timestamp": "2026-04-19T03:23:36.834Z",
"answer": 55961
},
{
... | 0 | [
{
"lemma": "B3_CLOSEST",
"status": "ok"
},
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"s... | {
"lo": 2.1,
"mid": 5.36,
"hi": 8.63
} | ||
6255e8 | nt_count_divisible_v1_1820931509_96 | Let $m=2$ and $n=49$. Let $u=46368$.
Let $p$ be the largest prime number with $2\le p\le 26$.
Let $R$ be the number of integers $k$ such that $1\le k\le u$ and $p$ divides $k$.
Let $N$ be the number of non-negative integers $j$ with $0\le j\le 19640$ such that $\binom{19640}{j}$ is odd.
Let $c$ be the maximum value... | 24,626 | graphs = [
Graph(
let={
"_m": Const(2),
"_n": Const(49),
"upper": Const(46368),
"divisor": MaxOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Ref("_m")), Leq(Var("n"), Const(26)), IsPrime(Var("n"))))),
"result": CountOverSet(set=... | NT | null | COUNT | sympy | V8 | [
"V8/B1",
"MAX_PRIME_BELOW"
] | 0c59ba | nt_count_divisible_v1 | quadratic_mod | 7 | 0 | [
"B1",
"MAX_PRIME_BELOW",
"V8"
] | 3 | 2.281 | 2026-02-08T11:20:26.517018Z | {
"verified": true,
"answer": 24626,
"timestamp": "2026-02-08T11:20:28.797868Z"
} | 774eb3 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 225,
"completion_tokens": 1527
},
"timestamp": "2026-02-14T12:13:21.640Z",
"answer": 24626
},
... | 1 | [
{
"lemma": "B1",
"status": "ok_later"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok"
... | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
59ac0f | alg_poly_orbit_count_v1_1218484723_3882 | For a non-negative integer $a$, define $N = (a^3 + 3a) \bmod 29$ and $M = (N^3 + 3N) \bmod 29$. Find the number of integers $a$ with $0 \le a \le 20821$ such that $M = a$ and $N \ne a$. | 4,308 | graphs = [
Graph(
let={
"p1": Mod(value=Sum(Pow(Var("a"), Const(3)), Mul(Const(3), Var("a"))), modulus=Const(29)),
"p2": Mod(value=Sum(Pow(Ref("p1"), Const(3)), Mul(Const(3), Ref("p1"))), modulus=Const(29)),
"result": CountOverSet(set=SolutionsSet(var=Var("a"), condition=... | ALG | null | COUNT | sympy | POLY_ORBIT_COUNT | [
"POLY_ORBIT_COUNT"
] | 4ad965 | alg_poly_orbit_count_v1 | null | 4 | null | [
"POLY_ORBIT_COUNT"
] | 1 | 0.009 | 2026-02-25T05:30:53.613816Z | {
"verified": true,
"answer": 4308,
"timestamp": "2026-02-25T05:30:53.622744Z"
} | 440a51 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 190,
"completion_tokens": 32768
},
"timestamp": "2026-03-29T12:44:57.069Z",
"answer": null
},
{
... | 1 | [
{
"lemma": "POLY_ORBIT_COUNT",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
}
] | {
"lo": 3.81,
"mid": 6.33,
"hi": 9.49
} | ||
fe7a8f | antilemma_cartesian_v1_1520064083_9665 | Let $A$ be the set of all ordered pairs $(i,j)$ such that $1 \leq i \leq 10$ and $1 \leq j \leq 16$. Let $x$ be the number of elements in $A$. Compute the remainder when $44121 \cdot x$ is divided by $90568$. | 85,624 | graphs = [
Graph(
let={
"x": CountOverSet(set=CartesianProduct(left=IntegerRange(start=Const(1), end=Const(10)), right=IntegerRange(start=Const(1), end=Const(16)))),
"Q": Mod(value=Mul(Const(44121), Ref("x")), modulus=Const(90568)),
},
goal=Ref("Q"),
)
] | COMB | GEOM | COMPUTE | sympy | COUNT_CARTESIAN | [
"COUNT_CARTESIAN"
] | 409d7d | antilemma_cartesian_v1 | null | 2 | 0 | [
"COUNT_CARTESIAN"
] | 1 | 0.001 | 2026-02-08T10:57:26.375698Z | {
"verified": true,
"answer": 85624,
"timestamp": "2026-02-08T10:57:26.376338Z"
} | 9b0783 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 184,
"completion_tokens": 816
},
"timestamp": "2026-02-24T12:33:47.558Z",
"answer": 85624
},
{
"i... | 1 | [
{
"lemma": "COUNT_CARTESIAN",
"status": "ok"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
},
{
"lemma": "V8_SUM",
"status"... | {
"lo": -2.35,
"mid": 1.22,
"hi": 4.84
} | ||
7c04ae | nt_sum_divisors_mod_v1_601307018_53 | Let $S$ be the sum of the positive divisors of $83160$, and let $T = S \bmod 11701$. Compute the remainder when $$T^2 + \min \{ d : d \geq 2, d \mid 15 \} \cdot T + \max \left\{ d_1 : d_1 \geq \sum_{d_2 \mid \gcd(3,5)} \mu(d_2),\ d_1 \mid 1009000,\ d_1^2 \leq 1009000 \right\}$$ is divided by $63925$. | 31,379 | graphs = [
Graph(
let={
"_m": Const(2),
"_n": Const(63925),
"n": Const(83160),
"M": Const(11701),
"sigma": SumDivisors(n=Ref("n")),
"result": Mod(value=Ref("sigma"), modulus=Ref("M")),
"Q": Mod(value=Sum(Pow(Ref("result"), R... | NT | null | COMPUTE | sympy | POLY_ORBIT_LEGENDRE | [
"MIN_PRIME_FACTOR",
"B3_CLOSEST",
"MOBIUS_COPRIME"
] | fec5d5 | nt_sum_divisors_mod_v1 | quadratic_mod | 6 | 0 | [
"B3_CLOSEST",
"MIN_PRIME_FACTOR",
"MOBIUS_COPRIME",
"POLY_ORBIT_LEGENDRE"
] | 4 | 0.119 | 2026-03-10T00:43:51.694054Z | {
"verified": true,
"answer": 31379,
"timestamp": "2026-03-10T00:43:51.812996Z"
} | 5fa4d9 | CC BY 4.0 | null | null | [
{
"lemma": "B3_CLOSEST",
"status": "ok"
},
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "MIN_PRIME_FACTOR",
"status": "ok"
},
{
"lemma": "MOBIUS_COPRIME",
"st... | {
"lo": -10,
"mid": 0,
"hi": 10
} | ||
5f3bfd | comb_sum_binomial_mod_v1_1116507919_56 | Let $n = 22$. Define $S$ to be the set of all integers $n$ such that $1 \leq n \leq 836$ and $n \equiv \left\lfloor \frac{n}{2} \right\rfloor \pmod{11}$. Let $N$ be the number of elements in $S$. Compute the remainder when $\sum_{k = n}^{N} \binom{77}{k}$ is divided by $11369$. | 7,624 | graphs = [
Graph(
let={
"_n": Const(22),
"sum": Summation(var="k", start=Ref("_n"), end=CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), EulerPhi(n=Const(1))), Leq(Var("n"), Const(836)), Congruent(a=Var(name='n'), b=Floor(arg=Div(left=Var(name='n'), right=Const... | NT | null | COMPUTE | sympy | ONE_PHI_1 | [
"ONE_PHI_1",
"L3C"
] | 2d2418 | comb_sum_binomial_mod_v1 | null | 6 | 0 | [
"L3C",
"ONE_PHI_1"
] | 2 | 0.007 | 2026-02-08T02:24:07.353940Z | {
"verified": true,
"answer": 7624,
"timestamp": "2026-02-08T02:24:07.360811Z"
} | 75b1bd | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 145,
"completion_tokens": 5221
},
"timestamp": "2026-02-09T14:42:14.300Z",
"answer": 0
},
{... | 0 | [
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "L3C",
"status": "ok"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "ONE_PHI_1",
"status": "ok"
},
{
"lemma": "V5"... | {
"lo": 2.52,
"mid": 6.26,
"hi": 10
} | ||
246666 | comb_count_derangements_v1_124444284_5657 | Let $m = 2$. Define $n$ to be the number of nonnegative integers $j \leq 66696$ such that
$$
\binom{66696}{j} \equiv 1 \pmod{2}.
$$
Let $s$ be the minimum value of $x + y$ over all ordered pairs $(x, y)$ of positive integers such that $xy = n$. Compute the number of derangements of $s$ elements. | 14,833 | graphs = [
Graph(
let={
"_m": Const(2),
"_n": CountOverSet(set=SolutionsSet(var=Var("j"), condition=And(Geq(Var("j"), Const(0)), Leq(Var("j"), Const(66696)), Eq(Mod(value=Binom(n=Const(66696), k=Var("j")), modulus=Ref("_m")), Const(1))), domain='nonnegative_integers')),
"... | COMB | null | COUNT | sympy | V8 | [
"V8/B3"
] | b4fc86 | comb_count_derangements_v1 | null | 6 | 0 | [
"B3",
"V8"
] | 2 | 0.002 | 2026-02-08T06:46:02.196341Z | {
"verified": true,
"answer": 14833,
"timestamp": "2026-02-08T06:46:02.198040Z"
} | 05c2a8 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 210,
"completion_tokens": 1331
},
"timestamp": "2026-02-24T06:59:56.914Z",
"answer": 14833
},
{
"... | 1 | [
{
"lemma": "B3",
"status": "ok_later"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "V8",
"status": "ok"
},
{
"lemm... | {
"lo": -2.46,
"mid": 0.47,
"hi": 3.59
} | ||
04b46c | antilemma_k2_v1_124444284_5283 | Compute $\sum_{k=1}^{193} \phi(k) \left\lfloor \frac{193}{k} \right\rfloor$, where $\phi$ denotes Euler's totient function. | 18,721 | graphs = [
Graph(
let={
"x": Summation(var="k", start=Div(Const(4), Const(4)), end=Const(193), expr=Mul(EulerPhi(n=Var("k")), Floor(Div(Const(193), Var("k"))))),
},
goal=Ref("x"),
)
] | NT | COMB | COMPUTE | sympy | K13 | [
"IDENTITY_DIV_SELF",
"K2"
] | 39e678 | antilemma_k2_v1 | null | 5 | 0 | [
"IDENTITY_DIV_SELF",
"K13",
"K2"
] | 3 | 0.049 | 2026-02-08T06:31:36.657247Z | {
"verified": true,
"answer": 18721,
"timestamp": "2026-02-08T06:31:36.706684Z"
} | 386e61 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 87,
"completion_tokens": 628
},
"timestamp": "2026-02-13T01:15:08.674Z",
"answer": 18721
},
{
... | 1 | [
{
"lemma": "IDENTITY_DIV_SELF",
"status": "ok"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "K2",
"status": "ok"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
... | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
5f623d | nt_num_divisors_compute_v1_1874849503_1499 | Let $T$ be the set of all ordered pairs of positive integers $(x, y)$ such that $xy = 1022121$, and let $n$ be the minimum value of $x + y$ over all such pairs. Let $d(n)$ denote the number of positive divisors of $n$. Let $c = \sum_{d \mid 100} \phi(d)$, where $\phi$ is Euler's totient function. Compute the value of $... | 108 | graphs = [
Graph(
let={
"_n": Const(2),
"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(1022121)))), expr=Sum(Var("x"), Var("y")))),... | NT | null | COMPUTE | sympy | K3 | [
"K3",
"B3"
] | 16dbe6 | nt_num_divisors_compute_v1 | digits_weighted_mod | 6 | 0 | [
"B3",
"K3"
] | 2 | 0.007 | 2026-02-08T13:56:34.052601Z | {
"verified": true,
"answer": 108,
"timestamp": "2026-02-08T13:56:34.059694Z"
} | 007cce | 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": 2234
},
"timestamp": "2026-02-10T04:50:47.731Z",
"answer": 108
},
{
"id... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "K3",
"status": "ok"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
},
{
"lemma": "VAL_SUM_EQ",
... | {
"lo": -5.49,
"mid": 0.03,
"hi": 6.12
} | ||
b0e2c9 | diophantine_fbi2_min_v1_1978505735_4797 | Let $n = 24649$ and $k = 6$. Let $S$ be the set of all ordered pairs $(x,y)$ of positive integers such that $xy = 64$. Define $u$ to be the minimum value of $x + y$ as $(x,y)$ ranges over $S$. Let $T$ be the set of all integers $d$ such that $2 \leq d \leq u$, $d$ divides $k$, and $\frac{k}{d} \geq 2$. Compute $n - \mi... | 24,647 | graphs = [
Graph(
let={
"_n": Const(24649),
"k": Const(6),
"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(64)))), e... | NT | null | EXTREMUM | sympy | B3 | [
"B3"
] | 0cd20d | diophantine_fbi2_min_v1 | null | 3 | 0 | [
"B3"
] | 1 | 0.004 | 2026-02-08T18:33:10.965543Z | {
"verified": true,
"answer": 24647,
"timestamp": "2026-02-08T18:33:10.970033Z"
} | 31281e | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 183,
"completion_tokens": 433
},
"timestamp": "2026-02-16T12:25:08.679Z",
"answer": 24647
},
{
"id": 11,
... | 2 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
}
] | {
"lo": -10,
"mid": -7.27,
"hi": -4.54
} | ||
ea6394_l | antilemma_sum_equals_v1_124444284_3109 | Let $n = 90$. Let $x$ be the number of ordered pairs $(i, j)$ of positive integers such that $1 \leq i \leq 88$, $1 \leq j \leq 88$, and $i + j = 90$. Compute the value of $x^2 + 36x + 512$. | 11,424 | COMB | GEOM | COMPUTE | sympy | COUNT_SUM_EQUALS | [
"COUNT_SUM_EQUALS"
] | 75ab0f | antilemma_sum_equals_v1 | null | 3 | 0 | [
"COUNT_SUM_EQUALS"
] | 1 | 0.005 | 2026-02-08T05:15:07.571970Z | {
"verified": false,
"answer": 11213,
"timestamp": "2026-02-08T05:15:07.577318Z"
} | 51f991 | ea6394 | legacy_text | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 186,
"completion_tokens": 786
},
"timestamp": "2026-02-24T02:57:22.230Z",
"answer": 11213
},
{
"i... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "ok"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8",
"status": "no... | {
"lo": -2.46,
"mid": 0.47,
"hi": 3.59
} | |
df2c50 | nt_max_prime_below_v1_1918700295_4148 | Let $S$ be the set of all positive integers $p$ for which there exists a positive integer $q$ such that $pq = 108$, $\gcd(p, q) = 1$, and $p < q$. Let $k$ be the number of elements in $S$. Determine the value of the largest prime number $n$ such that $k \leq n \leq 10816$. | 10,799 | graphs = [
Graph(
let={
"upper": Const(10816),
"result": MaxOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), CountOverSet(set=SolutionsSet(var=Var("p"), condition=And(IsPositive(arg=Var(name='p')), Exists(var=Var(name='q'), condition=And(Eq(left=Mul(Var(name='p'), V... | NT | null | EXTREMUM | sympy | COPRIME_PAIRS | [
"COPRIME_PAIRS"
] | 2bb3aa | nt_max_prime_below_v1 | null | 5 | 0 | [
"COPRIME_PAIRS"
] | 1 | 1.406 | 2026-02-08T09:09:58.180315Z | {
"verified": true,
"answer": 10799,
"timestamp": "2026-02-08T09:09:59.586684Z"
} | ca32ce | 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": 3428
},
"timestamp": "2026-02-14T01:47:58.720Z",
"answer": 10799
},
... | 1 | [
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
},
{
"lemma": "V8_... | {
"lo": -5.49,
"mid": 0.22,
"hi": 6.51
} | ||
bc2232 | lte_diff_endings_v1_124444284_33 | Let $a = 186$, $b = 11$, $p = 5$, and $n = 50134$. Let $v_p(a - b)$ denote the largest integer $k$ such that $p^k$ divides $a - b$. Let $v_p(n!)$ denote the largest integer $k$ such that $p^k$ divides $n!$. Compute the remainder when $n \cdot v_p(a - b) + v_p(n!)$ is divided by $100000$. | 12,799 | graphs = [
Graph(
let={
"a_val": Const(186),
"b_val": Const(11),
"p_val": Const(5),
"n_val": Const(50134),
"ab_diff": Sub(Ref("a_val"), Ref("b_val")),
"vp_ab": MaxKDivides(target=Ref("ab_diff"), base=Ref("p_val")),
"n_times_... | NT | null | COMPUTE | sympy | LTE_DIFF | [
"LTE_DIFF"
] | cf8260 | lte_diff_endings_v1 | null | 4 | null | [
"LTE_DIFF"
] | 1 | 0.001 | 2026-02-08T02:54:41.366266Z | {
"verified": true,
"answer": 12799,
"timestamp": "2026-02-08T02:54:41.367035Z"
} | c477f9 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 223,
"completion_tokens": 917
},
"timestamp": "2026-02-09T12:42:17.018Z",
"answer": 12799
},
{
"i... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "ok"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
}
] | {
"lo": -6.51,
"mid": -0.31,
"hi": 5.43
} | ||
0fdba8 | nt_sum_divisors_mod_v1_238844314_30 | Let $S$ be the set of all ordered pairs of positive odd integers $(x_1, x_2)$ such that $x_1 + x_2 = 16200$. Let $N$ be the number of elements in $S$. Let $n$ be the minimum value of $x + y$ over all ordered pairs of positive integers $(x, y)$ such that $xy = N$. Let $\sigma$ be the sum of all positive divisors of $n$,... | 546 | graphs = [
Graph(
let={
"n": MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(Mul(Var("x"), Var("y")), CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x1"), Var("x2")]), cond... | NT | null | COMPUTE | sympy | COMB1 | [
"COMB1/B3"
] | 014cfb | nt_sum_divisors_mod_v1 | null | 6 | 0 | [
"B3",
"COMB1"
] | 2 | 0.004 | 2026-02-08T13:05:46.875750Z | {
"verified": true,
"answer": 546,
"timestamp": "2026-02-08T13:05:46.879308Z"
} | d8d369 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 169,
"completion_tokens": 1036
},
"timestamp": "2026-02-15T09:29:35.837Z",
"answer": 546
},
{
... | 1 | [
{
"lemma": "B3",
"status": "ok_later"
},
{
"lemma": "COMB1",
"status": "ok"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "n... | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
50a56a | nt_sum_totient_over_divisors_v1_655260480_6204 | Let $n = 86243$. Define $\varphi(d)$ as Euler's totient function. Let $R$ be the sum of $\varphi(d)$ over all positive divisors $d$ of $n$. Let $S$ be the sum of $d_i \cdot (i+1)^2$ for $i$ from $0$ to the number of digits of $|R|$ minus one, where $d_i$ is the $i$-th decimal digit of $|R|$ (with $d_0$ being the units ... | 413 | graphs = [
Graph(
let={
"n": Const(86243),
"result": SumOverDivisors(n=Ref(name='n'), var='d', expr=EulerPhi(n=Var(name='d'))),
"Q": Sum(Summation(var="i", start=Const(0), end=Sub(NumDigits(x=Abs(arg=Ref(name='result')), base=None), Const(1)), expr=Mul(Digit(x=Abs(arg=Ref... | NT | null | COMPUTE | sympy | COUNT_CARTESIAN | [
"COUNT_CARTESIAN"
] | e44d3d | nt_sum_totient_over_divisors_v1 | digits_weighted_mod | 4 | 0 | [
"COUNT_CARTESIAN"
] | 1 | 0.002 | 2026-02-08T18:54:54.845624Z | {
"verified": true,
"answer": 413,
"timestamp": "2026-02-08T18:54:54.847620Z"
} | 4c0c49 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 207,
"completion_tokens": 4959
},
"timestamp": "2026-02-18T20:29:07.579Z",
"answer": 413
},
{
... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "ok"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "V3",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
5934a8 | lin_form_endings_v1_717093673_3060 | Let $a = 70$ and $b = 30$. Let $d$ be the greatest common divisor of $a$ and $b$. Define $k = \left\lfloor \frac{70}{d} \right\rfloor$. Let $s = 14246 \cdot k$, and let $M = 97778$. Compute the remainder when $s$ is divided by $M$. | 1,944 | graphs = [
Graph(
let={
"a_coeff": Const(70),
"b_coeff": Const(30),
"_inner_result": Floor(Div(Const(70), GCD(a=Ref("a_coeff"), b=Ref("b_coeff")))),
"_scale_k": Const(14246),
"_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 | 0.003 | 2026-02-08T17:21:15.360318Z | {
"verified": true,
"answer": 1944,
"timestamp": "2026-02-08T17:21:15.363488Z"
} | 57405c | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 151,
"completion_tokens": 304
},
"timestamp": "2026-02-16T09:38:14.548Z",
"answer": 1944
},
{
"id": 11,
... | 2 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
... | {
"lo": -10,
"mid": -7.27,
"hi": -4.54
} | ||
0393fb | nt_min_coprime_above_v1_124444284_7788 | Let $S$ be the set of all ordered pairs $(x, y)$ of positive integers such that $x + y = 176$. Define $P$ to be the maximum value of $xy$ over all pairs in $S$. Let $T$ be the set of all ordered pairs $(x, y)$ of positive integers such that $xy = P$. Define $m$ to be the minimum value of $x + y$ over all pairs in $T$. ... | 28,659 | graphs = [
Graph(
let={
"start": Const(28657),
"upper": Const(28843),
"modulus": MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(Mul(Var("x"), Var("y")), Ma... | NT | null | EXTREMUM | sympy | B1 | [
"B1/B3"
] | 80b49d | nt_min_coprime_above_v1 | null | 6 | 0 | [
"B1",
"B3"
] | 2 | 0.019 | 2026-02-08T09:22:40.206997Z | {
"verified": true,
"answer": 28659,
"timestamp": "2026-02-08T09:22:40.226083Z"
} | d2c451 | 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": 1749
},
"timestamp": "2026-02-14T03:34:40.994Z",
"answer": 28659
},
... | 1 | [
{
"lemma": "B1",
"status": "ok"
},
{
"lemma": "B3",
"status": "ok_later"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
... | {
"lo": -8.26,
"mid": -5.01,
"hi": -1.76
} | ||
53ce5f | modular_mod_compute_v1_677425708_3281 | Let $n = 142$. Consider the set of all ordered pairs $(x, y)$ of positive integers such that $x + y = n$. Let $m$ be the maximum value of $xy$ over all such pairs. Compute the remainder when $-23$ is divided by $m$. | 5,018 | graphs = [
Graph(
let={
"_n": Const(142),
"a": Const(-23),
"m": MaxOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(Sum(Var("x"), Var("y")), Ref("_n")))), expr=... | NT | null | COMPUTE | sympy | B1 | [
"B1"
] | 5b950e | modular_mod_compute_v1 | null | 4 | 0 | [
"B1"
] | 1 | 0.007 | 2026-02-08T05:38:12.200754Z | {
"verified": true,
"answer": 5018,
"timestamp": "2026-02-08T05:38:12.207648Z"
} | d081cf | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 108,
"completion_tokens": 633
},
"timestamp": "2026-02-12T11:35:11.271Z",
"answer": 5018
},
{
... | 1 | [
{
"lemma": "B1",
"status": "ok"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "V1",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
},
{
"lemma": "VAL_SUM_EQ",
"status": "no"
}
] | {
"lo": -7.01,
"mid": -4.68,
"hi": -2.15
} | ||
4699bf | sequence_count_fib_divisible_v1_865884756_189 | Let $U$ be the number of positive integers $n$ such that $1 \leq n \leq 653$ and $\gcd(n, 20) = 1$. Let $d$ be the smallest divisor of $10051$ that is at least $2$. Let $R$ be the number of positive integers $n_1$ such that $1 \leq n_1 \leq U$ and $d$ divides the $n_1$-th Fibonacci number. Compute $66666 - R$. | 66,652 | graphs = [
Graph(
let={
"upper": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Const(653)), Eq(GCD(a=Var("n"), b=Const(20)), Const(1))))),
"d": MinOverSet(set=SolutionsSet(var=Var("d1"), condition=And(Geq(Var("d1"), Const(2)), Divide... | NT | null | COUNT | sympy | MIN_PRIME_FACTOR | [
"MIN_PRIME_FACTOR",
"C4"
] | 90e51f | sequence_count_fib_divisible_v1 | null | 6 | 0 | [
"C4",
"MIN_PRIME_FACTOR"
] | 2 | 0.053 | 2026-02-08T15:15:21.151659Z | {
"verified": true,
"answer": 66652,
"timestamp": "2026-02-08T15:15:21.204194Z"
} | adb2cf | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 223,
"completion_tokens": 2296
},
"timestamp": "2026-02-10T05:17:56.771Z",
"answer": 66652
},
{
"... | 1 | [
{
"lemma": "C4",
"status": "ok"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "MIN_PRIME_FACTOR",
"status": "ok"
},
{
"... | {
"lo": -7.09,
"mid": -0.49,
"hi": 6.1
} | ||
674b86 | comb_count_derangements_v1_1742523217_3519 | Let $S$ be the set of all ordered pairs $(x, y)$ of positive integers such that $xy = 410881$. Let $s$ be the sum $x + y$ over the pair $(x, y) \in S$ that minimizes $x + y$. Let $n$ be the number of nonnegative integers $j$ such that $0 \leq j \leq 1282$ and the binomial coefficient $\binom{s}{j}$ is odd. Let $Q = !n$... | 14,833 | graphs = [
Graph(
let={
"_n": Const(1282),
"n": CountOverSet(set=SolutionsSet(var=Var("j"), condition=And(Geq(Var("j"), Const(0)), Leq(Var("j"), Ref("_n")), Eq(Mod(value=Binom(n=MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPosit... | COMB | null | COUNT | sympy | B3 | [
"B3/V8"
] | 4fad5b | comb_count_derangements_v1 | null | 7 | 0 | [
"B3",
"V8"
] | 2 | 0.002 | 2026-02-08T05:55:33.683578Z | {
"verified": true,
"answer": 14833,
"timestamp": "2026-02-08T05:55:33.685347Z"
} | 445bb7 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 235,
"completion_tokens": 32768
},
"timestamp": "2026-02-24T04:55:22.108Z",
"answer": null
},
{
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8",
"status": "ok_later"
},... | {
"lo": 1.97,
"mid": 4.36,
"hi": 6.69
} | ||
b5a88d | lin_form_endings_v1_397696148_970 | Let $a = 42$ and $b = 28$. Define $s = \gcd(a, b)$. Let $k = 39$ and compute $r = \left\lfloor \frac{k}{\gcd(k, s)} \right\rfloor$. Now let $x = (16118 \cdot r) \bmod 90518$. Find the value of $x$. | 85,494 | graphs = [
Graph(
let={
"a_coeff": Const(42),
"b_coeff": Const(28),
"k_val": Const(39),
"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(16... | COMB | NT | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | lin_form_endings_v1 | null | 2 | null | [
"LIN_FORM"
] | 1 | 0.001 | 2026-02-08T11:59:30.583904Z | {
"verified": true,
"answer": 85494,
"timestamp": "2026-02-08T11:59:30.584869Z"
} | e47749 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 127,
"completion_tokens": 447
},
"timestamp": "2026-02-14T23:43:37.102Z",
"answer": 85494
},
{... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
... | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
8bb633 | modular_sum_quadratic_residues_v1_601307018_7499 | Let $p$ be the number of ordered pairs $(a, b)$ of positive integers with $1 \le a, b \le 15$ such that $13a^2 - 2ab + 2b^2 \le \max\{ d : d \ge 1,\ d \le 2197,\ d \mid 4848779 \}$. Compute $\frac{p(p - 1)}{4}$. | 9,264 | graphs = [
Graph(
let={
"_m": Const(4),
"_n": Const(2),
"p": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("a"), Var("b")]), condition=And(Geq(Var("a"), Const(1)), Leq(Var("a"), Const(15)), Geq(Var("b"), Const(1)), Leq(Var("b"), Const(15)), Leq(Sum(Mul(Const(13), ... | NT | null | SUM | sympy | MAX_DIVISOR | [
"MAX_DIVISOR/QF_PSD_COUNT_LEQ"
] | 5c8342 | modular_sum_quadratic_residues_v1 | null | 5 | 0 | [
"MAX_DIVISOR",
"QF_PSD_COUNT_LEQ"
] | 2 | 0.005 | 2026-03-10T08:01:42.481518Z | {
"verified": true,
"answer": 9264,
"timestamp": "2026-03-10T08:01:42.486953Z"
} | d47a63 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 203,
"completion_tokens": 4409
},
"timestamp": "2026-04-19T06:53:08.045Z",
"answer": 9264
},
{
"... | 1 | [
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "MAX_DIVISOR",
"status": "ok"
},
{
"lemma": "QF_PSD_COUNT_LEQ",
"status": "ok_later"
},
{
"lemma": "V3",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
},
{
... | {
"lo": -5.34,
"mid": 1.1,
"hi": 7.53
} | ||
274885 | modular_inverse_v1_677425708_35 | Let $a$ be the number of integers $t$ such that $5 \leq t \leq 408$ and there exist positive integers $a$ and $b$ with $1 \leq a \leq 114$, $1 \leq b \leq 60$, and $t = 2a + 3b$. Let $m = 661$ and let $x_0$ be the smallest positive integer $x$ such that $1 \leq x \leq 660$ and $a \cdot x \equiv 1 \pmod{m}$. Compute the... | 21,485 | graphs = [
Graph(
let={
"_n": Const(44121),
"a": 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=114)), Geq(left=... | NT | null | EXTREMUM | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | modular_inverse_v1 | null | 6 | 0 | [
"LIN_FORM"
] | 1 | 0.029 | 2026-02-08T03:01:04.193280Z | {
"verified": true,
"answer": 21485,
"timestamp": "2026-02-08T03:01:04.222066Z"
} | 7bebd9 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 265,
"completion_tokens": 3818
},
"timestamp": "2026-02-08T20:16:42.391Z",
"answer": 57458
},
{
... | 1 | [
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
... | {
"lo": 3.7,
"mid": 5.49,
"hi": 7.55
} | ||
691489 | comb_sum_binomial_row_v1_865884756_5462 | Let $n$ be the number of ordered pairs $(i,j)$ of positive integers such that $i + j = 15$, $1 \le i \le 14$, and $1 \le j \le 15$. Compute $2^n$. | 16,384 | graphs = [
Graph(
let={
"_n": Const(2),
"n": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("i"), Var("j")]), condition=Eq(Sum(Var("i"), Var("j")), Const(15)), domain=CartesianProduct(left=IntegerRange(start=Const(1), end=Const(14)), right=IntegerRange(start=Const(1), end=Cons... | NT | null | SUM | sympy | COUNT_SUM_EQUALS | [
"COUNT_SUM_EQUALS"
] | 75ab0f | comb_sum_binomial_row_v1 | null | 2 | 0 | [
"COUNT_SUM_EQUALS"
] | 1 | 0.011 | 2026-02-08T18:37:42.159684Z | {
"verified": true,
"answer": 16384,
"timestamp": "2026-02-08T18:37:42.170994Z"
} | fbae70 | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 114,
"completion_tokens": 249
},
"timestamp": "2026-02-16T13:27:11.567Z",
"answer": 16384
},
{
"id": 11,
... | 2 | [
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "ok"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
}
] | {
"lo": -10,
"mid": -7.27,
"hi": -4.54
} | ||
6c3d28 | nt_num_divisors_compute_v1_655260480_168 | Let $n$ be the number of positive integers $p$ for which there exists a positive integer $q$ such that $pq = 2315250$, $\gcd(p, q) = 1$, and $p < q$. Compute the remainder when $44121 \cdot \tau(n)$ is divided by $99698$, where $\tau(n)$ denotes the number of positive divisors of $n$. | 76,786 | graphs = [
Graph(
let={
"_n": Const(99698),
"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=2315250)), Eq(left=GCD(a=Var(name='p'), b=Var... | NT | null | COMPUTE | sympy | COPRIME_PAIRS | [
"COPRIME_PAIRS"
] | 2bb3aa | nt_num_divisors_compute_v1 | null | 4 | 0 | [
"COPRIME_PAIRS"
] | 1 | 0.002 | 2026-02-08T15:14:45.317033Z | {
"verified": true,
"answer": 76786,
"timestamp": "2026-02-08T15:14:45.318663Z"
} | c69f86 | 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": 1315
},
"timestamp": "2026-02-16T02:51:35.080Z",
"answer": 76786
},
... | 1 | [
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
}... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
c7b1c1 | comb_count_partitions_v1_1218484723_1472 | Let $n$ be the number of positive integers $t$ with $27 \le t \le 156$ such that $t = 6a + 21b$ for some integers $a, b$ with $1 \le a \le 19$, $1 \le b \le 2$. Let $M = p(n)$, where $p(n)$ denotes the number of integer partitions of $n$. Find the remainder when $44121M$ is divided by $69158$. | 61,647 | graphs = [
Graph(
let={
"_n": Const(69158),
"n": CountOverSet(set=SolutionsSet(var=Var("t"), condition=Exists(var=Var(name='a'), condition=Exists(var=Var(name='b'), condition=And(Geq(left=Var(name='a'), right=Const(value=1)), Leq(left=Var(name='a'), right=Const(value=19)), Geq(left=V... | COMB | null | COUNT | sympy | STARS_BARS | [
"LIN_FORM"
] | 7b2633 | comb_count_partitions_v1 | null | 5 | 0 | [
"LIN_FORM",
"STARS_BARS"
] | 2 | 0.01 | 2026-02-25T03:10:51.066278Z | {
"verified": true,
"answer": 61647,
"timestamp": "2026-02-25T03:10:51.076360Z"
} | 0828a6 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 215,
"completion_tokens": 5101
},
"timestamp": "2026-03-10T03:55:37.546Z",
"answer": 61647
},
{
"... | 1 | [
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "V8",
"status": "no"
},
{
"lemma": "V8_SUM",
"st... | {
"lo": -2.47,
"mid": 1.2,
"hi": 4.81
} | ||
e7407a | antilemma_v1_legendre_2080023795_211 | Let $p$ be the largest prime number less than or equal to 18. Determine the largest integer $k$ such that $p^k$ divides $62577!$. | 3,909 | graphs = [
Graph(
let={
"_n": Const(18),
"x": MaxKDivides(target=Factorial(Const(62577)), base=MaxOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(2)), Leq(Var("n"), Ref("_n")), IsPrime(Var("n")))))),
},
goal=Ref("x"),
)
] | NT | null | COMPUTE | sympy | MAX_PRIME_BELOW | [
"MAX_PRIME_BELOW/V1",
"V1"
] | 8b2738 | antilemma_v1_legendre | null | 4 | 0 | [
"MAX_PRIME_BELOW",
"V1"
] | 2 | 0.001 | 2026-02-08T11:35:58.394669Z | {
"verified": true,
"answer": 3909,
"timestamp": "2026-02-08T11:35:58.395269Z"
} | 91dcf0 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 151,
"completion_tokens": 916
},
"timestamp": "2026-02-08T20:52:03.034Z",
"answer": 3908
},
{
... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "K5",
"status": "same_pattern_wrong"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "V1",
"status": "ok"
... | {
"lo": -2.06,
"mid": 1.85,
"hi": 5.2
} | ||
831114 | nt_min_coprime_above_v1_124444284_8215 | Let $s = \sum_{k=1}^{31} k$. Find the smallest integer $n$ such that $57121 < n \le 57627$ and $\gcd(n, s) = 1$. | 57,123 | graphs = [
Graph(
let={
"_n": Const(31),
"start": Const(57121),
"upper": Const(57627),
"modulus": Summation(var="k", start=Const(1), end=Ref("_n"), expr=Var("k")),
"result": MinOverSet(set=SolutionsSet(var=Var("n"), condition=And(Gt(Var("n"), Ref("... | NT | null | EXTREMUM | sympy | SUM_ARITHMETIC | [
"SUM_ARITHMETIC"
] | eb34f0 | nt_min_coprime_above_v1 | null | 3 | 0 | [
"SUM_ARITHMETIC"
] | 1 | 0.065 | 2026-02-08T09:36:24.649853Z | {
"verified": true,
"answer": 57123,
"timestamp": "2026-02-08T09:36:24.714703Z"
} | b1bfc0 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 93,
"completion_tokens": 616
},
"timestamp": "2026-02-14T05:10:20.866Z",
"answer": 57123
},
{
... | 1 | [
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "SUM_ARITHMETIC",
"status": "ok"
},
{
"lemma": "V3",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
}
] | {
"lo": -6.96,
"mid": -4.56,
"hi": -1.46
} | ||
be25ae | algebra_quadratic_discriminant_v1_677425708_3985 | Let $b$ be the maximum value of $xy$ over all ordered pairs $(x, y)$ of positive integers such that $x + y = 6$. Let $S$ be the set of all positive integers $p$ for which there exists a positive integer $q$ such that $pq = 216$, $\gcd(p, q) = 1$, and $p < q$. Let $k$ be the number of elements in $S$. Compute the value ... | 261 | graphs = [
Graph(
let={
"_n": Const(4),
"a": Const(-5),
"b": MaxOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(Sum(Var("x"), Var("y")), Const(6)))), expr=Mul(... | NT | null | COMPUTE | sympy | B3 | [
"COPRIME_PAIRS",
"B1"
] | aa8272 | algebra_quadratic_discriminant_v1 | null | 5 | 0 | [
"B1",
"B3",
"COPRIME_PAIRS"
] | 3 | 0.011 | 2026-02-08T06:07:35.111670Z | {
"verified": true,
"answer": 261,
"timestamp": "2026-02-08T06:07:35.123102Z"
} | eac00f | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 162,
"completion_tokens": 1045
},
"timestamp": "2026-02-12T19:35:42.533Z",
"answer": 261
},
{
... | 1 | [
{
"lemma": "B1",
"status": "ok"
},
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "V1",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
},
{
"lemma": "V8_SU... | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
81d343 | nt_min_crt_v1_1520064083_10048 | Let $m = 4$, $a = 3$, and $b = 1$. Let $k = 7$. Define $U$ to be the sum
$$
\sum_{k=1}^{d_{\text{min}}} \varphi(k) \left\lfloor \frac{7}{k} \right\rfloor,
$$
where $d_{\text{min}}$ is the smallest divisor of 11011 that is at least 2.
Let $x$ be the smallest positive integer not exceeding $U$ such that $x \equiv 3 \pmo... | 44,496 | graphs = [
Graph(
let={
"m": Const(4),
"k": Const(7),
"a": Const(3),
"b": Const(1),
"upper": Summation(var="k", start=Const(1), end=MinOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Const(2)), Divides(divisor=Var("d"), dividend=... | NT | null | EXTREMUM | sympy | MIN_PRIME_FACTOR | [
"MIN_PRIME_FACTOR/K2"
] | 352a97 | nt_min_crt_v1 | null | 7 | 0 | [
"K2",
"MIN_PRIME_FACTOR"
] | 2 | 0.006 | 2026-02-08T11:10:54.461571Z | {
"verified": true,
"answer": 44496,
"timestamp": "2026-02-08T11:10:54.467982Z"
} | 3a3a23 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 200,
"completion_tokens": 1420
},
"timestamp": "2026-02-14T10:48:24.229Z",
"answer": 44496
},
... | 1 | [
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K2",
"status": "ok_later"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "MIN_PRIME_FACTOR",
"status": "ok"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
... | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
24b258 | alg_poly_orbit_legendre_v1_601307018_2753 | Let $a$ be a non-negative integer with $0 \le a \le 40526$. Define $N = a^{39} \bmod 79$, $M = (a^4 + 2a^3 - a - 3) \bmod 79$, $R = M^{39} \bmod 79$, and $S = N + R$. Define $T = (M^4 + 2M^3 - M - 3) \bmod 79$. Find the number of such $a$ for which $T = a$, $S \equiv 0 \pmod{3}$, and $M \ne a$. | 1,026 | graphs = [
Graph(
let={
"p1": Mod(value=Sum(Pow(Var("a"), Const(4)), Mul(Const(2), Pow(Var("a"), Const(3))), Mul(Const(-1), Var("a")), Const(-3)), modulus=Const(79)),
"p2": Mod(value=Sum(Pow(Ref("p1"), Const(4)), Mul(Const(2), Pow(Ref("p1"), Const(3))), Mul(Const(-1), Ref("p1")), Con... | NT | null | COUNT | sympy | POLY_ORBIT_LEGENDRE_COUNT | [
"POLY_ORBIT_LEGENDRE_COUNT"
] | b47831 | alg_poly_orbit_legendre_v1 | null | 8 | null | [
"POLY_ORBIT_LEGENDRE_COUNT"
] | 1 | 0.048 | 2026-03-10T03:24:20.903358Z | {
"verified": true,
"answer": 1026,
"timestamp": "2026-03-10T03:24:20.951720Z"
} | 6569c1 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 1,
"correct": {
"strict": false,
"boxed": false,
"relaxed": true
},
"usage": {
"prompt_tokens": 253,
"completion_tokens": 12434
},
"timestamp": "2026-04-18T23:00:17.681Z",
"answer": 0
},
{
"... | 0 | [
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "POLY_ORBIT_LEGENDRE_COUNT",
"status": "ok"
},
{
"lemma": "V3",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
}
] | {
"lo": 2.12,
"mid": 5.37,
"hi": 8.63
} | ||
11e8b5 | sequence_fibonacci_compute_v1_124444284_1639 | Let $c$ be the minimum value of $x + y$ over all ordered pairs of positive integers $(x, y)$ such that $xy = 1827904$. Let $F_n$ denote the $n$th Fibonacci number, where $F_{22}$ is computed with $F_1 = 1$, $F_2 = 1$, and $F_n = F_{n-1} + F_{n-2}$ for $n \geq 3$. Find the remainder when $c - F_{22}$ is divided by $5811... | 43,108 | graphs = [
Graph(
let={
"_n": Const(58115),
"n": Const(22),
"result": Fibonacci(arg=Ref(name='n')),
"_c": MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name=... | NT | null | COMPUTE | sympy | B3 | [
"B3"
] | fc629c | sequence_fibonacci_compute_v1 | negation_mod | 4 | 0 | [
"B3"
] | 1 | 0.002 | 2026-02-08T04:03:55.941649Z | {
"verified": true,
"answer": 43108,
"timestamp": "2026-02-08T04:03:55.943603Z"
} | 3e3bca | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 230,
"completion_tokens": 1183
},
"timestamp": "2026-02-10T15:21:17.135Z",
"answer": 43108
},
{
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "V1",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
}
] | {
"lo": -3.42,
"mid": 1.86,
"hi": 7.55
} | ||
6bd8df | modular_mod_compute_v1_1915831931_903 | Let $a = -800$. Define $m$ to be the number of integers $t$ such that $8 \leq t \leq 6780$ and there exist positive integers $a'$ and $b'$ with $1 \leq a' \leq 561$, $1 \leq b' \leq 1325$, and $t = 5a' + 3b'$. Compute the remainder when $a$ is divided by $m$. | 5,965 | graphs = [
Graph(
let={
"a": Const(-800),
"m": CountOverSet(set=SolutionsSet(var=Var("t"), condition=Exists(var=Var(name='a'), condition=Exists(var=Var(name='b'), condition=And(Geq(left=Var(name='a'), right=Const(value=1)), Leq(left=Var(name='a'), right=Const(value=561)), Geq(left=Va... | NT | null | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | modular_mod_compute_v1 | null | 3 | 0 | [
"LIN_FORM"
] | 1 | 0.003 | 2026-02-08T15:45:43.042888Z | {
"verified": true,
"answer": 5965,
"timestamp": "2026-02-08T15:45:43.045543Z"
} | 940fd1 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 145,
"completion_tokens": 5213
},
"timestamp": "2026-02-16T12:25:18.594Z",
"answer": 5965
},
{... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
13a723 | comb_binomial_compute_v1_898971024_183 | Let $ n $ be the largest prime number less than or equal to 14. Let $ k = 6 $.
Compute $ \binom{n}{k} $, and then find the remainder when $ 69931 $ times this binomial coefficient is divided by 85379. | 44,101 | graphs = [
Graph(
let={
"_n": Const(2),
"n": MaxOverSet(set=SolutionsSet(var=Var("n1"), condition=And(Geq(Var("n1"), Ref("_n")), Leq(Var("n1"), Const(14)), IsPrime(Var("n1"))))),
"k": Const(6),
"result": Binom(n=Ref("n"), k=Ref("k")),
"_c": Const(6... | NT | null | COMPUTE | sympy | MAX_PRIME_BELOW | [
"MAX_PRIME_BELOW"
] | dc3ad3 | comb_binomial_compute_v1 | null | 3 | 0 | [
"MAX_PRIME_BELOW"
] | 1 | 0.003 | 2026-02-08T15:16:17.150157Z | {
"verified": true,
"answer": 44101,
"timestamp": "2026-02-08T15:16:17.153490Z"
} | 3ab009 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 104,
"completion_tokens": 795
},
"timestamp": "2026-02-16T02:42:33.063Z",
"answer": 44101
},
{... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok"
},
{
"lemma": "MAX_VAL",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
10b0e6 | nt_max_prime_below_v1_1520064083_3721 | Let $c$ 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 $n$ be the largest prime number such that $c \leq n \leq 36100$. Compute the remainder when $44121 \cdot n$ is divided by $59218$. | 26,845 | graphs = [
Graph(
let={
"upper": Const(36100),
"result": MaxOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), CountOverSet(set=SolutionsSet(var=Var("p"), condition=And(IsPositive(arg=Var(name='p')), Exists(var=Var(name='q'), condition=And(Eq(left=Mul(Var(name='p'), V... | NT | null | EXTREMUM | sympy | COPRIME_PAIRS | [
"COPRIME_PAIRS"
] | 2bb3aa | nt_max_prime_below_v1 | null | 4 | 0 | [
"COPRIME_PAIRS"
] | 1 | 0.856 | 2026-02-08T05:50:07.414878Z | {
"verified": true,
"answer": 26845,
"timestamp": "2026-02-08T05:50:08.271210Z"
} | 27965d | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 137,
"completion_tokens": 3178
},
"timestamp": "2026-02-12T16:16:30.021Z",
"answer": 26845
},
... | 1 | [
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "V1",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
},
{
"lemma": "VAL_SUM_EQ",
"status... | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
238130 | geo_count_lattice_rect_v1_153355830_313 | Let $a = 444$ and $b = 130$. Compute the number of lattice points $(x, y)$ such that $0 \leq x \leq a$ and $0 \leq y \leq b$. | 58,295 | graphs = [
Graph(
let={
"a": Const(444),
"b": Const(130),
"result": LatticePointsRect(a=Ref(name='a'), b=Ref(name='b')),
},
goal=Ref("result"),
)
] | GEOM | null | COUNT | sympy | [] | geo_count_lattice_rect_v1 | null | 4 | 0 | null | null | 0.007 | 2026-02-08T03:02:21.942225Z | {
"verified": true,
"answer": 58295,
"timestamp": "2026-02-08T03:02:21.949714Z"
} | 4a0da0 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 160,
"completion_tokens": 192
},
"timestamp": "2026-02-10T12:26:55.369Z",
"answer": 58295
},
{
"i... | 1 | [] | {
"lo": -7.18,
"mid": -4.99,
"hi": -3
} | ||||
860ada | comb_count_surjections_v1_124444284_10115 | Let $t$ be an integer between 5 and 12, inclusive. A pair of positive integers $(a, b)$ with $1 \le a \le 3$ and $1 \le b \le 2$ is called $t$-valid if $t = 2a + 3b$. Define $n$ to be the number of values of $t$ for which at least one $t$-valid pair exists. Let $k$ be the number of ordered pairs $(i, j)$ of positive in... | 1,800 | graphs = [
Graph(
let={
"_n": Const(6),
"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(na... | COMB | null | COUNT | sympy | COUNT_SUM_EQUALS | [
"COUNT_SUM_EQUALS",
"LIN_FORM"
] | 7b3310 | comb_count_surjections_v1 | null | 6 | 0 | [
"COUNT_SUM_EQUALS",
"LIN_FORM"
] | 2 | 0.02 | 2026-02-08T12:50:09.672251Z | {
"verified": true,
"answer": 1800,
"timestamp": "2026-02-08T12:50:09.692333Z"
} | 9e86ed | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 283,
"completion_tokens": 1135
},
"timestamp": "2026-02-24T16:30:39.772Z",
"answer": 1800
},
{
"i... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "ok"
},
{
"lemma": "LIN_F... | {
"lo": -2.35,
"mid": 1.22,
"hi": 4.84
} | ||
210fb5 | comb_binomial_compute_v1_1978505735_2925 | Let $n$ be the number of integers $t$ such that $10 \leq t \leq 38$ and $t = 4a + 6b$ for some integers $a$, $b$ with $1 \leq a \leq 5$ and $1 \leq b \leq 3$. Let $Q = \binom{n}{6}$. Find the remainder when $65500 \cdot Q$ is divided by $94183$. | 37,681 | 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=1... | ALG | COMB | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | comb_binomial_compute_v1 | null | 3 | 0 | [
"LIN_FORM"
] | 1 | 0.002 | 2026-02-08T17:15:46.685052Z | {
"verified": true,
"answer": 37681,
"timestamp": "2026-02-08T17:15:46.687072Z"
} | b1d81e | 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": 1650
},
"timestamp": "2026-02-17T22:49:58.510Z",
"answer": 37681
},
... | 1 | [
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
}
] | {
"lo": -2.38,
"mid": 1.74,
"hi": 6.59
} | ||
aec85e | modular_min_linear_v1_1742523217_515 | Let $S$ be the set of all ordered pairs $(x, y)$ of positive integers such that $xy = 11957764$. Let $a$ be the minimum value of $x + y$ over all such pairs. Let $b = 22118$ and $m = 26582$. Compute the smallest integer $x$ such that $x \geq \sum_{d\mid \gcd(15,22)} \mu(d)$, $x \leq m$, and $ax \equiv b \pmod{m}$. | 9,270 | graphs = [
Graph(
let={
"a": MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(Mul(Var("x"), Var("y")), Const(11957764)))), expr=Sum(Var("x"), Var("y")))),
"b": Const(221... | NT | null | EXTREMUM | sympy | MOBIUS_COPRIME | [
"MOBIUS_COPRIME",
"B3"
] | 233389 | modular_min_linear_v1 | null | 7 | 0 | [
"B3",
"MOBIUS_COPRIME"
] | 2 | 2.212 | 2026-02-08T03:05:33.685156Z | {
"verified": true,
"answer": 9270,
"timestamp": "2026-02-08T03:05:35.897190Z"
} | 9a024a | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 228,
"completion_tokens": 5231
},
"timestamp": "2026-02-09T19:02:27.874Z",
"answer": 9270
},
{
"i... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "MOBIUS_COPRIME",
"status": "ok"
},
{
"lemma": "MOD_MUL",
"status... | {
"lo": -6.51,
"mid": -0.31,
"hi": 5.43
} | ||
db5cfa | geo_count_lattice_rect_v1_1125832087_2370 | Compute the number of lattice points in the rectangle $[0, 300] \times [0, 288]$, including the boundary. | 86,989 | graphs = [
Graph(
let={
"a": Const(300),
"b": Const(288),
"result": LatticePointsRect(a=Ref(name='a'), b=Ref(name='b')),
"Q": Abs(arg=Ref(name='result')),
},
goal=Ref("Q"),
)
] | GEOM | null | COUNT | sympy | [] | geo_count_lattice_rect_v1 | null | 3 | 0 | null | null | 0.001 | 2026-02-08T04:34:30.430373Z | {
"verified": true,
"answer": 86989,
"timestamp": "2026-02-08T04:34:30.430974Z"
} | 37e466 | 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": 335
},
"timestamp": "2026-02-24T01:00:54.575Z",
"answer": 86989
},
{
"i... | 1 | [] | {
"lo": -2.46,
"mid": 0.47,
"hi": 3.59
} | ||||
acb8e2 | nt_sum_gcd_range_mod_v1_124444284_10078 | Let $P$ be the set of all ordered pairs $(x, y)$ of positive integers such that $xy = 23059204$. Define $N$ to be the minimum value of $x + y$ as $(x, y)$ ranges over $P$. Let $k$ be the number of positive integers $n$ such that $1 \leq n \leq 673$ and the sum of the digits of $n$ is even. Define $S = \sum_{n=1}^{N} \g... | 8,601 | graphs = [
Graph(
let={
"_n": Const(673),
"N": MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(Mul(Var("x"), Var("y")), Const(23059204)))), expr=Sum(Var("x"), Var("y"))... | NT | null | COMPUTE | sympy | L3B | [
"L3B",
"B3"
] | e8deef | nt_sum_gcd_range_mod_v1 | null | 6 | 0 | [
"B3",
"L3B"
] | 2 | 0.463 | 2026-02-08T12:48:55.984716Z | {
"verified": true,
"answer": 8601,
"timestamp": "2026-02-08T12:48:56.448005Z"
} | f0261a | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 173,
"completion_tokens": 5022
},
"timestamp": "2026-02-15T05:33:06.543Z",
"answer": 8601
},
{... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "L3B",
"status": "ok"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma"... | {
"lo": -5.49,
"mid": 0.22,
"hi": 6.51
} | ||
19ed30 | comb_count_derangements_v1_548369836_332 | Let $n$ be the minimum value of $x + y$ over all ordered pairs $(x, y)$ of positive integers such that $xy = 16$. Let $Q$ be the remainder when $44121 \cdot !n$ is divided by $67490$, where $!n$ denotes the subfactorial of $n$. Compute $Q$. | 63,753 | graphs = [
Graph(
let={
"_n": Const(44121),
"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")))),
... | COMB | null | COUNT | sympy | B3 | [
"B3"
] | 0cd20d | comb_count_derangements_v1 | null | 4 | 0 | [
"B3"
] | 1 | 0.001 | 2026-02-08T02:52:09.781241Z | {
"verified": true,
"answer": 63753,
"timestamp": "2026-02-08T02:52:09.782178Z"
} | 94be5f | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 190,
"completion_tokens": 4156
},
"timestamp": "2026-02-08T20:21:44.541Z",
"answer": 63753
},
{
"... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "V8",
"status": "n... | {
"lo": 0.04,
"mid": 1.71,
"hi": 3.18
} | ||
f0d793 | comb_count_permutations_fixed_v1_677425708_2667 | Let $n = 7$ and $k = \sum_{k=1}^{2} k$. Compute $\binom{n}{k} \cdot !{(n-k)}$, where $!m$ denotes the number of derangements of $m$ elements. Let $Q$ be the sum of the number of positive divisors of all integers from 1 to the absolute value of this result. Find the value of $Q$. | 1,867 | graphs = [
Graph(
let={
"_n": Const(2),
"n": Const(7),
"k": Summation(var="k", start=Const(1), end=Ref("_n"), expr=Var("k")),
"result": Mul(Binom(n=Ref("n"), k=Ref("k")), Subfactorial(arg=Sub(left=Ref(name='n'), right=Ref(name='k')))),
"Q": Summati... | NT | COMB | COUNT | sympy | SUM_ARITHMETIC | [
"SUM_ARITHMETIC"
] | eb34f0 | comb_count_permutations_fixed_v1 | null | 6 | 0 | [
"SUM_ARITHMETIC"
] | 1 | 0.001 | 2026-02-08T05:10:50.477718Z | {
"verified": true,
"answer": 1867,
"timestamp": "2026-02-08T05:10:50.478839Z"
} | 2cf353 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 203,
"completion_tokens": 1802
},
"timestamp": "2026-02-11T23:03:56.744Z",
"answer": 1867
},
{
"... | 1 | [
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "SUM_ARITHMETIC",
"status": "ok"
}
] | {
"lo": -3.49,
"mid": 1.84,
"hi": 7.55
} | ||
6cfec4 | lin_form_endings_v1_1520064083_7772 | Let $a = 24$ and $b = 42$. Define $d = \gcd(a, b)$. Let $x$ be the remainder when $7516 \cdot d$ is divided by $57480$. Find the value of $x$. | 45,096 | graphs = [
Graph(
let={
"a_coeff": Const(24),
"b_coeff": Const(42),
"_inner_result": GCD(a=Ref("a_coeff"), b=Ref("b_coeff")),
"_scale_k": Const(7516),
"_scaled": Mul(Ref("_scale_k"), Ref("_inner_result")),
"_mod_M": Const(57480),
... | COMB | NT | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | lin_form_endings_v1 | null | 2 | null | [
"LIN_FORM"
] | 1 | 0 | 2026-02-08T09:18:17.745495Z | {
"verified": true,
"answer": 45096,
"timestamp": "2026-02-08T09:18:17.745890Z"
} | 3d9e34 | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 116,
"completion_tokens": 307
},
"timestamp": "2026-02-15T20:36:51.385Z",
"answer": 45096
},
{
"id": 11,
... | 2 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "V8",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
... | {
"lo": -9.12,
"mid": -6.02,
"hi": -3.62
} | ||
1c6ae4 | antilemma_sum_factor_cartesian_v1_677425708_1027 | Let $a = \gcd(3, 5)$. Compute $\sum_{d\mid a} \mu(d)$, where $\mu$ is the M\"obius function. Let $T$ be the set of all ordered pairs $(i, j)$ of positive integers with $1 \leq i \leq 7$ and $1 \leq j \leq 27$. Define $S$ as the subset of $T$ consisting of all pairs $(i, j)$ for which the computed sum equals 1. For each... | 57,834 | graphs = [
Graph(
let={
"x": SumOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("i"), Var("j")]), condition=SumOverDivisors(n=GCD(a=Const(value=3), b=Const(value=5)), var='d', expr=MoebiusMu(n=Var(name='d'))), domain=CartesianProduct(left=IntegerRange(start=Const(1), end=Const(7)... | NT | null | COMPUTE | sympy | SUM_FACTOR_CARTESIAN | [
"SUM_FACTOR_CARTESIAN",
"MOBIUS_COPRIME"
] | 1428b5 | antilemma_sum_factor_cartesian_v1 | null | 3 | 0 | [
"MOBIUS_COPRIME",
"SUM_FACTOR_CARTESIAN"
] | 2 | 0.001 | 2026-02-08T03:57:21.582906Z | {
"verified": true,
"answer": 57834,
"timestamp": "2026-02-08T03:57:21.583665Z"
} | 3efd5c | 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": 1567
},
"timestamp": "2026-02-09T15:01:03.955Z",
"answer": 57834
},
{
"... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MOBIUS_COPRIME",
"status": "ok"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
... | {
"lo": -6.5,
"mid": -0.2,
"hi": 6.11
} | ||
caa00d | nt_sum_divisors_range_v1_1248542787_506 | Let $S$ be the set of all positive integers $n$ such that $n \geq \sum_{d \mid \gcd(5,7)} \mu(d)$ and $n \leq 10080$, where $\mu$ denotes the M\"obius function. Let $\text{result}$ be the sum of the number of positive divisors of each element in $S$. Compute the remainder when $44121 \cdot \text{result}$ is divided by ... | 7,806 | graphs = [
Graph(
let={
"upper": Const(10080),
"result": SumOverSet(set=MapOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), SumOverDivisors(n=GCD(a=Const(value=5), b=Const(value=7)), var='d', expr=MoebiusMu(n=Var(name='d')))), Leq(Var("n"), Ref("upper")))), expr=Num... | NT | null | SUM | sympy | MOBIUS_COPRIME | [
"MOBIUS_COPRIME"
] | ac54ac | nt_sum_divisors_range_v1 | null | 4 | 0 | [
"MOBIUS_COPRIME"
] | 1 | 0.585 | 2026-02-08T03:10:54.491140Z | {
"verified": true,
"answer": 7806,
"timestamp": "2026-02-08T03:10:55.076352Z"
} | 4c0b76 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 216,
"completion_tokens": 7045
},
"timestamp": "2026-02-09T17:38:20.945Z",
"answer": 7806
},
{
"... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "MOBIUS_COPRIME",
"status": "ok"
},
{
"lemma": "V8_SUM",
"status": "no"
}
] | {
"lo": -6.49,
"mid": 0.51,
"hi": 7.52
} | ||
d8ffd1 | algebra_poly_eval_v1_2051736721_1726 | Let $t = 5$. Consider the set of all ordered pairs $(x, y)$ of positive integers such that $x + y = 4$. Let $P$ be the set of all products $xy$ for such pairs. Let $M$ be the maximum value in $P$. Define $\text{result} = 2 \cdot t^M - 9 \cdot t^3 + t^2 + t + 6$. Compute the remainder when $82778 \cdot \text{result}$ is... | 24,733 | graphs = [
Graph(
let={
"_n": Const(2),
"t": Const(5),
"result": Sum(Mul(Const(2), Pow(Ref("t"), MaxOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(Sum(Var("x"... | NT | null | COMPUTE | sympy | B1 | [
"B1"
] | 5b950e | algebra_poly_eval_v1 | null | 3 | 0 | [
"B1"
] | 1 | 0.004 | 2026-02-08T16:10:50.651788Z | {
"verified": true,
"answer": 24733,
"timestamp": "2026-02-08T16:10:50.655418Z"
} | 67b159 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 161,
"completion_tokens": 872
},
"timestamp": "2026-02-16T22:37:19.069Z",
"answer": 24733
},
{... | 1 | [
{
"lemma": "B1",
"status": "ok"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
468db2 | alg_poly4_min_v1_1419126231_1736 | Let $Q$ be the minimum value of the expression $3050016a^4 - 15250080a^3b + 29737656a^2b^2 - 26687640ab^3 + 9245361b^4$ over all ordered pairs $(a, b)$ of positive integers such that $1 \leq a \leq \min\{x + y \mid x, y > 0,\, xy = 22500\}$ and $1 \leq b \leq 300$. Find $Q$. | 95,313 | graphs = [
Graph(
let={
"_n": Const(4),
"result": MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("a"), Var("b")]), condition=And(Geq(Var("a"), Const(1)), Leq(Var("a"), MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=A... | ALG | null | COMPUTE | sympy | B3 | [
"B3"
] | 0cd20d | alg_poly4_min_v1 | null | 6 | 0 | [
"B3"
] | 1 | 0.224 | 2026-02-25T11:14:50.685373Z | {
"verified": true,
"answer": 95313,
"timestamp": "2026-02-25T11:14:50.909580Z"
} | 87b942 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 1,
"correct": {
"strict": false,
"boxed": false,
"relaxed": true
},
"usage": {
"prompt_tokens": 229,
"completion_tokens": 13387
},
"timestamp": "2026-03-30T13:39:42.602Z",
"answer": 103121
},
{
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
}
] | {
"lo": 3.8,
"mid": 6.33,
"hi": 9.49
} | ||
b44900 | modular_count_residue_v1_717093673_2619 | Let $m = 12$ and $r = 0$. Define $\text{result}$ to be the number of integers $n$ such that $1 \leq n \leq 67600$ and $n \equiv r \pmod{m}$. Let $S$ be the set of all positive integers $d$ such that $1 \leq d \leq 14$ and $d$ divides the number of positive integers $n_1$ satisfying $1 \leq n_1 \leq 797$ and $\gcd(n_1, ... | 5,665 | graphs = [
Graph(
let={
"_m": Const(12),
"_n": Const(75130),
"upper": Const(67600),
"m": Const(12),
"r": Const(0),
"result": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Ref("upper")),... | NT | null | COUNT | sympy | C4 | [
"C4/MAX_DIVISOR"
] | 911b84 | modular_count_residue_v1 | mod_exp | 4 | 0 | [
"C4",
"MAX_DIVISOR"
] | 2 | 4.06 | 2026-02-08T17:00:41.528229Z | {
"verified": true,
"answer": 5665,
"timestamp": "2026-02-08T17:00:45.588132Z"
} | 95c5d1 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 202,
"completion_tokens": 1172
},
"timestamp": "2026-02-17T17:05:29.475Z",
"answer": 5665
},
{... | 1 | [
{
"lemma": "C4",
"status": "ok"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MAX_DIVISOR",
"status": "ok_later"
},
{
"lemma": "V8",
"status": "... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
bf3909 | algebra_quadratic_discriminant_v1_784195855_2236 | Let $a = -5$, $b = -7$, and $n = 2$. Define $c = \sum_{k=1}^{2} \phi(k) \left\lfloor \frac{n}{k} \right\rfloor$. Let $D = b^2 - 4ac$. Define $r = 2$ if $D > 0$, $r = 1$ if $D = 0$, and $r = 0$ if $D < 0$. Compute $41708 \cdot r$. | 83,416 | graphs = [
Graph(
let={
"_n": Const(2),
"a": Const(-5),
"b": Const(-7),
"c": Summation(var="k", start=Const(1), end=Const(2), expr=Mul(EulerPhi(n=Var("k")), Floor(Div(Ref("_n"), Var("k"))))),
"D": Sub(Pow(Ref("b"), Const(2)), Mul(Const(4), Ref("a")... | NT | null | COMPUTE | sympy | K2 | [
"K2"
] | 6897ab | algebra_quadratic_discriminant_v1 | null | 5 | 0 | [
"K2"
] | 1 | 0.003 | 2026-02-08T05:37:13.975612Z | {
"verified": true,
"answer": 83416,
"timestamp": "2026-02-08T05:37:13.978714Z"
} | 3fa189 | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 175,
"completion_tokens": 376
},
"timestamp": "2026-02-11T22:56:02.652Z",
"answer": 83416
},
{
"id": 11,
... | 2 | [
{
"lemma": "K2",
"status": "ok"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "V3",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
}
] | {
"lo": -10,
"mid": -7.73,
"hi": -5.46
} | ||
96902c | antilemma_k3_v1_717093673_3803 | Let $n = 70063$. Define $x = \sum_{d \mid n} \phi(d)$, where $\phi$ is Euler's totient function. Find the value of $63822x \mod 77249$. | 2,421 | graphs = [
Graph(
let={
"_n": Const(70063),
"x": SumOverDivisors(n=Ref(name='_n'), var='d', expr=EulerPhi(n=Var(name='d'))),
"Q": Mod(value=Mul(Const(63822), Ref("x")), modulus=Const(77249)),
},
goal=Ref("Q"),
)
] | NT | COMB | COMPUTE | sympy | K3 | [
"K3"
] | 54c41e | antilemma_k3_v1 | null | 3 | 0 | [
"K3"
] | 1 | 0.001 | 2026-02-08T17:52:21.428006Z | {
"verified": true,
"answer": 2421,
"timestamp": "2026-02-08T17:52:21.428888Z"
} | a7443d | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 95,
"completion_tokens": 1556
},
"timestamp": "2026-02-18T09:00:33.012Z",
"answer": 2421
},
{
... | 1 | [
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "K3",
"status": "ok"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
0eaed5 | comb_count_derangements_v1_784195855_4987 | Let $T$ be the set of all integers $t$ such that $5 \le t \le 15$ and there exist positive integers $a \le 3$ and $b \le 3$ satisfying $t = 3a + 2b$. Let $m$ be the number of elements in $T$. Let $n$ be the largest prime number satisfying $2 \le n \le m$. Compute the number of derangements of $n$ elements. | 1,854 | graphs = [
Graph(
let={
"_n": Const(2),
"n": MaxOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Ref("_n")), Leq(Var("n"), CountOverSet(set=SolutionsSet(var=Var("t"), condition=Exists(var=Var(name='a'), condition=Exists(var=Var(name='b'), condition=And(Geq(left=Var(... | NT | COMB | COUNT | sympy | LIN_FORM | [
"LIN_FORM/MAX_PRIME_BELOW"
] | 47006e | comb_count_derangements_v1 | null | 5 | 0 | [
"LIN_FORM",
"MAX_PRIME_BELOW"
] | 2 | 0.002 | 2026-02-08T07:32:41.609012Z | {
"verified": true,
"answer": 1854,
"timestamp": "2026-02-08T07:32:41.610581Z"
} | 4265fe | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 148,
"completion_tokens": 942
},
"timestamp": "2026-02-13T11:13:46.540Z",
"answer": 1854
},
{
... | 1 | [
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok_later"
},
{
"lemma": "MAX_VA... | {
"lo": -7.01,
"mid": -4.68,
"hi": -2.15
} | ||
730483 | geo_count_lattice_rect_v1_1915831931_3426 | Compute the number of lattice points $(x, y)$ satisfying $0 \le x \le 77$ and $0 \le y \le 137$. | 10,764 | graphs = [
Graph(
let={
"a": Const(77),
"b": Const(137),
"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 | 2026-02-08T17:39:45.668339Z | {
"verified": true,
"answer": 10764,
"timestamp": "2026-02-08T17:39:45.669716Z"
} | c4c635 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 80,
"completion_tokens": 707
},
"timestamp": "2026-02-24T22:50:05.699Z",
"answer": 10764
},
{
... | 1 | [] | {
"lo": -8.52,
"mid": -5.43,
"hi": -3.2
} | ||||
85809a | comb_catalan_compute_v1_2051736721_3195 | Let $n$ be the number of ordered pairs $(x_1, x_2)$ of positive odd integers such that $x_1 + x_2 = 22$. Let $C_n$ denote the $n$th Catalan number. Compute the remainder when
$$
50625 - C_n
$$
is divided by $54519$. | 46,358 | graphs = [
Graph(
let={
"_n": Const(22),
"n": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x1"), Var("x2")]), condition=And(IsPositive(arg=Var(name='x1')), IsPositive(arg=Var(name='x2')), IsOdd(arg=Var(name='x1')), IsOdd(arg=Var(name='x2')), Eq(Sum(Var("x1"), Var("x2")), Re... | COMB | null | COMPUTE | sympy | COMB1 | [
"COMB1"
] | 567f58 | comb_catalan_compute_v1 | null | 4 | 0 | [
"COMB1"
] | 1 | 0.002 | 2026-02-08T17:10:20.413447Z | {
"verified": true,
"answer": 46358,
"timestamp": "2026-02-08T17:10:20.415424Z"
} | bd5764 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 118,
"completion_tokens": 746
},
"timestamp": "2026-02-17T20:45:39.479Z",
"answer": 46358
},
{... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COMB1",
"status": "ok"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
... | {
"lo": -5.64,
"mid": -3.17,
"hi": -0.81
} | ||
82d1d2 | nt_count_gcd_equals_v1_124444284_7403 | Let $a$ and $b$ be positive integers such that $ab = 56169$. Define $k$ to be the minimum value of $a + b$ over all such pairs $(a, b)$. Let $d = 3$ and $U = 29584$. Compute the number of positive integers $n \leq U$ such that $\gcd(n, k) = d$, and denote this count by $C$. Find the value of $11664 - C$. | 6,795 | graphs = [
Graph(
let={
"upper": Const(29584),
"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(56169)))), expr=Sum(Var("x"), Var("y"... | NT | null | COUNT | sympy | B3 | [
"B3"
] | 0cd20d | nt_count_gcd_equals_v1 | null | 5 | 0 | [
"B3"
] | 1 | 2.748 | 2026-02-08T09:06:29.593967Z | {
"verified": true,
"answer": 6795,
"timestamp": "2026-02-08T09:06:32.342102Z"
} | 6c3558 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 147,
"completion_tokens": 1225
},
"timestamp": "2026-02-14T00:30:29.911Z",
"answer": 6795
},
{... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
}
] | {
"lo": -3.51,
"mid": 1.33,
"hi": 6.56
} | ||
88b798 | sequence_count_fib_divisible_v1_784195855_6108 | Let $P$ be the number of prime numbers $p$ such that $2 \leq p \leq 4679$. Compute the remainder when $88185$ times the number of positive integers $n \leq P$ for which the $n$th Fibonacci number is divisible by $13$, is divided by $99974$. | 38,704 | graphs = [
Graph(
let={
"_n": Const(4679),
"upper": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(2)), Leq(Var("n"), Ref("_n")), IsPrime(Var("n"))))),
"d": Const(13),
"result": CountOverSet(set=SolutionsSet(var=Var("n"), conditi... | NT | null | COUNT | sympy | COUNT_PRIMES | [
"COUNT_PRIMES"
] | 07c874 | sequence_count_fib_divisible_v1 | null | 6 | 0 | [
"COUNT_PRIMES"
] | 1 | 0.078 | 2026-02-08T08:20:07.657979Z | {
"verified": true,
"answer": 38704,
"timestamp": "2026-02-08T08:20:07.736248Z"
} | b240c8 | 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": 1969
},
"timestamp": "2026-02-13T18:15:36.367Z",
"answer": 38704
},
... | 1 | [
{
"lemma": "COUNT_PRIMES",
"status": "ok"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "V1",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
}
] | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
d704dc | antilemma_v1_legendre_1116507919_251 | Determine the largest integer $x$ such that $2^x$ divides $1818!$. | 1,812 | graphs = [
Graph(
let={
"_n": Const(2),
"x": MaxKDivides(target=Factorial(Const(1818)), base=Ref("_n")),
},
goal=Ref("x"),
)
] | NT | null | COMPUTE | sympy | V1 | [
"V1"
] | dae96f | antilemma_v1_legendre | null | 3 | 0 | [
"V1"
] | 1 | 0 | 2026-02-08T02:29:53.727143Z | {
"verified": true,
"answer": 1812,
"timestamp": "2026-02-08T02:29:53.727385Z"
} | 577cd4 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 134,
"completion_tokens": 780
},
"timestamp": "2026-02-08T19:16:39.404Z",
"answer": 1812
},
{
"id... | 1 | [
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K5",
"status": "same_pattern_wrong"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
... | {
"lo": -4.6,
"mid": 0.19,
"hi": 4.77
} | ||
06ba1f | nt_count_divisible_v1_1439011603_2928 | Let $n = 8$. Consider the set of all ordered pairs $(x, y)$ of positive integers such that $x + y = n$. Let $P$ be the set of all values of $xy$ as $(x, y)$ ranges over this set. Let $d$ be the maximum element of $P$.
Now, let $S$ be the set of all positive integers $n$ such that $1 \leq n \leq 39204$ and
$$
n \equi... | 2,450 | graphs = [
Graph(
let={
"_n": Const(8),
"upper": Const(39204),
"divisor": MaxOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(Sum(Var("x"), Var("y")), Ref("_n")... | COMB | null | COUNT | sympy | BINOMIAL_ALTERNATING | [
"BINOMIAL_ALTERNATING",
"B1"
] | 6d96ac | nt_count_divisible_v1 | null | 5 | 0 | [
"B1",
"BINOMIAL_ALTERNATING"
] | 2 | 1.401 | 2026-02-08T17:05:43.285101Z | {
"verified": true,
"answer": 2450,
"timestamp": "2026-02-08T17:05:44.686057Z"
} | 37fcdf | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 186,
"completion_tokens": 809
},
"timestamp": "2026-02-24T22:12:03.622Z",
"answer": 2450
},
{
... | 1 | [
{
"lemma": "B1",
"status": "ok"
},
{
"lemma": "BINOMIAL_ALTERNATING",
"status": "ok"
},
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS"... | {
"lo": -8.52,
"mid": -5.43,
"hi": -3.2
} | ||
6651ba | nt_count_coprime_and_v1_1439011603_1877 | Let $p$ be the largest prime number less than or equal to 7888. Compute the number of positive integers $n$ such that $1 \leq n \leq p$, $\gcd(n, 5) = 1$, and $\gcd(n, 7) = 1$. | 5,406 | graphs = [
Graph(
let={
"upper": MaxOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(2)), Leq(Var("n"), Const(7888)), IsPrime(Var("n"))))),
"k1": Const(5),
"k2": Const(7),
"result": CountOverSet(set=SolutionsSet(var=Var("n1"), condition... | NT | null | COUNT | sympy | MAX_PRIME_BELOW | [
"MAX_PRIME_BELOW"
] | dc3ad3 | nt_count_coprime_and_v1 | null | 4 | 0 | [
"MAX_PRIME_BELOW"
] | 1 | 1.045 | 2026-02-08T16:20:36.919488Z | {
"verified": true,
"answer": 5406,
"timestamp": "2026-02-08T16:20:37.964201Z"
} | 5ec460 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 108,
"completion_tokens": 1288
},
"timestamp": "2026-02-17T01:40:33.871Z",
"answer": 5406
},
{... | 1 | [
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
},
{
"lemma": "V7",
"stat... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
992491 | diophantine_fbi2_count_v1_1470522791_162 | Let $m = 9$ and $k = 240$. Define $S$ as the set of all positive integers $x$ and $y$ such that $xy = m$. Let $T$ be the set of all sums $x + y$ where $(x, y) \in S$. Let $a$ be the minimum element of $T$.
Let $D$ be the sum of $\phi(d)$ over all positive divisors $d$ of $1049$. Consider the set of integers $n$ such t... | 65,496 | graphs = [
Graph(
let={
"_m": Const(9),
"_n": Const(92303),
"k": Const(240),
"result": CountOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(Is... | NT | null | COUNT | sympy | K3 | [
"K3/L3C",
"B3"
] | 0cdb86 | diophantine_fbi2_count_v1 | null | 7 | 0 | [
"B3",
"K3",
"L3C"
] | 3 | 0.024 | 2026-02-08T12:51:33.383681Z | {
"verified": true,
"answer": 65496,
"timestamp": "2026-02-08T12:51:33.407483Z"
} | 1fed94 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 299,
"completion_tokens": 3676
},
"timestamp": "2026-02-15T07:08:54.736Z",
"answer": 65496
},
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K3",
"status": "ok"
},
{
"lemma": "L3C",
"status": "ok_later"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "... | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
40a43c | nt_count_phi_equals_v1_2051736721_1945 | Let $S$ be the set of all ordered pairs $(x, y)$ of positive integers such that $x + y = 78$. Define $P$ to be the maximum value of $xy$ over all such pairs. Let $k = 1102$. Determine the number of positive integers $n$ such that $1 \leq n \leq P$ and $\phi(n) = k$, where $\phi$ denotes Euler's totient function. Comput... | 17,710 | graphs = [
Graph(
let={
"upper": MaxOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(Sum(Var("x"), Var("y")), Const(78)))), expr=Mul(Var("x"), Var("y")))),
"k": Const(1102)... | NT | null | COUNT | sympy | B1 | [
"B1"
] | 5b950e | nt_count_phi_equals_v1 | null | 6 | 0 | [
"B1"
] | 1 | 0.183 | 2026-02-08T16:22:43.066578Z | {
"verified": true,
"answer": 17710,
"timestamp": "2026-02-08T16:22:43.249647Z"
} | 150071 | 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": 4267
},
"timestamp": "2026-02-17T02:39:49.300Z",
"answer": 17710
},
... | 1 | [
{
"lemma": "B1",
"status": "ok"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
f6cc18 | antilemma_k3_v1_2051736721_2825 | Let $ n = 95895 $. Define $$
\sum_{d \mid n} \phi(d),
$$ where $ \phi $ denotes Euler's totient function and the sum is taken over all positive divisors $ d $ of $ n $. Compute this sum. | 95,895 | graphs = [
Graph(
let={
"x": SumOverDivisors(n=Const(value=95895), var='d', expr=EulerPhi(n=Var(name='d'))),
},
goal=Ref("x"),
)
] | NT | COMB | COMPUTE | sympy | K3 | [
"K3"
] | 54c41e | antilemma_k3_v1 | null | 3 | 0 | [
"K3"
] | 1 | 0.001 | 2026-02-08T16:55:27.654647Z | {
"verified": true,
"answer": 95895,
"timestamp": "2026-02-08T16:55:27.655221Z"
} | af02c7 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 99,
"completion_tokens": 789
},
"timestamp": "2026-02-17T14:54:16.451Z",
"answer": 95895
},
{
... | 1 | [
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "K3",
"status": "ok"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
a295f7 | nt_sum_over_divisible_v1_1431428450_1058 | Let $u = 49284$ and $d = 172$. Define $S$ to be the set of all positive integers $n$ such that $1 \leq n \leq u$ and $n$ is divisible by $d$. Let $s$ be the sum of all elements in $S$. Compute the remainder when $37157 \cdot s$ is divided by $83138$. | 38,170 | graphs = [
Graph(
let={
"upper": Const(49284),
"divisor": Const(172),
"result": SumOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Ref("upper")), Eq(Mod(value=Var("n"), modulus=Ref("divisor")), Const(0))))),
"_c": Co... | NT | null | SUM | sympy | LIN_FORM | [
"LIN_FORM/COUNT_SUM_EQUALS",
"BINOMIAL_ALTERNATING"
] | bf26d3 | nt_sum_over_divisible_v1 | null | 3 | 0 | [
"BINOMIAL_ALTERNATING",
"COUNT_SUM_EQUALS",
"LIN_FORM"
] | 3 | 4.312 | 2026-02-08T13:52:50.415015Z | {
"verified": true,
"answer": 38170,
"timestamp": "2026-02-08T13:52:54.727343Z"
} | ed52e8 | 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": 2929
},
"timestamp": "2026-02-15T21:33:29.158Z",
"answer": 38170
},
... | 1 | [
{
"lemma": "BINOMIAL_ALTERNATING",
"status": "ok"
},
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "ok_later"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": ... | {
"lo": -5.49,
"mid": 0.22,
"hi": 6.51
} | ||
d21415_l | comb_sum_binomial_mod_v1_458359167_21 | Let $n = 143$. Define
$$
S = \sum_{k=20}^{122} \binom{172}{k}.
$$
Let $r$ be the remainder when $S$ is divided by $10729$. Let $d_{\text{min}}$ be the smallest divisor of $n$ that is at least $2$. Compute the Bell number $B_r$, where the index is taken modulo $d_{\text{min}}$. That is, compute $B_{r \bmod d_{\text{min}... | 1 | NT | COMB | COMPUTE | sympy | MIN_PRIME_FACTOR | [
"MIN_PRIME_FACTOR"
] | 58d7e9 | comb_sum_binomial_mod_v1 | bell_mod | 7 | 0 | [
"MIN_PRIME_FACTOR"
] | 1 | 0.07 | 2026-02-08T02:57:08.111914Z | {
"verified": false,
"answer": 52,
"timestamp": "2026-02-08T02:57:08.182304Z"
} | 86062e | d21415 | 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": 233,
"completion_tokens": 32768
},
"timestamp": "2026-02-23T20:34:59.789Z",
"answer": null
},
{
... | 0 | [
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "MIN_PRIME_FACTOR",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
... | {
"lo": 4.56,
"mid": 6.51,
"hi": 9.5
} |
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