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 |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
652bbb | nt_max_prime_below_v1_1520064083_4846 | Let $r$ be the largest prime number $n$ such that $2 \le n \le 57600$. Let $M$ be the maximum value of $xy$ over all ordered pairs of positive integers $(x, y)$ such that $x + y = 154$. Compute the remainder when $M - r$ is divided by $76536$. | 24,872 | graphs = [
Graph(
let={
"_n": Const(2),
"upper": Const(57600),
"result": MaxOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Ref("_n")), Leq(Var("n"), Ref("upper")), IsPrime(Var("n"))))),
"Q": Mod(value=Sub(MaxOverSet(set=MapOverSet(set=Solut... | NT | null | EXTREMUM | sympy | B1 | [
"B1"
] | d2b6e1 | nt_max_prime_below_v1 | negation_mod | 6 | 0 | [
"B1"
] | 1 | 1.333 | 2026-02-08T06:27:42.376399Z | {
"verified": true,
"answer": 24872,
"timestamp": "2026-02-08T06:27:43.709691Z"
} | 93b018 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 122,
"completion_tokens": 1701
},
"timestamp": "2026-02-13T00:22:49.211Z",
"answer": 24872
},
... | 1 | [
{
"lemma": "B1",
"status": "ok"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
}
] | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
2c54bb_n | comb_count_permutations_fixed_v1_1419126231_195 | A secure messaging system uses permutations of 8 symbols. A subset of keys satisfies a quadratic hash condition modulo 7921, producing a set $S$ of size $|S|$. Let $k = \binom{|S|}{0} - 1$. The number of valid encryption schemes using $k$ fixed symbols and deranging the rest is $\binom{8}{k} \cdot D_{8-k}$. Compute thi... | 14,833 | COMB | null | COUNT | sympy | COMB1 | [
"POLY_ORBIT_HENSEL/ZERO_BINOM_0"
] | 4267fe | comb_count_permutations_fixed_v1 | null | 6 | null | [
"COMB1",
"POLY_ORBIT_HENSEL",
"ZERO_BINOM_0"
] | 3 | 0.434 | 2026-02-25T09:45:32.740626Z | null | d782fc | 2c54bb | narrative | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 204,
"completion_tokens": 1360
},
"timestamp": "2026-03-31T03:20:06.659Z",
"answer": 14833
},
{
"... | 1 | [
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "POLY_ORBIT_HENSEL",
"status": "ok"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8_S... | {
"lo": -5.37,
"mid": 0.23,
"hi": 5.22
} | |
1ae395 | comb_binomial_compute_v1_124444284_2201 | Let $n$ be the number of integers $t$ with $42 \leq t \leq 99$ for which there exist integers $a$ and $b$ such that $1 \leq a \leq 2$, $1 \leq b \leq 7$, and $t = 21a + 6b + 15$. Let $k = \sum_{k=1}^{3} \phi(k) \left\lfloor \frac{3}{k} \right\rfloor$, where $\phi$ denotes Euler's totient function. Compute $\binom{n}{k}... | 3,003 | graphs = [
Graph(
let={
"_n": Const(3),
"n": CountOverSet(set=SolutionsSet(var=Var("t"), condition=Exists(var=Var(name='a'), condition=Exists(var=Var(name='b'), condition=And(Geq(left=Var(name='a'), right=Const(value=1)), Leq(left=Var(name='a'), right=Const(value=2)), Geq(left=Var(na... | NT | null | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM",
"K2"
] | b46b5e | comb_binomial_compute_v1 | null | 5 | 0 | [
"K2",
"LIN_FORM"
] | 2 | 0.003 | 2026-02-08T04:31:01.579600Z | {
"verified": true,
"answer": 3003,
"timestamp": "2026-02-08T04:31:01.583018Z"
} | 7f9a80 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 244,
"completion_tokens": 1199
},
"timestamp": "2026-02-10T16:58:26.433Z",
"answer": 3003
},
{
"... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "K2",
"status": "ok"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "V1",
"status": "no"
},
{
"lemma": "V7... | {
"lo": -3.42,
"mid": 1.86,
"hi": 7.55
} | ||
8c51a8 | comb_bell_compute_v1_397696148_1955 | Let $n$ be the number of positive integers $k$ such that $1 \leq k \leq 640$ and $80$ divides $k$. Compute the Bell number $B_n$, which counts the number of partitions of a set of size $n$. | 4,140 | graphs = [
Graph(
let={
"_n": Const(80),
"n": CountOverSet(set=SolutionsSet(var=Var("k"), condition=And(Geq(Var("k"), Const(1)), Leq(Var("k"), Const(640)), Divides(divisor=Ref("_n"), dividend=Var("k"))), domain='positive_integers')),
"result": Bell(Ref("n")),
},
... | NT | COMB | COMPUTE | sympy | C2 | [
"C2"
] | 9685eb | comb_bell_compute_v1 | null | 6 | 0 | [
"C2"
] | 1 | 0.001 | 2026-02-08T12:51:40.118213Z | {
"verified": true,
"answer": 4140,
"timestamp": "2026-02-08T12:51:40.119274Z"
} | c9c8b4 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 102,
"completion_tokens": 1645
},
"timestamp": "2026-02-15T06:40:56.996Z",
"answer": 4140
},
{... | 1 | [
{
"lemma": "C2",
"status": "ok"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "VAL_SUM_EQ",
"status": "no"
}
] | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
0d34d7 | sequence_lucas_compute_v1_2051736721_4886 | Let $n$ be the number of prime numbers between 2 and 79, inclusive. Compute the $n$-th Lucas number. | 39,603 | graphs = [
Graph(
let={
"_n": Const(79),
"n": CountOverSet(set=SolutionsSet(var=Var("n1"), condition=And(Geq(Var("n1"), Const(2)), Leq(Var("n1"), Ref("_n")), IsPrime(Var("n1"))))),
"result": Lucas(arg=Ref(name='n')),
},
goal=Ref("result"),
)
] | NT | null | COMPUTE | sympy | COUNT_PRIMES | [
"COUNT_PRIMES"
] | 07c874 | sequence_lucas_compute_v1 | null | 3 | 0 | [
"COUNT_PRIMES"
] | 1 | 0.001 | 2026-02-08T18:15:12.205288Z | {
"verified": true,
"answer": 39603,
"timestamp": "2026-02-08T18:15:12.206206Z"
} | 565f88 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 75,
"completion_tokens": 980
},
"timestamp": "2026-02-18T15:19:02.987Z",
"answer": 39603
},
{
... | 1 | [
{
"lemma": "COUNT_PRIMES",
"status": "ok"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
066d56 | nt_lcm_compute_v1_655260480_1649 | Let $a$ be the sum of all real solutions $x$ to the equation $x^2 - 1190x + 88800 = 0$. Let $b$ be the minimum value of $x_1 + y$ over all ordered pairs $(x_1, y)$ of positive integers such that $x_1 y = 115600$. Compute the least common multiple of $a$ and $b$. | 4,760 | graphs = [
Graph(
let={
"_n": Const(2),
"a": SumOverSet(set=SolutionsSet(var=Var("x"), condition=Eq(Sum(Pow(Var("x"), Ref("_n")), Mul(Const(-1190), Var("x")), Const(88800)), Const(0)))),
"b": MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x1"), Var("y... | NT | null | COMPUTE | sympy | V5 | [
"VIETA_SUM",
"B3"
] | 018050 | nt_lcm_compute_v1 | null | 5 | 0 | [
"B3",
"V5",
"VIETA_SUM"
] | 3 | 0.007 | 2026-02-08T16:16:25.662335Z | {
"verified": true,
"answer": 4760,
"timestamp": "2026-02-08T16:16:25.669013Z"
} | 65c0c2 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 136,
"completion_tokens": 875
},
"timestamp": "2026-02-17T00:05:54.166Z",
"answer": 4760
},
{
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
9e8404 | nt_sum_divisors_mod_v1_458359167_3993 | Let $n = \sum_{k=1}^{15} \phi(k) \left\lfloor \frac{15}{k} \right\rfloor$, where $\phi(k)$ denotes Euler's totient function. Let $\sigma$ be the sum of all positive divisors of $n$. Compute the remainder when $\sigma$ is divided by $11657$. | 360 | graphs = [
Graph(
let={
"_n": Const(15),
"n": Summation(var="k", start=Const(1), end=Const(15), expr=Mul(EulerPhi(n=Var("k")), Floor(Div(Ref("_n"), Var("k"))))),
"M": Const(11657),
"sigma": SumDivisors(n=Ref("n")),
"result": Mod(value=Ref("sigma"),... | NT | null | COMPUTE | sympy | K2 | [
"K2"
] | 6897ab | nt_sum_divisors_mod_v1 | null | 5 | 0 | [
"K2"
] | 1 | 0.003 | 2026-02-08T11:28:13.892362Z | {
"verified": true,
"answer": 360,
"timestamp": "2026-02-08T11:28:13.895688Z"
} | 59ba80 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 120,
"completion_tokens": 1223
},
"timestamp": "2026-02-14T14:28:41.603Z",
"answer": 360
},
{
... | 1 | [
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K2",
"status": "ok"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
}
] | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
391a17 | antilemma_k3_v1_1431428450_627 | Let $n = 61616$. Define $x = \sum_{d \mid n} \phi(d)$, where $\phi$ denotes Euler's totient function. Find the remainder when $20164x$ is divided by $89451$. | 40,085 | graphs = [
Graph(
let={
"_n": Const(61616),
"x": SumOverDivisors(n=Ref(name='_n'), var='d', expr=EulerPhi(n=Var(name='d'))),
"Q": Mod(value=Mul(Const(20164), Ref("x")), modulus=Const(89451)),
},
goal=Ref("Q"),
)
] | NT | COMB | COMPUTE | sympy | K3 | [
"K3"
] | 54c41e | antilemma_k3_v1 | null | 3 | 0 | [
"K3"
] | 1 | 0.001 | 2026-02-08T13:34:10.845325Z | {
"verified": true,
"answer": 40085,
"timestamp": "2026-02-08T13:34:10.845846Z"
} | ac45a0 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 97,
"completion_tokens": 1193
},
"timestamp": "2026-02-15T18:09:06.612Z",
"answer": 40085
},
{... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "K3",
"status": "ok"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "VAL_SUM_EQ",
"status": "no"
... | {
"lo": -5.49,
"mid": 0.22,
"hi": 6.51
} | ||
1f5207 | nt_count_gcd_equals_v1_865884756_167 | Let $k = \sum_{k1=1}^{25} \phi(k1) \left\lfloor \frac{25}{k1} \right\rfloor$, where $\phi$ denotes Euler's totient function. Let $P$ be the set of all ordered pairs $(x, y)$ of positive integers such that $x + y = 10$. Let $d$ be the maximum value of $xy$ as $(x, y)$ ranges over $P$. Determine the number of positive in... | 410 | graphs = [
Graph(
let={
"_n": Const(25),
"upper": Const(11111),
"k": Summation(var="k1", start=Const(1), end=Ref("_n"), expr=Mul(EulerPhi(n=Var("k1")), Floor(Div(Const(25), Var("k1"))))),
"d": MaxOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var(... | NT | null | COUNT | sympy | B3 | [
"K2",
"B1"
] | 7fde97 | nt_count_gcd_equals_v1 | null | 7 | 0 | [
"B1",
"B3",
"K2"
] | 3 | 11.067 | 2026-02-08T15:13:47.858143Z | {
"verified": true,
"answer": 410,
"timestamp": "2026-02-08T15:13:58.925130Z"
} | 242514 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 246,
"completion_tokens": 3142
},
"timestamp": "2026-02-10T05:01:34.037Z",
"answer": 410
},
{
"id... | 1 | [
{
"lemma": "B1",
"status": "ok"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "K2",
"status": "ok"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
},
{
"lem... | {
"lo": -7.09,
"mid": -0.49,
"hi": 6.1
} | ||
3dc2f9 | modular_min_linear_v1_124444284_625 | Let $a = 47007$, $b = 26330$, and $m = 81548$. Let $d$ be the greatest common divisor of $15$ and the sum of the Möbius function $\mu(d)$ over all positive divisors $d$ of $\gcd(11^{19487171} + 1^{19487171}, 10^{19487171})$. Determine the smallest integer $x$ such that $d \leq x \leq m$ and $ax \equiv b \pmod{m}$. | 11,282 | graphs = [
Graph(
let={
"_n": Const(10),
"a": Const(47007),
"b": Const(26330),
"m": Const(81548),
"result": MinOverSet(set=SolutionsSet(var=Var("x"), condition=And(Geq(Var("x"), SumOverDivisors(n=GCD(a=MaxKDivides(target=Sum(Pow(base=Ref(name='_n')... | NT | null | EXTREMUM | sympy | LTE_SUM | [
"LTE_SUM/MOBIUS_COPRIME"
] | 6cc2c0 | modular_min_linear_v1 | null | 6 | 0 | [
"LTE_SUM",
"MOBIUS_COPRIME"
] | 2 | 5.612 | 2026-02-08T03:24:28.401665Z | {
"verified": true,
"answer": 11282,
"timestamp": "2026-02-08T03:24:34.013964Z"
} | cb4aa1 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 228,
"completion_tokens": 3500
},
"timestamp": "2026-02-09T19:58:43.338Z",
"answer": 20570
},
{
... | 1 | [
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "ok"
},
{
"lemma": "MOBIUS_COPRIME",
"status": "ok_later"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
},
{
... | {
"lo": 1.69,
"mid": 5.03,
"hi": 8.38
} | ||
6bc3e0 | sequence_lucas_compute_v1_717093673_1949 | Let $m = 121$. Consider all pairs of positive integers $(x, y)$ such that $xy = 121$. Let $s$ be the sum $x + y$ for each such pair, and let $s_{\min}$ be the smallest such sum. Let $n$ be the largest prime number $n_1$ such that $2 \leq n_1 \leq s_{\min}$. Compute the $n$-th Lucas number. | 9,349 | graphs = [
Graph(
let={
"_m": Const(121),
"_n": Const(2),
"n": MaxOverSet(set=SolutionsSet(var=Var("n1"), condition=And(Geq(Var("n1"), Ref("_n")), Leq(Var("n1"), MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(... | NT | null | COMPUTE | sympy | B3 | [
"B3/MAX_PRIME_BELOW"
] | f253c0 | sequence_lucas_compute_v1 | null | 6 | 0 | [
"B3",
"MAX_PRIME_BELOW"
] | 2 | 0.004 | 2026-02-08T16:24:52.597350Z | {
"verified": true,
"answer": 9349,
"timestamp": "2026-02-08T16:24:52.600931Z"
} | c8741b | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 141,
"completion_tokens": 877
},
"timestamp": "2026-02-17T03:03:05.218Z",
"answer": 9349
},
{
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok_later"
},
{
"lemma": "MOD_MUL",
"status": "no"
... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
d47e47 | nt_sum_divisors_mod_v1_784195855_749 | Let $n$ be the minimum value of $x + y$ over all ordered pairs $(x, y)$ of positive integers such that $xy = 396900$. Let $\sigma$ denote the sum of the positive divisors of $n$. Compute the remainder when $\sigma$ is divided by $10223$. | 4,368 | 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(396900)))), expr=Sum(Var("x"), Var("y")))),
"M": Const(10223... | NT | null | COMPUTE | sympy | B3 | [
"B3"
] | 0cd20d | nt_sum_divisors_mod_v1 | null | 6 | 0 | [
"B3"
] | 1 | 0.001 | 2026-02-08T04:34:31.519796Z | {
"verified": true,
"answer": 4368,
"timestamp": "2026-02-08T04:34:31.521015Z"
} | dbeb6d | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 175,
"completion_tokens": 1145
},
"timestamp": "2026-02-10T17:25:05.558Z",
"answer": 4368
},
{
"... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"... | {
"lo": -3.42,
"mid": 1.86,
"hi": 7.55
} | ||
0e3357 | nt_sum_totient_over_divisors_v1_784195855_4163 | Let $n = 67621$. Compute $$\sum_{d \mid n} \phi(d),$$ where $\phi$ denotes Euler's totient function. Let $m$ be the maximum prime number less than or equal to $12$. Compute the Bell number $B_r$, where $r$ is the remainder when the sum is divided by $m$. | 15 | graphs = [
Graph(
let={
"n": Const(67621),
"result": SumOverDivisors(n=Ref(name='n'), var='d', expr=EulerPhi(n=Var(name='d'))),
"Q": Bell(Mod(value=Abs(arg=Ref(name='result')), modulus=MaxOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(2)), Leq(Va... | NT | COMB | COMPUTE | sympy | MAX_PRIME_BELOW | [
"MAX_PRIME_BELOW"
] | 88ea9c | nt_sum_totient_over_divisors_v1 | bell_mod | 5 | 0 | [
"MAX_PRIME_BELOW"
] | 1 | 0.001 | 2026-02-08T06:52:35.845239Z | {
"verified": true,
"answer": 15,
"timestamp": "2026-02-08T06:52:35.846436Z"
} | fac71e | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 120,
"completion_tokens": 598
},
"timestamp": "2026-02-13T05:44:31.567Z",
"answer": 15
},
{
... | 1 | [
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok"
},
{
"lemma": "MOD_SUB",
"status": "no"
}
... | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
be2340_n | alg_poly4_min_v1_1419126231_1327 | An engineer designs a composite material whose strength is modeled by $3444a^4 + 9072a^3b + 672b^4 + 9072a^2b^2 + ab^3 \cdot \min\{x + y : x,y > 0,\ xy = 4064256\}$, where $a$ and $b$ are positive integers between 1 and 294 representing layer thicknesses. The term $\min\{x + y\}$ represents the minimal perimeter for a ... | 26,292 | ALG | null | COMPUTE | sympy | B3 | [
"B3"
] | 0cd20d | alg_poly4_min_v1 | null | 6 | null | [
"B3"
] | 1 | 0.199 | 2026-02-25T10:44:59.007519Z | null | d6a064 | be2340 | narrative | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 239,
"completion_tokens": 1963
},
"timestamp": "2026-03-31T04:34:15.257Z",
"answer": 26292
},
{
"... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
}
] | {
"lo": -5.37,
"mid": 0.23,
"hi": 5.22
} | |
f5c5c0 | lte_diff_endings_v1_1742523217_274 | Let $a = 153$, $b = 3$, $p = 5$, $K = 6$, and $N = 54740986$. Let $d = a - b$, and let $v$ be the largest integer $k$ such that $5^k$ divides $d$. Define $t = K - v$ and let $P = 5^t$. Compute the number of positive integers $n \leq N$ that are divisible by $P$ but not divisible by $5P$. | 70,068 | graphs = [
Graph(
let={
"a_val": Const(153),
"b_val": Const(3),
"p_val": Const(5),
"K_val": Const(6),
"N_val": Const(54740986),
"ab_diff": Sub(Ref("a_val"), Ref("b_val")),
"vp_diff": MaxKDivides(target=Ref("ab_diff"), base=R... | NT | null | COMPUTE | sympy | LTE_DIFF | [
"LTE_DIFF"
] | cf8260 | lte_diff_endings_v1 | null | 5 | null | [
"LTE_DIFF"
] | 1 | 0.001 | 2026-02-08T02:57:29.429901Z | {
"verified": true,
"answer": 70068,
"timestamp": "2026-02-08T02:57:29.431062Z"
} | 7baf1e | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 221,
"completion_tokens": 981
},
"timestamp": "2026-02-09T15:50:11.138Z",
"answer": 70068
},
{
"i... | 1 | [
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "ok"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "V1",
"status": "no"
... | {
"lo": -6.51,
"mid": -0.31,
"hi": 5.43
} | ||
d46b34 | nt_count_divisors_in_range_v1_1520064083_6662 | Let $n = 20160$ and $m = 86915$. Define $a$ to be the number of positive integers $p$ for which there exists a positive integer $q$ such that $pq = 108$, $\gcd(p, q) = 1$, and $p < q$. Define $b$ to be the number of positive integers $t$ between $12$ and $543$, inclusive, such that there exist positive integers $a \leq... | 51,460 | graphs = [
Graph(
let={
"_n": Const(86915),
"n": Const(20160),
"a": CountOverSet(set=SolutionsSet(var=Var("p"), condition=And(IsPositive(arg=Var(name='p')), Exists(var=Var(name='q'), condition=And(Eq(left=Mul(Var(name='p'), Var(name='q')), right=Const(value=108)), Eq(left... | NT | null | COUNT | sympy | COPRIME_PAIRS | [
"COPRIME_PAIRS",
"LIN_FORM"
] | 67610e | nt_count_divisors_in_range_v1 | null | 6 | 0 | [
"COPRIME_PAIRS",
"LIN_FORM"
] | 2 | 0.009 | 2026-02-08T08:15:30.989857Z | {
"verified": true,
"answer": 51460,
"timestamp": "2026-02-08T08:15:30.999117Z"
} | 4e5522 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 213,
"completion_tokens": 6513
},
"timestamp": "2026-02-13T16:52:19.515Z",
"answer": 51460
},
... | 1 | [
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "... | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
308051 | lin_form_endings_v1_349078426_1647 | Let $a = 12$ and $b = 15$. Let $k = 33$ and define $d = \gcd(a, b)$. Let $s = \left\lfloor \frac{k}{\gcd(k, d)} \right\rfloor$. Compute the remainder when $19546 \cdot s$ is divided by $63180$. | 25,466 | graphs = [
Graph(
let={
"a_coeff": Const(12),
"b_coeff": Const(15),
"k_val": Const(33),
"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(19... | COMB | NT | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | lin_form_endings_v1 | null | 3 | null | [
"LIN_FORM"
] | 1 | 0.001 | 2026-02-08T13:49:11.928393Z | {
"verified": true,
"answer": 25466,
"timestamp": "2026-02-08T13:49:11.929721Z"
} | fd61e5 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 119,
"completion_tokens": 577
},
"timestamp": "2026-02-15T20:48:15.981Z",
"answer": 25466
},
{... | 1 | [
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "V8",
"status": "no"
},
{
"lemma": "V8_SUM",
... | {
"lo": -5.49,
"mid": 0.22,
"hi": 6.51
} | ||
b88671 | alg_sum_powers_v1_1218484723_6560 | Let $B$ be the number of ordered pairs $(a_1, b_1)$ of positive integers with $1 \le a_1, b_1 \le 35$ satisfying
$$
12a_1^2b_1^2 + 8a_1^3b_1 + 2b_1^4 + 2a_1^4 + 8a_1b_1^3 = 3359232.
$$
Let $S$ be the number of ordered pairs $(a, b)$ of positive integers with $1 \le a \le 35$ and $1 \le b \le B$ such that
$$
-2ab + 2a^2... | 36,175 | graphs = [
Graph(
let={
"_d": Const(3),
"_m": Const(90044),
"_n": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("a"), Var("b")]), condition=And(Geq(Var("a"), Const(1)), Leq(Var("a"), Const(35)), Geq(Var("b"), Const(1)), Leq(Var("b"), CountOverSet(set=SolutionsSet(... | ALG | null | COMPUTE | sympy | POLY4_COUNT | [
"POLY4_COUNT/QF_PSD_COUNT_LEQ/B3"
] | 213607 | alg_sum_powers_v1 | null | 6 | 0 | [
"B3",
"POLY4_COUNT",
"QF_PSD_COUNT_LEQ"
] | 3 | 0.042 | 2026-02-25T08:06:46.254542Z | {
"verified": true,
"answer": 36175,
"timestamp": "2026-02-25T08:06:46.296117Z"
} | 3d9c86 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 347,
"completion_tokens": 32768
},
"timestamp": "2026-03-30T02:13:22.481Z",
"answer": null
},
{
... | 1 | [
{
"lemma": "B3",
"status": "ok_later"
},
{
"lemma": "POLY4_COUNT",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "QF_PSD_COUNT_LEQ",
"status": "ok_later"
}
] | {
"lo": 1.53,
"mid": 4.7,
"hi": 7.23
} | ||
cc1693 | alg_poly_orbit_count_v1_601307018_6152 | Let $N = 2a^3 \bmod 53$, $M = 2N^3 \bmod 53$, $R = 2M^3 \bmod 53$, $S = 2R^3 \bmod 53$, $T = 2S^3 \bmod 53$, and $K = 2T^3 \bmod 53$. Find the number of non-negative integers $a$ with $0 \le a \le 63546$ such that $K = a$, but $N \ne a$, $M \ne a$, $R \ne a$, $S \ne a$, and $T \ne a$. | 57,552 | graphs = [
Graph(
let={
"p1": Mod(value=Mul(Const(2), Pow(Var("a"), Const(3))), modulus=Const(53)),
"p2": Mod(value=Mul(Const(2), Pow(Ref("p1"), Const(3))), modulus=Const(53)),
"p3": Mod(value=Mul(Const(2), Pow(Ref("p2"), Const(3))), modulus=Const(53)),
"p4": ... | ALG | null | COUNT | sympy | POLY_ORBIT_COUNT | [
"POLY_ORBIT_COUNT"
] | 4ad965 | alg_poly_orbit_count_v1 | null | 6 | null | [
"POLY_ORBIT_COUNT"
] | 1 | 0.031 | 2026-03-10T06:44:47.597218Z | {
"verified": true,
"answer": 57552,
"timestamp": "2026-03-10T06:44:47.627927Z"
} | 47f702 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 257,
"completion_tokens": 7316
},
"timestamp": "2026-04-19T03:45:44.629Z",
"answer": 57552
},
{
... | 1 | [
{
"lemma": "POLY_ORBIT_COUNT",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
}
] | {
"lo": 2.1,
"mid": 5.36,
"hi": 8.63
} | ||
8063f6 | antilemma_cartesian_v1_1520064083_3517 | Let $x$ be the number of ordered pairs $(a,b)$ such that $1 \leq a \leq 35$ and $1 \leq b \leq 50$. Compute the remainder when $29233 \cdot x$ is divided by $79797$. | 7,873 | graphs = [
Graph(
let={
"x": CountOverSet(set=CartesianProduct(left=IntegerRange(start=Const(1), end=Const(35)), right=IntegerRange(start=Const(1), end=Const(50)))),
"_c": Const(29233),
"Q": Mod(value=Mul(Ref("_c"), Ref("x")), modulus=Const(79797)),
},
goa... | COMB | GEOM | COMPUTE | sympy | COUNT_CARTESIAN | [
"COUNT_CARTESIAN"
] | 409d7d | antilemma_cartesian_v1 | null | 2 | 0 | [
"COUNT_CARTESIAN"
] | 1 | 0.001 | 2026-02-08T05:43:34.355969Z | {
"verified": true,
"answer": 7873,
"timestamp": "2026-02-08T05:43:34.356606Z"
} | 86476e | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 1,
"correct": {
"strict": false,
"boxed": false,
"relaxed": true
},
"usage": {
"prompt_tokens": 170,
"completion_tokens": 32768
},
"timestamp": "2026-02-24T04:30:28.957Z",
"answer": null
},
{
... | 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": "no"
},
{
"lemma": "V8_SU... | {
"lo": 1.97,
"mid": 4.36,
"hi": 6.69
} | ||
fa4157 | comb_sum_binomial_row_v1_1218484723_1999 | Let $M = \left|\left\{ p > 0 : \exists\, q \in \mathbb{Z},\, pq = 6,\, \gcd(p, q) = 1,\, p < q \right\}\right|^{10}$. Find the remainder when $44317 \cdot M$ is divided by $50007$. | 24,259 | graphs = [
Graph(
let={
"n": Const(10),
"result": Pow(CountOverSet(set=SolutionsSet(var=Var("p"), condition=And(IsPositive(arg=Var(name='p')), Exists(var=Var(name='q'), condition=And(Eq(left=Mul(Var(name='p'), Var(name='q')), right=Const(value=6)), Eq(left=GCD(a=Var(name='p'), b=Var(... | COMB | NT | SUM | sympy | COPRIME_PAIRS | [
"COPRIME_PAIRS"
] | 2bb3aa | comb_sum_binomial_row_v1 | null | 3 | 0 | [
"COPRIME_PAIRS"
] | 1 | 0.001 | 2026-02-25T03:42:46.968973Z | {
"verified": true,
"answer": 24259,
"timestamp": "2026-02-25T03:42:46.970356Z"
} | 6db784 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 188,
"completion_tokens": 1243
},
"timestamp": "2026-03-29T02:26:24.658Z",
"answer": 24259
},
{
"... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "... | {
"lo": -2.47,
"mid": 1.2,
"hi": 4.81
} | ||
e17181 | modular_min_linear_v1_238844314_57 | Let $a = 30440$ and $m = 70464$. Let $b$ be the sum of all real solutions $x$ to the equation $x^2 - 3968x + 67167 = 0$. Let $\text{result}$ be the smallest positive integer $x$ such that $1 \leq x \leq m$ and $a \cdot x \equiv b \pmod{m}$. Compute $\text{result}$. | 4,984 | graphs = [
Graph(
let={
"_n": Const(2),
"a": Const(30440),
"b": SumOverSet(set=SolutionsSet(var=Var("x"), condition=Eq(Sum(Pow(Var("x"), Ref("_n")), Mul(Const(-3968), Var("x")), Const(67167)), Const(0)))),
"m": Const(70464),
"result": MinOverSet(se... | NT | null | EXTREMUM | sympy | VIETA_SUM | [
"VIETA_SUM"
] | b33a7a | modular_min_linear_v1 | null | 5 | 0 | [
"VIETA_SUM"
] | 1 | 2.84 | 2026-02-08T13:06:25.360606Z | {
"verified": true,
"answer": 4984,
"timestamp": "2026-02-08T13:06:28.200779Z"
} | ff2100 | 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": 2058
},
"timestamp": "2026-02-15T09:32:41.541Z",
"answer": 4984
},
{... | 1 | [
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "V1",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
},
{
"lemma": "VIETA_SUM",
"status": "ok"
}
] | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
1c9bc1 | antilemma_sum_equals_v1_1080341949_218 | Let $n = 32$. Consider the set of all ordered pairs $(i,j)$ of integers such that $1 \leq i \leq 31$, $1 \leq j \leq 31$, and $i + j = n$. Let $x$ be the number of elements in this set. Let $c = 77975$. Compute the remainder when $c \cdot x$ is divided by $77934$. | 1,271 | graphs = [
Graph(
let={
"_n": Const(32),
"x": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("i"), Var("j")]), condition=Eq(Sum(Var("i"), Var("j")), Ref("_n")), domain=CartesianProduct(left=IntegerRange(start=Const(1), end=Const(31)), right=IntegerRange(start=Const(1), end=Con... | COMB | GEOM | COMPUTE | sympy | COUNT_SUM_EQUALS | [
"COUNT_SUM_EQUALS"
] | 75ab0f | antilemma_sum_equals_v1 | null | 2 | 0 | [
"COUNT_SUM_EQUALS"
] | 1 | 0.015 | 2026-02-08T13:18:13.541368Z | {
"verified": true,
"answer": 1271,
"timestamp": "2026-02-08T13:18:13.556462Z"
} | 0335f5 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 203,
"completion_tokens": 1021
},
"timestamp": "2026-02-24T18:06:26.005Z",
"answer": 1271
},
{
"i... | 1 | [
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "ok"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
},
{
"lemma": "V8_SUM",
"status"... | {
"lo": -2.35,
"mid": 1.22,
"hi": 4.84
} | ||
38dc6a | nt_min_coprime_above_v1_458359167_3669 | Let $S$ be the set of all positive integers $p$ for which there exists a positive integer $q$ such that $p \cdot q = 36$, $\gcd(p, q) = 1$, and $p < q$. Let $d$ be the smallest divisor of $5543093$ that is at least the number of elements in $S$. Let $T$ be the set of all integers $n$ such that $17956 < n \leq 18139$ an... | 17,957 | graphs = [
Graph(
let={
"start": Const(17956),
"upper": Const(18139),
"modulus": MinOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), CountOverSet(set=SolutionsSet(var=Var("p"), condition=And(IsPositive(arg=Var(name='p')), Exists(var=Var(name='q'), condit... | NT | null | EXTREMUM | sympy | COPRIME_PAIRS | [
"COPRIME_PAIRS/MIN_PRIME_FACTOR"
] | 52cee2 | nt_min_coprime_above_v1 | null | 5 | 0 | [
"COPRIME_PAIRS",
"MIN_PRIME_FACTOR"
] | 2 | 0.029 | 2026-02-08T11:15:08.666937Z | {
"verified": true,
"answer": 17957,
"timestamp": "2026-02-08T11:15:08.695480Z"
} | cdb5de | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 172,
"completion_tokens": 6435
},
"timestamp": "2026-02-14T11:20:21.242Z",
"answer": 17957
},
... | 1 | [
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "MIN_PRIME_FACTOR",
"status": "ok_later"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "V3",
"... | {
"lo": -9.12,
"mid": -6.02,
"hi": -3.62
} | ||
db7521 | diophantine_product_count_v1_1978505735_965 | Let $k = 480$ and $U = 369$. Define $r$ to be the number of positive integers $x$ such that $1 \leq x \leq U$, $x$ divides $k$, and $\frac{k}{x} \leq U$. Let $s$ be the minimum value of $x_1 + y$ over all ordered pairs $(x_1, y)$ of positive integers such that $x_1 \cdot y = 19518724$. Compute $r^2 + 30r + s$. | 9,980 | graphs = [
Graph(
let={
"k": Const(480),
"upper": Const(369),
"result": CountOverSet(set=SolutionsSet(var=Var("x"), condition=And(Geq(Var("x"), Const(1)), Leq(Var("x"), Ref("upper")), Divides(divisor=Var("x"), dividend=Ref("k")), Leq(Div(Ref("k"), Var("x")), Ref("upper"))... | NT | null | COUNT | sympy | B3 | [
"B3"
] | d720b5 | diophantine_product_count_v1 | quadratic_mod | 4 | 0 | [
"B3"
] | 1 | 0.024 | 2026-02-08T15:43:14.769246Z | {
"verified": true,
"answer": 9980,
"timestamp": "2026-02-08T15:43:14.793400Z"
} | 6c3b2b | 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": 1528
},
"timestamp": "2026-02-16T11:40:17.495Z",
"answer": 9980
},
{... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "V1",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
d4b9df | modular_count_residue_v1_349078426_155 | Let $m = 8$ and $U = 75076$. Define $S$ to be the set of all positive integers $n$ such that $n \le U$ and $n \equiv 0 \pmod{m}$. Let $c$ be the number of elements in $S$. Let $s = \sum_{k=1}^{8} k$. Compute the remainder when $s - c$ is divided by 64698. | 55,350 | graphs = [
Graph(
let={
"upper": Const(75076),
"m": Const(8),
"r": Const(0),
"result": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Ref("upper")), Eq(Mod(value=Var("n"), modulus=Ref("m")), Ref("r"))))),
... | NT | null | COUNT | sympy | SUM_ARITHMETIC | [
"SUM_ARITHMETIC"
] | 5c63b0 | modular_count_residue_v1 | negation_mod | 2 | 0 | [
"SUM_ARITHMETIC"
] | 1 | 6.906 | 2026-02-08T12:51:24.409254Z | {
"verified": true,
"answer": 55350,
"timestamp": "2026-02-08T12:51:31.315408Z"
} | a0cd2e | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 157,
"completion_tokens": 705
},
"timestamp": "2026-02-16T04:07:19.758Z",
"answer": 55350
},
{
"id": 11,
... | 2 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "SUM_ARITHMETIC",
"status": "ok"
},
{
"lemma": "V8_SUM",
"status": "no"
}
] | {
"lo": -9.12,
"mid": -6.02,
"hi": -3.62
} | ||
b6ff34 | comb_sum_binomial_row_v1_1520064083_6132 | Let $S$ be the set of all positive integers $p$ for which there exists a positive integer $q$ such that $pq = 36$, $\gcd(p, q) = 1$, and $p < q$. Let $m$ be the number of elements in $S$. Define $n$ to be the largest prime number that is at least $m$ and at most $13$. Compute the smallest positive integer $k$ such that... | 360 | graphs = [
Graph(
let={
"_m": Const(13),
"_n": Const(2),
"n": 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... | NT | null | SUM | sympy | COPRIME_PAIRS | [
"COPRIME_PAIRS/MAX_PRIME_BELOW"
] | 2248fc | comb_sum_binomial_row_v1 | null | 6 | 0 | [
"COPRIME_PAIRS",
"MAX_PRIME_BELOW"
] | 2 | 0.006 | 2026-02-08T07:52:58.378043Z | {
"verified": true,
"answer": 360,
"timestamp": "2026-02-08T07:52:58.384283Z"
} | 754a41 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 158,
"completion_tokens": 3702
},
"timestamp": "2026-02-13T13:24:16.375Z",
"answer": 360
},
{
... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok_later"
},
{
"lemma": "V3",
"status": "no"
},
{
... | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
32cd70 | nt_sum_over_divisible_v1_784195855_2547 | Let $P$ be the set of all ordered pairs $(x, y)$ of positive integers such that $x \cdot y = 6350400$. For each such pair, compute $x + y$. Let $s$ be the minimum value of $x + y$ over all such pairs. Compute the sum of all positive integers $n \leq s$ that are divisible by $192$. | 67,392 | graphs = [
Graph(
let={
"upper": MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(Mul(Var("x"), Var("y")), Const(6350400)))), expr=Sum(Var("x"), Var("y")))),
"divisor": ... | NT | null | SUM | sympy | LIN_FORM | [
"B3"
] | 0cd20d | nt_sum_over_divisible_v1 | null | 5 | 0 | [
"B3",
"LIN_FORM"
] | 2 | 13.218 | 2026-02-08T05:50:55.469141Z | {
"verified": true,
"answer": 67392,
"timestamp": "2026-02-08T05:51:08.686809Z"
} | 1d086e | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 129,
"completion_tokens": 1750
},
"timestamp": "2026-02-12T16:00:55.080Z",
"answer": 67392
},
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
}
] | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
6a47fb | nt_min_with_divisor_count_v1_1520064083_466 | Let $n$ be a positive integer such that the number of positive divisors of $n$ is exactly 9. The maximum possible value of $n$ under this condition is 40320. Determine the value of the smallest such $n$. | 36 | graphs = [
Graph(
let={
"upper": Const(40320),
"div_count": Const(9),
"result": MinOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Ref("upper")), Eq(NumDivisors(n=Var("n")), Ref("div_count"))))),
},
goal=Ref("res... | NT | null | EXTREMUM | sympy | MIN_PRIME_FACTOR | [
"LTE_SUM"
] | de3c48 | nt_min_with_divisor_count_v1 | null | 6 | 0 | [
"LTE_SUM",
"MIN_PRIME_FACTOR"
] | 2 | 10.238 | 2026-02-08T03:25:19.481370Z | {
"verified": true,
"answer": 36,
"timestamp": "2026-02-08T03:25:29.719497Z"
} | 916d18 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 161,
"completion_tokens": 1421
},
"timestamp": "2026-02-10T14:24:25.309Z",
"answer": 36
},
{
"id"... | 1 | [
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "ok"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "V1",
"status": "no"
},
{
"lemma": "V3",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
}
] | {
"lo": -7.01,
"mid": -4.68,
"hi": -2.15
} | ||
5aa47a | modular_count_residue_v1_1978505735_3936 | Let $m$ be the smallest divisor of $48841$ that is at least $2$. Let $r = 4$ and let $U = 77284$. Compute the number of positive integers $n$ such that $1 \leq n \leq U$ and $n \equiv r \pmod{m}$. | 5,945 | graphs = [
Graph(
let={
"upper": Const(77284),
"m": MinOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Const(2)), Divides(divisor=Var("d"), dividend=Const(48841))))),
"r": Const(4),
"result": CountOverSet(set=SolutionsSet(var=Var("n"), condi... | NT | null | COUNT | sympy | MIN_PRIME_FACTOR | [
"MIN_PRIME_FACTOR"
] | bc3776 | modular_count_residue_v1 | null | 3 | 0 | [
"MIN_PRIME_FACTOR"
] | 1 | 2.528 | 2026-02-08T17:55:46.064118Z | {
"verified": true,
"answer": 5945,
"timestamp": "2026-02-08T17:55:48.592085Z"
} | a352db | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 114,
"completion_tokens": 786
},
"timestamp": "2026-02-18T09:56:08.104Z",
"answer": 5945
},
{
... | 1 | [
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MIN_PRIME_FACTOR",
"status": "ok"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
5a0c03 | antilemma_v1_legendre_168721529_926 | Let $m = 2$, and let $n$ be the largest prime number such that $m \leq n \leq 17$. Determine the largest integer $k$ such that $n^k$ divides $126752!$. Find the remainder when this $k$ is divided by $83852$. | 7,920 | graphs = [
Graph(
let={
"_m": Const(2),
"_n": MaxOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Ref("_m")), Leq(Var("n"), Const(17)), IsPrime(Var("n"))))),
"x": MaxKDivides(target=Factorial(Const(126752)), base=Ref("_n")),
"Q": Mod(value=Ab... | NT | null | COMPUTE | sympy | MAX_PRIME_BELOW | [
"MAX_PRIME_BELOW/V1",
"V1"
] | 8b2738 | antilemma_v1_legendre | null | 4 | 0 | [
"MAX_PRIME_BELOW",
"V1"
] | 2 | 0.002 | 2026-02-08T13:20:52.629757Z | {
"verified": true,
"answer": 7920,
"timestamp": "2026-02-08T13:20:52.631349Z"
} | db78dc | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 180,
"completion_tokens": 1219
},
"timestamp": "2026-02-09T10:51:56.833Z",
"answer": 7920
},
{
"i... | 1 | [
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "K5",
"status": "same_pattern_wrong"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status"... | {
"lo": -6.69,
"mid": -2.39,
"hi": 1.83
} | ||
e04055 | comb_count_partitions_v1_1918700295_4322 | Let $n$ be the number of prime numbers $p$ such that $2 \leq p \leq 197$. Let $P(n)$ denote the number of integer partitions of $n$.
Compute the remainder when $39601 - P(n)$ is divided by $96095$. | 46,562 | graphs = [
Graph(
let={
"_n": Const(2),
"n": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Ref("_n")), Leq(Var("n"), Const(197)), IsPrime(Var("n"))))),
"result": Partition(arg=Ref(name='n')),
"Q": Mod(value=Sub(Const(39601), Ref("resu... | NT | COMB | COUNT | sympy | COUNT_PRIMES | [
"COUNT_PRIMES"
] | 07c874 | comb_count_partitions_v1 | null | 5 | 0 | [
"COUNT_PRIMES"
] | 1 | 0.001 | 2026-02-08T09:17:41.817261Z | {
"verified": true,
"answer": 46562,
"timestamp": "2026-02-08T09:17:41.818165Z"
} | a20d2b | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 105,
"completion_tokens": 1248
},
"timestamp": "2026-02-14T02:26:12.001Z",
"answer": 46562
},
... | 1 | [
{
"lemma": "COUNT_PRIMES",
"status": "ok"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
}
] | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
37fb7c | antilemma_k3_v1_1874849503_223 | Let $n = 20502$. Compute the remainder when
$$
44121 \cdot \sum_{d \mid n} \phi(d)
$$
is divided by $85447$. | 26,800 | graphs = [
Graph(
let={
"_n": Const(20502),
"x": SumOverDivisors(n=Ref(name='_n'), var='d', expr=EulerPhi(n=Var(name='d'))),
"Q": Mod(value=Mul(Const(44121), Ref("x")), modulus=Const(85447)),
},
goal=Ref("Q"),
)
] | NT | COMB | COMPUTE | sympy | K3 | [
"K3"
] | 54c41e | antilemma_k3_v1 | null | 3 | 0 | [
"K3"
] | 1 | 0.001 | 2026-02-08T12:53:11.858417Z | {
"verified": true,
"answer": 26800,
"timestamp": "2026-02-08T12:53:11.859032Z"
} | d3d1f0 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 155,
"completion_tokens": 1044
},
"timestamp": "2026-02-09T14:49:36.279Z",
"answer": 26800
},
{
"... | 1 | [
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K3",
"status": "ok"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
}
] | {
"lo": -5.15,
"mid": 0.01,
"hi": 5.44
} | ||
bcfa41 | modular_inverse_v1_898971024_732 | Let $m$ be the number of positive integers $n$ such that $1 \le n \le 1709$ and $n \equiv \left\lfloor \frac{n}{2} \right\rfloor \pmod{3}$. Let $x$ be the smallest positive integer such that $1 \le x \le 568$ and $98x \equiv 1 \pmod{m}$. Compute $x$. | 180 | graphs = [
Graph(
let={
"_n": Const(1709),
"a": Const(98),
"m": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Ref("_n")), Congruent(a=Var(name='n'), b=Floor(arg=Div(left=Var(name='n'), right=Const(value=2))), modulus=Cons... | NT | null | EXTREMUM | sympy | L3C | [
"L3C"
] | 73f8b0 | modular_inverse_v1 | null | 6 | 0 | [
"L3C"
] | 1 | 0.13 | 2026-02-08T15:37:34.576277Z | {
"verified": true,
"answer": 180,
"timestamp": "2026-02-08T15:37:34.705967Z"
} | c68e61 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 136,
"completion_tokens": 1271
},
"timestamp": "2026-02-16T09:19:59.836Z",
"answer": 180
},
{
... | 1 | [
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "L3C",
"status": "ok"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "V3",
"status": "no... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
13b6a4 | comb_sum_binomial_mod_v1_655260480_891 | Let $n = 11251$. Let $S$ be the set of positive integers $m$ such that $1 \leq m \leq 282$ and $m \equiv 0 \pmod{141}$. Define $N$ to be the sum of all elements in $S$. Let $\text{sum} = \sum_{k=36}^{415} \binom{N}{k}$. Define $\text{result}$ to be the remainder when $\text{sum}$ is divided by $n$.\n\nCompute the value... | 2,310 | graphs = [
Graph(
let={
"_n": Const(11251),
"sum": Summation(var="k", start=Const(36), end=Const(415), expr=Binom(n=SumOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Const(282)), Eq(Mod(value=Var("n"), modulus=Const(141)), Const(0))))), k=... | ALG | COMB | COMPUTE | sympy | SUM_DIVISIBLE | [
"SUM_DIVISIBLE"
] | 02dbe3 | comb_sum_binomial_mod_v1 | null | 4 | 0 | [
"SUM_DIVISIBLE"
] | 1 | 0.031 | 2026-02-08T15:42:18.066794Z | {
"verified": true,
"answer": 2310,
"timestamp": "2026-02-08T15:42:18.097799Z"
} | 608e06 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 235,
"completion_tokens": 25102
},
"timestamp": "2026-02-24T18:32:04.731Z",
"answer": 2310
},
{
... | 1 | [
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "SUM_DIVISIBLE",
"status": "ok"
}
] | {
"lo": 1.98,
"mid": 5.23,
"hi": 8.52
} | ||
efaa3c | diophantine_fbi2_min_v1_1431428450_978 | Let $k$ be the number of integers $t$ in the range $18 \leq t \leq 290$ for which there exist positive integers $a \leq 25$ and $b \leq 9$ such that $t = 8a + 10b$. Let $d_{\min}$ be the smallest divisor $d$ of $k$ such that $5 \leq d \leq 135$ and $\frac{k}{d} \geq 6$. Determine the value of $d_{\min}$. | 5 | graphs = [
Graph(
let={
"k": CountOverSet(set=SolutionsSet(var=Var("t"), condition=Exists(var=Var(name='a'), condition=Exists(var=Var(name='b'), condition=And(Geq(left=Var(name='a'), right=Const(value=1)), Leq(left=Var(name='a'), right=Const(value=25)), Geq(left=Var(name='b'), right=Const(value=... | NT | null | EXTREMUM | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | diophantine_fbi2_min_v1 | null | 5 | 0 | [
"LIN_FORM"
] | 1 | 0.008 | 2026-02-08T13:50:18.273064Z | {
"verified": true,
"answer": 5,
"timestamp": "2026-02-08T13:50:18.281012Z"
} | 845e75 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 156,
"completion_tokens": 5119
},
"timestamp": "2026-02-15T21:28:14.655Z",
"answer": 5
},
{
... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
}
] | {
"lo": -5.49,
"mid": 0.22,
"hi": 6.51
} | ||
9d58e3 | nt_count_intersection_v1_1470522791_86 | Let $S$ be the set of all ordered pairs $(x, y)$ of positive integers such that $xy = 6250000$. Define $N$ to be the minimum value of $x + y$ as $(x, y)$ ranges over $S$.
Let $r$ be the number of positive integers $n$ such that $1 \leq n \leq N$, $7$ divides $n$, and $\gcd(n, 15) = 1$.
Let $c$ be the largest prime nu... | 67 | 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(6250000)))), expr=Sum(Var("x"), Var("y")))),... | NT | null | COUNT | sympy | B3 | [
"MAX_PRIME_BELOW",
"B3"
] | 6886fa | nt_count_intersection_v1 | digits_weighted_mod | 6 | 0 | [
"B3",
"MAX_PRIME_BELOW"
] | 2 | 3.375 | 2026-02-08T12:49:13.726413Z | {
"verified": true,
"answer": 67,
"timestamp": "2026-02-08T12:49:17.101857Z"
} | f0a289 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 223,
"completion_tokens": 1835
},
"timestamp": "2026-02-15T05:20:18.940Z",
"answer": 67
},
{
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok"
},
... | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
a7774d | nt_count_coprime_v1_971394319_231 | Let $m = 2$ and define $n$ to be the number of ordered pairs $(i,j)$ with $1 \leq i \leq 2$ and $1 \leq j \leq 43$. Let $k$ be the number of positive integers $n$ with $1 \leq n \leq n$ such that the sum of the decimal digits of $n$ is divisible by $m$. Let $\text{result}$ be the number of positive integers $n$ with $1... | 19,974 | graphs = [
Graph(
let={
"_m": Const(2),
"_n": CountOverSet(set=CartesianProduct(left=IntegerRange(start=Const(1), end=Const(2)), right=IntegerRange(start=Const(1), end=Const(43)))),
"upper": Const(20449),
"k": CountOverSet(set=SolutionsSet(var=Var("n"), condit... | NT | null | COUNT | sympy | COUNT_CARTESIAN | [
"COUNT_CARTESIAN/L3B"
] | fb8c6f | nt_count_coprime_v1 | null | 5 | 0 | [
"COUNT_CARTESIAN",
"L3B"
] | 2 | 1.883 | 2026-02-08T12:54:24.636702Z | {
"verified": true,
"answer": 19974,
"timestamp": "2026-02-08T12:54:26.520025Z"
} | 10f40e | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 174,
"completion_tokens": 1536
},
"timestamp": "2026-02-15T08:02:13.477Z",
"answer": 19974
},
... | 1 | [
{
"lemma": "COUNT_CARTESIAN",
"status": "ok"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "L3B",
"status": "ok_later"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lem... | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
d4b834 | comb_count_permutations_fixed_v1_1520064083_2178 | Let $m = 10$. Define $n'$ to be the number of positive integers $p$ for which there exists an integer $q$ such that $p \cdot q = 24$, $\gcd(p, q) = 1$, and $p < q$. Let $n$ be the largest prime number satisfying $n' \leq n \leq m$. Compute $\binom{n}{0} \cdot !n$, where $!n$ denotes the number of derangements of $n$ el... | 1,854 | graphs = [
Graph(
let={
"_m": Const(10),
"_n": CountOverSet(set=SolutionsSet(var=Var("p"), condition=And(IsPositive(arg=Var(name='p')), Exists(var=Var(name='q'), condition=And(Eq(left=Mul(Var(name='p'), Var(name='q')), right=Const(value=24)), Eq(left=GCD(a=Var(name='p'), b=Var(name='... | NT | COMB | COUNT | sympy | COPRIME_PAIRS | [
"COPRIME_PAIRS/MAX_PRIME_BELOW"
] | 2248fc | comb_count_permutations_fixed_v1 | null | 5 | 0 | [
"COPRIME_PAIRS",
"MAX_PRIME_BELOW"
] | 2 | 0.002 | 2026-02-08T04:33:07.534662Z | {
"verified": true,
"answer": 1854,
"timestamp": "2026-02-08T04:33:07.536464Z"
} | 4d6044 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 223,
"completion_tokens": 1200
},
"timestamp": "2026-02-10T17:07:47.625Z",
"answer": 1854
},
{
"... | 1 | [
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok_later"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONS... | {
"lo": -8.32,
"mid": -5.11,
"hi": -2.37
} | ||
c54c6a | algebra_quadratic_discriminant_v1_168721529_1407 | Let $a = 2$. Let $b$ be the number of ordered pairs $(x_1, x_2)$ of positive odd integers such that $x_1 + x_2 = 40$. Let $c = 18$. Compute $b^2 - 4ac$. | 256 | graphs = [
Graph(
let={
"a": Const(2),
"b": 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")), Cons... | NT | null | COMPUTE | sympy | COMB1 | [
"COMB1"
] | 567f58 | algebra_quadratic_discriminant_v1 | null | 4 | 0 | [
"COMB1"
] | 1 | 0.002 | 2026-02-08T13:41:08.324542Z | {
"verified": true,
"answer": 256,
"timestamp": "2026-02-08T13:41:08.326825Z"
} | 01bcdb | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 171,
"completion_tokens": 521
},
"timestamp": "2026-02-09T16:32:01.465Z",
"answer": 256
},
{
"id"... | 2 | [
{
"lemma": "COMB1",
"status": "ok"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
}
] | {
"lo": -10,
"mid": -7.28,
"hi": -4.55
} | ||
fb7222 | antilemma_k3_v1_2080023795_178 | Compute the sum of Euler's totient function $\phi(d)$ over all positive divisors $d$ of $40284$. | 40,284 | graphs = [
Graph(
let={
"_n": Const(40284),
"x": SumOverDivisors(n=Ref(name='_n'), var='d', expr=EulerPhi(n=Var(name='d'))),
},
goal=Ref("x"),
)
] | NT | COMB | COMPUTE | sympy | K3 | [
"K3"
] | 54c41e | antilemma_k3_v1 | null | 3 | 0 | [
"K3"
] | 1 | 0.001 | 2026-02-08T11:35:16.880758Z | {
"verified": true,
"answer": 40284,
"timestamp": "2026-02-08T11:35:16.881472Z"
} | 7db5cd | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 140,
"completion_tokens": 448
},
"timestamp": "2026-02-08T20:50:23.609Z",
"answer": 40284
},
{
"i... | 1 | [
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "K3",
"status": "ok"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
}
] | {
"lo": -3.9,
"mid": -1.13,
"hi": 1.31
} | ||
2d3193 | geo_count_lattice_rect_v1_1915831931_790 | Compute the number of lattice points in the rectangle $[0, 196] \times [0, 414]$. | 81,755 | graphs = [
Graph(
let={
"a": Const(196),
"b": Const(414),
"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 | 0.002 | 2026-02-08T15:40:49.086944Z | {
"verified": true,
"answer": 81755,
"timestamp": "2026-02-08T15:40:49.088536Z"
} | 8d34e8 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 135,
"completion_tokens": 233
},
"timestamp": "2026-02-24T18:22:32.153Z",
"answer": 81755
},
{
"... | 1 | [] | {
"lo": -8,
"mid": -4.75,
"hi": -2.28
} | ||||
cc7b3e | nt_max_prime_below_v1_971394319_1271 | 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 $n_0$ be the number of elements in $S$. Let $T$ be the set of all prime numbers $n$ such that $n \geq n_0$ and $n \leq 81225$. Determine the value of $|\max(T)| \bmod 89... | 81,223 | graphs = [
Graph(
let={
"_n": Const(89682),
"upper": Const(81225),
"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=... | NT | null | EXTREMUM | sympy | COPRIME_PAIRS | [
"COPRIME_PAIRS"
] | 2bb3aa | nt_max_prime_below_v1 | null | 5 | 0 | [
"COPRIME_PAIRS"
] | 1 | 2.423 | 2026-02-08T13:34:11.963076Z | {
"verified": true,
"answer": 81223,
"timestamp": "2026-02-08T13:34:14.386112Z"
} | c03d7f | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 159,
"completion_tokens": 2777
},
"timestamp": "2026-02-15T17:49:12.976Z",
"answer": 81223
},
... | 1 | [
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
... | {
"lo": -5.49,
"mid": 0.22,
"hi": 6.51
} | ||
fd1b63 | algebra_poly_eval_v1_1218484723_298 | Let $E = \left|\{ (a_1, b_1) : 1 \leq a_1, b_1 \leq 40,\ 17b_1^4 = 1377 \}\right|$ and $F = \left|\{ t \in \mathbb{Z} : \exists\, a,b \in \mathbb{Z}^+ \text{ with } 1 \leq a \leq 900,\ 1 \leq b \leq 56,\ t = 2a + 7b,\ 9 \leq t \leq 2192 \}\right|$. Compute the value of $$\left|\left\{ (a, b) : 1 \leq a \leq b \leq 40,\... | 29,402 | graphs = [
Graph(
let={
"_c": Const(40),
"_m": Const(2),
"_n": Const(10),
"m": Const(16),
"result": Sum(Mul(CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("a"), Var("b")]), condition=And(Geq(Var("a"), Const(1)), Leq(Var("a"), Const(40)), Geq... | ALG | null | COMPUTE | sympy | POLY4_COUNT | [
"POLY4_COUNT/QF_PSD_ORBIT",
"LIN_FORM/QF_PSD_ORBIT"
] | a4b73b | algebra_poly_eval_v1 | null | 6 | 0 | [
"LIN_FORM",
"POLY4_COUNT",
"QF_PSD_ORBIT"
] | 3 | 0.018 | 2026-02-25T01:59:24.653767Z | {
"verified": true,
"answer": 29402,
"timestamp": "2026-02-25T01:59:24.671813Z"
} | 519522 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 336,
"completion_tokens": 26988
},
"timestamp": "2026-03-10T09:28:47.825Z",
"answer": 29402
},
{
... | 1 | [
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "POLY4_COUNT",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "QF_PSD_ORBIT",
"status": "ok_later"
}
] | {
"lo": 1.22,
"mid": 3.76,
"hi": 5.73
} | ||
96e3da | modular_min_linear_v1_2080023795_10 | Let $A$ be the set of all positive integers $n$ such that $1 \leq n \leq 15128$, $8$ divides $n$, and $\gcd(n, 15) = 1$. Let $a = 26701$, $b = 13166$, and $m = 35540$. Let $x_0$ be the smallest positive integer $x$ such that $1 \leq x \leq m$ and
\[
26701x \equiv 13166 \pmod{35540}.
\]
Let $c$ be the largest prime numb... | 18,420 | graphs = [
Graph(
let={
"_n": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Const(15128)), Divides(divisor=Const(8), dividend=Var("n")), Eq(GCD(a=Var("n"), b=Const(15)), Const(1))))),
"a": Const(26701),
"b": Const(13166),... | NT | null | EXTREMUM | sympy | C5 | [
"C5/MAX_PRIME_BELOW"
] | d42db4 | modular_min_linear_v1 | two_moduli | 6 | 0 | [
"C5",
"MAX_PRIME_BELOW"
] | 2 | 1.59 | 2026-02-08T11:29:59.123067Z | {
"verified": true,
"answer": 18420,
"timestamp": "2026-02-08T11:30:00.712863Z"
} | 286cac | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 294,
"completion_tokens": 3468
},
"timestamp": "2026-02-10T03:42:06.603Z",
"answer": 18420
},
{
... | 1 | [
{
"lemma": "C5",
"status": "ok"
},
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok_later"
},
{
"lemma": "POLY_PADIC_VAL_CONS... | {
"lo": 2.06,
"mid": 5.24,
"hi": 8.53
} | ||
e76a4d | comb_count_permutations_fixed_v1_458359167_3472 | Let $n$ be the smallest divisor of 537251 that is greater than or equal to 2. Let $k$ be the number of integers $t$ such that $15 \leq t \leq 25$ and there exist integers $a, b$ with $1 \leq a \leq 3$, $1 \leq b \leq 3$, and $t = 3a + 2b + 10$. Compute the remainder when $44121 \cdot \binom{n}{k} \cdot !(n-k)$ is divid... | 1,239 | graphs = [
Graph(
let={
"_n": Const(57748),
"n": MinOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Const(2)), Divides(divisor=Var("d"), dividend=Const(537251))))),
"k": CountOverSet(set=SolutionsSet(var=Var("t"), condition=Exists(var=Var(name='a'), con... | NT | COMB | COUNT | sympy | MIN_PRIME_FACTOR | [
"MIN_PRIME_FACTOR",
"LIN_FORM"
] | 41af5a | comb_count_permutations_fixed_v1 | null | 5 | 0 | [
"LIN_FORM",
"MIN_PRIME_FACTOR"
] | 2 | 0.003 | 2026-02-08T08:22:57.799740Z | {
"verified": true,
"answer": 1239,
"timestamp": "2026-02-08T08:22:57.802248Z"
} | d1019c | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 184,
"completion_tokens": 2228
},
"timestamp": "2026-02-13T18:00:59.163Z",
"answer": 1239
},
{... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "MIN_PRIME_FACTOR",
"status": "ok"
},
{
"lemm... | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
d120ea | comb_bell_compute_v1_124444284_6381 | Let $ n $ be the number of positive integers $ j $ such that $ 1 \leq j \leq 9 $ and $ j^5 \leq 59049 $. Compute the Bell number $ B_n $, which counts the number of partitions of a set of size $ n $. | 21,147 | graphs = [
Graph(
let={
"_n": Const(5),
"n": CountOverSet(set=SolutionsSet(var=Var("j"), condition=And(Geq(Var("j"), Const(1)), Leq(Var("j"), Const(9)), Leq(Pow(Var("j"), Ref("_n")), Const(59049))), domain='positive_integers')),
"result": Bell(Ref("n")),
},
... | COMB | null | COMPUTE | sympy | C3 | [
"C3"
] | 8a214c | comb_bell_compute_v1 | null | 4 | 0 | [
"C3"
] | 1 | 0.001 | 2026-02-08T08:18:57.009524Z | {
"verified": true,
"answer": 21147,
"timestamp": "2026-02-08T08:18:57.010779Z"
} | 207e21 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 172,
"completion_tokens": 708
},
"timestamp": "2026-02-24T09:21:56.841Z",
"answer": 21147
},
{
"i... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "C3",
"status": "ok"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
}
] | {
"lo": -4.92,
"mid": -2.91,
"hi": -0.68
} | ||
59bd3f | comb_catalan_compute_v1_655260480_2750 | Let $n = 10$, and let $C_n$ denote the $n$-th Catalan number. Compute $C_{10}$. Let $d_i$ denote the $i$-th decimal digit of $|C_{10}|$ (with $d_0$ being the units digit). Let $s$ be the sum of $d_i \cdot (i+1)^2$ over all $i$ from $0$ to $\text{number of digits of } |C_{10}| - 1$. Then compute $s + 12996$.
Find the v... | 13,222 | graphs = [
Graph(
let={
"n": Const(10),
"result": Catalan(Ref("n")),
"Q": Sum(Summation(var="i", start=Summation(var="k", start=Const(0), end=Const(2), expr=Mul(Pow(Const(-1), Var("k")), Binom(n=Const(2), k=Var("k")))), end=Sub(NumDigits(x=Abs(arg=Ref(name='result')), bas... | COMB | null | COMPUTE | sympy | BINOMIAL_ALTERNATING | [
"BINOMIAL_ALTERNATING",
"ONE_FACTORIAL_0"
] | 8794cb | comb_catalan_compute_v1 | null | 4 | 0 | [
"BINOMIAL_ALTERNATING",
"ONE_FACTORIAL_0"
] | 2 | 0.004 | 2026-02-08T16:58:29.749442Z | {
"verified": true,
"answer": 13222,
"timestamp": "2026-02-08T16:58:29.753770Z"
} | 091dc2 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 171,
"completion_tokens": 835
},
"timestamp": "2026-02-17T16:51:00.617Z",
"answer": 13222
},
{... | 1 | [
{
"lemma": "BINOMIAL_ALTERNATING",
"status": "ok"
},
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "... | {
"lo": -4.1,
"mid": -1.76,
"hi": 1.32
} | ||
2f88d3 | diophantine_product_count_v1_1918700295_3492 | Let $k = 1260$. Let $u$ be the sum of all positive integers $n$ such that $n \leq 85$ and $n$ is divisible by 17. Define $S$ as the set of all positive integers $x$ such that $x \leq u$, $x$ divides $k$, and $\frac{k}{x} \leq u$. Let $r$ be the number of elements in $S$. Compute the remainder when $50509 \cdot r$ is di... | 41,518 | graphs = [
Graph(
let={
"k": Const(1260),
"upper": SumOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Const(85)), Eq(Mod(value=Var("n"), modulus=Const(17)), Const(0))))),
"result": CountOverSet(set=SolutionsSet(var=Var("x"), con... | NT | null | COUNT | sympy | SUM_DIVISIBLE | [
"SUM_DIVISIBLE"
] | 02dbe3 | diophantine_product_count_v1 | null | 5 | 0 | [
"SUM_DIVISIBLE"
] | 1 | 0.016 | 2026-02-08T08:40:02.206452Z | {
"verified": true,
"answer": 41518,
"timestamp": "2026-02-08T08:40:02.222327Z"
} | eb0df8 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 159,
"completion_tokens": 1867
},
"timestamp": "2026-02-13T20:25:03.528Z",
"answer": 41518
},
... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "SUM_DIVISIBLE",
"status": "ok"
}
] | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
aad930 | geo_count_lattice_triangle_v1_1978505735_7315 | Let $P$ be the set of all positive integers $p$ for which there exists a positive integer $q$ such that $pq = 27081081027000$, $\gcd(p, q) = 1$, and $p < q$. Let $c = 100 \cdot 196 + 50 \cdot (0 - |P|)$. Define $b = \gcd(100, 32) + \gcd(50, 164) + \gcd(50, 196)$. Compute $\frac{c + 2 - b}{2}$. | 8,997 | graphs = [
Graph(
let={
"_m": Const(17),
"_n": Const(2),
"area_2x": Abs(arg=Sum(Mul(Const(value=100), Const(value=196)), Mul(Const(value=50), Sub(left=Const(value=0), right=CountOverSet(set=SolutionsSet(var=Var(name='p'), condition=And(IsPositive(arg=Var(name='p')), Exist... | NT | null | COUNT | sympy | COPRIME_PAIRS | [
"COPRIME_PAIRS",
"V1"
] | cee0c3 | geo_count_lattice_triangle_v1 | null | 6 | 0 | [
"COPRIME_PAIRS",
"V1"
] | 2 | 0.008 | 2026-02-08T20:10:01.201378Z | {
"verified": true,
"answer": 8997,
"timestamp": "2026-02-08T20:10:01.209310Z"
} | ca5268 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 163,
"completion_tokens": 4804
},
"timestamp": "2026-02-19T00:07:15.768Z",
"answer": 8997
},
{... | 1 | [
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "K5",
"status": "same_pattern_wrong"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "V1",
"status"... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
8b6bc0 | nt_count_coprime_v1_717093673_160 | Let $k$ be the number of prime numbers $n$ such that $2 \leq n \leq 103$. Let $\text{result}$ be the number of positive integers $n_1$ with $1 \leq n_1 \leq 51984$ such that $\gcd(n_1, k) = 1$. Compute the remainder when $44121 \cdot \text{result}$ is divided by $77633$. | 75,441 | graphs = [
Graph(
let={
"_n": Const(103),
"upper": Const(51984),
"k": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(2)), Leq(Var("n"), Ref("_n")), IsPrime(Var("n"))))),
"result": CountOverSet(set=SolutionsSet(var=Var("n1"), cond... | NT | null | COUNT | sympy | COUNT_PRIMES | [
"COUNT_PRIMES"
] | 07c874 | nt_count_coprime_v1 | null | 4 | 0 | [
"COUNT_PRIMES"
] | 1 | 4.149 | 2026-02-08T15:12:49.704251Z | {
"verified": true,
"answer": 75441,
"timestamp": "2026-02-08T15:12:53.853330Z"
} | 3fbd20 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 138,
"completion_tokens": 1766
},
"timestamp": "2026-02-16T01:37:16.033Z",
"answer": 75441
},
... | 1 | [
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "COUNT_PRIMES",
"status": "ok"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "V3",
"statu... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
b8069e | antilemma_k3_v1_48377204_135 | Let $n = 45354$. Compute the sum of $\phi(d)$ over all positive divisors $d$ of $n$, where $\phi$ denotes Euler's totient function. | 45,354 | graphs = [
Graph(
let={
"_n": Const(45354),
"x": SumOverDivisors(n=Ref(name='_n'), var='d', expr=EulerPhi(n=Var(name='d'))),
},
goal=Ref("x"),
)
] | NT | COMB | COMPUTE | sympy | K3 | [
"K3"
] | 54c41e | antilemma_k3_v1 | null | 2 | 0 | [
"K3"
] | 1 | 0.001 | 2026-02-08T15:14:44.104745Z | {
"verified": true,
"answer": 45354,
"timestamp": "2026-02-08T15:14:44.105330Z"
} | 19e0f7 | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 1,
"correct": {
"strict": false,
"boxed": false,
"relaxed": true
},
"usage": {
"prompt_tokens": 100,
"completion_tokens": 465
},
"timestamp": "2026-02-16T05:21:44.496Z",
"answer": 358035
},
{
"id": 11... | 1 | [
{
"lemma": "K3",
"status": "ok"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"... | {
"lo": -8.26,
"mid": -5.01,
"hi": -1.76
} | ||
df1e43 | nt_sum_divisors_mod_v1_397696148_204 | Let $S$ be the set of all ordered pairs $(x, y)$ of positive integers such that $xy = 14288400$. Let $n$ be the minimum value of $x + y$ over all such pairs. Let $\sigma(n)$ denote the sum of all positive divisors of $n$. Define $M = 10939$ and let $r = \sigma(n) \bmod M$. Compute the value of $80761 \cdot r \bmod 8596... | 57,204 | graphs = [
Graph(
let={
"_n": Const(85969),
"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(14288400)))), expr=Sum(Var("x"), Var("y"... | NT | null | COMPUTE | sympy | B3 | [
"B3"
] | 0cd20d | nt_sum_divisors_mod_v1 | null | 6 | 0 | [
"B3"
] | 1 | 0.003 | 2026-02-08T11:22:40.343935Z | {
"verified": true,
"answer": 57204,
"timestamp": "2026-02-08T11:22:40.346902Z"
} | 02f1aa | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 150,
"completion_tokens": 1917
},
"timestamp": "2026-02-14T12:23:43.598Z",
"answer": 57204
},
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
}
] | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
28dadd_n | sequence_count_fib_divisible_v1_601307018_3904 | A drone flies a route shaped like a rectangle with area $544$ square kilometers, where both side lengths are positive integers. The pilot chooses the dimensions that minimize the difference between the two side lengths. Let $d$ be this minimal difference. Separately, a researcher studies signal cycles of length $F_n$, ... | 2,419 | ALG | null | COUNT | sympy | B3_CLOSEST | [
"B3_CLOSEST",
"B3_DIFF"
] | e18306 | sequence_count_fib_divisible_v1 | null | 4 | null | [
"B3_CLOSEST",
"B3_DIFF"
] | 2 | 0.01 | 2026-03-10T04:30:51.744614Z | null | 006975 | 28dadd | narrative | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 261,
"completion_tokens": 11690
},
"timestamp": "2026-03-29T18:09:13.982Z",
"answer": 0
},
{
"... | 1 | [
{
"lemma": "B3_CLOSEST",
"status": "ok"
},
{
"lemma": "B3_DIFF",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
}
] | {
"lo": 1.7,
"mid": 5.03,
"hi": 8.38
} | |
00b4fe | geo_count_lattice_rect_v1_784195855_2885 | Let $a = 406$ and $b = 120$. Define $\text{result}$ to be the number of lattice points $(x, y)$ such that $0 \leq x \leq a$ and $0 \leq y \leq b$. Let $Q$ be the remainder when $52170 \cdot \text{result}$ is divided by $84707$. Find the value of $Q$. | 52,680 | graphs = [
Graph(
let={
"a": Const(406),
"b": Const(120),
"result": LatticePointsRect(a=Ref(name='a'), b=Ref(name='b')),
"Q": Mod(value=Mul(Const(52170), Ref("result")), modulus=Const(84707)),
},
goal=Ref("Q"),
)
] | GEOM | null | COUNT | sympy | [] | geo_count_lattice_rect_v1 | null | 3 | 0 | null | null | 0.001 | 2026-02-08T06:06:26.726252Z | {
"verified": true,
"answer": 52680,
"timestamp": "2026-02-08T06:06:26.726878Z"
} | f44149 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 200,
"completion_tokens": 32768
},
"timestamp": "2026-02-24T05:26:30.051Z",
"answer": null
},
{
... | 1 | [] | {
"lo": -0.06,
"mid": 2.89,
"hi": 5.27
} | ||||
8b863e | algebra_poly_eval_v1_601307018_4123 | Let $f(x) = 3x^3 + x^2 + 4x - 5$. Define $R = f(a) \bmod 961$ for some integer $a$. Then define $S = f(R) \bmod 961$ and $T = f(S) \bmod d$, where $d = \min\{ |x - y| : x, y > 0,\ xy = 1864376 \}$. Let $K$ be the number of non-negative integers $a$ with $0 \leq a \leq 960$ such that $T = a$, $R \ne a$, and $S \ne a$. C... | 9,884 | graphs = [
Graph(
let={
"_c": Const(15),
"_m": Const(2),
"_n": CountOverSet(set=SolutionsSet(var=Var("a"), condition=And(Geq(Var("a"), Const(0)), Leq(Var("a"), Const(960)), Eq(Ref("_po_p3"), Var("a")), Neq(Ref("_po_p1"), Var("a")), Neq(Ref("_po_p2"), Var("a"))))),
... | ALG | null | COMPUTE | sympy | B3_DIFF | [
"B3_DIFF/POLY_ORBIT_HENSEL/SUM_ARITHMETIC"
] | 3713ec | algebra_poly_eval_v1 | null | 7 | 0 | [
"B3_DIFF",
"POLY_ORBIT_HENSEL",
"SUM_ARITHMETIC"
] | 3 | 0.014 | 2026-03-10T04:43:21.691760Z | {
"verified": true,
"answer": 9884,
"timestamp": "2026-03-10T04:43:21.705545Z"
} | 13efff | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 310,
"completion_tokens": 32768
},
"timestamp": "2026-03-29T11:07:59.891Z",
"answer": null
},
{
... | 1 | [
{
"lemma": "B3_DIFF",
"status": "ok"
},
{
"lemma": "POLY_ORBIT_HENSEL",
"status": "ok_later"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "SUM_ARITHMETIC",
"status": "ok_later"
}
] | {
"lo": 3.34,
"mid": 5.77,
"hi": 8.89
} | ||
249140 | alg_poly4_sum_v1_601307018_1648 | Find the remainder when $$\sum_{\substack{a=1 \\ b=1}}^{468} \left( 337 \cdot a^{\min\left\{ \left|\left\{ (a_2, b_2) : 1 \leq a_2, b_2 \leq 25,\ -189 a_2^3 = -189 \right\}\right| \cdot b_1^2 + 41 a_1^2 - 62 a_1 b_1 \ :\ 1 \leq a_1, b_1 \leq 11 \right\}} - 28a b^3 - 364 a^3 b + 150 a^2 b^2 + 2 b^4 \right)$$ is divided ... | 29,802 | graphs = [
Graph(
let={
"_m": Const(2),
"_n": Const(3),
"result": Mod(value=SumOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("a"), Var("b")]), condition=And(Geq(Var("a"), Const(1)), Leq(Var("a"), Const(468)), Geq(Var("b"), Const(1)), Leq(Var("b"), Const(... | ALG | null | COMPUTE | sympy | POLY3_COUNT | [
"POLY3_COUNT/QF_PSD_MIN"
] | 3d4951 | alg_poly4_sum_v1 | null | 7 | 0 | [
"POLY3_COUNT",
"QF_PSD_MIN"
] | 2 | 1.275 | 2026-03-10T02:23:45.500625Z | {
"verified": true,
"answer": 29802,
"timestamp": "2026-03-10T02:23:46.775518Z"
} | ee09f4 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 287,
"completion_tokens": 8779
},
"timestamp": "2026-03-29T02:57:48.279Z",
"answer": 53556
},
{
... | 1 | [
{
"lemma": "POLY3_COUNT",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "QF_PSD_MIN",
"status": "ok_later"
}
] | {
"lo": 3.99,
"mid": 6.11,
"hi": 9.15
} | ||
20c622 | geo_count_lattice_triangle_v1_655260480_3735 | Let $A$ be the area of the triangle with vertices at $(0, 0)$, $(169, 225)$, and $(256, 256)$, multiplied by $2$. Let $B$ be the sum of the number of lattice points on the boundary of this triangle, computed as follows: for each side from $(x_1, y_1)$ to $(x_2, y_2)$, the number of lattice points on that side (includin... | 7,040 | graphs = [
Graph(
let={
"_n": Const(256),
"area_2x": Abs(arg=Sum(Mul(Const(value=169), Ref(name='_n')), Mul(Const(value=256), Sub(left=Const(value=0), right=Const(value=225))))),
"boundary": Sum(GCD(a=Abs(arg=Const(value=169)), b=Abs(arg=Const(value=225))), GCD(a=Abs(arg=... | ALG | NT | COUNT | sympy | B1 | [
"B1"
] | 5b950e | geo_count_lattice_triangle_v1 | null | 5 | 0 | [
"B1"
] | 1 | 0.007 | 2026-02-08T17:31:11.835905Z | {
"verified": true,
"answer": 7040,
"timestamp": "2026-02-08T17:31:11.842506Z"
} | a3743a | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 249,
"completion_tokens": 1323
},
"timestamp": "2026-02-18T03:29:04.961Z",
"answer": 7040
},
{... | 1 | [
{
"lemma": "B1",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
c744d6 | comb_binomial_compute_v1_809748730_1149 | Let $n = 13$. Let $k$ be the largest prime number such that $2 \leq k \leq 9$. Define $\text{result} = \binom{n}{k}$. Let $c = 96574$. Compute the remainder when $c \cdot \text{result}$ is divided by $83119$. Determine the value of this remainder. | 64,817 | graphs = [
Graph(
let={
"n": Const(13),
"k": MaxOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(2)), Leq(Var("n"), Const(9)), IsPrime(Var("n"))))),
"result": Binom(n=Ref("n"), k=Ref("k")),
"_c": Const(96574),
"Q": Mod(value... | NT | null | COMPUTE | sympy | MAX_PRIME_BELOW | [
"MAX_PRIME_BELOW"
] | dc3ad3 | comb_binomial_compute_v1 | null | 2 | 0 | [
"MAX_PRIME_BELOW"
] | 1 | 0.002 | 2026-02-08T12:11:52.674027Z | {
"verified": true,
"answer": 64817,
"timestamp": "2026-02-08T12:11:52.675631Z"
} | a4cb55 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 123,
"completion_tokens": 1003
},
"timestamp": "2026-02-14T22:51:32.419Z",
"answer": 64817
},
... | 1 | [
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
}... | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
6459cc | nt_count_digit_sum_v1_458359167_546 | Let $s$ be the minimum value of $x + y$ over all ordered pairs $(x,y)$ of positive integers such that $xy = 144$. Let $N$ be the number of positive integers $n$ such that $1 \le n \le 448900$ and the sum of the decimal digits of $n$ is equal to $s$. Compute the value of $N$. | 26,970 | graphs = [
Graph(
let={
"_n": Const(144),
"upper": Const(448900),
"target_sum": 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... | NT | null | COUNT | sympy | B3 | [
"B3"
] | 0cd20d | nt_count_digit_sum_v1 | null | 5 | 0 | [
"B3"
] | 1 | 21.185 | 2026-02-08T03:24:15.083223Z | {
"verified": true,
"answer": 26970,
"timestamp": "2026-02-08T03:24:36.268569Z"
} | 12454e | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 193,
"completion_tokens": 4083
},
"timestamp": "2026-02-10T14:19:42.446Z",
"answer": 26070
},
{
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "V1",
"status": "no"
},
{
"lemma": "VAL_SUM_EQ",
"status": "no"
}
] | {
"lo": 1.71,
"mid": 5.04,
"hi": 8.38
} | ||
9d367b | comb_catalan_compute_v1_1918700295_562 | Let $m$ be the number of integers $t$ such that $16 \leq t \leq 66$ and there exist positive integers $a$ and $b$ with $1 \leq a \leq 11$, $1 \leq b \leq 2$, and $t = 4a + 10b + 2$. Let $n$ be the number of ordered pairs $(x_1, x_2)$ of positive odd integers such that $x_1 + x_2 = m$. Let $k$ be the number of ordered p... | 16,796 | graphs = [
Graph(
let={
"_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=11)), Geq(left=Var(name='b'), right=Const(value... | COMB | null | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM/COMB1/COUNT_SUM_EQUALS"
] | eb862e | comb_catalan_compute_v1 | null | 6 | 0 | [
"COMB1",
"COUNT_SUM_EQUALS",
"LIN_FORM"
] | 3 | 0.022 | 2026-02-08T03:18:56.861735Z | {
"verified": true,
"answer": 16796,
"timestamp": "2026-02-08T03:18:56.883625Z"
} | 86ebce | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 285,
"completion_tokens": 2513
},
"timestamp": "2026-02-10T13:55:28.940Z",
"answer": 16796
},
{
"... | 1 | [
{
"lemma": "COMB1",
"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": "ok_later"
},
{
... | {
"lo": -3.83,
"mid": -1.68,
"hi": 1.09
} | ||
e58f28 | nt_count_divisible_v1_2051736721_4306 | Let $n = 86789$. Define $d$ to be the largest prime number between $2$ and $12$, inclusive. Let $r$ be the number of positive integers $n_1$ such that $1 \leq n_1 \leq 78400$ and $n_1$ is divisible by $d$. Let $m$ be the smallest divisor of $347633$ that is at least $2$. Compute the remainder when the Bell number $B_{r... | 29,186 | graphs = [
Graph(
let={
"_n": Const(86789),
"upper": Const(78400),
"divisor": MaxOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(2)), Leq(Var("n"), Const(12)), IsPrime(Var("n"))))),
"result": CountOverSet(set=SolutionsSet(var=Var("n1")... | NT | COMB | COUNT | sympy | MIN_PRIME_FACTOR | [
"MIN_PRIME_FACTOR",
"MAX_PRIME_BELOW"
] | d2be59 | nt_count_divisible_v1 | bell_mod | 5 | 0 | [
"MAX_PRIME_BELOW",
"MIN_PRIME_FACTOR"
] | 2 | 2.538 | 2026-02-08T17:53:30.914607Z | {
"verified": true,
"answer": 29186,
"timestamp": "2026-02-08T17:53:33.452843Z"
} | d9ae9a | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 159,
"completion_tokens": 965
},
"timestamp": "2026-02-18T10:02:51.702Z",
"answer": 29186
},
{... | 1 | [
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "MIN_PRIME_FACTOR",
"status": "ok... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
c7cb0f | comb_sum_binomial_row_v1_1125832087_982 | Let $p_{\max}$ be the largest prime number not exceeding $11$. Let $d_{\min}$ be the smallest divisor of $150$ that is at least $2$. Let $q_{\max}$ be the largest prime number $q$ such that $d_{\min} \leq q \leq p_{\max}$. Compute the remainder when $91360 \cdot 2^{q_{\max}}$ is divided by $51487$. | 1,522 | graphs = [
Graph(
let={
"_c": Const(2),
"_m": Const(51487),
"_n": MaxOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(2)), Leq(Var("n"), Const(11)), IsPrime(Var("n"))))),
"n": MaxOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(... | NT | null | SUM | sympy | MIN_PRIME_FACTOR | [
"MIN_PRIME_FACTOR/MAX_PRIME_BELOW",
"MAX_PRIME_BELOW/MAX_PRIME_BELOW"
] | f15075 | comb_sum_binomial_row_v1 | null | 4 | 0 | [
"MAX_PRIME_BELOW",
"MIN_PRIME_FACTOR"
] | 2 | 0.003 | 2026-02-08T03:24:14.534331Z | {
"verified": true,
"answer": 1522,
"timestamp": "2026-02-08T03:24:14.537124Z"
} | 928f07 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 205,
"completion_tokens": 1098
},
"timestamp": "2026-02-10T14:28:02.958Z",
"answer": 1522
},
{
"i... | 1 | [
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok"
},
{
"lemma": "MIN_PRIME_FACTOR",
"statu... | {
"lo": -3.53,
"mid": 1.02,
"hi": 5.49
} | ||
016f12 | alg_qf_psd_min_v1_1419126231_1857 | Find the minimum value of $-18ab - 48ac + 18ad + 69a^2 + 150d^2 + 129b^2 + 138cd + 222bd + 126c^2$ over all ordered quadruples $(a, b, c, d)$ of positive integers such that $1 \le a \le 14$, $1 \le c \le 14$, $1 \le d \le 14$, and $1 \le b \le \left|\{ (a_1, b_1) : a_1, b_1 \in \mathbb{Z}^+, 1 \le a_1, b_1 \le 35,\ -8a... | 786 | graphs = [
Graph(
let={
"_n": Const(16),
"result": MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("a"), Var("b"), Var("c"), Var("d")]), condition=And(Geq(Var("a"), Const(1)), Leq(Var("a"), Const(14)), Geq(Var("b"), Const(1)), Leq(Var("b"), CountOverSet(set=Solutio... | ALG | null | COMPUTE | sympy | QF_PSD_COUNT | [
"QF_PSD_COUNT"
] | 09ce67 | alg_qf_psd_min_v1 | null | 6 | 0 | [
"QF_PSD_COUNT"
] | 1 | 0.443 | 2026-02-25T11:24:23.110340Z | {
"verified": true,
"answer": 786,
"timestamp": "2026-02-25T11:24:23.553815Z"
} | 8b0688 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 294,
"completion_tokens": 32768
},
"timestamp": "2026-03-30T14:25:37.322Z",
"answer": null
},
{
... | 1 | [
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "QF_PSD_COUNT",
"status": "ok"
}
] | {
"lo": 1.5,
"mid": 4.69,
"hi": 7.23
} | ||
43483e | nt_min_coprime_above_v1_1439011603_1628 | Let $S$ be the set of all ordered pairs $(x, y)$ of positive integers such that $xy = 24649$. Let $T$ be the set of all values $x + y$ as $(x, y)$ ranges over $S$. Let $m$ be the minimum element of $T$. Let $A$ be the set of all positive integers $n$ such that $1 \leq n \leq m$ and $n$ is divisible by $157$. Let $M$ be... | 34,970 | graphs = [
Graph(
let={
"_n": Const(157),
"start": Const(34969),
"upper": Const(35450),
"modulus": SumOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var... | NT | null | EXTREMUM | sympy | B3 | [
"B3/SUM_DIVISIBLE"
] | 138b1a | nt_min_coprime_above_v1 | null | 6 | 0 | [
"B3",
"SUM_DIVISIBLE"
] | 2 | 0.077 | 2026-02-08T16:11:44.090018Z | {
"verified": true,
"answer": 34970,
"timestamp": "2026-02-08T16:11:44.166533Z"
} | d2a02e | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 208,
"completion_tokens": 1317
},
"timestamp": "2026-02-16T22:53:29.043Z",
"answer": 34970
},
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "SUM_DIVISIBLE",
"status": "ok_later"
},
{... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
e9bb90 | nt_min_with_divisor_count_v1_1353956133_458 | Let $S$ be the set of all ordered pairs $(x,y)$ of positive integers such that $x + y = 94$. Define $u$ to be the maximum value of $xy$ as $(x,y)$ ranges over $S$. Let $d = 9$. Compute the smallest positive integer $n \leq u$ that has exactly $d$ positive divisors. Let this integer be $m$. Find the remainder when $4412... | 75,316 | 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(94)))), expr=Mul(Var("x"), Var("y")))),
"div_count": Con... | NT | null | EXTREMUM | sympy | B1 | [
"B1"
] | 5b950e | nt_min_with_divisor_count_v1 | null | 4 | 0 | [
"B1"
] | 1 | 0.09 | 2026-02-08T11:27:27.719578Z | {
"verified": true,
"answer": 75316,
"timestamp": "2026-02-08T11:27:27.809920Z"
} | 763774 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 150,
"completion_tokens": 1321
},
"timestamp": "2026-02-14T14:44:48.611Z",
"answer": 75316
},
... | 1 | [
{
"lemma": "B1",
"status": "ok"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
}
] | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
b1041c | nt_sum_totient_over_divisors_v1_1470522791_539 | Let $n$ be the sum of $\phi(d)$ over all positive divisors $d$ of $6471$. Let $m$ be the sum of $\phi(d)$ over all positive divisors $d$ of $n$. Compute $m$. | 6,471 | graphs = [
Graph(
let={
"_n": Const(6471),
"n": SumOverDivisors(n=Ref(name='_n'), var='d', expr=EulerPhi(n=Var(name='d'))),
"result": SumOverDivisors(n=Ref(name='n'), var='d', expr=EulerPhi(n=Var(name='d'))),
"Q": Ref("result"),
},
goal=Ref("Q"... | NT | null | COMPUTE | sympy | K3 | [
"K3"
] | 54c41e | nt_sum_totient_over_divisors_v1 | null | 3 | 0 | [
"K3"
] | 1 | 0.005 | 2026-02-08T13:04:32.136121Z | {
"verified": true,
"answer": 6471,
"timestamp": "2026-02-08T13:04:32.141069Z"
} | 9ded3a | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 98,
"completion_tokens": 1365
},
"timestamp": "2026-02-15T08:49:38.350Z",
"answer": 6471
},
{
... | 1 | [
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "K3",
"status": "ok"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
}
] | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
0c5dd4 | nt_sum_divisors_range_v1_151522320_1588 | Let $p$ and $q$ be positive integers such that $pq = 18$, $\gcd(p, q) = 1$, and $p < q$. Let $n_0$ be the number of such integers $p$. Let $S$ be the set of all primes $n$ satisfying $n \geq n_0$ and
$$
n \leq \left| \left\{ t \in \mathbb{Z}^+ : 8 \leq t \leq 5136 \text{ and } t = 5a + 3b \text{ for some } a, b \in \m... | 44,507 | graphs = [
Graph(
let={
"_n": CountOverSet(set=SolutionsSet(var=Var("p"), condition=And(IsPositive(arg=Var(name='p')), Exists(var=Var(name='q'), condition=And(Eq(left=Mul(Var(name='p'), Var(name='q')), right=Const(value=18)), Eq(left=GCD(a=Var(name='p'), b=Var(name='q')), right=Const(value=1)), ... | NT | null | SUM | sympy | COPRIME_PAIRS | [
"COPRIME_PAIRS/MAX_PRIME_BELOW",
"LIN_FORM/MAX_PRIME_BELOW"
] | d6bd1c | nt_sum_divisors_range_v1 | null | 6 | 0 | [
"COPRIME_PAIRS",
"LIN_FORM",
"MAX_PRIME_BELOW"
] | 3 | 0.76 | 2026-02-08T04:07:02.077146Z | {
"verified": true,
"answer": 44507,
"timestamp": "2026-02-08T04:07:02.836830Z"
} | 9f9484 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 326,
"completion_tokens": 5819
},
"timestamp": "2026-02-10T15:21:12.025Z",
"answer": 44507
},
{
... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok_later"
}... | {
"lo": -3.49,
"mid": 1.84,
"hi": 7.55
} | ||
df8587_n | comb_binomial_compute_v1_292587783_2 | A game designer assigns points to character pairs $(a, b)$, where $a$ and $b$ are integers from 1 to 5 representing strength and agility. The score for a pair is $-50ab + p a^2 + 34b^2$, with $p$ the largest prime at most 29. Let $n$ be the minimum achievable score. A reward is unlocked if exactly 6 items are chosen fr... | 1,716 | COMB | null | COMPUTE | sympy | MAX_PRIME_BELOW | [
"MAX_PRIME_BELOW/QF_PSD_MIN"
] | db757a | comb_binomial_compute_v1 | null | 6 | null | [
"MAX_PRIME_BELOW",
"QF_PSD_MIN"
] | 2 | 0.003 | 2026-02-25T01:35:03.980383Z | null | aeb4b1 | df8587 | narrative | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 232,
"completion_tokens": 1716
},
"timestamp": "2026-03-30T14:36:37.368Z",
"answer": 1716
},
{
"i... | 1 | [
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "QF_PSD_MIN",
"status": "ok_... | {
"lo": -5.37,
"mid": 0.23,
"hi": 5.22
} | |
6ec1f0 | antilemma_k2_v1_784195855_7607 | Let $m = 2$, and let $n$ be the sum of all real solutions $x$ to the equation $x^2 - 389x + 16660 = 0$. Compute
$$
\sum_{k=1}^{389} \phi(k) \left\lfloor \frac{n}{k} \right\rfloor,
$$
where $\phi(k)$ denotes the number of positive integers at most $k$ that are relatively prime to $k$. | 75,855 | graphs = [
Graph(
let={
"_m": Const(2),
"_n": SumOverSet(set=SolutionsSet(var=Var("x"), condition=Eq(Sum(Pow(Var("x"), Ref("_m")), Mul(Const(-389), Var("x")), Const(16660)), Const(0)))),
"x": Summation(var="k", start=Const(1), end=Const(389), expr=Mul(EulerPhi(n=Var("k"))... | NT | COMB | COMPUTE | sympy | VIETA_SUM | [
"VIETA_SUM/K2",
"K2"
] | 6be084 | antilemma_k2_v1 | null | 4 | 0 | [
"K2",
"VIETA_SUM"
] | 2 | 0.001 | 2026-02-08T09:25:03.259597Z | {
"verified": true,
"answer": 75855,
"timestamp": "2026-02-08T09:25:03.260967Z"
} | 13f8f6 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 143,
"completion_tokens": 763
},
"timestamp": "2026-02-14T03:48:04.756Z",
"answer": 75855
},
{... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "K2",
"status": "ok"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "VI... | {
"lo": -5.49,
"mid": 0.22,
"hi": 6.51
} | ||
413aed | diophantine_fbi2_min_v1_784195855_6574 | Let $j$ be a positive integer such that $1 \leq j \leq 84$ and
$$
j^\left( \sum_{k=1}^{2} \varphi(k) \left\lfloor \frac{2}{k} \right\rfloor \right) \leq 592704.
$$
Let $k$ be the number of such integers $j$. Let $d$ be the smallest integer such that $6 \leq d \leq 94$, $d$ divides $k$, and $\frac{k}{d} \geq 3$. Determi... | 6 | graphs = [
Graph(
let={
"k": CountOverSet(set=SolutionsSet(var=Var("j"), condition=And(Geq(Var("j"), Const(1)), Leq(Var("j"), Const(84)), Leq(Pow(Var("j"), Summation(var="k", start=Const(1), end=Const(2), expr=Mul(EulerPhi(n=Var("k")), Floor(Div(Const(2), Var("k")))))), Const(592704))), domain='... | NT | null | EXTREMUM | sympy | K2 | [
"K2/C3"
] | 2f11e4 | diophantine_fbi2_min_v1 | null | 6 | 0 | [
"C3",
"K2"
] | 2 | 0.008 | 2026-02-08T08:44:14.309537Z | {
"verified": true,
"answer": 6,
"timestamp": "2026-02-08T08:44:14.317116Z"
} | c8e6b5 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 171,
"completion_tokens": 990
},
"timestamp": "2026-02-13T21:02:05.910Z",
"answer": 6
},
{
... | 1 | [
{
"lemma": "C3",
"status": "ok_later"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K2",
"status": "ok"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
... | {
"lo": -8.32,
"mid": -5.11,
"hi": -2.37
} | ||
8c29d0 | nt_min_phi_inverse_v1_784195855_6702 | Let $n$ be a positive integer such that $1 \leq n \leq 20$. Define $k = \sum_{i=1}^{3} \phi(i) \left\lfloor \frac{3}{i} \right\rfloor$, where $\phi$ denotes Euler's totient function. Determine the value of $n$ for which $\phi(n) = k$, assuming such an $n$ exists and is unique. | 7 | graphs = [
Graph(
let={
"_n": Const(3),
"upper": Const(20),
"k": Summation(var="k", start=Const(1), end=Const(3), expr=Mul(EulerPhi(n=Var("k")), Floor(Div(Ref("_n"), Var("k"))))),
"result": MinOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), ... | NT | null | EXTREMUM | sympy | C4 | [
"K2"
] | 6897ab | nt_min_phi_inverse_v1 | null | 6 | 0 | [
"C4",
"K2"
] | 2 | 0.059 | 2026-02-08T08:48:53.279759Z | {
"verified": true,
"answer": 7,
"timestamp": "2026-02-08T08:48:53.338692Z"
} | 15ee0f | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 1,
"correct": {
"strict": false,
"boxed": false,
"relaxed": true
},
"usage": {
"prompt_tokens": 137,
"completion_tokens": 3478
},
"timestamp": "2026-02-13T21:56:12.390Z",
"answer": 1
},
{
... | 1 | [
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "K2",
"status": "ok"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
}
] | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
847b88 | comb_binomial_compute_v1_601307018_10136 | Find the number of positive integers $t$ with $10 \le t \le 36$ that can be expressed as $t = 6a + 4b$ for some integers $a, b$ satisfying $1 \le a \le 2$ and $1 \le b \le 6$. Let $n$ denote this count, and let $R = \binom{n}{6}$. Compute the remainder when $91346 \cdot R$ is divided by $84901$. | 12,110 | graphs = [
Graph(
let={
"_n": Const(84901),
"n": CountOverSet(set=SolutionsSet(var=Var("t"), condition=Exists(var=Var(name='a'), condition=Exists(var=Var(name='b'), condition=And(Geq(left=Var(name='a'), right=Const(value=1)), Leq(left=Var(name='a'), right=Const(value=2)), Geq(left=Va... | COMB | null | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | comb_binomial_compute_v1 | null | 3 | 0 | [
"LIN_FORM"
] | 1 | 0.003 | 2026-03-10T10:36:37.088400Z | {
"verified": true,
"answer": 12110,
"timestamp": "2026-03-10T10:36:37.090964Z"
} | b27d86 | 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": 845
},
"timestamp": "2026-04-19T13:05:50.636Z",
"answer": 12110
},
{
"... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "V8",
"sta... | {
"lo": -5.34,
"mid": 1.1,
"hi": 7.53
} | ||
b31e40 | algebra_quadratic_discriminant_v1_971394319_1230 | Let $a = 2$ and $b = -1$. Define $c$ to be the sum $\sum_{k=1}^{4} k$. Let $\Delta = b^2 - 4ac$. Compute the remainder when $41874 \cdot \Delta$ is divided by $54973$. | 45,307 | graphs = [
Graph(
let={
"a": Const(2),
"b": Const(-1),
"c": Summation(var="k", start=Const(1), end=Const(4), expr=Var("k")),
"result": Sub(Pow(Ref("b"), Const(2)), Mul(Const(4), Ref("a"), Ref("c"))),
"Q": Mod(value=Mul(Const(41874), Ref("result")),... | NT | null | COMPUTE | sympy | SUM_ARITHMETIC | [
"SUM_ARITHMETIC"
] | eb34f0 | algebra_quadratic_discriminant_v1 | null | 2 | 0 | [
"SUM_ARITHMETIC"
] | 1 | 0.001 | 2026-02-08T13:32:13.017020Z | {
"verified": true,
"answer": 45307,
"timestamp": "2026-02-08T13:32:13.017998Z"
} | 625856 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 111,
"completion_tokens": 539
},
"timestamp": "2026-02-15T17:46:54.259Z",
"answer": 45307
},
{... | 1 | [
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "SUM_ARITHMETIC",
"status": "ok"
},
{
"lemma": "V1",
"status":... | {
"lo": -5.49,
"mid": 0.22,
"hi": 6.51
} | ||
8803f8 | nt_count_coprime_and_v1_1470522791_998 | Let $n$ be a positive integer such that $1 \leq n \leq 69806$, $\gcd(n, 8) = 1$, and $\gcd(n, 15) = 1$. Compute the number of such integers $n$. Let $Q$ be the remainder when $54701$ times this count is divided by $67783$. Find the value of $Q$. | 22,889 | graphs = [
Graph(
let={
"upper": Const(69806),
"k1": Const(8),
"k2": Summation(var="k", start=Const(1), end=Const(5), expr=Var("k")),
"result": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Ref("upper")), Eq(G... | NT | null | COUNT | sympy | SUM_ARITHMETIC | [
"SUM_ARITHMETIC"
] | eb34f0 | nt_count_coprime_and_v1 | null | 4 | 0 | [
"SUM_ARITHMETIC"
] | 1 | 10.947 | 2026-02-08T13:22:11.096683Z | {
"verified": true,
"answer": 22889,
"timestamp": "2026-02-08T13:22:22.043345Z"
} | 9f7da4 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 129,
"completion_tokens": 2066
},
"timestamp": "2026-02-15T14:03:59.386Z",
"answer": 22889
},
... | 1 | [
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "SUM_ARITHMETIC",
"status": "ok"
},
{
"lemma": "V8",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
}
] | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
184d81 | comb_sum_binomial_row_v1_1116507919_382 | Let $ n = \sum_{k=1}^{5} \phi(k) \left\lfloor \frac{5}{k} \right\rfloor $, where $ \phi $ denotes Euler's totient function. Compute $ 2^n $. | 32,768 | graphs = [
Graph(
let={
"_n": Const(5),
"n": Summation(var="k", start=Const(1), end=Ref("_n"), expr=Mul(EulerPhi(n=Var("k")), Floor(Div(Const(5), Var("k"))))),
"result": Pow(Const(2), Ref("n")),
},
goal=Ref("result"),
)
] | NT | null | SUM | sympy | SUM_ARITHMETIC | [
"K2"
] | 6897ab | comb_sum_binomial_row_v1 | null | 4 | 0 | [
"K2",
"SUM_ARITHMETIC"
] | 2 | 0.006 | 2026-02-08T02:33:07.882251Z | {
"verified": true,
"answer": 32768,
"timestamp": "2026-02-08T02:33:07.888556Z"
} | 266e3c | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 168,
"completion_tokens": 610
},
"timestamp": "2026-02-08T19:27:57.223Z",
"answer": 32768
},
{
"i... | 2 | [
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "K2",
"status": "ok"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "V3",
"status": "no"
}
] | {
"lo": -10,
"mid": -8.03,
"hi": -6.06
} | ||
53c92f | nt_max_prime_below_v1_1080341949_306 | Let $S_1$ be the set of integers $n$ such that $1 \le n \le 10$ and $n \equiv \left\lfloor \frac{n}{2} \right\rfloor \pmod{5}$. Let $k = |S_1|$. Let $S_2$ be the set of integers $n$ such that $1 \le n \le 5$ and the sum of the digits of $n$ is divisible by $k$. Let $L = |S_2|$. Find the largest prime number $n$ such th... | 38,803 | graphs = [
Graph(
let={
"upper": Const(38809),
"result": MaxOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Const(5)), Eq(Mod(value=DigitSum(Var("n")), modulus=CountOve... | NT | null | EXTREMUM | sympy | L3C | [
"L3C/L3B"
] | 88e2a6 | nt_max_prime_below_v1 | null | 6 | 0 | [
"L3B",
"L3C"
] | 2 | 1.031 | 2026-02-08T13:25:02.222661Z | {
"verified": true,
"answer": 38803,
"timestamp": "2026-02-08T13:25:03.253313Z"
} | 6b4ef7 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 181,
"completion_tokens": 4210
},
"timestamp": "2026-02-15T14:51:35.974Z",
"answer": 38803
},
... | 1 | [
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "L3B",
"status": "ok_later"
},
{
"lemma": "L3C",
"status": "ok"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
... | {
"lo": -5.49,
"mid": 0.22,
"hi": 6.51
} | ||
fefca6 | antilemma_k2_v1_655260480_3139 | Let
$$
x = \sum_{k=1}^{399} \phi(k) \left\lfloor \frac{399}{k} \right\rfloor,
$$
where $\phi$ denotes Euler's totient function. Compute the value of
$$
x + \left(2^{(x \bmod 14)} \bmod 96563\right).$$ | 79,801 | graphs = [
Graph(
let={
"x": Summation(var="k", start=Const(1), end=Const(399), expr=Mul(EulerPhi(n=Var("k")), Floor(Div(Const(399), Var("k"))))),
"Q": Sum(Ref("x"), Mod(value=Pow(Const(2), Mod(value=Ref("x"), modulus=Const(14))), modulus=Const(96563))),
},
goal=Ref("... | NT | COMB | COMPUTE | sympy | K2 | [
"K2"
] | 6897ab | antilemma_k2_v1 | null | 6 | 0 | [
"K2"
] | 1 | 0.001 | 2026-02-08T17:12:10.650225Z | {
"verified": true,
"answer": 79801,
"timestamp": "2026-02-08T17:12:10.650811Z"
} | b73fc4 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 121,
"completion_tokens": 904
},
"timestamp": "2026-02-17T21:06:54.324Z",
"answer": 79801
},
{... | 1 | [
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K2",
"status": "ok"
},
{
"lemma": "V8_SUM",
"status": "no"
},
{
"lemma": "VAL_SUM_EQ",
"status": ... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
62ede3 | algebra_quadratic_discriminant_v1_1218484723_231 | Let $D = -9^2 - 4(-7)\cdot 7$. Define $R = 2$ if $D > 0$, $R = 1$ if $D = 0$, and $R = 0$ otherwise. Compute $$ R^2 + \left| \left\{ (a_1, b_1) : 1 \leq a_1 \leq 40,\ 1 \leq b_1 \leq \left| \left\{ (a_2, b_2) : 1 \leq a_2, b_2 \leq 40,\ 17 b_2^4 = 17 \right\} \right|,\ -189 a_1^3 = -1512 \right\} \right| \cdot R + 25. ... | 109 | graphs = [
Graph(
let={
"_m": Const(17),
"_n": Const(3),
"a": Const(-7),
"b": Const(-9),
"c": Const(7),
"D": Sub(Pow(Ref("b"), Const(2)), Mul(Const(4), Ref("a"), Ref("c"))),
"result": Sum(Mul(Const(2), Iverson(condition=Gt(R... | ALG | null | COMPUTE | sympy | LIN_FORM | [
"POLY4_COUNT/POLY3_COUNT"
] | d92d74 | algebra_quadratic_discriminant_v1 | quadratic_mod | 5 | 0 | [
"LIN_FORM",
"POLY3_COUNT",
"POLY4_COUNT"
] | 3 | 0.424 | 2026-02-25T01:55:10.259238Z | {
"verified": true,
"answer": 109,
"timestamp": "2026-02-25T01:55:10.682761Z"
} | 21d2e0 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 293,
"completion_tokens": 1363
},
"timestamp": "2026-03-10T09:04:37.124Z",
"answer": 109
},
{
"id... | 1 | [
{
"lemma": "POLY3_COUNT",
"status": "ok_later"
},
{
"lemma": "POLY4_COUNT",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
}
] | {
"lo": -2.78,
"mid": -0.24,
"hi": 2.7
} | ||
d22c4b_n | comb_count_derangements_v1_601307018_122 | Seven friends each bring a gift to a party and place them in a pile. After a game, they redistribute the gifts so that no one receives their own. In how many ways can this happen? Let $M$ be that number. Compute the remainder when $1471 \cdot M$ is divided by $59604$. | 45,054 | COMB | null | COUNT | sympy | LIN_FORM | [
"LIN_FORM",
"POLY_ORBIT_LEGENDRE"
] | db0012 | comb_count_derangements_v1 | affine_mod | 3 | null | [
"LIN_FORM",
"POLY_ORBIT_LEGENDRE"
] | 2 | 0.006 | 2026-03-10T00:46:01.395523Z | null | ac0b0d | d22c4b | narrative | 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": 1406
},
"timestamp": "2026-03-29T13:51:51.733Z",
"answer": 45054
},
{
"... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "POLY_ORBIT_LEGE... | {
"lo": -5.36,
"mid": 0.27,
"hi": 5.45
} | |
c4e890 | nt_num_divisors_compute_v1_865884756_5289 | Let $n$ be the sum of all real solutions $x$ to the equation $x^2 - 1680x - 133456 = 0$. Let $r$ be the number of positive divisors of $n$. Compute the remainder when $95869 \cdot r$ is divided by $75390$. | 65,260 | graphs = [
Graph(
let={
"_n": Const(75390),
"n": SumOverSet(set=SolutionsSet(var=Var("x"), condition=Eq(Sum(Pow(Var("x"), Const(2)), Mul(Const(-1680), Var("x")), Const(-133456)), Const(0)))),
"result": NumDivisors(n=Ref("n")),
"_c": Const(95869),
"... | NT | null | COMPUTE | sympy | VIETA_SUM | [
"VIETA_SUM"
] | b33a7a | nt_num_divisors_compute_v1 | null | 4 | 0 | [
"VIETA_SUM"
] | 1 | 0.002 | 2026-02-08T18:30:24.872721Z | {
"verified": true,
"answer": 65260,
"timestamp": "2026-02-08T18:30:24.874258Z"
} | 1b516d | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 113,
"completion_tokens": 980
},
"timestamp": "2026-02-18T17:45:54.523Z",
"answer": 65260
},
{... | 1 | [
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
},
{
"lemma": "VIETA_SUM",
"status": "ok"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
996e81 | sequence_count_fib_divisible_v1_1978505735_7063 | Let $T$ be the set of all positive integers $t$ such that $11 \le t \le 333$ and there exist positive integers $a$, $b$ with $1 \le a \le 33$, $1 \le b \le 87$, and $t = 2a + 3b + 6$. Let $u$ be the number of elements in $T$. Let $r$ be the number of positive integers $n$ with $1 \le n \le u$ such that $20$ divides the... | 6,859 | graphs = [
Graph(
let={
"upper": CountOverSet(set=SolutionsSet(var=Var("t"), condition=Exists(var=Var(name='a'), condition=Exists(var=Var(name='b'), condition=And(Geq(left=Var(name='a'), right=Const(value=1)), Leq(left=Var(name='a'), right=Const(value=33)), Geq(left=Var(name='b'), right=Const(va... | NT | null | COUNT | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | sequence_count_fib_divisible_v1 | null | 5 | 0 | [
"LIN_FORM"
] | 1 | 0.064 | 2026-02-08T20:02:11.418241Z | {
"verified": true,
"answer": 6859,
"timestamp": "2026-02-08T20:02:11.481921Z"
} | 42c84b | 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": 7145
},
"timestamp": "2026-02-18T23:50:48.344Z",
"answer": 6859
},
{... | 1 | [
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "V1",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
fd036d | nt_max_prime_below_v1_124444284_1979 | Let $S$ be the set of all positive integers $p$ for which there exists a positive integer $q > p$ such that $pq = 36$ and $\gcd(p, q) = 1$. Let $L$ be the number of elements in $S$. Determine the largest prime number $n$ such that $L \leq n \leq 60516$. | 60,509 | graphs = [
Graph(
let={
"upper": Const(60516),
"result": MaxOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), CountOverSet(set=SolutionsSet(var=Var("p"), condition=And(IsPositive(arg=Var(name='p')), Exists(var=Var(name='q'), condition=And(Eq(left=Mul(Var(name='p'), V... | NT | null | EXTREMUM | sympy | COPRIME_PAIRS | [
"COPRIME_PAIRS"
] | 2bb3aa | nt_max_prime_below_v1 | null | 4 | 0 | [
"COPRIME_PAIRS"
] | 1 | 1.412 | 2026-02-08T04:14:01.215022Z | {
"verified": true,
"answer": 60509,
"timestamp": "2026-02-08T04:14:02.626948Z"
} | 000793 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 192,
"completion_tokens": 7806
},
"timestamp": "2026-02-10T15:58:12.103Z",
"answer": 60509
},
{
... | 1 | [
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "n... | {
"lo": -3.42,
"mid": 1.86,
"hi": 7.55
} | ||
725ddc | nt_sum_divisors_compute_v1_1918700295_3059 | Let $m$ be the maximum value of $xy$ over all pairs of positive integers $(x, y)$ such that $x + y = 32$. Let $n = 30976$ and let $\sigma(n)$ denote the sum of the positive divisors of $n$. Let $s$ be the minimum value of $x + y$ over all pairs of positive integers $(x, y)$ such that $xy = m$. Let $p$ be the maximum va... | 55,932 | graphs = [
Graph(
let={
"_m": MaxOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(Sum(Var("x"), Var("y")), Const(32)))), expr=Mul(Var("x"), Var("y")))),
"_n": Const(75763),... | NT | null | COMPUTE | sympy | B1 | [
"B1/B1/B3",
"B1"
] | 2a5778 | nt_sum_divisors_compute_v1 | quadratic_mod | 4 | 0 | [
"B1",
"B3"
] | 2 | 0.004 | 2026-02-08T08:22:17.676107Z | {
"verified": true,
"answer": 55932,
"timestamp": "2026-02-08T08:22:17.680412Z"
} | a3ac00 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 197,
"completion_tokens": 1574
},
"timestamp": "2026-02-13T17:50:09.979Z",
"answer": 55932
},
... | 1 | [
{
"lemma": "B1",
"status": "ok"
},
{
"lemma": "B3",
"status": "ok_later"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": ... | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
e1a435 | diophantine_sum_product_min_v1_1125832087_2287 | Let $S$ be the number of positive integers $j \leq 54$ such that $j^4 \leq 8503056$. Let $P$ be the minimum value of $x + y$ over all pairs of positive integers $(x, y)$ such that $xy = 132496$. Determine the value of the smallest positive integer $x \leq 53$ such that $x(S - x) = P$. | 26 | graphs = [
Graph(
let={
"_n": Const(53),
"S": CountOverSet(set=SolutionsSet(var=Var("j"), condition=And(Geq(Var("j"), Const(1)), Leq(Var("j"), Const(54)), Leq(Pow(Var("j"), Const(4)), Const(8503056))), domain='positive_integers')),
"P": MinOverSet(set=MapOverSet(set=Solut... | NT | null | EXTREMUM | sympy | MOBIUS_COPRIME | [
"B3",
"C3"
] | 5d1796 | diophantine_sum_product_min_v1 | null | 7 | 0 | [
"B3",
"C3",
"MOBIUS_COPRIME"
] | 3 | 0.029 | 2026-02-08T04:30:02.917951Z | {
"verified": true,
"answer": 26,
"timestamp": "2026-02-08T04:30:02.946619Z"
} | 22739c | 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": 1246
},
"timestamp": "2026-02-10T16:47:21.504Z",
"answer": 26
},
{
"id... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "C3",
"status": "ok"
},
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
... | {
"lo": -5.13,
"mid": 0.83,
"hi": 7.52
} | ||
8a7057 | comb_sum_binomial_row_v1_601307018_11385 | Find the number of ordered pairs $(a, b)$ of positive integers with $1 \le a \le 15$ and $1 \le b \le 15$ such that $16 \cdot b^{2} = 784$. Let $n$ be this number. Compute $2^n$. | 32,768 | graphs = [
Graph(
let={
"_n": Const(2),
"n": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("a"), Var("b")]), condition=And(Geq(Var("a"), Const(1)), Leq(Var("a"), Const(15)), Geq(Var("b"), Const(1)), Leq(Var("b"), Const(15)), Eq(Mul(Const(16), Pow(Var("b"), Ref("_n"))), Const(... | COMB | null | SUM | sympy | QF_PSD_COUNT | [
"QF_PSD_COUNT"
] | 09ce67 | comb_sum_binomial_row_v1 | null | 3 | 0 | [
"QF_PSD_COUNT"
] | 1 | 0.001 | 2026-03-10T11:49:53.460437Z | {
"verified": true,
"answer": 32768,
"timestamp": "2026-03-10T11:49:53.461929Z"
} | 339da0 | CC BY 4.0 | [
{
"id": 36,
"model": "qwen2.5:3b-32k",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 124,
"completion_tokens": 546
},
"timestamp": "2026-04-23T00:28:51.934Z",
"answer": 32768
}
] | 2 | [
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "QF_PSD_COUNT",
"status": "ok"
},
{
"lemm... | {
"lo": -10,
"mid": -5.89,
"hi": -1.79
} | ||
abbd0e | nt_count_intersection_v1_2051736721_982 | Let $a$ be the largest prime number not exceeding 12. Let $N = 50000$ and $b = 15$. Let $S$ be the set of all positive integers $n_1$ such that $1 \leq n_1 \leq N$, $a$ divides $n_1$, and $\gcd(n_1, b) = 1$. Let $R$ be the number of elements in $S$. Compute the remainder when $68893 \cdot R$ is divided by $53441$. | 46,948 | graphs = [
Graph(
let={
"N": Const(50000),
"a": MaxOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(2)), Leq(Var("n"), Const(12)), IsPrime(Var("n"))))),
"b": Const(15),
"result": CountOverSet(set=SolutionsSet(var=Var("n1"), condition=An... | NT | null | COUNT | sympy | MAX_PRIME_BELOW | [
"MAX_PRIME_BELOW"
] | dc3ad3 | nt_count_intersection_v1 | null | 5 | 0 | [
"MAX_PRIME_BELOW"
] | 1 | 1.787 | 2026-02-08T15:46:40.684255Z | {
"verified": true,
"answer": 46948,
"timestamp": "2026-02-08T15:46:42.471540Z"
} | 6e3672 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 158,
"completion_tokens": 1119
},
"timestamp": "2026-02-16T13:44:13.400Z",
"answer": 46948
},
... | 1 | [
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "VAL_SUM_EQ",
"status": "no"
... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
0a41b8 | nt_count_divisible_and_v1_784195855_6298 | Let $S$ be the set of all integers $t$ such that $9 \leq t \leq 8342$ and there exist positive integers $a$ and $b$ with $1 \leq a \leq 2960$, $1 \leq b \leq 346$, and $t = 2a + 7b$. Let $N$ be the number of elements in $S$. Compute the number of positive integers $n$ such that $1 \leq n \leq N$, $n$ is divisible by 8,... | 347 | graphs = [
Graph(
let={
"upper": CountOverSet(set=SolutionsSet(var=Var("t"), condition=Exists(var=Var(name='a'), condition=Exists(var=Var(name='b'), condition=And(Geq(left=Var(name='a'), right=Const(value=1)), Leq(left=Var(name='a'), right=Const(value=2960)), Geq(left=Var(name='b'), right=Const(... | NT | null | COUNT | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | nt_count_divisible_and_v1 | null | 4 | 0 | [
"LIN_FORM"
] | 1 | 0.357 | 2026-02-08T08:33:25.057635Z | {
"verified": true,
"answer": 347,
"timestamp": "2026-02-08T08:33:25.414730Z"
} | 1940f9 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 171,
"completion_tokens": 3264
},
"timestamp": "2026-02-13T19:34:32.004Z",
"answer": 347
},
{
... | 1 | [
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
}
] | {
"lo": -8.32,
"mid": -5.11,
"hi": -2.37
} | ||
4e00ba | nt_num_divisors_compute_v1_1918700295_4296 | Let $n = 108$. Let $p$ be the maximum value of $x \cdot y$ over all ordered pairs $(x, y)$ of positive integers such that $x + y = n$. Compute the number of positive divisors of $p$. | 21 | graphs = [
Graph(
let={
"_n": Const(108),
"n": MaxOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(Sum(Var("x"), Var("y")), Ref("_n")))), expr=Mul(Var("x"), Var("y")))),
... | NT | null | COMPUTE | sympy | B1 | [
"B1"
] | 5b950e | nt_num_divisors_compute_v1 | null | 4 | 0 | [
"B1"
] | 1 | 0.001 | 2026-02-08T09:17:13.174952Z | {
"verified": true,
"answer": 21,
"timestamp": "2026-02-08T09:17:13.176394Z"
} | cedd49 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 100,
"completion_tokens": 581
},
"timestamp": "2026-02-14T02:20:47.350Z",
"answer": 21
},
{
... | 1 | [
{
"lemma": "B1",
"status": "ok"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": ... | {
"lo": -5.49,
"mid": 0.22,
"hi": 6.51
} | ||
ae3739 | comb_binomial_compute_v1_1874849503_17 | Let $n = 14$ and $k = 7$. Define $P$ to be the maximum value of $xy$ over all pairs of positive integers $(x, y)$ such that $x + y = 128$. Compute $P - \binom{14}{7}$. | 664 | graphs = [
Graph(
let={
"_n": Const(128),
"n": Const(14),
"k": Const(7),
"result": Binom(n=Ref("n"), k=Ref("k")),
"Q": Sub(MaxOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x... | ALG | COMB | COMPUTE | sympy | B1 | [
"B1"
] | d2b6e1 | comb_binomial_compute_v1 | negation_mod | 5 | 0 | [
"B1"
] | 1 | 0.002 | 2026-02-08T12:45:55.284490Z | {
"verified": true,
"answer": 664,
"timestamp": "2026-02-08T12:45:55.286549Z"
} | fae43d | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 175,
"completion_tokens": 803
},
"timestamp": "2026-02-09T12:53:42.586Z",
"answer": 664
},
{
"id"... | 2 | [
{
"lemma": "B1",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
}
] | {
"lo": -9.23,
"mid": -6.18,
"hi": -4.06
} | ||
b83b80 | diophantine_fbi2_count_v1_655260480_1135 | Let $k = 120$. Determine the number of positive integers $d$ such that $4 \le d \le 103$, $d$ divides $k$, $\frac{k}{d} \ge 4$, and $\frac{k}{d} \le \max\{n \mid 2 \le n \le 103,\ n\text{ is prime}\}$. | 10 | graphs = [
Graph(
let={
"_n": Const(4),
"k": Const(120),
"result": CountOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Const(4)), Leq(Var("d"), Const(103)), Divides(divisor=Var("d"), dividend=Ref("k")), Geq(Div(Ref("k"), Var("d")), Ref("_n")), Leq(Div(... | NT | null | COUNT | sympy | B1 | [
"MAX_PRIME_BELOW"
] | dc3ad3 | diophantine_fbi2_count_v1 | null | 4 | 0 | [
"B1",
"MAX_PRIME_BELOW"
] | 2 | 0.081 | 2026-02-08T15:55:40.235543Z | {
"verified": true,
"answer": 10,
"timestamp": "2026-02-08T15:55:40.316531Z"
} | 256fe7 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 125,
"completion_tokens": 1186
},
"timestamp": "2026-02-16T17:06:35.806Z",
"answer": 10
},
{
... | 1 | [
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok"
},
{
"lemma": "MOD_ADD",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
d9884a | nt_count_gcd_equals_v1_1520064083_3363 | Let $\varphi(n)$ denote Euler's totient function. Define $k = \sum_{d\mid 402} \varphi(d)$ and $d = 6$. Let $S$ be the set of all integers $n$ such that $1 \leq n \leq 49284$ and $\mathrm{gcd}(n, k) = d$. Compute the number of elements in $S$. | 8,092 | graphs = [
Graph(
let={
"upper": Const(49284),
"k": SumOverDivisors(n=Const(value=402), var='d', expr=EulerPhi(n=Var(name='d'))),
"d": Const(6),
"result": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Ref("upp... | NT | null | COUNT | sympy | K3 | [
"K3"
] | 54c41e | nt_count_gcd_equals_v1 | null | 4 | 0 | [
"K3"
] | 1 | 5.653 | 2026-02-08T05:36:18.305305Z | {
"verified": true,
"answer": 8092,
"timestamp": "2026-02-08T05:36:23.958273Z"
} | 049746 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 129,
"completion_tokens": 916
},
"timestamp": "2026-02-12T10:53:40.661Z",
"answer": 8092
},
{
... | 1 | [
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "K3",
"status": "ok"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
}
] | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
51bcf6 | lin_form_endings_v1_1520064083_3935 | Let $a = 30$, $b = 20$, and $k = 39$. Let $d = \gcd(a, b)$, and let $m = \left\lfloor \frac{k}{\gcd(k, d)} \right\rfloor$. Let $s = 15762 \cdot m$. Compute the remainder when $s$ is divided by $64702$. | 32,400 | graphs = [
Graph(
let={
"a_coeff": Const(30),
"b_coeff": Const(20),
"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(15... | COMB | NT | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | lin_form_endings_v1 | null | 3 | null | [
"LIN_FORM"
] | 1 | 0.001 | 2026-02-08T05:59:20.821669Z | {
"verified": true,
"answer": 32400,
"timestamp": "2026-02-08T05:59:20.822599Z"
} | 2d223c | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 125,
"completion_tokens": 544
},
"timestamp": "2026-02-12T17:55:13.842Z",
"answer": 32400
},
{... | 1 | [
{
"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",
"status": "no"
}
] | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
f12604 | antilemma_k3_v1_124444284_4487 | Let $x$ be the sum of $\phi(d)$ over all positive divisors $d$ of $43341$, where $\phi$ denotes Euler's totient function. Compute the remainder when $78977x$ is divided by $69223$. | 3,253 | graphs = [
Graph(
let={
"x": SumOverDivisors(n=Const(value=43341), var='d', expr=EulerPhi(n=Var(name='d'))),
"Q": Mod(value=Mul(Const(78977), Ref("x")), modulus=Const(69223)),
},
goal=Ref("Q"),
)
] | NT | COMB | COMPUTE | sympy | K3 | [
"K3"
] | 54c41e | antilemma_k3_v1 | null | 3 | 0 | [
"K3"
] | 1 | 0.001 | 2026-02-08T06:03:04.902606Z | {
"verified": true,
"answer": 3253,
"timestamp": "2026-02-08T06:03:04.903189Z"
} | 85cbf9 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 97,
"completion_tokens": 962
},
"timestamp": "2026-02-12T18:57:34.999Z",
"answer": 3253
},
{
... | 1 | [
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "K3",
"status": "ok"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
}
] | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
2c6c27 | antilemma_sum_equals_v1_1742523217_2629 | Let $m$ be the number of integers $t$ with $27 \leq t \leq 313$ such that there exist positive integers $a$ and $b$ with $1 \leq a \leq 18$, $1 \leq b \leq 7$, and $t = 14a + 8b + 5$. Let $n$ be the number of ordered pairs $(x_1, x_2)$ of positive odd integers such that $x_1 + x_2 = m$. Let $x$ be the number of ordered... | 44,140 | graphs = [
Graph(
let={
"_c": Const(81440),
"_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=18)), Geq(left=... | COMB | GEOM | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM/COMB1/COUNT_SUM_EQUALS",
"COUNT_SUM_EQUALS"
] | b14821 | antilemma_sum_equals_v1 | null | 7 | 0 | [
"COMB1",
"COUNT_SUM_EQUALS",
"LIN_FORM"
] | 3 | 0.012 | 2026-02-08T04:53:17.969107Z | {
"verified": true,
"answer": 44140,
"timestamp": "2026-02-08T04:53:17.980872Z"
} | 886eb6 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 299,
"completion_tokens": 16515
},
"timestamp": "2026-02-24T02:11:40.950Z",
"answer": 44140
},
{
... | 1 | [
{
"lemma": "COMB1",
"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": "ok"
},
{
"lemma... | {
"lo": -0.05,
"mid": 2.89,
"hi": 5.27
} | ||
f97482 | modular_sum_quadratic_residues_v1_151522320_1971 | Let $p = 577$ and define $\text{result} = \frac{p(p-1)}{4}$. Let $c$ be the largest prime number $n$ such that $2 \leq n \leq 8607$. Compute the remainder when $c \cdot \text{result}$ is divided by $69692$. Find the value of this remainder. | 61,020 | graphs = [
Graph(
let={
"_n": Const(2),
"p": Const(577),
"result": Div(Mul(Ref("p"), Sub(Ref("p"), Const(1))), Const(4)),
"_c": MaxOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Ref("_n")), Leq(Var("n"), Const(8607)), IsPrime(Var("n"))))),
... | NT | null | SUM | sympy | MAX_PRIME_BELOW | [
"MAX_PRIME_BELOW"
] | 183c11 | modular_sum_quadratic_residues_v1 | affine_mod | 4 | 0 | [
"MAX_PRIME_BELOW"
] | 1 | 0.001 | 2026-02-08T04:29:44.845901Z | {
"verified": true,
"answer": 61020,
"timestamp": "2026-02-08T04:29:44.847303Z"
} | e660e3 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 192,
"completion_tokens": 2516
},
"timestamp": "2026-02-10T16:49:40.277Z",
"answer": 61020
},
{
... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok"
},
{
"lemma": "V3",
"status": "no"
}
] | {
"lo": -3.49,
"mid": 1.84,
"hi": 7.55
} | ||
0a21c1 | alg_poly3_sum_v1_1218484723_4847 | Let $R$ be the number of ordered pairs $(a, b)$ of positive integers with $1 \le a \le b$ and
$$1 \le b \le \left|\left\{v : 4 \le v \le 1306,\ \text{there exist integers } a, b \text{ with } 1 \le a \le 8,\ 1 \le b \le 8 \text{ such that } 26a^{2} - 48ab + 26b^{2} = v\right\}\right|$$
such that
$$50a^{2} + 50b^{2} - 1... | 58,837 | graphs = [
Graph(
let={
"_c": Const(4),
"_m": Const(50),
"_n": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("a"), Var("b")]), condition=And(Geq(Var("a"), Const(1)), Leq(Var("a"), Const(35)), Geq(Var("b"), Const(1)), Leq(Var("b"), CountOverSet(set=SolutionsSet(var... | ALG | null | COMPUTE | sympy | QF_PSD_DISTINCT | [
"QF_PSD_DISTINCT/QF_PSD_ORBIT/B3"
] | d167d5 | alg_poly3_sum_v1 | null | 7 | 0 | [
"B3",
"QF_PSD_DISTINCT",
"QF_PSD_ORBIT"
] | 3 | 0.501 | 2026-02-25T06:29:03.060627Z | {
"verified": true,
"answer": 58837,
"timestamp": "2026-02-25T06:29:03.561820Z"
} | f0cd29 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 392,
"completion_tokens": 32768
},
"timestamp": "2026-03-29T18:02:35.525Z",
"answer": null
},
{
... | 1 | [
{
"lemma": "B3",
"status": "ok_later"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "QF_PSD_DISTINCT",
"status": "ok"
},
{
"lemma": "QF_PSD_ORBIT",
"status": "ok_later"
}
] | {
"lo": 3.81,
"mid": 6.33,
"hi": 9.49
} | ||
2e71b6 | comb_binomial_compute_v1_1125832087_181 | Let $n$ be the minimum value of $x + y$ over all ordered pairs $(x, y)$ of positive integers such that $xy = 49$. Let $k$ be the number of integers $t$ with $5 \leq t \leq 12$ for which there exist integers $a$ and $b$ such that $1 \leq a \leq 3$, $1 \leq b \leq 2$, and $t = 2a + 3b$. Compute $\binom{n}{k}$. | 3,003 | graphs = [
Graph(
let={
"_n": Const(49),
"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")))),
... | ALG | COMB | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM",
"B3"
] | 688dbe | comb_binomial_compute_v1 | null | 4 | 0 | [
"B3",
"LIN_FORM"
] | 2 | 0.004 | 2026-02-08T02:55:26.200064Z | {
"verified": true,
"answer": 3003,
"timestamp": "2026-02-08T02:55:26.203844Z"
} | 6bb99a | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 229,
"completion_tokens": 880
},
"timestamp": "2026-02-10T11:47:57.403Z",
"answer": 3003
},
{
"id... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
}
] | {
"lo": -1.87,
"mid": 0.05,
"hi": 1.73
} | ||
5805b6 | lin_form_endings_v1_1520064083_6495 | Let $a = 14$ and $b = 21$. Define $A = 30$ and $B = 16$. Let $g = \gcd(a, b)$, and set $a' = \left\lfloor \frac{a}{g} \right\rfloor$ and $b' = \left\lfloor \frac{b}{g} \right\rfloor$. Compute the value of
\[
( a' \cdot A + b' \cdot B - a' \cdot b' ) \cdot 14320
\]
and let $x$ be the remainder when this value is divided... | 33,512 | graphs = [
Graph(
let={
"a_coeff": Const(14),
"b_coeff": Const(21),
"A_val": Const(30),
"B_val": Const(16),
"g_step": GCD(a=Ref("a_coeff"), b=Ref("b_coeff")),
"ap_node": Floor(Div(Ref("a_coeff"), Ref("g_step"))),
"bp_node": ... | COMB | NT | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | lin_form_endings_v1 | null | 3 | null | [
"LIN_FORM"
] | 1 | 0 | 2026-02-08T08:07:00.401843Z | {
"verified": true,
"answer": 33512,
"timestamp": "2026-02-08T08:07:00.402324Z"
} | cb62f2 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 183,
"completion_tokens": 670
},
"timestamp": "2026-02-13T15:08:53.249Z",
"answer": 33512
},
{... | 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": -3.51,
"mid": 1.33,
"hi": 6.56
} | ||
a422a6 | alg_qf_psd_sum_v1_1218484723_2069 | Let $T = \left\{ (a_1, b_1) : 1 \leq a_1, b_1 \leq 40,\ 257a_1^4 - 1028a_1 b_1^3 + 257b_1^4 - 1028a_1^3 b_1 + 1542a_1^2 b_1^2 = 65792 \right\}$. Compute the remainder when
$$
\sum_{a=1}^{14} \sum_{b=1}^{14} \sum_{c=1}^{14} \sum_{d=1}^{14} \left( 40b^2 - 8ab + 18ac + 10ad + 21a^2 + 60c^2 - 40cd - 16bd + 36d^2 + |T| \cdo... | 2,066 | graphs = [
Graph(
let={
"_n": Const(80642),
"result": Mod(value=SumOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("a"), Var("b"), Var("c"), Var("d")]), condition=And(Geq(Var("a"), Const(1)), Leq(Var("a"), Const(14)), Geq(Var("b"), Const(1)), Leq(Var("b"), Const(14)),... | ALG | null | COMPUTE | sympy | POLY4_COUNT | [
"POLY4_COUNT"
] | 861d91 | alg_qf_psd_sum_v1 | null | 6 | 0 | [
"POLY4_COUNT"
] | 1 | 0.448 | 2026-02-25T03:46:46.593534Z | {
"verified": true,
"answer": 2066,
"timestamp": "2026-02-25T03:46:47.041540Z"
} | c8dcc9 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 318,
"completion_tokens": 3215
},
"timestamp": "2026-03-29T02:48:24.312Z",
"answer": 2066
},
{
"i... | 1 | [
{
"lemma": "POLY4_COUNT",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
}
] | {
"lo": -2.47,
"mid": 1.2,
"hi": 4.81
} |
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