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 |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
1567ef | diophantine_fbi2_count_v1_153355830_2640 | Let $S$ be the set of all ordered pairs $(i, j)$ of integers such that $1 \leq i \leq 21$, $1 \leq j \leq 64$, and $\gcd(i, j) = 1$. Let $k$ be the number of elements in $S$. Let $T$ be the set of all positive integers $d$ such that:
- $4 \leq d \leq 91$,
- $d$ divides $k$,
- $\frac{k}{d} \geq \max\{ n \mid 2 \leq n \... | 12 | graphs = [
Graph(
let={
"_n": Const(2),
"k": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("i"), Var("j")]), condition=Eq(GCD(a=Var("i"), b=Var("j")), Const(1)), domain=CartesianProduct(left=IntegerRange(start=Const(1), end=Const(21)), right=IntegerRange(start=Const(1), end=C... | NT | null | COUNT | sympy | SUM_DIVISIBLE | [
"COUNT_COPRIME_GRID",
"MAX_PRIME_BELOW"
] | 2b0ad4 | diophantine_fbi2_count_v1 | null | 6 | 0 | [
"COUNT_COPRIME_GRID",
"MAX_PRIME_BELOW",
"SUM_DIVISIBLE"
] | 3 | 0.126 | 2026-02-08T07:15:14.163863Z | {
"verified": true,
"answer": 12,
"timestamp": "2026-02-08T07:15:14.290135Z"
} | 811f40 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 287,
"completion_tokens": 3116
},
"timestamp": "2026-02-13T09:14:51.233Z",
"answer": 12
},
{
... | 1 | [
{
"lemma": "COUNT_COPRIME_GRID",
"status": "ok"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok"
},
{
"lemma": "V5",
"statu... | {
"lo": -5.55,
"mid": -3.01,
"hi": 0.32
} | ||
909244 | nt_sum_divisors_compute_v1_865884756_6259 | Let $A$ be the set of all ordered pairs $(x, y)$ of positive integers such that $xy = 5929$. Let $s_1$ be the minimum value of $x + y$ over all pairs $(x, y) \in A$. Let $B$ be the set of all ordered pairs $(x_1, y_1)$ of positive integers such that $x_1 + y_1 = s_1$. Let $p_1$ be the maximum value of $x_1 y_1$ over al... | 48,630 | graphs = [
Graph(
let={
"_m": Const(51106),
"_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")), MaxOverSet(set=MapOverSet(set=SolutionsSet(va... | NT | null | COMPUTE | sympy | B1 | [
"B1/B3/B1",
"B3/B3/B1"
] | 3ef7ee | nt_sum_divisors_compute_v1 | negation_mod | 7 | 0 | [
"B1",
"B3"
] | 2 | 0.005 | 2026-02-08T19:07:16.932628Z | {
"verified": true,
"answer": 48630,
"timestamp": "2026-02-08T19:07:16.938027Z"
} | a43ad9 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 340,
"completion_tokens": 2490
},
"timestamp": "2026-02-18T21:17:06.849Z",
"answer": 48630
},
... | 1 | [
{
"lemma": "B1",
"status": "ok"
},
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
efe04b_l | comb_binomial_compute_v1_1520064083_6390 | Let $j$ be a positive integer such that $1 \leq j \leq 14$ and $j^5 \leq 537824$. Let $n$ be the number of such integers $j$. Compute the value of
$$
\binom{n}{7} + \varphi\left(\left|\binom{n}{7}\right| + 1\right) + \tau\left(\left|\binom{n}{7}\right| + 1\right),
$$
where $\varphi(m)$ denotes the number of positive in... | 17 | NT | null | COMPUTE | sympy | C3 | [
"C3"
] | 8a214c | comb_binomial_compute_v1 | null | 4 | 0 | [
"C3"
] | 1 | 0.003 | 2026-02-08T08:02:50.512285Z | {
"verified": false,
"answer": 6866,
"timestamp": "2026-02-08T08:02:50.514985Z"
} | dee327 | efe04b | legacy_text | 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": 1352
},
"timestamp": "2026-02-13T14:19:22.222Z",
"answer": 6866
},
{... | 1 | [
{
"lemma": "C3",
"status": "ok"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
}
] | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | |
489592 | geo_count_lattice_rect_v1_601307018_3544 | Let $a = \sum_{k=0}^{2} 10^k$. Find the number of lattice points $(x,y)$ such that $0 \le x \le a$ and $0 \le y \le 88$. | 9,968 | graphs = [
Graph(
let={
"_n": Const(10),
"a": Summation(var="k", start=Const(0), end=Const(2), expr=Pow(Ref("_n"), Var("k"))),
"b": Const(88),
"result": LatticePointsRect(a=Ref(name='a'), b=Ref(name='b')),
},
goal=Ref("result"),
)
] | GEOM | GEOM | COUNT | sympy | POLY_ORBIT_HENSEL | [
"SUM_GEOM"
] | 04214c | geo_count_lattice_rect_v1 | null | 2 | 0 | [
"POLY_ORBIT_HENSEL",
"SUM_GEOM"
] | 2 | 0.306 | 2026-03-10T04:08:20.710074Z | {
"verified": true,
"answer": 9968,
"timestamp": "2026-03-10T04:08:21.016436Z"
} | 0a6c1a | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 160,
"completion_tokens": 523
},
"timestamp": "2026-03-29T09:02:54.922Z",
"answer": 9968
},
{
"id... | 1 | [
{
"lemma": "SUM_GEOM",
"status": "ok"
}
] | {
"lo": -6.5,
"mid": -3.34,
"hi": -0.89
} | ||
fdf31a | antilemma_k2_v1_1116507919_308 | Compute the value of
$$
\sum_{k=1}^{56} \phi(k) \left\lfloor \frac{56}{k} \right\rfloor,
$$
where $\phi$ denotes Euler's totient function. | 1,596 | graphs = [
Graph(
let={
"x": Summation(var="k", start=Const(1), end=Const(56), expr=Mul(EulerPhi(n=Var("k")), Floor(Div(Const(56), Var("k"))))),
},
goal=Ref("x"),
)
] | NT | COMB | COMPUTE | sympy | K2 | [
"K2"
] | 6897ab | antilemma_k2_v1 | null | 4 | 0 | [
"K2"
] | 1 | 0 | 2026-02-08T02:30:45.164802Z | {
"verified": true,
"answer": 1596,
"timestamp": "2026-02-08T02:30:45.165071Z"
} | abd156 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 165,
"completion_tokens": 887
},
"timestamp": "2026-02-08T19:21:31.572Z",
"answer": 1596
},
{
"id... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K2",
"status": "ok"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "VAL_SUM_EQ",
"status": "no"
}
] | {
"lo": -1.75,
"mid": 0.26,
"hi": 2.09
} | ||
c027c4 | geo_count_lattice_triangle_v1_2051736721_738 | Let $A$ be the area of the triangle with vertices at $(256, 233)$, $(32, 100)$, and $(0, 0)$, multiplied by $2$. Let $B$ be the sum
$$
\gcd(256, 233) + \gcd(|32 - 256|, |100 - 233|) + \gcd(32, 100).
$$
Compute the value of
$$
\frac{A + 2 - B}{2}.
$$ | 9,067 | graphs = [
Graph(
let={
"_n": Const(235),
"area_2x": Abs(arg=Sum(Mul(Const(value=256), Const(value=100)), Mul(Const(value=32), Sub(left=Const(value=0), right=Const(value=233))))),
"boundary": Sum(GCD(a=Abs(arg=Const(value=256)), b=Abs(arg=Const(value=233))), GCD(a=Abs(arg... | ALG | NT | COUNT | sympy | MAX_PRIME_BELOW | [
"MAX_PRIME_BELOW"
] | dc3ad3 | geo_count_lattice_triangle_v1 | null | 4 | 0 | [
"MAX_PRIME_BELOW"
] | 1 | 0.006 | 2026-02-08T15:39:08.285901Z | {
"verified": true,
"answer": 9067,
"timestamp": "2026-02-08T15:39:08.291614Z"
} | cf67a6 | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 184,
"completion_tokens": 592
},
"timestamp": "2026-02-16T06:11:32.349Z",
"answer": 9070
},
{
"id": 11,... | 1 | [
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok"
},
{
"lemma": "V8",
"status": "no"
},
{
"lemma": "VAL_SUM_EQ",
"status": "no"
... | {
"lo": -8.26,
"mid": -5.01,
"hi": -1.76
} | ||
3b3c81 | nt_count_divisible_v1_458359167_2323 | Let $S$ be the set of all integers $t$ such that $27 \leq t \leq 90$ and $t = 6a + 21b$ for some integers $a$ and $b$ satisfying $1 \leq a \leq 8$ and $1 \leq b \leq 2$. Let $d$ be the number of elements in $S$. Let $x = \sum_{k=0}^{7} (-1)^k \binom{7}{k}$. Determine the number of positive integers $n$ such that $1 \le... | 3,249 | graphs = [
Graph(
let={
"_n": Const(7),
"upper": Const(51984),
"divisor": 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'... | COMB | null | COUNT | sympy | BINOMIAL_ALTERNATING | [
"BINOMIAL_ALTERNATING",
"LIN_FORM"
] | 10f694 | nt_count_divisible_v1 | null | 6 | 0 | [
"BINOMIAL_ALTERNATING",
"LIN_FORM"
] | 2 | 1.66 | 2026-02-08T05:18:44.408175Z | {
"verified": true,
"answer": 3249,
"timestamp": "2026-02-08T05:18:46.067758Z"
} | fffab2 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 266,
"completion_tokens": 3256
},
"timestamp": "2026-02-24T03:06:43.915Z",
"answer": 3249
},
{
"i... | 1 | [
{
"lemma": "BINOMIAL_ALTERNATING",
"status": "ok"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8",
"... | {
"lo": -2.46,
"mid": 0.47,
"hi": 3.59
} | ||
155d81 | modular_inverse_v1_458359167_448 | Let $ a $ be the number of ordered pairs $ (i, j) $ with $ 1 \leq i \leq 20 $, $ 1 \leq j \leq 51 $, and $ \gcd(i, j) = 1 $. Let $ m $ be the number of integers $ t $ such that $ 21 \leq t \leq 3213 $ and $ t = 6a' + 15b' $ for some positive integers $ a' \leq 203 $, $ b' \leq 133 $. Let $ x $ be the smallest positive ... | 904 | graphs = [
Graph(
let={
"a": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("i"), Var("j")]), condition=Eq(GCD(a=Var("i"), b=Var("j")), Const(1)), domain=CartesianProduct(left=IntegerRange(start=Const(1), end=Const(20)), right=IntegerRange(start=Const(1), end=Const(51))))),
"m... | NT | null | EXTREMUM | sympy | COPRIME_PAIRS | [
"COUNT_COPRIME_GRID",
"LIN_FORM"
] | 66e6c4 | modular_inverse_v1 | null | 7 | 0 | [
"COPRIME_PAIRS",
"COUNT_COPRIME_GRID",
"LIN_FORM"
] | 3 | 0.077 | 2026-02-08T03:19:59.294960Z | {
"verified": true,
"answer": 904,
"timestamp": "2026-02-08T03:19:59.372060Z"
} | a3d5ae | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 286,
"completion_tokens": 4152
},
"timestamp": "2026-02-10T14:06:27.155Z",
"answer": 904
},
{
"id... | 1 | [
{
"lemma": "COUNT_COPRIME_GRID",
"status": "ok"
},
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "LTE_DIFF... | {
"lo": 1.71,
"mid": 5.04,
"hi": 8.38
} | ||
946e92 | diophantine_fbi2_count_v1_1918700295_4570 | Let $T$ be the set of all integers $t$ such that $19 \leq t \leq 1699$ and $t = 3a + 2b + 14$ for some integers $a$, $b$ with $1 \leq a \leq 509$ and $1 \leq b \leq 79$. Let $k$ be the number of positive integers $n \leq |T|$ such that the sum of the decimal digits of $n$ is odd. Determine the number of divisors $d$ of... | 52,567 | graphs = [
Graph(
let={
"_n": Const(82),
"k": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), CountOverSet(set=SolutionsSet(var=Var("t"), condition=Exists(var=Var(name='a'), condition=Exists(var=Var(name='b'), condition=And(Geq(left=Va... | NT | null | COUNT | sympy | LIN_FORM | [
"LIN_FORM/L3B"
] | db250f | diophantine_fbi2_count_v1 | null | 7 | 0 | [
"L3B",
"LIN_FORM"
] | 2 | 0.012 | 2026-02-08T09:28:07.748006Z | {
"verified": true,
"answer": 52567,
"timestamp": "2026-02-08T09:28:07.759826Z"
} | c21ecb | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 217,
"completion_tokens": 6197
},
"timestamp": "2026-02-14T04:29:49.338Z",
"answer": 52567
},
... | 1 | [
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "L3B",
"status": "ok_later"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "V1",
"status": "no"
},
{
"lem... | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
141885 | modular_count_residue_v1_865884756_564 | Let $r$ be the smallest divisor of $875$ that is at least $2$. Compute the number of positive integers $n$ at most $60025$ such that $n \equiv r \pmod{23}$. | 2,610 | graphs = [
Graph(
let={
"_n": Const(2),
"upper": Const(60025),
"m": Const(23),
"r": MinOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Ref("_n")), Divides(divisor=Var("d"), dividend=Const(875))))),
"result": CountOverSet(set=Solu... | NT | null | COUNT | sympy | MIN_PRIME_FACTOR | [
"MIN_PRIME_FACTOR"
] | bc3776 | modular_count_residue_v1 | null | 3 | 0 | [
"MIN_PRIME_FACTOR"
] | 1 | 3.844 | 2026-02-08T15:30:52.465855Z | {
"verified": true,
"answer": 2610,
"timestamp": "2026-02-08T15:30:56.310030Z"
} | 9f7832 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 94,
"completion_tokens": 655
},
"timestamp": "2026-02-16T07:38:00.824Z",
"answer": 2610
},
{
... | 1 | [
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "MIN_PRIME_FACTOR",
"status": "ok"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
}... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
1ac5d2 | nt_count_gcd_equals_v1_1439011603_2619 | Let $k$ be the number of prime numbers $n$ such that $2 \leq n \leq 1427$. Let $d = 1$. Define $S$ as the set of all positive integers $n_1$ such that $1 \leq n_1 \leq 16384$ and $\gcd(n_1, k) = d$. Let $Q = 44121 \times |S|$. Find the remainder when $Q$ is divided by $93470$. | 9,669 | graphs = [
Graph(
let={
"_n": Const(93470),
"upper": Const(16384),
"k": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(2)), Leq(Var("n"), Const(1427)), IsPrime(Var("n"))))),
"d": Const(1),
"result": CountOverSet(set=S... | NT | null | COUNT | sympy | COUNT_PRIMES | [
"COUNT_PRIMES"
] | 07c874 | nt_count_gcd_equals_v1 | null | 5 | 0 | [
"COUNT_PRIMES"
] | 1 | 1.655 | 2026-02-08T16:53:05.806067Z | {
"verified": true,
"answer": 9669,
"timestamp": "2026-02-08T16:53:07.461448Z"
} | cb2021 | 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": 1637
},
"timestamp": "2026-02-17T14:21:25.706Z",
"answer": 9669
},
{... | 1 | [
{
"lemma": "COUNT_PRIMES",
"status": "ok"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "V1",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
724db6 | sequence_lucas_compute_v1_151522320_43 | Let $ n = \sum_{k=1}^{6} \phi(k) \left\lfloor \frac{6}{k} \right\rfloor $, where $ \phi(k) $ denotes Euler's totient function. Define $ L_n $ to be the $ n $-th Lucas number, with $ L_1 = 1 $, $ L_2 = 3 $, and $ L_k = L_{k-1} + L_{k-2} $ for $ k \geq 3 $. Compute $ L_n $. | 24,476 | graphs = [
Graph(
let={
"_n": Const(6),
"n": Summation(var="k", start=Const(1), end=Ref("_n"), expr=Mul(EulerPhi(n=Var("k")), Floor(Div(Const(6), Var("k"))))),
"result": Lucas(arg=Ref(name='n')),
},
goal=Ref("result"),
)
] | NT | null | COMPUTE | sympy | K2 | [
"K2"
] | 6897ab | sequence_lucas_compute_v1 | null | 4 | 0 | [
"K2"
] | 1 | 0.001 | 2026-02-08T02:56:17.311245Z | {
"verified": true,
"answer": 24476,
"timestamp": "2026-02-08T02:56:17.312190Z"
} | 4f3615 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 225,
"completion_tokens": 1173
},
"timestamp": "2026-02-10T11:57:17.731Z",
"answer": 24476
},
{
"... | 1 | [
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "K2",
"status": "ok"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
}
] | {
"lo": -7.01,
"mid": -4.67,
"hi": -2.18
} | ||
487bbc | nt_count_divisible_and_v1_717093673_3435 | Let $d_1 = 9$. Let $s$ be the minimum value of $x_1 + y_1$ over all ordered pairs $(x_1, y_1)$ of positive integers such that $x_1 y_1 = 324$. Let $d_2$ be the minimum value of $x + y$ over all ordered pairs $(x, y)$ of positive integers such that $x y = s$. Compute the number of positive integers $n$ such that $1 \leq... | 2,472 | graphs = [
Graph(
let={
"upper": Const(88992),
"d1": Const(9),
"d2": 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")), MinOverSet(set... | NT | null | COUNT | sympy | B3 | [
"B3/B3"
] | 8ffef9 | nt_count_divisible_and_v1 | null | 4 | 0 | [
"B3"
] | 1 | 3.033 | 2026-02-08T17:37:10.186343Z | {
"verified": true,
"answer": 2472,
"timestamp": "2026-02-08T17:37:13.219782Z"
} | cfd21c | 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": 1012
},
"timestamp": "2026-02-18T05:14:44.029Z",
"answer": 2472
},
{... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "VAL_SUM_EQ",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
0ea7a9 | geo_count_lattice_rect_v1_1978505735_3512 | Compute the remainder when $44121$ times the number of lattice points in the rectangle $[0, 289] \times [0, 224]$ is divided by $56092$. | 29,442 | graphs = [
Graph(
let={
"a": Const(289),
"b": Const(224),
"result": LatticePointsRect(a=Ref(name='a'), b=Ref(name='b')),
"Q": Mod(value=Mul(Const(44121), Ref("result")), modulus=Const(56092)),
},
goal=Ref("Q"),
)
] | GEOM | null | COUNT | sympy | [] | geo_count_lattice_rect_v1 | null | 2 | 0 | null | null | 0.003 | 2026-02-08T17:42:02.613513Z | {
"verified": true,
"answer": 29442,
"timestamp": "2026-02-08T17:42:02.616869Z"
} | 5b47ce | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 86,
"completion_tokens": 2898
},
"timestamp": "2026-02-18T06:15:29.971Z",
"answer": 29442
},
{... | 1 | [] | {
"lo": -2.38,
"mid": 1.74,
"hi": 6.59
} | ||||
ef8ba8 | comb_factorial_compute_v1_655260480_3226 | Let $n$ be the number of ordered pairs $(i,j)$ of integers with $1 \leq i \leq 3$ and $1 \leq j \leq 3$ such that $\gcd(i,j) = 1$.
Define $Q$ to be the remainder when $72835 \cdot n!$ is divided by $82168$.
Find the value of $Q$. | 43,944 | graphs = [
Graph(
let={
"n": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("i"), Var("j")]), condition=Eq(GCD(a=Var("i"), b=Var("j")), Const(1)), domain=CartesianProduct(left=IntegerRange(start=Const(1), end=Const(3)), right=IntegerRange(start=Const(1), end=Const(3))))),
"res... | NT | null | COMPUTE | sympy | COUNT_COPRIME_GRID | [
"COUNT_COPRIME_GRID"
] | 20ec03 | comb_factorial_compute_v1 | null | 4 | 0 | [
"COUNT_COPRIME_GRID"
] | 1 | 0.002 | 2026-02-08T17:15:47.833608Z | {
"verified": true,
"answer": 43944,
"timestamp": "2026-02-08T17:15:47.835704Z"
} | a857aa | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 127,
"completion_tokens": 1824
},
"timestamp": "2026-02-17T22:45:11.174Z",
"answer": 43944
},
... | 1 | [
{
"lemma": "COUNT_COPRIME_GRID",
"status": "ok"
},
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "V5",
"sta... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
8c3d30 | lin_form_endings_v1_153355830_564 | Let $a = 28$, $b = 98$, $A = 30$, and $B = 38$. Let $g = \gcd(a, b)$. Define $$
n = \left\lfloor \frac{aA + bB - a - b}{g} \right\rfloor + 1.
$$ Let $k = 13121$ and $M = 64878$. Compute the remainder when $k \cdot n$ is divided by $M$. | 20,286 | graphs = [
Graph(
let={
"a_coeff": Const(28),
"b_coeff": Const(98),
"A_val": Const(30),
"B_val": Const(38),
"g_step": GCD(a=Ref("a_coeff"), b=Ref("b_coeff")),
"numerator": Sub(Sum(Mul(Ref("a_coeff"), Ref("A_val")), Mul(Ref("b_coeff"), R... | COMB | NT | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | lin_form_endings_v1 | null | 3 | null | [
"LIN_FORM"
] | 1 | 0 | 2026-02-08T03:10:17.612010Z | {
"verified": true,
"answer": 20286,
"timestamp": "2026-02-08T03:10:17.612506Z"
} | 27c58d | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 216,
"completion_tokens": 756
},
"timestamp": "2026-02-10T15:14:27.699Z",
"answer": 20286
},
{
"... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
}
] | {
"lo": -3.42,
"mid": 1.86,
"hi": 7.55
} | ||
4cd899 | modular_modexp_compute_v1_1431428450_501 | Let $d$ be the smallest integer greater than or equal to 2 that divides 48841. Compute the remainder when $d^{233}$ is divided by 11175. | 4,078 | graphs = [
Graph(
let={
"a": MinOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Const(2)), Divides(divisor=Var("d"), dividend=Const(48841))))),
"e": Const(233),
"m": Const(11175),
"result": ModExp(base=Ref("a"), exp=Ref("e"), mod=Ref("m")),
... | NT | null | COMPUTE | sympy | MIN_PRIME_FACTOR | [
"MIN_PRIME_FACTOR"
] | bc3776 | modular_modexp_compute_v1 | null | 4 | 0 | [
"MIN_PRIME_FACTOR"
] | 1 | 0.001 | 2026-02-08T13:29:44.633481Z | {
"verified": true,
"answer": 4078,
"timestamp": "2026-02-08T13:29:44.634818Z"
} | 7f2ef9 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 84,
"completion_tokens": 2645
},
"timestamp": "2026-02-15T16:26:38.514Z",
"answer": 4078
},
{
... | 1 | [
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "MIN_PRIME_FACTOR",
"status": "ok"
},
{
"lemma": "V1",
"status": "no"
},
{
"lemma": "V3",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
}
] | {
"lo": -5.49,
"mid": 0.22,
"hi": 6.51
} | ||
8488a8 | nt_sum_divisors_mod_v1_238844314_452 | Let $n$ be the number of integers $t$ such that $9 \leq t \leq 1700$ and there exist positive integers $a$ and $b$ with $1 \leq a \leq 40$, $1 \leq b \leq 375$, and $t = 5a + 4b$. Let $\sigma$ be the sum of all positive divisors of $n$. Compute the remainder when $\sigma$ is divided by $11587$. | 5,952 | graphs = [
Graph(
let={
"n": CountOverSet(set=SolutionsSet(var=Var("t"), condition=Exists(var=Var(name='a'), condition=Exists(var=Var(name='b'), condition=And(Geq(left=Var(name='a'), right=Const(value=1)), Leq(left=Var(name='a'), right=Const(value=40)), Geq(left=Var(name='b'), right=Const(value=... | NT | null | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | nt_sum_divisors_mod_v1 | null | 5 | 0 | [
"LIN_FORM"
] | 1 | 0.003 | 2026-02-08T13:21:15.483431Z | {
"verified": true,
"answer": 5952,
"timestamp": "2026-02-08T13:21:15.486550Z"
} | 5a14f2 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 146,
"completion_tokens": 6051
},
"timestamp": "2026-02-15T13:44:33.115Z",
"answer": 5952
},
{... | 1 | [
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "MOD_MUL",
"status": "no"
}
] | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
1fa65c | antilemma_k3_v1_168721529_842 | Let $x = \sum_{d \mid 34799} \phi(d)$, where $\phi$ denotes Euler's totient function. Compute the remainder when $8 - x$ is divided by $72121$. | 37,330 | graphs = [
Graph(
let={
"x": SumOverDivisors(n=Const(value=34799), var='d', expr=EulerPhi(n=Var(name='d'))),
"Q": Mod(value=Sub(Const(8), Ref("x")), modulus=Const(72121)),
},
goal=Ref("Q"),
)
] | NT | COMB | COMPUTE | sympy | K3 | [
"K3"
] | 54c41e | antilemma_k3_v1 | null | 3 | 0 | [
"K3"
] | 1 | 0 | 2026-02-08T13:19:09.694633Z | {
"verified": true,
"answer": 37330,
"timestamp": "2026-02-08T13:19:09.695017Z"
} | dd9587 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 160,
"completion_tokens": 437
},
"timestamp": "2026-02-09T09:49:23.644Z",
"answer": 37330
},
{
"i... | 2 | [
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K3",
"status": "ok"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "V1",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
}
] | {
"lo": -9.12,
"mid": -6.02,
"hi": -3.64
} | ||
e94235 | antilemma_sum_equals_v1_1520064083_10069 | Let $m = 106$. 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 pairs $(i, j)$ with $1 \leq i \leq 52$ and $1 \leq j \leq 53$ such that $i + j = n$. Let $Q$ be the remainder when $98919 \cdot x$ is divided by $69994$. Find $Q$. | 34,226 | graphs = [
Graph(
let={
"_m": Const(106),
"_n": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x1"), Var("x2")]), condition=And(IsPositive(arg=Var(name='x1')), IsPositive(arg=Var(name='x2')), IsOdd(arg=Var(name='x1')), IsOdd(arg=Var(name='x2')), Eq(Sum(Var("x1"), Var("x2")), ... | COMB | GEOM | COMPUTE | sympy | COMB1 | [
"COMB1/COUNT_SUM_EQUALS",
"COUNT_SUM_EQUALS"
] | 3e1adf | antilemma_sum_equals_v1 | null | 4 | 0 | [
"COMB1",
"COUNT_SUM_EQUALS"
] | 2 | 0.008 | 2026-02-08T11:11:52.706193Z | {
"verified": true,
"answer": 34226,
"timestamp": "2026-02-08T11:11:52.714025Z"
} | 07fc4c | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 230,
"completion_tokens": 1250
},
"timestamp": "2026-02-24T12:54:22.164Z",
"answer": 34226
},
{
"... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COMB1",
"status": "ok"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "ok"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
},
{... | {
"lo": -2.35,
"mid": 1.22,
"hi": 4.84
} | ||
1c212f | diophantine_fbi2_min_v1_1978505735_8448 | Let $n = 169$. Consider the set of all ordered pairs of positive integers $(x, y)$ such that $xy = n$. Let $s$ be the minimum value of $x + y$ over all such pairs.
Now, let $k = 16$. Consider the set of all positive integers $d$ such that $3 \leq d \leq s$, $d$ divides $k$, and $\frac{k}{d} \geq 2$. Let $r$ be the sma... | 55,560 | graphs = [
Graph(
let={
"_n": Const(169),
"k": Const(16),
"upper": MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(Mul(Var("x"), Var("y")), Ref("_n")))), ex... | NT | null | EXTREMUM | sympy | B3 | [
"B3"
] | 0cd20d | diophantine_fbi2_min_v1 | null | 5 | 0 | [
"B3"
] | 1 | 0.011 | 2026-02-08T20:49:50.024573Z | {
"verified": true,
"answer": 55560,
"timestamp": "2026-02-08T20:49:50.035820Z"
} | 29c552 | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 197,
"completion_tokens": 803
},
"timestamp": "2026-02-16T18:54:49.183Z",
"answer": 1
},
{
"id": 11,
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
... | {
"lo": -8.26,
"mid": -5.01,
"hi": -1.76
} | ||
2473a9 | comb_binomial_compute_v1_1978505735_3247 | Let $n = 15$ and $k = 8$. Define $\text{result} = \binom{n}{k}$. Let $S$ be the set of all positive integers $n_1$ such that $1 \leq n_1 \leq 400$ and $n_1$ is divisible by $100$. Define $Q$ as the sum of two terms: the first term is $\sum_{i=0}^{d-1} \left(\text{the } i\text{-th decimal digit of } |\text{result}|\righ... | 1,149 | graphs = [
Graph(
let={
"_n": Const(400),
"n": Const(15),
"k": Const(8),
"result": Binom(n=Ref("n"), k=Ref("k")),
"Q": Sum(Summation(var="i", start=Const(0), end=Sub(NumDigits(x=Abs(arg=Ref(name='result')), base=None), Const(1)), expr=Mul(Digit(x=A... | ALG | COMB | COMPUTE | sympy | SUM_DIVISIBLE | [
"SUM_DIVISIBLE"
] | d92c90 | comb_binomial_compute_v1 | digits_weighted_mod | 4 | 0 | [
"SUM_DIVISIBLE"
] | 1 | 0.004 | 2026-02-08T17:31:17.046009Z | {
"verified": true,
"answer": 1149,
"timestamp": "2026-02-08T17:31:17.049725Z"
} | 658693 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 210,
"completion_tokens": 1129
},
"timestamp": "2026-02-18T03:43:55.970Z",
"answer": 1149
},
{... | 1 | [
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "SUM_DIVISIBLE",
"status": "ok"
}
] | {
"lo": -2.38,
"mid": 1.74,
"hi": 6.59
} | ||
41b089 | geo_count_lattice_rect_v1_168721529_826 | Let $a = 24$ and $b = 61$. Define $Q$ to be the number of lattice points in the rectangle $[0, a] \times [0, b]$, including the boundary. Compute $Q$. | 1,550 | graphs = [
Graph(
let={
"a": Const(24),
"b": Const(61),
"result": LatticePointsRect(a=Ref(name='a'), b=Ref(name='b')),
"Q": Ref("result"),
},
goal=Ref("Q"),
)
] | GEOM | null | COUNT | sympy | [] | geo_count_lattice_rect_v1 | null | 4 | 0 | null | null | 0.006 | 2026-02-08T13:19:01.227787Z | {
"verified": true,
"answer": 1550,
"timestamp": "2026-02-08T13:19:01.233308Z"
} | 951669 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 164,
"completion_tokens": 396
},
"timestamp": "2026-02-09T09:38:08.282Z",
"answer": 1550
},
{
"id... | 1 | [] | {
"lo": -9.23,
"mid": -6.18,
"hi": -4.07
} | ||||
59437b | diophantine_fbi2_min_v1_784195855_10035 | Let $d$ be the smallest integer $d$ such that $5 \leq d \leq 370$, $d$ divides $360$, and $\frac{360}{d} \geq 4$. Let $c$ be the number of positive integers $n \leq 2401$ such that $\gcd(n, 20) = 1$. Compute $c - d$. | 956 | graphs = [
Graph(
let={
"k": Const(360),
"upper": Const(370),
"result": MinOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Const(5)), Leq(Var("d"), Ref("upper")), Divides(divisor=Var("d"), dividend=Ref("k")), Geq(Div(Ref("k"), Var("d")), Const(4))))),
... | NT | null | EXTREMUM | sympy | C4 | [
"C4"
] | acb85c | diophantine_fbi2_min_v1 | negation_mod | 4 | 0 | [
"C4"
] | 1 | 0.017 | 2026-02-08T17:23:14.732225Z | {
"verified": true,
"answer": 956,
"timestamp": "2026-02-08T17:23:14.748900Z"
} | 5d4c85 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 127,
"completion_tokens": 812
},
"timestamp": "2026-02-18T00:47:00.171Z",
"answer": 956
},
{
... | 1 | [
{
"lemma": "C4",
"status": "ok"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
d23749 | comb_count_permutations_fixed_v1_655260480_4038 | Let $n$ be the largest prime number between $2$ and $12$, inclusive. Compute the value of $\binom{n}{9} \cdot !(n - 9)$, where $!k$ denotes the number of derangements of $k$ elements. | 55 | graphs = [
Graph(
let={
"n": MaxOverSet(set=SolutionsSet(var=Var("n1"), condition=And(Geq(Var("n1"), Const(2)), Leq(Var("n1"), Const(12)), IsPrime(Var("n1"))))),
"k": Const(9),
"result": Mul(Binom(n=Ref("n"), k=Ref("k")), Subfactorial(arg=Sub(left=Ref(name='n'), right=Ref... | NT | COMB | COUNT | sympy | SUM_ARITHMETIC | [
"MAX_PRIME_BELOW"
] | dc3ad3 | comb_count_permutations_fixed_v1 | null | 3 | 0 | [
"MAX_PRIME_BELOW",
"SUM_ARITHMETIC"
] | 2 | 0.01 | 2026-02-08T17:40:31.770722Z | {
"verified": true,
"answer": 55,
"timestamp": "2026-02-08T17:40:31.781019Z"
} | 9f0cc6 | 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": 517
},
"timestamp": "2026-02-18T06:45:10.151Z",
"answer": 55
},
{
... | 1 | [
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "V1",
"st... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
6cab20 | nt_min_coprime_above_v1_238844314_344 | Let $m = 3$. Let $N$ be the number of integers $t$ such that $7 \leq t \leq 197$ and there exist positive integers $a \leq 29$, $b \leq 27$ satisfying $t = 4a + 3b$. Let $M$ be the number of positive integers $n \leq N$ such that $\gcd\left(n, \sum_{k=1}^{m} \varphi(k) \cdot \left\lfloor \frac{3}{k} \right\rfloor\right... | 77,285 | graphs = [
Graph(
let={
"_m": 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=29)), Geq(left=Var(... | NT | null | EXTREMUM | sympy | LIN_FORM | [
"LIN_FORM/C4",
"K2/C4"
] | a30854 | nt_min_coprime_above_v1 | null | 7 | 0 | [
"C4",
"K2",
"LIN_FORM"
] | 3 | 0.021 | 2026-02-08T13:17:55.390350Z | {
"verified": true,
"answer": 77285,
"timestamp": "2026-02-08T13:17:55.411757Z"
} | 82cfa0 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 211,
"completion_tokens": 6004
},
"timestamp": "2026-02-15T13:03:04.442Z",
"answer": 77285
},
... | 1 | [
{
"lemma": "C4",
"status": "ok_later"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "K2",
"status": "ok"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "... | {
"lo": -6.96,
"mid": -4.56,
"hi": -1.46
} | ||
7cde8a | nt_max_prime_below_v1_2051736721_5761 | Let $P$ 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 $L$ be the number of elements in $P$. Determine the largest prime number $n$ such that $L \leq n \leq 18225$. Let $Q$ be the remainder when $85801$ times this prime is di... | 71,923 | graphs = [
Graph(
let={
"_n": Const(95919),
"upper": Const(18225),
"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 | 4 | 0 | [
"COPRIME_PAIRS"
] | 1 | 5.453 | 2026-02-08T18:47:27.058445Z | {
"verified": true,
"answer": 71923,
"timestamp": "2026-02-08T18:47:32.511369Z"
} | 26a9a4 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 155,
"completion_tokens": 3554
},
"timestamp": "2026-02-18T19:36:08.500Z",
"answer": 71923
},
... | 1 | [
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "V8_SUM",
"... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
beca8e | comb_sum_binomial_row_v1_1218484723_2744 | Let $R$ be the minimum value of
\[
24a^{2}b + 98b^{3} - 96ab^{2}
\]
over all ordered pairs $(a, b)$ of positive integers with $1 \le a \le 17$ and $1 \le b \le 17$.
Define
\[
V = \bigl|\{v : v \ge 0,\ v \le 8978,\ \text{there exist integers } a_1, b_1 \text{ with } 1 \le a_1 \le 17,\ 1 \le b_1 \le 17 \\ \text{such tha... | 16,384 | graphs = [
Graph(
let={
"_c": Const(8978),
"_m": Const(17),
"_n": MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("a"), Var("b")]), condition=And(Geq(Var("a"), Const(1)), Leq(Var("a"), Const(17)), Geq(Var("b"), Const(1)), Leq(Var("b"), Const(17)))), exp... | COMB | null | SUM | sympy | QF_PSD_DISTINCT | [
"QF_PSD_DISTINCT/POLY4_COUNT",
"POLY3_MIN/POLY4_COUNT"
] | 61dd34 | comb_sum_binomial_row_v1 | null | 7 | 0 | [
"POLY3_MIN",
"POLY4_COUNT",
"QF_PSD_DISTINCT"
] | 3 | 0.012 | 2026-02-25T04:27:32.886128Z | {
"verified": true,
"answer": 16384,
"timestamp": "2026-02-25T04:27:32.898336Z"
} | a4df4c | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 411,
"completion_tokens": 16823
},
"timestamp": "2026-03-29T06:19:46.195Z",
"answer": 16384
},
{
... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "POLY3_MIN",
"status": "ok"
},
{
"lemma": "POLY4_COUNT",
"status": "ok_later"
},
{
"lemma": "QF_PSD_DIS... | {
"lo": -2.45,
"mid": 1.37,
"hi": 5.29
} | ||
c5a40a | nt_count_divisible_and_v1_168721529_1212 | Let $d_1 = 10$. Let $d_2$ be the number of integers $t$ such that $5 \leq t \leq 18$ and there exist positive integers $a$ and $b$ with $1 \leq a \leq 4$, $1 \leq b \leq 3$, and $t = 3a + 2b$. Define $S$ to be the set of all positive integers $n \leq 180960$ such that $n$ is divisible by $d_1$ and the remainder when $n... | 3,016 | graphs = [
Graph(
let={
"upper": Const(180960),
"d1": Const(10),
"d2": CountOverSet(set=SolutionsSet(var=Var("t"), condition=Exists(var=Var(name='a'), condition=Exists(var=Var(name='b'), condition=And(Geq(left=Var(name='a'), right=Const(value=1)), Leq(left=Var(name='a'), ... | COMB | null | COUNT | sympy | BINOMIAL_ALTERNATING | [
"BINOMIAL_ALTERNATING",
"LIN_FORM"
] | 10f694 | nt_count_divisible_and_v1 | null | 6 | 0 | [
"BINOMIAL_ALTERNATING",
"LIN_FORM"
] | 2 | 6.681 | 2026-02-08T13:31:40.618865Z | {
"verified": true,
"answer": 3016,
"timestamp": "2026-02-08T13:31:47.299790Z"
} | 8bc041 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 281,
"completion_tokens": 1029
},
"timestamp": "2026-02-09T14:40:59.470Z",
"answer": 3016
},
{
"i... | 1 | [
{
"lemma": "BINOMIAL_ALTERNATING",
"status": "ok"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma":... | {
"lo": -4.95,
"mid": -2.96,
"hi": -0.89
} | ||
800b2f | lin_form_endings_v1_1125832087_1798 | Let $a = 30$ and $b = 20$. Let $g = \gcd(a, b)$. Compute the remainder when $17625 \cdot g$ is divided by $55288$. | 10,386 | graphs = [
Graph(
let={
"a_coeff": Const(30),
"b_coeff": Const(20),
"_inner_result": GCD(a=Ref("a_coeff"), b=Ref("b_coeff")),
"_scale_k": Const(17625),
"_scaled": Mul(Ref("_scale_k"), Ref("_inner_result")),
"_mod_M": Const(55288),
... | COMB | NT | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | lin_form_endings_v1 | null | 2 | null | [
"LIN_FORM"
] | 1 | 0.001 | 2026-02-08T03:57:10.548824Z | {
"verified": true,
"answer": 10386,
"timestamp": "2026-02-08T03:57:10.549610Z"
} | 009117 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 155,
"completion_tokens": 349
},
"timestamp": "2026-02-10T16:22:38.464Z",
"answer": 10486
},
{
... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "V8",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
}
... | {
"lo": -5.55,
"mid": -3.02,
"hi": 0.31
} | ||
f43104 | antilemma_cartesian_v1_784195855_5668 | Let $x$ be the number of ordered pairs $(a,b)$ of positive integers such that $1 \leq a \leq 17$ and $1 \leq b \leq 35$. Let $Q$ be the difference between the number of ordered pairs $(a,b)$ with $1 \leq a \leq 24$, $1 \leq b \leq 37$, and $x$. Find the value of $Q$. | 293 | graphs = [
Graph(
let={
"x": CountOverSet(set=CartesianProduct(left=IntegerRange(start=Const(1), end=Const(17)), right=IntegerRange(start=Const(1), end=Const(35)))),
"Q": Sub(CountOverSet(set=CartesianProduct(left=IntegerRange(start=Const(1), end=Const(24)), right=IntegerRange(start=... | COMB | GEOM | COMPUTE | sympy | COUNT_CARTESIAN | [
"COUNT_CARTESIAN",
"COUNT_CARTESIAN"
] | f9c395 | antilemma_cartesian_v1 | negation_mod | 2 | 0 | [
"COUNT_CARTESIAN"
] | 1 | 0.001 | 2026-02-08T08:01:53.904416Z | {
"verified": true,
"answer": 293,
"timestamp": "2026-02-08T08:01:53.905688Z"
} | b9365b | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 207,
"completion_tokens": 1013
},
"timestamp": "2026-02-24T08:43:44.331Z",
"answer": 293
},
{
"id... | 2 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "ok"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8",
"status": ... | {
"lo": -9.23,
"mid": -6.18,
"hi": -4.06
} | ||
05e44f | comb_binomial_compute_v1_1520064083_2376 | Let $n = 15$. Let $k$ be the number of positive integers between $1$ and $288$ inclusive that are divisible by $36$. Compute $\binom{n}{k}$. | 6,435 | graphs = [
Graph(
let={
"_n": Const(36),
"n": Const(15),
"k": CountOverSet(set=SolutionsSet(var=Var("k"), condition=And(Geq(Var("k"), Const(1)), Leq(Var("k"), Const(288)), Divides(divisor=Ref("_n"), dividend=Var("k"))), domain='positive_integers')),
"result": ... | NT | null | COMPUTE | sympy | C2 | [
"C2"
] | 9685eb | comb_binomial_compute_v1 | null | 3 | 0 | [
"C2"
] | 1 | 0.001 | 2026-02-08T04:41:25.454263Z | {
"verified": true,
"answer": 6435,
"timestamp": "2026-02-08T04:41:25.455237Z"
} | 9ee92a | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 153,
"completion_tokens": 654
},
"timestamp": "2026-02-11T21:49:31.747Z",
"answer": 6435
},
{
"id... | 1 | [
{
"lemma": "C2",
"status": "ok"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "V1",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
... | {
"lo": -7.01,
"mid": -4.68,
"hi": -2.15
} | ||
2a27b6 | nt_count_coprime_v1_124444284_6090 | Let $S$ be the set of all ordered pairs of positive integers $(x, y)$ such that $xy = 441$. Let $k$ be the minimum value of $x + y$ over all pairs in $S$. Determine the number of positive integers $n$ such that $1 \leq n \leq 65536$ and $\gcd(n, k) = 1$. | 18,724 | graphs = [
Graph(
let={
"upper": Const(65536),
"k": MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(Mul(Var("x"), Var("y")), Const(441)))), expr=Sum(Var("x"), Var("y"))... | NT | null | COUNT | sympy | B3 | [
"B3"
] | 0cd20d | nt_count_coprime_v1 | null | 4 | 0 | [
"B3"
] | 1 | 16.5 | 2026-02-08T08:07:28.795117Z | {
"verified": true,
"answer": 18724,
"timestamp": "2026-02-08T08:07:45.295244Z"
} | 967f5d | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 128,
"completion_tokens": 1637
},
"timestamp": "2026-02-13T14:46:57.535Z",
"answer": 18724
},
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "V1",
"status": "no"
},
{
"lemma": "V3",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
}
] | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
bb8515 | nt_count_digit_sum_v1_1520064083_10331 | Let $d$ be the smallest divisor of 47027 that is at least 2. Let $T$ be the number of ordered pairs $(i, j)$ of integers such that $1 \leq i \leq 30$, $1 \leq j \leq 30$, and $i + j = d$. Define $S$ as the set of all positive integers $n$ such that $n \leq 22500$ and the sum of the decimal digits of $n$ equals $T$. Let... | 52,345 | graphs = [
Graph(
let={
"_n": MinOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Const(2)), Divides(divisor=Var("d"), dividend=Const(47027))))),
"upper": Const(22500),
"target_sum": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("i"), Var("j")]),... | NT | null | COUNT | sympy | MIN_PRIME_FACTOR | [
"MIN_PRIME_FACTOR/COUNT_SUM_EQUALS"
] | ca7168 | nt_count_digit_sum_v1 | null | 5 | 0 | [
"COUNT_SUM_EQUALS",
"MIN_PRIME_FACTOR"
] | 2 | 0.923 | 2026-02-08T11:21:20.477307Z | {
"verified": true,
"answer": 52345,
"timestamp": "2026-02-08T11:21:21.399983Z"
} | 2854c0 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 198,
"completion_tokens": 5630
},
"timestamp": "2026-02-14T12:09:53.681Z",
"answer": 52345
},
... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "ok_later"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
... | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
93774b | nt_count_divisible_and_v1_1520064083_5585 | Let $m = 35$. Let $P$ be the set of all ordered pairs of positive integers $(x, y)$ such that $x + y = 34$. Let $M$ be the maximum value of $xy$ over all such pairs. Let $Q$ be the set of all ordered pairs of positive integers $(x, y)$ such that $xy = M$. Let $s$ be the minimum value of $x + y$ over all pairs in $Q$. L... | 47,596 | graphs = [
Graph(
let={
"_n": Const(35),
"upper": Const(157968),
"d1": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPos... | NT | null | COUNT | sympy | B1 | [
"B1/B3/C5"
] | 4cc6b9 | nt_count_divisible_and_v1 | null | 6 | 0 | [
"B1",
"B3",
"C5"
] | 3 | 10.591 | 2026-02-08T07:26:36.689733Z | {
"verified": true,
"answer": 47596,
"timestamp": "2026-02-08T07:26:47.280878Z"
} | ee3575 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 275,
"completion_tokens": 1122
},
"timestamp": "2026-02-13T10:22:46.121Z",
"answer": 47596
},
... | 1 | [
{
"lemma": "B1",
"status": "ok"
},
{
"lemma": "B3",
"status": "ok_later"
},
{
"lemma": "C5",
"status": "ok_later"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "L3c... | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
769b60 | diophantine_fbi2_count_v1_2051736721_2870 | Let $k = 60$. Compute the number of positive integers $d$ such that $2 \leq d \leq 56$, $d$ divides $60$, $\frac{60}{d} \geq 6$, and $\frac{60}{d} \leq \min\{x + y \mid x, y \text{ are positive integers and } xy = 900\}$. Let $r$ be this number. Compute $r^2 + 8r + 33$. | 117 | graphs = [
Graph(
let={
"k": Const(60),
"result": CountOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Const(2)), Leq(Var("d"), Const(56)), Divides(divisor=Var("d"), dividend=Ref("k")), Geq(Div(Ref("k"), Var("d")), Const(6)), Leq(Div(Ref("k"), Var("d")), MinOverSet... | NT | null | COUNT | sympy | LIN_FORM | [
"LIN_FORM",
"B3"
] | 688dbe | diophantine_fbi2_count_v1 | null | 5 | 0 | [
"B3",
"LIN_FORM"
] | 2 | 0.011 | 2026-02-08T16:58:45.753110Z | {
"verified": true,
"answer": 117,
"timestamp": "2026-02-08T16:58:45.763717Z"
} | b76aaa | 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": 998
},
"timestamp": "2026-02-17T16:41:47.943Z",
"answer": 117
},
{
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
ac3ea4 | modular_min_modexp_v1_153355830_1170 | Let $a = \sum_{k=1}^{2} \varphi(k) \left\lfloor \frac{2}{k} \right\rfloor$, and let $b = 34$. Let $m$ be the smallest divisor $d$ of $125142874424741$ such that $d \geq 2$. Let $\text{result}$ be the smallest positive integer $x \leq 100$ such that $a^x \equiv b \pmod{m}$. Compute the remainder when $81167 \cdot \text{... | 83,043 | graphs = [
Graph(
let={
"_n": Const(2),
"a": Summation(var="k", start=Const(1), end=Const(2), expr=Mul(EulerPhi(n=Var("k")), Floor(Div(Const(2), Var("k"))))),
"b": Const(34),
"m": MinOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Ref("_n"))... | NT | null | EXTREMUM | sympy | MIN_PRIME_FACTOR | [
"MIN_PRIME_FACTOR",
"K2"
] | 8f7f24 | modular_min_modexp_v1 | null | 7 | 0 | [
"K2",
"MIN_PRIME_FACTOR"
] | 2 | 0.008 | 2026-02-08T06:10:32.356183Z | {
"verified": true,
"answer": 83043,
"timestamp": "2026-02-08T06:10:32.364418Z"
} | 72000e | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 168,
"completion_tokens": 4385
},
"timestamp": "2026-02-12T20:31:38.711Z",
"answer": 83043
},
... | 1 | [
{
"lemma": "K2",
"status": "ok"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "MIN_PRIME_FACTOR",
"status": "ok"
},
{
"lemma": "V7",
"status": "no"... | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
bea78c | comb_bell_compute_v1_784195855_8509 | Let $n$ be the number of positive integers less than or equal to $112$ that are divisible by $8$ and relatively prime to $15$. Let $B_n$ denote the $n$th Bell number, which counts the number of partitions of a set of $n$ elements. Compute the remainder when $1 - B_n$ is divided by $63110$. | 58,971 | graphs = [
Graph(
let={
"_n": Const(15),
"n": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Const(112)), Divides(divisor=Const(8), dividend=Var("n")), Eq(GCD(a=Var("n"), b=Ref("_n")), Const(1))))),
"result": Bell(Ref("n")... | NT | COMB | COMPUTE | sympy | C5 | [
"C5"
] | 1d9668 | comb_bell_compute_v1 | null | 5 | 0 | [
"C5"
] | 1 | 0.002 | 2026-02-08T16:07:58.688135Z | {
"verified": true,
"answer": 58971,
"timestamp": "2026-02-08T16:07:58.690167Z"
} | 6ce57b | 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": 761
},
"timestamp": "2026-02-16T22:18:56.397Z",
"answer": 58971
},
{... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "C5",
"status": "ok"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
7c9fc3 | antilemma_k2_v1_1978505735_7666 | Let $n = 424$. Define
$$
x = \sum_{k=1}^{n} \varphi(k) \left\lfloor \frac{424}{k} \right\rfloor,
$$
where $\varphi(k)$ denotes Euler's totient function. Compute $x$. | 90,100 | graphs = [
Graph(
let={
"_n": Const(424),
"x": Summation(var="k", start=Const(1), end=Ref("_n"), expr=Mul(EulerPhi(n=Var("k")), Floor(Div(Const(424), Var("k"))))),
},
goal=Ref("x"),
)
] | NT | COMB | COMPUTE | sympy | K2 | [
"K2"
] | 6897ab | antilemma_k2_v1 | null | 6 | 0 | [
"K2"
] | 1 | 0.001 | 2026-02-08T20:22:53.650622Z | {
"verified": true,
"answer": 90100,
"timestamp": "2026-02-08T20:22:53.651225Z"
} | 48f7cd | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 104,
"completion_tokens": 1296
},
"timestamp": "2026-02-19T00:28:16.127Z",
"answer": 90100
},
... | 1 | [
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "K2",
"status": "ok"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
87cd52 | diophantine_fbi2_min_v1_1439011603_684 | Let $k = 33$, $a = 3$, $b = 1$, and $U = 43$. Find the smallest integer $d$ such that $4 \leq d \leq U$, $d$ divides $k$, and $\frac{k}{d} \geq 2$. Compute the value of this integer. | 11 | graphs = [
Graph(
let={
"k": Const(33),
"a": Const(3),
"b": Const(1),
"upper": Const(43),
"result": MinOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Const(4)), Leq(Var("d"), Ref("upper")), Divides(divisor=Var("d"), dividend=Ref... | NT | null | EXTREMUM | sympy | COPRIME_PAIRS | [
"LIN_FORM"
] | 7b2633 | diophantine_fbi2_min_v1 | null | 2 | 0 | [
"COPRIME_PAIRS",
"LIN_FORM"
] | 2 | 0.06 | 2026-02-08T15:40:16.926728Z | {
"verified": true,
"answer": 11,
"timestamp": "2026-02-08T15:40:16.986825Z"
} | a120fd | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 129,
"completion_tokens": 485
},
"timestamp": "2026-02-16T06:14:15.501Z",
"answer": 11
},
{
"id": 11,
... | 2 | [
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "V1",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
}
] | {
"lo": -10,
"mid": -7.27,
"hi": -4.54
} | ||
ff2a6e | comb_sum_binomial_row_v1_124444284_5688 | Let $n$ be the minimum value of $x + y$ over all ordered pairs $(x, y)$ of positive integers such that $xy = 49$. Compute the value of $2^n$. | 16,384 | 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(49)))), expr=Sum(Var("x"), Var("y")))),
... | NT | null | SUM | sympy | B3 | [
"B3"
] | 0cd20d | comb_sum_binomial_row_v1 | null | 3 | 0 | [
"B3"
] | 1 | 0.001 | 2026-02-08T06:46:18.711924Z | {
"verified": true,
"answer": 16384,
"timestamp": "2026-02-08T06:46:18.712671Z"
} | 202d81 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 89,
"completion_tokens": 334
},
"timestamp": "2026-02-13T04:25:28.234Z",
"answer": 16384
},
{
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
}
] | {
"lo": -9.14,
"mid": -6.05,
"hi": -3.73
} | ||
a7660b | nt_euler_phi_compute_v1_548369836_322 | Let $n=77777$, and let $\varphi(n)$ denote the number of positive integers less than or equal to $n$ that are relatively prime to $n$.
Let $r$ be the remainder when $\lvert\varphi(n)\rvert$ is divided by $11$, so that $0\le r<11$ and $r\equiv \lvert\varphi(n)\rvert\pmod{11}$.
Let $B_r$ be the $r$-th Bell number, that... | 57,559 | graphs = [
Graph(
let={
"n": Const(77777),
"result": EulerPhi(n=Ref("n")),
"Q": Mod(value=Bell(Mod(value=Abs(arg=Ref(name='result')), modulus=Const(11))), modulus=Const(58416)),
},
goal=Ref("Q"),
)
] | NT | COMB | COMPUTE | sympy | COPRIME_PAIRS | [
"COPRIME_PAIRS/MAX_PRIME_BELOW",
"B3/MAX_PRIME_BELOW"
] | f0e487 | nt_euler_phi_compute_v1 | bell_mod | 5 | 0 | [
"B3",
"COPRIME_PAIRS",
"MAX_PRIME_BELOW"
] | 3 | 0.03 | 2026-02-08T02:51:56.792047Z | {
"verified": true,
"answer": 57559,
"timestamp": "2026-02-08T02:51:56.822308Z"
} | 57a2e7 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 298,
"completion_tokens": 1140
},
"timestamp": "2026-02-08T20:19:44.511Z",
"answer": 57559
},
{
"... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok_... | {
"lo": -0.86,
"mid": 1,
"hi": 2.65
} | ||
dda788 | nt_count_divisible_v1_1742523217_1908 | Let $n = 76019$ and $u = 82944$. Consider the quadratic equation $x^2 - 437x - 11550 = 0$. Let $s$ be the sum of all integer solutions to this equation. Let $d$ be the smallest divisor of $s$ that is at least 2. Compute the number of positive integers $m \leq u$ that are divisible by $d$. Then, compute the remainder wh... | 32,038 | graphs = [
Graph(
let={
"_n": Const(76019),
"upper": Const(82944),
"divisor": MinOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Const(2)), Divides(divisor=Var("d"), dividend=SumOverSet(set=SolutionsSet(var=Var("x"), condition=Eq(Sum(Pow(Var("x"), Const... | NT | null | COUNT | sympy | VIETA_SUM | [
"VIETA_SUM/MIN_PRIME_FACTOR"
] | b1c8ca | nt_count_divisible_v1 | null | 5 | 0 | [
"MIN_PRIME_FACTOR",
"VIETA_SUM"
] | 2 | 2.707 | 2026-02-08T04:20:31.959912Z | {
"verified": true,
"answer": 32038,
"timestamp": "2026-02-08T04:20:34.666516Z"
} | 2cf35d | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 219,
"completion_tokens": 1478
},
"timestamp": "2026-02-10T16:10:57.373Z",
"answer": 32038
},
{
... | 1 | [
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "MIN_PRIME_FACTOR",
"status": "ok_later"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
}... | {
"lo": -3.42,
"mid": 1.86,
"hi": 7.55
} | ||
40a733 | diophantine_sum_product_min_v1_349078426_1576 | Let $S = 23$. Let $T$ be the set of all integers $t$ such that $5 \leq t \leq 3975$ and $t = 2a + 3b$ for some positive integers $a \leq 474$ and $b \leq 1009$. Let $P$ be the minimum value of $x + y$ over all pairs of positive integers $(x, y)$ such that $xy = |T|$, the number of elements in $T$. Find the value of the... | 9 | graphs = [
Graph(
let={
"_n": Const(22),
"S": Const(23),
"P": MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(Mul(Var("x"), Var("y")), CountOverSet(set=Solu... | NT | null | EXTREMUM | sympy | LIN_FORM | [
"LIN_FORM/B3"
] | 05313e | diophantine_sum_product_min_v1 | null | 7 | 0 | [
"B3",
"LIN_FORM"
] | 2 | 0.006 | 2026-02-08T13:43:53.529730Z | {
"verified": true,
"answer": 9,
"timestamp": "2026-02-08T13:43:53.535447Z"
} | 05e8f9 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 180,
"completion_tokens": 4976
},
"timestamp": "2026-02-15T20:06:38.403Z",
"answer": 9
},
{
... | 1 | [
{
"lemma": "B3",
"status": "ok_later"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
... | {
"lo": -5.49,
"mid": 0.22,
"hi": 6.51
} | ||
39378f | sequence_lucas_compute_v1_168721529_1774 | Let $m = 32215$. Let $x$ be a solution to the equation $x^2 - 6x - 3960 = 0$. Define $n$ as the sum
$$
\sum_{k=1}^{x} \phi(k) \left\lfloor \frac{1}{k} \sum_{k=1}^{3} \phi(k) \left\lfloor \frac{3}{k} \right\rfloor \right\rfloor,
$$
where $\phi$ denotes Euler's totient function. Let $L_n$ be the $n$-th Lucas number, def... | 35,042 | graphs = [
Graph(
let={
"_m": Const(32215),
"_n": SumOverSet(set=SolutionsSet(var=Var("x"), condition=Eq(Sum(Pow(Var("x"), Const(2)), Mul(Const(-6), Var("x")), Const(-3960)), Const(0)))),
"n": Summation(var="k", start=Const(1), end=Ref("_n"), expr=Mul(EulerPhi(n=Var("k"))... | NT | null | COMPUTE | sympy | VIETA_SUM | [
"VIETA_SUM/K2",
"K2/K2"
] | 451831 | sequence_lucas_compute_v1 | null | 7 | 0 | [
"K2",
"VIETA_SUM"
] | 2 | 0.007 | 2026-02-08T13:54:54.087312Z | {
"verified": true,
"answer": 35042,
"timestamp": "2026-02-08T13:54:54.093988Z"
} | a8f218 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 307,
"completion_tokens": 2095
},
"timestamp": "2026-02-09T21:30:37.383Z",
"answer": 35042
},
{
"... | 1 | [
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "K2",
"status": "ok"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "VAL_SUM_EQ",
"status": "no"
},
{
"lemma": "VIE... | {
"lo": -5.49,
"mid": 0.03,
"hi": 6.12
} | ||
4b060a | diophantine_fbi2_min_v1_168721529_880 | Let $d$ be an integer satisfying the following conditions: $d \geq \sum_{k=1}^{2} k$, $d \leq 31$, $d$ divides $21$, and $\frac{21}{d} \geq 5$. Let $r$ be the smallest such $d$. Compute $13311 \cdot r$. | 39,933 | graphs = [
Graph(
let={
"k": Const(21),
"upper": Const(31),
"result": MinOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Summation(var="k", start=EulerPhi(n=Const(1)), end=Const(2), expr=Var("k"))), Leq(Var("d"), Ref("upper")), Divides(divisor=Var("d"),... | NT | null | EXTREMUM | sympy | SUM_ARITHMETIC | [
"SUM_ARITHMETIC",
"ONE_PHI_1"
] | 342157 | diophantine_fbi2_min_v1 | null | 3 | 0 | [
"ONE_PHI_1",
"SUM_ARITHMETIC"
] | 2 | 0.007 | 2026-02-08T13:20:04.615452Z | {
"verified": true,
"answer": 39933,
"timestamp": "2026-02-08T13:20:04.622393Z"
} | 3bc8d3 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 191,
"completion_tokens": 554
},
"timestamp": "2026-02-09T10:11:08.027Z",
"answer": 39933
},
{
"i... | 2 | [
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "ONE_PHI_1",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "SUM_ARITHMETIC",
"status": "ok"
},
{
"lemma": "V5",
"stat... | {
"lo": -10,
"mid": -6.5,
"hi": -3.01
} | ||
04d56e | nt_count_divisible_v1_2051736721_3607 | Let $S$ be the set of all ordered pairs $(x_1, y_1)$ of positive integers such that $x_1 + y_1 = 26$. Define $P$ to be the maximum value of $x_1 y_1$ as $(x_1, y_1)$ ranges over $S$. Now let $T$ be the set of all ordered pairs $(x, y)$ of positive integers such that $xy = P$. Define $d$ to be the minimum value of $x + ... | 1,218 | graphs = [
Graph(
let={
"_n": Const(77392),
"upper": Const(31684),
"divisor": 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")), MaxOv... | NT | null | COUNT | sympy | B1 | [
"B1/B3"
] | 80b49d | nt_count_divisible_v1 | null | 6 | 0 | [
"B1",
"B3"
] | 2 | 1.001 | 2026-02-08T17:25:14.324406Z | {
"verified": true,
"answer": 1218,
"timestamp": "2026-02-08T17:25:15.325062Z"
} | 23f1a1 | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 239,
"completion_tokens": 591
},
"timestamp": "2026-02-16T09:41:32.908Z",
"answer": 1217
},
{
"id": 11,... | 1 | [
{
"lemma": "B1",
"status": "ok"
},
{
"lemma": "B3",
"status": "ok_later"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "V3",
"status": "no"
},
{
"lemma... | {
"lo": -8.26,
"mid": -5.01,
"hi": -1.76
} | ||
aeee7f | nt_max_prime_below_v1_1470522791_469 | Let $S$ be the set of all positive integers $p$ for which there exists a positive integer $q$ such that $pq = 6$, $\gcd(p, q) = 1$, and $p < q$. Let $N$ be the number of elements in $S$. Determine the largest prime number $n$ such that $N \leq n \leq 87616$. | 87,613 | graphs = [
Graph(
let={
"upper": Const(87616),
"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 | 2.45 | 2026-02-08T13:01:55.910025Z | {
"verified": true,
"answer": 87613,
"timestamp": "2026-02-08T13:01:58.360012Z"
} | 7c839f | 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": 2235
},
"timestamp": "2026-02-15T08:42:11.352Z",
"answer": 87613
},
... | 1 | [
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
}
] | {
"lo": -9.12,
"mid": -6.02,
"hi": -3.62
} | ||
0f4237 | alg_poly_preperiod_count_v1_1419126231_418 | Let $f(x) = (x^2 + x - 9) \bmod 17$. For a non-negative integer $a$, define the sequence $N = f(a)$, $M = f(N)$, $R = f(M)$, $S = f(R)$. Let $Q$ be the number of integers $a$ with $0 \le a \le 6442$ such that $S = M$ and $R \ne M$. Find $Q$. | 1,895 | graphs = [
Graph(
let={
"p1": Mod(value=Sum(Pow(Var("a"), Const(2)), Var("a"), Const(-9)), modulus=Const(17)),
"p2": Mod(value=Sum(Pow(Ref("p1"), Const(2)), Ref("p1"), Const(-9)), modulus=Const(17)),
"p3": Mod(value=Sum(Pow(Ref("p2"), Const(2)), Ref("p2"), Const(-9)), mod... | ALG | null | COUNT | sympy | POLY_ORBIT_COUNT | [
"POLY_ORBIT_COUNT"
] | 4ad965 | alg_poly_preperiod_count_v1 | null | 5 | null | [
"POLY_ORBIT_COUNT"
] | 1 | 0.023 | 2026-02-25T09:57:49.628957Z | {
"verified": true,
"answer": 1895,
"timestamp": "2026-02-25T09:57:49.651495Z"
} | 40783d | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 213,
"completion_tokens": 9308
},
"timestamp": "2026-03-30T08:25:44.860Z",
"answer": 1895
},
{
"i... | 1 | [
{
"lemma": "POLY_ORBIT_COUNT",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
}
] | {
"lo": -5.37,
"mid": 0.23,
"hi": 5.22
} | ||
638a43 | comb_catalan_compute_v1_784195855_6852 | Let $n$ be the number of ordered pairs $(i,j)$ of integers with $1 \le i \le 10$ and $1 \le j \le 10$ such that $i + j = m$, where $m$ is the number of integers $t$ in the range $5 \le t \le 17$ for which there exist integers $a$ and $b$ satisfying $1 \le a \le 4$, $1 \le b \le 3$, and $t = 2a + 3b$. Compute the $n$-th... | 16,796 | graphs = [
Graph(
let={
"_n": CountOverSet(set=SolutionsSet(var=Var("t"), condition=Exists(var=Var(name='a'), condition=Exists(var=Var(name='b'), condition=And(Geq(left=Var(name='a'), right=Const(value=1)), Leq(left=Var(name='a'), right=Const(value=4)), Geq(left=Var(name='b'), right=Const(value=... | COMB | null | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM/COUNT_SUM_EQUALS"
] | 8a3f7a | comb_catalan_compute_v1 | null | 6 | 0 | [
"COUNT_SUM_EQUALS",
"LIN_FORM"
] | 2 | 0.011 | 2026-02-08T08:55:36.890447Z | {
"verified": true,
"answer": 16796,
"timestamp": "2026-02-08T08:55:36.901746Z"
} | b4e748 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 268,
"completion_tokens": 1100
},
"timestamp": "2026-02-24T10:16:28.125Z",
"answer": 16796
},
{
"... | 1 | [
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "ok_later"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"le... | {
"lo": -3.84,
"mid": -1.67,
"hi": 1.32
} | ||
25ce63 | antilemma_sum_equals_v1_458359167_4442 | Let $n$ be the number of ordered pairs $(i, j)$ such that $1 \leq i \leq 7$ and $1 \leq j \leq 14$. Compute the number of ordered pairs $(i, j)$ of positive integers such that $i + j = n$ and $1 \leq i, j \leq 96$. | 95 | graphs = [
Graph(
let={
"_n": CountOverSet(set=CartesianProduct(left=IntegerRange(start=Const(1), end=Const(7)), right=IntegerRange(start=Const(1), end=Const(14)))),
"x": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("i"), Var("j")]), condition=Eq(Sum(Var("i"), Var("j")), Ref... | COMB | GEOM | COMPUTE | sympy | COUNT_CARTESIAN | [
"COUNT_CARTESIAN/COUNT_SUM_EQUALS",
"COUNT_SUM_EQUALS"
] | 8bee9e | antilemma_sum_equals_v1 | null | 4 | 0 | [
"COUNT_CARTESIAN",
"COUNT_SUM_EQUALS"
] | 2 | 0.004 | 2026-02-08T11:47:46.885895Z | {
"verified": true,
"answer": 95,
"timestamp": "2026-02-08T11:47:46.890348Z"
} | b0b2d0 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 190,
"completion_tokens": 723
},
"timestamp": "2026-02-24T14:42:22.774Z",
"answer": 95
},
{
"id":... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "ok"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "ok"
},
{
"lemma": "V7",
... | {
"lo": -4.92,
"mid": -2.91,
"hi": -0.68
} | ||
03731a | diophantine_product_count_v1_1874849503_581 | Let $s$ be the minimum value of $x + y$ over all ordered pairs $(x, y)$ of positive integers such that $xy = 202500$. Let $k$ be the minimum value of $x + y$ over all ordered pairs $(x, y)$ of positive integers such that $xy = s$. Compute the number of positive integers $x$ such that $1 \leq x \leq 45$, $x$ divides $k$... | 10 | graphs = [
Graph(
let={
"k": MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(Mul(Var("x"), Var("y")), MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("... | NT | null | COUNT | sympy | B3 | [
"B3/B3"
] | 8ffef9 | diophantine_product_count_v1 | null | 6 | 0 | [
"B3"
] | 1 | 0.019 | 2026-02-08T13:11:49.562945Z | {
"verified": true,
"answer": 10,
"timestamp": "2026-02-08T13:11:49.582128Z"
} | cf8575 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 221,
"completion_tokens": 1439
},
"timestamp": "2026-02-11T07:36:15.418Z",
"answer": 10
},
{
"id... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
}
] | {
"lo": -5.13,
"mid": 0.83,
"hi": 7.52
} | ||
bfb2bd | nt_sum_totient_over_divisors_v1_655260480_466 | Let $n$ be the number of integers $t$ such that $28 \leq t \leq 4046$ and there exist positive integers $a \leq 258$ and $b \leq 912$ satisfying $t = 5a + 3b + 20$. Compute $\sum_{d \mid n} \phi(d)$, where $\phi$ denotes Euler's totient function. | 4,011 | graphs = [
Graph(
let={
"n": CountOverSet(set=SolutionsSet(var=Var("t"), condition=Exists(var=Var(name='a'), condition=Exists(var=Var(name='b'), condition=And(Geq(left=Var(name='a'), right=Const(value=1)), Leq(left=Var(name='a'), right=Const(value=258)), Geq(left=Var(name='b'), right=Const(value... | NT | null | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | nt_sum_totient_over_divisors_v1 | null | 5 | 0 | [
"LIN_FORM"
] | 1 | 0.005 | 2026-02-08T15:24:08.470532Z | {
"verified": true,
"answer": 4011,
"timestamp": "2026-02-08T15:24:08.475252Z"
} | 2b87b5 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 130,
"completion_tokens": 6020
},
"timestamp": "2026-02-16T05:32:48.893Z",
"answer": 4011
},
{... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "V3",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
57a55a | modular_count_residue_v1_1918700295_1889 | Let $N$ be the number of positive integers $n$ such that $n \leq 82944$ and $n \equiv 10 \pmod{29}$. Let $c$ be the largest positive divisor of $4108725$ that is at most $2025$. Compute the remainder when $c - N$ is divided by $50731$. | 49,896 | graphs = [
Graph(
let={
"upper": Const(82944),
"m": Const(29),
"r": Const(10),
"result": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Ref("upper")), Eq(Mod(value=Var("n"), modulus=Ref("m")), Ref("r"))))),
... | NT | null | COUNT | sympy | MAX_DIVISOR | [
"MAX_DIVISOR"
] | ad1a9b | modular_count_residue_v1 | negation_mod | 3 | 0 | [
"MAX_DIVISOR"
] | 1 | 5.086 | 2026-02-08T06:09:32.218310Z | {
"verified": true,
"answer": 49896,
"timestamp": "2026-02-08T06:09:37.304724Z"
} | 3bfade | 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": 1769
},
"timestamp": "2026-02-12T20:48:34.415Z",
"answer": 49896
},
... | 1 | [
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "MAX_DIVISOR",
"status": "ok"
},
{
"lemma": "V3",
"status": "no"
}
] | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
f72122 | modular_product_range_v1_601307018_7317 | Let $M = \prod_{i=49}^{k} i$, where $$k = \min\left\{ 41a^2 + 64ab + 25b^2 \mid a, b \in \mathbb{Z}^+,\, 1 \leq a \leq 17,\, 1 \leq b \leq 17 \right\}.$$ Find the remainder when $M$ is divided by $11261$. | 3,649 | graphs = [
Graph(
let={
"_n": Const(41),
"prod": MathProduct(expr=Var("i"), var="i", start=Const(49), end=MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("a"), Var("b")]), condition=And(Geq(Var("a"), Const(1)), Leq(Var("a"), Const(17)), Geq(Var("b"), Const(1)), Leq... | NT | null | COMPUTE | sympy | QF_PSD_MIN | [
"QF_PSD_MIN"
] | c66ce3 | modular_product_range_v1 | null | 5 | 0 | [
"QF_PSD_MIN"
] | 1 | 0.004 | 2026-03-10T07:55:11.366345Z | {
"verified": true,
"answer": 3649,
"timestamp": "2026-03-10T07:55:11.370803Z"
} | e53d34 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 209,
"completion_tokens": 9778
},
"timestamp": "2026-04-19T06:25:42.607Z",
"answer": 3649
},
{
"... | 1 | [
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "QF_PSD_MIN",
"status": "ok"
}... | {
"lo": -5.34,
"mid": 1.1,
"hi": 7.53
} | ||
c504e3_l | nt_sum_over_divisible_v1_153355830_1108 | Let $n = 78544$. Define $d = \sum_{k=1}^{12} \phi(k) \left\lfloor \frac{12}{k} \right\rfloor$, where $\phi$ is Euler's totient function. Let $S$ be the set of all integers $n$ with $1 \le n \le 38416$ such that $n$ is divisible by $d$. Let $R$ be the sum of all elements in $S$. Compute the remainder when $55879 \cdot R... | 0 | NT | null | SUM | sympy | K2 | [
"K2"
] | 6897ab | nt_sum_over_divisible_v1 | null | 4 | 0 | [
"K2"
] | 1 | 2.117 | 2026-02-08T04:24:10.836515Z | {
"verified": false,
"answer": 18172,
"timestamp": "2026-02-08T04:24:12.953746Z"
} | a48b9e | c504e3 | legacy_text | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 165,
"completion_tokens": 1939
},
"timestamp": "2026-02-12T20:23:08.591Z",
"answer": 18172
},
... | 1 | [
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "K2",
"status": "ok"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "VAL_SUM_EQ",
"status": "... | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | |
fcb9f0 | modular_inverse_v1_124444284_5393 | Let $n = 2$ and $a = 417$. Let $m$ be the smallest divisor of $134770649251057$ that is at least $n$. Let the upper bound be $660$. Define $S$ as the set of all integers $x$ such that $1 \le x \le 660$ and
$$
417x \equiv 1 \pmod{m}.
$$
Compute the smallest element of $S$. | 512 | graphs = [
Graph(
let={
"_n": Const(2),
"a": Const(417),
"m": MinOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Ref("_n")), Divides(divisor=Var("d"), dividend=Const(134770649251057))))),
"upper": Const(660),
"result": MinOverSet... | NT | null | EXTREMUM | sympy | MIN_PRIME_FACTOR | [
"MIN_PRIME_FACTOR"
] | bc3776 | modular_inverse_v1 | null | 6 | 0 | [
"MIN_PRIME_FACTOR"
] | 1 | 0.029 | 2026-02-08T06:34:21.916225Z | {
"verified": true,
"answer": 512,
"timestamp": "2026-02-08T06:34:21.945651Z"
} | 55919e | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 140,
"completion_tokens": 4270
},
"timestamp": "2026-02-13T02:13:36.257Z",
"answer": 512
},
{
... | 1 | [
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "MIN_PRIME_FACTOR",
"status": "ok"
},
{
"lemma": "V1",
"status": "no"
}
] | {
"lo": -3.51,
"mid": 1.33,
"hi": 6.56
} | ||
ab084a | antilemma_k2_v1_1520064083_5894 | Let $x_1$ and $x_2$ be the roots of the quadratic equation $x^2 - 165x + 800 = 0$. Let $s$ be the sum of all integers $x$ that satisfy this equation. Compute the value of
$$
\sum_{k=1}^{s} \phi(k) \left\lfloor \frac{165}{k} \right\rfloor,
$$
where $\phi$ denotes Euler's totient function. | 13,695 | graphs = [
Graph(
let={
"_n": Const(165),
"x": Summation(var="k", start=Const(1), end=SumOverSet(set=SolutionsSet(var=Var("x"), condition=Eq(Sum(Pow(Var("x"), Const(2)), Mul(Const(-165), Var("x")), Const(800)), Const(0)))), expr=Mul(EulerPhi(n=Var("k")), Floor(Div(Ref("_n"), Var("k")... | NT | COMB | COMPUTE | sympy | VIETA_SUM | [
"VIETA_SUM/K2",
"K2"
] | 6be084 | antilemma_k2_v1 | null | 6 | 0 | [
"K2",
"VIETA_SUM"
] | 2 | 0.001 | 2026-02-08T07:42:22.817017Z | {
"verified": true,
"answer": 13695,
"timestamp": "2026-02-08T07:42:22.817777Z"
} | fb0208 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 144,
"completion_tokens": 1542
},
"timestamp": "2026-02-13T11:37:33.256Z",
"answer": 13695
},
... | 1 | [
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K2",
"status": "ok"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
... | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
7c8d5e | geo_count_lattice_rect_v1_397696148_1445 | Compute the number of lattice points in the rectangle $[0, 89] \times [0, 159]$, including the boundary. | 14,400 | graphs = [
Graph(
let={
"a": Const(89),
"b": Const(159),
"result": LatticePointsRect(a=Ref(name='a'), b=Ref(name='b')),
},
goal=Ref("result"),
)
] | GEOM | null | COUNT | sympy | [] | geo_count_lattice_rect_v1 | null | 3 | 0 | null | null | 0.002 | 2026-02-08T12:33:16.183639Z | {
"verified": true,
"answer": 14400,
"timestamp": "2026-02-08T12:33:16.185300Z"
} | 04c32a | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 139,
"completion_tokens": 209
},
"timestamp": "2026-02-24T15:46:54.102Z",
"answer": 14400
},
{
"i... | 1 | [] | {
"lo": -7.18,
"mid": -5,
"hi": -3.01
} | ||||
be99e2 | diophantine_fbi2_count_v1_1431428450_85 | Let $s$ be the minimum value of $x + y$ over all pairs of positive integers $(x, y)$ such that $xy = 9$. Let $k$ be the minimum value of $x + y$ over all pairs of positive integers $(x, y)$ such that $xy = 396900$. Determine the number of positive integers $d$ such that $s \leq d \leq 69$, $d$ divides $k$, and $\frac{k... | 10 | graphs = [
Graph(
let={
"_m": Const(5),
"_n": MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(Mul(Var("x"), Var("y")), Const(9)))), expr=Sum(Var("x"), Var("y")))),
... | NT | null | COUNT | sympy | MIN_PRIME_FACTOR | [
"B3/B3"
] | 8ffef9 | diophantine_fbi2_count_v1 | null | 5 | 0 | [
"B3",
"MIN_PRIME_FACTOR"
] | 2 | 0.056 | 2026-02-08T13:10:50.944812Z | {
"verified": true,
"answer": 10,
"timestamp": "2026-02-08T13:10:51.000624Z"
} | ad1880 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 175,
"completion_tokens": 1542
},
"timestamp": "2026-02-15T11:07:02.180Z",
"answer": 10
},
{
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "VAL_SUM_EQ",
"status": "no"
}
] | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
f89827 | comb_count_derangements_v1_124444284_3171 | Let $n$ be the number of positive integers $p$ for which there exists a positive integer $q$ such that $pq = 1323000$, $\gcd(p, q) = 1$, and $p < q$. Compute the subfactorial of $n$, denoted $!n$. | 14,833 | graphs = [
Graph(
let={
"n": CountOverSet(set=SolutionsSet(var=Var("p"), condition=And(IsPositive(arg=Var(name='p')), Exists(var=Var(name='q'), condition=And(Eq(left=Mul(Var(name='p'), Var(name='q')), right=Const(value=1323000)), Eq(left=GCD(a=Var(name='p'), b=Var(name='q')), right=Const(value=1... | NT | COMB | COUNT | sympy | COPRIME_PAIRS | [
"COPRIME_PAIRS"
] | 2bb3aa | comb_count_derangements_v1 | null | 6 | 0 | [
"COPRIME_PAIRS"
] | 1 | 0.001 | 2026-02-08T05:17:04.662711Z | {
"verified": true,
"answer": 14833,
"timestamp": "2026-02-08T05:17:04.663473Z"
} | eef214 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 110,
"completion_tokens": 1658
},
"timestamp": "2026-02-12T05:52:29.952Z",
"answer": 14833
},
... | 1 | [
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "V1",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
... | {
"lo": -3.51,
"mid": 1.33,
"hi": 6.56
} | ||
286214 | algebra_poly_eval_v1_1470522791_109 | Let $m = 10$ and $n = 60$. Define $s$ to be the minimum value of $x + y$ over all ordered pairs $(x, y)$ of positive integers such that $xy = 1600$. Define $t$ to be the minimum value of $x + y$ over all ordered pairs $(x, y)$ of positive integers such that $xy = 11022400$. Let $d_{\max}$ be the largest positive diviso... | 5,175 | graphs = [
Graph(
let={
"_m": Const(2),
"_n": Const(60),
"m": Const(10),
"result": Div(Sum(Mul(Ref("_n"), Pow(Ref("m"), Const(4))), Mul(Const(-186), Pow(Ref("m"), Const(3))), Mul(Const(224), Pow(Ref("m"), Ref("_m"))), Mul(Const(-178), Ref("m")), MaxOverSet(set... | NT | null | COMPUTE | sympy | B3 | [
"B3/MAX_DIVISOR"
] | 33b851 | algebra_poly_eval_v1 | null | 5 | 0 | [
"B3",
"MAX_DIVISOR"
] | 2 | 0.012 | 2026-02-08T12:49:55.025000Z | {
"verified": true,
"answer": 5175,
"timestamp": "2026-02-08T12:49:55.037113Z"
} | eaeb6f | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 202,
"completion_tokens": 1725
},
"timestamp": "2026-02-15T07:01:48.403Z",
"answer": 5175
},
{... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "MAX_DIVISOR",
"status": "... | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
3eb2d5 | algebra_quadratic_discriminant_v1_458359167_1041 | Let $a = -2$ and $b = -14$. Let $c$ be the number of integers $t$ with $23 \leq t \leq 65$ such that $t = 8a' + 6b' + 9$ for some integers $a', b'$ with $1 \leq a' \leq 4$ and $1 \leq b' \leq 4$. Let $k$ be the number of positive integers $j \leq 4$ such that $j^5 \leq 1024$. Define $r = b^2 - k \cdot a \cdot c$. Compu... | 27,982 | graphs = [
Graph(
let={
"_m": Const(4),
"_n": Const(53038),
"a": Const(-2),
"b": Const(-14),
"c": CountOverSet(set=SolutionsSet(var=Var("t"), condition=Exists(var=Var(name='a'), condition=Exists(var=Var(name='b'), condition=And(Geq(left=Var(name='a... | NT | null | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM",
"C3"
] | ea43fe | algebra_quadratic_discriminant_v1 | null | 5 | 0 | [
"C3",
"LIN_FORM"
] | 2 | 0.005 | 2026-02-08T04:14:46.533174Z | {
"verified": true,
"answer": 27982,
"timestamp": "2026-02-08T04:14:46.537700Z"
} | a8c1e1 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 271,
"completion_tokens": 2090
},
"timestamp": "2026-02-10T15:53:42.876Z",
"answer": 27982
},
{
... | 1 | [
{
"lemma": "C3",
"status": "ok"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"l... | {
"lo": -3.49,
"mid": 1.84,
"hi": 7.55
} | ||
72ece8 | algebra_poly_eval_v1_1915831931_845 | Let $c = 4$. Compute the sum
$$
\sum_{k=1}^{4} \varphi(k) \left\lfloor \frac{c}{k} \right\rfloor,
$$
where $\varphi(k)$ is Euler's totient function.
Let $m = 25$. Let $P$ 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 $t$ be... | 69,007 | graphs = [
Graph(
let={
"_c": Const(4),
"_m": Const(2),
"_n": Summation(var="k", start=Const(1), end=Const(4), expr=Mul(EulerPhi(n=Var("k")), Floor(Div(Ref("_c"), Var("k"))))),
"m": Const(25),
"result": Sum(Mul(Const(4), Pow(Ref("m"), Const(3))), M... | NT | null | COMPUTE | sympy | K2 | [
"K2/COPRIME_PAIRS",
"MAX_PRIME_BELOW"
] | 653990 | algebra_poly_eval_v1 | null | 6 | 0 | [
"COPRIME_PAIRS",
"K2",
"MAX_PRIME_BELOW"
] | 3 | 0.007 | 2026-02-08T15:42:49.803015Z | {
"verified": true,
"answer": 69007,
"timestamp": "2026-02-08T15:42:49.809889Z"
} | 6a0fa3 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 242,
"completion_tokens": 1363
},
"timestamp": "2026-02-16T11:31:12.197Z",
"answer": 69007
},
... | 1 | [
{
"lemma": "COPRIME_PAIRS",
"status": "ok_later"
},
{
"lemma": "K2",
"status": "ok"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok"
},
{
"lemma": "MAX_VAL",
"statu... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
f69cf6 | modular_sum_quadratic_residues_v1_1520064083_5774 | Let $p = 541$. Define $S$ as the set of all positive integers $p$ such that there exists an integer $q$ satisfying $pq = 150$, $\gcd(p, q) = 1$, and $p < q$. Compute the value of $\frac{p(p-1)}{|S|}$, and let $n = 44121$. Find the remainder when $n$ times this value is divided by $69353$. | 28,796 | graphs = [
Graph(
let={
"_n": Const(44121),
"p": Const(541),
"result": Div(Mul(Ref("p"), Sub(Ref("p"), Const(1))), 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 | SUM | sympy | COPRIME_PAIRS | [
"COPRIME_PAIRS"
] | 2bb3aa | modular_sum_quadratic_residues_v1 | null | 5 | 0 | [
"COPRIME_PAIRS"
] | 1 | 0.003 | 2026-02-08T07:37:19.018597Z | {
"verified": true,
"answer": 28796,
"timestamp": "2026-02-08T07:37:19.021623Z"
} | bdfe0c | 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": 1710
},
"timestamp": "2026-02-13T11:12:52.084Z",
"answer": 28796
},
... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
}
] | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
d01175 | antilemma_k2_v1_151522320_1320 | Let $m = 18$ and let $n = \sum_{k=1}^{18} k$. Define $$x = \sum_{k=1}^{n} \phi(k) \left\lfloor \frac{\sum_{k=1}^{m} k}{k} \right\rfloor.$$ Let $Q$ be the smallest positive integer such that the $Q$-th Fibonacci number is divisible by $|x| + 2$. Compute $Q$. | 3,678 | graphs = [
Graph(
let={
"_m": Const(18),
"_n": Summation(var="k", start=Const(1), end=Const(18), expr=Var("k")),
"x": Summation(var="k", start=Const(1), end=Ref("_n"), expr=Mul(EulerPhi(n=Var("k")), Floor(Div(Summation(var="k", start=Const(1), end=Ref("_m"), expr=Var("k")... | NT | COMB | COMPUTE | sympy | SUM_ARITHMETIC | [
"SUM_ARITHMETIC/K2",
"IDENTITY_POW_ZERO",
"K2"
] | 996d4f | antilemma_k2_v1 | null | 6 | 0 | [
"IDENTITY_POW_ZERO",
"K2",
"SUM_ARITHMETIC"
] | 3 | 0.002 | 2026-02-08T03:52:55.915780Z | {
"verified": true,
"answer": 3678,
"timestamp": "2026-02-08T03:52:55.917941Z"
} | 8b5f93 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 145,
"completion_tokens": 4688
},
"timestamp": "2026-02-11T20:22:41.852Z",
"answer": 3678
},
{... | 1 | [
{
"lemma": "IDENTITY_POW_ZERO",
"status": "ok"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "K2",
"status": "ok"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "SUM_ARITHMETIC",
"status": "ok"
},
{... | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
6e3a99 | alg_poly_orbit_hensel_v1_1218484723_2621 | For a non-negative integer $a$, define $N = a^4 + 4a^3 + 3a^2 - 3a + 4 \bmod 49$, $M = N^4 + 4N^3 + 3N^2 - 3N + 4 \bmod 49$, and $R = M^4 + 4M^3 + 3M^2 - 3M + 4 \bmod 49$. Find the number of integers $a$ with $0 \le a \le 57280$ such that $R = a$, $N \ne a$, and $M \ne a$. | 3,507 | graphs = [
Graph(
let={
"p1": Mod(value=Sum(Pow(Var("a"), Const(4)), Mul(Const(4), Pow(Var("a"), Const(3))), Mul(Const(3), Pow(Var("a"), Const(2))), Mul(Const(-3), Var("a")), Const(4)), modulus=Const(49)),
"p2": Mod(value=Sum(Pow(Ref("p1"), Const(4)), Mul(Const(4), Pow(Ref("p1"), Con... | ALG | null | COUNT | sympy | POLY_ORBIT_COUNT | [
"POLY_ORBIT_COUNT"
] | 4ad965 | alg_poly_orbit_hensel_v1 | null | 5 | null | [
"POLY_ORBIT_COUNT"
] | 1 | 0.057 | 2026-02-25T04:22:15.922786Z | {
"verified": true,
"answer": 3507,
"timestamp": "2026-02-25T04:22:15.979437Z"
} | b74a23 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 253,
"completion_tokens": 32768
},
"timestamp": "2026-03-29T05:44:46.488Z",
"answer": null
},
{
... | 1 | [
{
"lemma": "POLY_ORBIT_COUNT",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
}
] | {
"lo": 1.55,
"mid": 4.7,
"hi": 7.23
} | ||
7bd05f | antilemma_sum_equals_v1_784195855_135 | Compute the number of ordered pairs $(i, j)$ of positive integers such that $i + j = 66$, $1 \leq i \leq 64$, and $1 \leq j \leq 65$. | 64 | graphs = [
Graph(
let={
"_n": Const(66),
"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(64)), right=IntegerRange(start=Const(1), end=Con... | COMB | GEOM | COMPUTE | sympy | COUNT_SUM_EQUALS | [
"COUNT_SUM_EQUALS"
] | 75ab0f | antilemma_sum_equals_v1 | null | 3 | 0 | [
"COUNT_SUM_EQUALS"
] | 1 | 0.007 | 2026-02-08T02:59:11.355902Z | {
"verified": true,
"answer": 64,
"timestamp": "2026-02-08T02:59:11.362931Z"
} | 3f3a21 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 159,
"completion_tokens": 535
},
"timestamp": "2026-02-10T12:27:21.633Z",
"answer": 64
},
{
"id":... | 2 | [
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "ok"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
},
{
"lemma": "V8_SUM",
"status":... | {
"lo": -10,
"mid": -7.78,
"hi": -5.56
} | ||
1a930a | antilemma_v7_kummer_1742523217_1266 | Let $c = 225$ and $m = 3$. Let $n$ be the number of positive integers $k$ such that $1 \leq k \leq 88650$ and $c$ divides $k$. Let $S$ be the set of positive integers $t$ such that $18 \leq t \leq 1998$ and there exist positive integers $a \leq 349$, $b \leq 43$ satisfying $t = 4a + 14b$. Let $N$ be the number of eleme... | 54,125 | graphs = [
Graph(
let={
"_c": Const(225),
"_m": Const(3),
"_n": CountOverSet(set=SolutionsSet(var=Var("k"), condition=And(Geq(Var("k"), Const(1)), Leq(Var("k"), Const(88650)), Divides(divisor=Ref("_c"), dividend=Var("k"))), domain='positive_integers')),
"x": M... | NT | null | COMPUTE | sympy | B1 | [
"LIN_FORM/V7",
"C2/V7",
"V7"
] | 824f3b | antilemma_v7_kummer | null | 6 | 0 | [
"B1",
"C2",
"LIN_FORM",
"V7"
] | 4 | 0.01 | 2026-02-08T03:35:09.110742Z | {
"verified": true,
"answer": 54125,
"timestamp": "2026-02-08T03:35:09.120665Z"
} | d57654 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 267,
"completion_tokens": 7908
},
"timestamp": "2026-02-10T05:56:32.232Z",
"answer": 54125
},
{
"... | 1 | [
{
"lemma": "C2",
"status": "ok"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": ... | {
"lo": -6.5,
"mid": -0.2,
"hi": 6.11
} | ||
c6c7b5 | nt_count_intersection_v1_1915831931_2236 | Let $N = 20000$. Let $a$ be the smallest divisor of $1573$ that is at least $2$. Let $b = 6$. Define $\text{result}$ to be the number of positive integers $n$ such that $1 \leq n \leq N$, $a$ divides $n$, and $\gcd(n, b) = 1$. Compute $30122 \times \text{result}$, and then find the remainder when this product is divide... | 62,923 | graphs = [
Graph(
let={
"_n": Const(30122),
"N": Const(20000),
"a": MinOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Const(2)), Divides(divisor=Var("d"), dividend=Const(1573))))),
"b": Const(6),
"result": CountOverSet(set=Solut... | NT | null | COUNT | sympy | MIN_PRIME_FACTOR | [
"MIN_PRIME_FACTOR"
] | bc3776 | nt_count_intersection_v1 | null | 3 | 0 | [
"MIN_PRIME_FACTOR"
] | 1 | 0.762 | 2026-02-08T16:40:58.910087Z | {
"verified": true,
"answer": 62923,
"timestamp": "2026-02-08T16:40:59.671781Z"
} | ebc4bc | 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": 1416
},
"timestamp": "2026-02-17T09:53:37.479Z",
"answer": 62923
},
... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "MIN_PRIME_FACTOR",
"status": "ok"
},
{
"lemma": "VAL_SUM_EQ",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
6abd58 | lin_form_endings_v1_168721529_660 | Let $a = 70$, $b = 40$, $A = 28$, and $B = 50$. Let $g = \gcd(a, b)$. Define $$N = \left\lfloor \frac{aA + bB - a - b}{g} \right\rfloor + 1.$$ Compute the remainder when $15136 \cdot N$ is divided by $66222$. | 14,960 | graphs = [
Graph(
let={
"a_coeff": Const(70),
"b_coeff": Const(40),
"A_val": Const(28),
"B_val": Const(50),
"g_step": GCD(a=Ref("a_coeff"), b=Ref("b_coeff")),
"numerator": Sub(Sum(Mul(Ref("a_coeff"), Ref("A_val")), Mul(Ref("b_coeff"), R... | COMB | NT | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | lin_form_endings_v1 | null | 3 | null | [
"LIN_FORM"
] | 1 | 0.002 | 2026-02-08T13:10:46.285963Z | {
"verified": true,
"answer": 14960,
"timestamp": "2026-02-08T13:10:46.287858Z"
} | 0f8d8e | 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": 471
},
"timestamp": "2026-02-09T07:33:48.700Z",
"answer": 14960
},
{
"i... | 1 | [
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
... | {
"lo": -1.93,
"mid": 2.14,
"hi": 6.33
} | ||
049a20 | sequence_lucas_compute_v1_1520064083_7451 | Let $n$ be the number of integers $t$ such that $10 \leq t \leq 50$ and there exist positive integers $a$ and $b$ with $1 \leq a \leq 8$, $1 \leq b \leq 3$, and $t = 4a + 6b$. Compute the $n$th Lucas number. | 9,349 | graphs = [
Graph(
let={
"n": CountOverSet(set=SolutionsSet(var=Var("t"), condition=Exists(var=Var(name='a'), condition=Exists(var=Var(name='b'), condition=And(Geq(left=Var(name='a'), right=Const(value=1)), Leq(left=Var(name='a'), right=Const(value=8)), Geq(left=Var(name='b'), right=Const(value=1... | NT | null | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | sequence_lucas_compute_v1 | null | 4 | 0 | [
"LIN_FORM"
] | 1 | 0.001 | 2026-02-08T09:03:20.147872Z | {
"verified": true,
"answer": 9349,
"timestamp": "2026-02-08T09:03:20.148839Z"
} | 1eb2e4 | 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": 1677
},
"timestamp": "2026-02-13T23:38:04.182Z",
"answer": 9349
},
{... | 1 | [
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "V3",
"status": "no"
}
] | {
"lo": -5.55,
"mid": -3.01,
"hi": 0.32
} | ||
45189f | sequence_fibonacci_compute_v1_151522320_1878 | Let $d=2$, and let $M$ be the sum of all prime numbers $n$ such that $2\le n\le 28$.
Consider all ordered pairs $(x,y)$ of positive integers such that $xy=M$. For each such pair, form the sum $x+y$. Let $n$ be the smallest value of $x+y$ obtained in this way.
Let $F$ be the $n$th Fibonacci number.
Let $N=49999$, and... | 3,234 | graphs = [
Graph(
let={
"_d": Const(2),
"_m": SumOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Ref("_d")), Leq(Var("n"), Const(28)), IsPrime(Var("n"))))),
"_n": Const(49999),
"n": MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elemen... | NT | null | COMPUTE | sympy | L3C | [
"L3C",
"SUM_PRIMES/B3"
] | cc7d82 | sequence_fibonacci_compute_v1 | negation_mod | 8 | 0 | [
"B3",
"L3C",
"SUM_PRIMES"
] | 3 | 0.003 | 2026-02-08T04:26:28.196435Z | {
"verified": true,
"answer": 3234,
"timestamp": "2026-02-08T04:26:28.199086Z"
} | 446f31 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 294,
"completion_tokens": 1544
},
"timestamp": "2026-02-11T23:36:26.425Z",
"answer": 3234
},
{
"i... | 1 | [
{
"lemma": "B3",
"status": "ok_later"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "L3C",
"status": "ok"
},
{
"lemma": "MOD_FACTORIAL",
"status": ... | {
"lo": -1.75,
"mid": 1.03,
"hi": 3.64
} | ||
770ae3 | sequence_lucas_compute_v1_784195855_2003 | Let $n$ be the number of integers $t$ with $5 \leq t \leq 28$ such that there exist integers $a$ and $b$ satisfying $1 \leq a \leq 4$, $1 \leq b \leq 8$, and $t = 3a + 2b$. Compute the $n$-th Lucas number. | 39,603 | graphs = [
Graph(
let={
"n": CountOverSet(set=SolutionsSet(var=Var("t"), condition=Exists(var=Var(name='a'), condition=Exists(var=Var(name='b'), condition=And(Geq(left=Var(name='a'), right=Const(value=1)), Leq(left=Var(name='a'), right=Const(value=4)), Geq(left=Var(name='b'), right=Const(value=1... | NT | null | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | sequence_lucas_compute_v1 | null | 4 | 0 | [
"LIN_FORM"
] | 1 | 0.001 | 2026-02-08T05:25:27.764945Z | {
"verified": true,
"answer": 39603,
"timestamp": "2026-02-08T05:25:27.765807Z"
} | 23fdcd | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 124,
"completion_tokens": 2230
},
"timestamp": "2026-02-12T08:19:52.085Z",
"answer": 39603
},
... | 1 | [
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no... | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
bf30b1 | comb_bell_compute_v1_124444284_8205 | Let $c$ be the minimum value of $x + y$ over all ordered pairs $(x, y)$ of positive integers such that $xy = 2458624$. Let $m$ be the minimum value of $x + y$ over all ordered pairs $(x, y)$ of positive integers such that $xy = c$. Let $n$ be the number of positive integers $k$ with $1 \leq k \leq m$ such that $k \equi... | 4,140 | graphs = [
Graph(
let={
"_c": MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(Mul(Var("x"), Var("y")), Const(2458624)))), expr=Sum(Var("x"), Var("y")))),
"_m": MinOverS... | NT | COMB | COMPUTE | sympy | B3 | [
"B3/L3C/B3"
] | 8ff600 | comb_bell_compute_v1 | null | 7 | 0 | [
"B3",
"L3C"
] | 2 | 0.003 | 2026-02-08T09:36:06.996655Z | {
"verified": true,
"answer": 4140,
"timestamp": "2026-02-08T09:36:06.999980Z"
} | a5f81b | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 214,
"completion_tokens": 1716
},
"timestamp": "2026-02-14T05:08:05.660Z",
"answer": 4140
},
{... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "L3C",
"status": "ok_later"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma":... | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
eb2b1a | nt_sum_divisors_mod_v1_1431428450_49 | Let $x$ and $y$ be positive integers such that $xy = 14288400$. Define $n$ to be the minimum value of $x + y$ over all such pairs.
Let $\sigma(n)$ denote the sum of all positive divisors of $n$.
Compute the remainder when $\sigma(n)$ is divided by $10391$. | 8,018 | 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(14288400)))), expr=Sum(Var("x"), Var("y")))),
"M": Const(103... | NT | null | COMPUTE | sympy | B3 | [
"B3"
] | 0cd20d | nt_sum_divisors_mod_v1 | null | 4 | 0 | [
"B3"
] | 1 | 0.004 | 2026-02-08T13:09:42.413007Z | {
"verified": true,
"answer": 8018,
"timestamp": "2026-02-08T13:09:42.416824Z"
} | 544a9d | 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": 1122
},
"timestamp": "2026-02-15T11:04:13.652Z",
"answer": 8018
},
{... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
}
] | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
e49303 | comb_count_derangements_v1_1915831931_3531 | Let $n_2 = 0$ and define $$w = \sum_{k=0}^{n_2} (-1)^k \binom{n_2}{k}.$$ Let $n_1 = 0$ and define $$h = \sum_{k_1=0}^{n_1} (-1)^{k_1} \binom{n_1}{k_1}.$$ Let $n = 7 \cdot w \cdot h$. Compute the subfactorial of $n$, denoted $!n$, which counts the number of derangements of $n$ elements. | 1,854 | graphs = [
Graph(
let={
"n2": Const(0),
"w": Summation(var="k", start=Const(0), end=Ref("n2"), expr=Mul(Pow(Const(-1), Var("k")), Binom(n=Ref("n2"), k=Var("k")))),
"n1": Const(0),
"h": Summation(var="k1", start=Const(0), end=Ref("n1"), expr=Mul(Pow(Const(-1), ... | COMB | null | COUNT | sympy | BINOMIAL_ALTERNATING | [
"BINOMIAL_ALTERNATING"
] | c21569 | comb_count_derangements_v1 | null | 2 | 2 | [
"BINOMIAL_ALTERNATING"
] | 1 | 0.001 | 2026-02-08T17:42:54.579893Z | {
"verified": true,
"answer": 1854,
"timestamp": "2026-02-08T17:42:54.581192Z"
} | c1d8ec | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 170,
"completion_tokens": 1075
},
"timestamp": "2026-02-18T07:05:10.046Z",
"answer": 1854
},
{... | 1 | [
{
"lemma": "BINOMIAL_ALTERNATING",
"status": "ok"
},
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "V7"... | {
"lo": -5.64,
"mid": -3.17,
"hi": -0.81
} | ||
9c5aae | comb_count_partitions_v1_238844314_624 | Let $n$ be the number of integers $t$ with $21 \leq t \leq 150$ such that there exist positive integers $a$, $b$ with $1 \leq a \leq 10$, $1 \leq b \leq 6$, and $t = 6a + 15b$. Compute the number of integer partitions of $n$. | 37,338 | graphs = [
Graph(
let={
"n": CountOverSet(set=SolutionsSet(var=Var("t"), condition=Exists(var=Var(name='a'), condition=Exists(var=Var(name='b'), condition=And(Geq(left=Var(name='a'), right=Const(value=1)), Leq(left=Var(name='a'), right=Const(value=10)), Geq(left=Var(name='b'), right=Const(value=... | COMB | null | COUNT | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | comb_count_partitions_v1 | null | 6 | 0 | [
"LIN_FORM"
] | 1 | 0.003 | 2026-02-08T13:27:06.983967Z | {
"verified": true,
"answer": 37338,
"timestamp": "2026-02-08T13:27:06.986608Z"
} | 6d8f27 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 194,
"completion_tokens": 32768
},
"timestamp": "2026-02-24T18:17:55.451Z",
"answer": null
},
{
... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
}
] | {
"lo": 3.25,
"mid": 5.68,
"hi": 8.81
} | ||
098d01 | nt_max_prime_below_v1_865884756_4009 | Let $S$ be the set of positive integers $p$ for which there exists a positive integer $q$ such that $pq = 216$, $\gcd(p, q) = 1$, and $p < q$. Let $N$ be the number of elements in $S$. Find the largest prime number $n$ such that $N \le n \le 56953$. | 56,951 | graphs = [
Graph(
let={
"upper": Const(56953),
"result": MaxOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), CountOverSet(set=SolutionsSet(var=Var("p"), condition=And(IsPositive(arg=Var(name='p')), Exists(var=Var(name='q'), condition=And(Eq(left=Mul(Var(name='p'), V... | NT | null | EXTREMUM | sympy | COPRIME_PAIRS | [
"COPRIME_PAIRS"
] | 2bb3aa | nt_max_prime_below_v1 | null | 5 | 0 | [
"COPRIME_PAIRS"
] | 1 | 1.344 | 2026-02-08T17:41:20.230181Z | {
"verified": true,
"answer": 56951,
"timestamp": "2026-02-08T17:41:21.573790Z"
} | b71555 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 128,
"completion_tokens": 2730
},
"timestamp": "2026-02-18T06:39:33.418Z",
"answer": 56951
},
... | 1 | [
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
},
{
"lemma": "VAL_SUM_EQ",
"status": "no"
}... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
036041 | comb_count_partitions_v1_458359167_31 | Let $n$ be the minimum value of $x + y$ over all ordered pairs $(x, y)$ of positive integers such that $xy = 484$. Compute the number of integer partitions of $n$. (An integer partition of a positive integer $n$ is a way of writing $n$ as a sum of positive integers, disregarding order.) | 75,175 | graphs = [
Graph(
let={
"_n": Const(484),
"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")))),
... | COMB | null | COUNT | sympy | B3 | [
"B3"
] | 0cd20d | comb_count_partitions_v1 | null | 5 | 0 | [
"B3"
] | 1 | 0.001 | 2026-02-08T02:57:22.885927Z | {
"verified": true,
"answer": 75175,
"timestamp": "2026-02-08T02:57:22.887220Z"
} | d0d6a3 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 184,
"completion_tokens": 966
},
"timestamp": "2026-02-23T20:30:37.185Z",
"answer": 75175
},
{
"i... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
}
] | {
"lo": 1.97,
"mid": 4.36,
"hi": 6.69
} | ||
91041b | modular_mod_compute_v1_1918700295_2132 | Let $m$ be the maximum value of $xy$ over all pairs of positive integers $(x, y)$ such that $$
x + y = \min\left\{ x' + y' \mid x', y' \text{ are positive integers and } x'y' = \sum_{d \mid 4489} \phi(d) \right\}.
$$
Compute the remainder when $16900$ is divided by $m$, and then find the remainder when $44121$ times t... | 47,793 | graphs = [
Graph(
let={
"_m": Const(4489),
"_n": Const(84122),
"a": Const(16900),
"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("... | NT | null | COMPUTE | sympy | K3 | [
"K3/B3/B1"
] | cf22e8 | modular_mod_compute_v1 | null | 7 | 0 | [
"B1",
"B3",
"K3"
] | 3 | 0.006 | 2026-02-08T07:42:50.151998Z | {
"verified": true,
"answer": 47793,
"timestamp": "2026-02-08T07:42:50.157763Z"
} | c943a4 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 157,
"completion_tokens": 1409
},
"timestamp": "2026-02-13T11:54:53.996Z",
"answer": 47793
},
... | 1 | [
{
"lemma": "B1",
"status": "ok_later"
},
{
"lemma": "B3",
"status": "ok_later"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"le... | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
cf1ed6 | geo_count_lattice_rect_v1_1353956133_761 | Let $a = 144$ and $b = 54$. Define $L$ to be the number of lattice points $(x, y)$ such that $0 \leq x \leq 144$ and $0 \leq y \leq 54$. Compute the absolute value of $L$, find the remainder when this value is divided by $11$, and then compute the Bell number corresponding to this remainder. Determine the value of this... | 1 | graphs = [
Graph(
let={
"a": Const(144),
"b": Const(54),
"result": LatticePointsRect(a=Ref(name='a'), b=Ref(name='b')),
"Q": Bell(Mod(value=Abs(arg=Ref(name='result')), modulus=Const(11))),
},
goal=Ref("Q"),
)
] | GEOM | COMB | COUNT | sympy | [] | geo_count_lattice_rect_v1 | null | 5 | 0 | null | null | 0.004 | 2026-02-08T11:50:53.458477Z | {
"verified": true,
"answer": 1,
"timestamp": "2026-02-08T11:50:53.462339Z"
} | 6ea8da | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 206,
"completion_tokens": 611
},
"timestamp": "2026-02-24T14:52:51.736Z",
"answer": 1
},
{
"id": ... | 1 | [] | {
"lo": -4.92,
"mid": -2.91,
"hi": -0.68
} | ||||
446965 | alg_poly_preperiod_count_v1_1419126231_1397 | Let $f(x) = x^3 - 3x \bmod 59$. For a non-negative integer $a$, define the sequence $N = f(a)$, $M = f(N)$, $R = f(M)$, $S = f(R)$, $T = f(S)$. Find the number of integers $a$ with $0 \leq a \leq 83484$ such that $T = N$, $M \neq N$, $R \neq N$, and $S \neq N$. | 16,980 | graphs = [
Graph(
let={
"p1": Mod(value=Sum(Pow(Var("a"), Const(3)), Mul(Const(-3), Var("a"))), modulus=Const(59)),
"p2": Mod(value=Sum(Pow(Ref("p1"), Const(3)), Mul(Const(-3), Ref("p1"))), modulus=Const(59)),
"p3": Mod(value=Sum(Pow(Ref("p2"), Const(3)), Mul(Const(-3), R... | ALG | null | COUNT | sympy | POLY_ORBIT_COUNT | [
"POLY_ORBIT_COUNT"
] | 4ad965 | alg_poly_preperiod_count_v1 | null | 6 | null | [
"POLY_ORBIT_COUNT"
] | 1 | 0.024 | 2026-02-25T10:48:29.015627Z | {
"verified": true,
"answer": 16980,
"timestamp": "2026-02-25T10:48:29.039213Z"
} | a8c8dd | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 223,
"completion_tokens": 17518
},
"timestamp": "2026-03-30T12:19:40.440Z",
"answer": 16980
},
{
... | 1 | [
{
"lemma": "POLY_ORBIT_COUNT",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
}
] | {
"lo": 3.8,
"mid": 6.33,
"hi": 9.49
} | ||
4626b9 | modular_modexp_compute_v1_601307018_10401 | Let $e$ be the largest prime number $n$ such that $2 \leq n \leq \min\{ x + y \mid x, y > 0,\, xy = 5184,\, x \leq y \}$. Compute $13^e \bmod 48516$. | 33,709 | graphs = [
Graph(
let={
"_n": Const(2),
"a": Const(13),
"e": MaxOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Ref("_n")), Leq(Var("n"), MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=V... | NT | null | COMPUTE | sympy | B3 | [
"B3/MAX_PRIME_BELOW"
] | f253c0 | modular_modexp_compute_v1 | null | 5 | 0 | [
"B3",
"MAX_PRIME_BELOW"
] | 2 | 0.003 | 2026-03-10T10:53:21.994663Z | {
"verified": true,
"answer": 33709,
"timestamp": "2026-03-10T10:53:21.997565Z"
} | d7c0eb | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 177,
"completion_tokens": 3212
},
"timestamp": "2026-04-19T13:42:27.095Z",
"answer": 33709
},
{
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok_later"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status"... | {
"lo": -5.34,
"mid": 1.1,
"hi": 7.53
} | ||
e08a6d | comb_sum_binomial_row_v1_2051736721_1262 | Let $n$ be the number of positive integers $n_1$ at most $102$ such that $6$ divides $n_1$ and $\gcd(n_1, 35) = 1$. Compute $2^n$. | 4,096 | graphs = [
Graph(
let={
"_n": Const(35),
"n": CountOverSet(set=SolutionsSet(var=Var("n1"), condition=And(Geq(Var("n1"), Const(1)), Leq(Var("n1"), Const(102)), Divides(divisor=Const(6), dividend=Var("n1")), Eq(GCD(a=Var("n1"), b=Ref("_n")), Const(1))))),
"result": Pow(Cons... | NT | null | SUM | sympy | C5 | [
"C5"
] | 1d9668 | comb_sum_binomial_row_v1 | null | 4 | 0 | [
"C5"
] | 1 | 0.001 | 2026-02-08T15:55:22.279529Z | {
"verified": true,
"answer": 4096,
"timestamp": "2026-02-08T15:55:22.280760Z"
} | dd2184 | 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": 857
},
"timestamp": "2026-02-16T16:04:11.720Z",
"answer": 4096
},
{
... | 1 | [
{
"lemma": "C5",
"status": "ok"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
2490cd | lin_form_endings_v1_1820931509_69 | Let $a = 63$ and $b = 18$. Let $A = 33$ and $B = 46$. Define $g = \gcd(a, b)$. Compute the value of $$\left(15868 \left( \left\lfloor \frac{aA + bB - (a + b)}{g} \right\rfloor + 1 \right)\right) \bmod{94505}.$$ | 84,160 | graphs = [
Graph(
let={
"a_coeff": Const(63),
"b_coeff": Const(18),
"A_val": Const(33),
"B_val": Const(46),
"g_step": GCD(a=Ref("a_coeff"), b=Ref("b_coeff")),
"numerator": Sub(Sum(Mul(Ref("a_coeff"), Ref("A_val")), Mul(Ref("b_coeff"), R... | COMB | NT | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | lin_form_endings_v1 | null | 3 | null | [
"LIN_FORM"
] | 1 | 0.002 | 2026-02-08T11:19:44.395668Z | {
"verified": true,
"answer": 84160,
"timestamp": "2026-02-08T11:19:44.397573Z"
} | c9ae40 | 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": 748
},
"timestamp": "2026-02-14T12:12:46.616Z",
"answer": 84160
},
{... | 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": "V8",
"statu... | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
7d68c5 | nt_max_prime_below_v1_124444284_2314 | 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 $t$ be the number of elements in $S$. Consider the set of all prime numbers $n$ such that $t \leq n \leq 50400$. Compute the largest element of this set. | 50,387 | graphs = [
Graph(
let={
"upper": Const(50400),
"result": MaxOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), CountOverSet(set=SolutionsSet(var=Var("p"), condition=And(IsPositive(arg=Var(name='p')), Exists(var=Var(name='q'), condition=And(Eq(left=Mul(Var(name='p'), V... | NT | null | EXTREMUM | sympy | COPRIME_PAIRS | [
"COPRIME_PAIRS"
] | 2bb3aa | nt_max_prime_below_v1 | null | 5 | 0 | [
"COPRIME_PAIRS"
] | 1 | 1.195 | 2026-02-08T04:35:39.853632Z | {
"verified": true,
"answer": 50387,
"timestamp": "2026-02-08T04:35:41.048954Z"
} | b2f031 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 205,
"completion_tokens": 4666
},
"timestamp": "2026-02-10T17:15:39.461Z",
"answer": 50387
},
{
... | 1 | [
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
... | {
"lo": -3.49,
"mid": 1.84,
"hi": 7.55
} | ||
68f39a | comb_bell_compute_v1_238844314_350 | Let $m = 35$. Define $n'$ to be the number of positive integers $n$ at most $1287$ that are divisible by $9$ and satisfy $\gcd(n, m) = 1$. Let $n$ be the largest positive divisor of $n'$ that is at most $9$. Compute the Bell number $B_n$. Find the value of this Bell number. | 21,147 | graphs = [
Graph(
let={
"_m": Const(35),
"_n": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Const(1287)), Divides(divisor=Const(9), dividend=Var("n")), Eq(GCD(a=Var("n"), b=Ref("_m")), Const(1))))),
"n": MaxOverSet(set=S... | NT | COMB | COMPUTE | sympy | C5 | [
"C5/MAX_DIVISOR"
] | 454bdd | comb_bell_compute_v1 | null | 6 | 0 | [
"C5",
"MAX_DIVISOR"
] | 2 | 0.002 | 2026-02-08T13:18:00.696404Z | {
"verified": true,
"answer": 21147,
"timestamp": "2026-02-08T13:18:00.698085Z"
} | a784cb | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 132,
"completion_tokens": 795
},
"timestamp": "2026-02-15T12:58:34.068Z",
"answer": 21147
},
{... | 1 | [
{
"lemma": "C5",
"status": "ok"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "MAX_DIVISOR",
"status... | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
8f6f37_n | alg_qf_psd_sum_v1_601307018_548 | A game board has positions labeled by integers from $1$ to $41$ for three different attributes: agility ($a$), balance ($b$), and coordination ($c$). A player's score for a position $(a,b,c)$ is given by $45a^2 + 14b^2 + 57c^2 - 30ab + 34ac - 6bc$. The player may only use values of $c$ no greater than the smallest poss... | 44,842 | ALG | null | COMPUTE | sympy | POLY_ORBIT_HENSEL | [
"B3_DIFF"
] | b47ea7 | alg_qf_psd_sum_v1 | null | 6 | null | [
"B3_DIFF",
"POLY_ORBIT_HENSEL"
] | 2 | 0.375 | 2026-03-10T01:04:55.258328Z | null | deb8c9 | 8f6f37 | 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": 14839
},
"timestamp": "2026-03-29T14:11:02.221Z",
"answer": 44842
},
{
... | 1 | [
{
"lemma": "B3_DIFF",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
}
] | {
"lo": -5.36,
"mid": 0.27,
"hi": 5.45
} | |
c498bf | geo_count_lattice_rect_v1_784195855_9812 | Let $ a = 120 $ and $ b = 44 $. Define $ L $ to be the number of lattice points in the rectangle $ [0, a] \times [0, b] $, including the boundaries. Compute $ 12100 - L $. | 6,655 | graphs = [
Graph(
let={
"a": Const(120),
"b": Const(44),
"result": LatticePointsRect(a=Ref(name='a'), b=Ref(name='b')),
"_c": Const(12100),
"Q": Sub(Ref("_c"), Ref("result")),
},
goal=Ref("Q"),
)
] | GEOM | null | COUNT | sympy | [] | geo_count_lattice_rect_v1 | null | 3 | 0 | null | null | 0.001 | 2026-02-08T17:06:02.117055Z | {
"verified": true,
"answer": 6655,
"timestamp": "2026-02-08T17:06:02.117893Z"
} | 34ffb6 | 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": 456
},
"timestamp": "2026-02-17T21:16:12.341Z",
"answer": 6655
},
{
... | 1 | [] | {
"lo": -8,
"mid": -4.75,
"hi": -2.28
} | ||||
800093 | nt_euler_phi_compute_v1_153355830_570 | Let $m = 4661$ and $n = 65536$. Let $x$ be the sum of $\phi(d)$ over all positive divisors $d$ of $m$, where $\phi$ denotes Euler's totient function. Let $y = \phi(n)$. Let $Q$ be the remainder when $x \cdot y$ is divided by $64540$. Compute $Q$. | 30,008 | graphs = [
Graph(
let={
"_n": Const(4661),
"n": Const(65536),
"result": EulerPhi(n=Ref("n")),
"Q": Mod(value=Mul(SumOverDivisors(n=Ref(name='_n'), var='d', expr=EulerPhi(n=Var(name='d'))), Ref("result")), modulus=Const(64540)),
},
goal=Ref("Q")... | NT | null | COMPUTE | sympy | K3 | [
"K3"
] | fd5c4e | nt_euler_phi_compute_v1 | affine_mod | 4 | 0 | [
"K3"
] | 1 | 0.002 | 2026-02-08T03:10:18.593290Z | {
"verified": true,
"answer": 30008,
"timestamp": "2026-02-08T03:10:18.594992Z"
} | 637942 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 196,
"completion_tokens": 1093
},
"timestamp": "2026-02-10T15:14:38.782Z",
"answer": 30008
},
{
... | 1 | [
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K3",
"status": "ok"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "MOD_MUL",
"statu... | {
"lo": -3.42,
"mid": 1.86,
"hi": 7.55
} | ||
098cd7 | geo_count_lattice_rect_v1_151522320_1985 | Let $a = 128$ and $b = 275$. Compute the number of lattice points $(x, y)$ such that $0 \leq x \leq a$ and $0 \leq y \leq b$. | 35,604 | graphs = [
Graph(
let={
"a": Const(128),
"b": Const(275),
"result": LatticePointsRect(a=Ref(name='a'), b=Ref(name='b')),
},
goal=Ref("result"),
)
] | GEOM | null | COUNT | sympy | [] | geo_count_lattice_rect_v1 | null | 3 | 0 | null | null | 0.001 | 2026-02-08T04:30:13.815354Z | {
"verified": true,
"answer": 35604,
"timestamp": "2026-02-08T04:30:13.815987Z"
} | cfc4d9 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 160,
"completion_tokens": 242
},
"timestamp": "2026-02-24T00:46:01.671Z",
"answer": 35604
},
{
"i... | 1 | [] | {
"lo": -3.83,
"mid": -1.68,
"hi": 1.09
} | ||||
aba09a | comb_bell_compute_v1_1353956133_831 | Let $a = \sum_{k=0}^{7} (-1)^k \binom{7}{k}$ and $b = \sum_{k=a}^{7} (-1)^k \binom{7}{k}$. Define $e = \sum_{k=0}^{b} (-1)^k \binom{b}{k}$ and $n = 8e$. Compute the $n$th Bell number. | 4,140 | graphs = [
Graph(
let={
"a": Const(5),
"b": Const(2),
"n2": Sum(Ref("a"), Ref("b")),
"h": Summation(var="k", start=Summation(var="k", start=Const(0), end=Const(7), expr=Mul(Pow(Const(-1), Var("k")), Binom(n=Const(7), k=Var("k")))), end=Ref("n2"), expr=Mul(Pow(... | COMB | null | COMPUTE | sympy | BINOMIAL_ALTERNATING | [
"BINOMIAL_ALTERNATING"
] | c21569 | comb_bell_compute_v1 | null | 6 | 2 | [
"BINOMIAL_ALTERNATING"
] | 1 | 0.002 | 2026-02-08T11:52:55.286285Z | {
"verified": true,
"answer": 4140,
"timestamp": "2026-02-08T11:52:55.287975Z"
} | cd6eb7 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 202,
"completion_tokens": 569
},
"timestamp": "2026-02-24T14:53:00.631Z",
"answer": 4140
},
{
"id... | 1 | [
{
"lemma": "BINOMIAL_ALTERNATING",
"status": "ok"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8",... | {
"lo": -5.97,
"mid": -3.97,
"hi": -1.93
} | ||
cb63a2 | modular_mod_compute_v1_48377204_278 | Let $m$ be the number of integers $t$ with $20 \le t \le 8672$ such that there exist integers $a$ and $b$ satisfying $1 \le a \le 642$, $1 \le b \le 1475$, and $t = 2a + 5b + 13$. Let $r$ be the remainder when $-5329$ is divided by $m$. Find the value of $51821r \bmod 96900$. | 48,220 | graphs = [
Graph(
let={
"_n": Const(96900),
"a": Const(-5329),
"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'), rig... | NT | null | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | modular_mod_compute_v1 | null | 4 | 0 | [
"LIN_FORM"
] | 1 | 0.003 | 2026-02-08T15:19:56.949189Z | {
"verified": true,
"answer": 48220,
"timestamp": "2026-02-08T15:19:56.952500Z"
} | ebdf0e | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 153,
"completion_tokens": 4305
},
"timestamp": "2026-02-16T03:10:02.910Z",
"answer": 48220
},
... | 1 | [
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
}... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
88ecc8 | nt_min_coprime_above_v1_865884756_4835 | Let $S$ be the set of all ordered pairs $(a,b)$ of positive integers such that $1 \leq a \leq 3$ and $1 \leq b \leq 149$. Let $m$ be the number of elements in $S$. Determine the smallest integer $n$ such that $37636 < n \leq 38093$ and $\gcd(n, m) = 1$. Compute $n$. | 37,637 | graphs = [
Graph(
let={
"start": Const(37636),
"upper": Const(38093),
"modulus": CountOverSet(set=CartesianProduct(left=IntegerRange(start=Const(1), end=Const(3)), right=IntegerRange(start=Const(1), end=Const(149)))),
"result": MinOverSet(set=SolutionsSet(var=... | NT | null | EXTREMUM | sympy | COUNT_CARTESIAN | [
"COUNT_CARTESIAN"
] | 409d7d | nt_min_coprime_above_v1 | null | 3 | 0 | [
"COUNT_CARTESIAN"
] | 1 | 0.038 | 2026-02-08T18:09:55.677152Z | {
"verified": true,
"answer": 37637,
"timestamp": "2026-02-08T18:09:55.715641Z"
} | 1e3aab | 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": 1197
},
"timestamp": "2026-02-18T14:51:44.669Z",
"answer": 37637
},
... | 1 | [
{
"lemma": "COUNT_CARTESIAN",
"status": "ok"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
}... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
1e5644 | nt_count_intersection_v1_865884756_738 | Let $N$ be the number of integers $t$ such that $10 \leq t \leq 5021$ and there exist positive integers $a \leq 1382$ and $b \leq 125$ satisfying $t = 3a + 7b$. Let $a = 7$ and $b = 15$. Define $S$ as the set of all positive integers $n \leq N$ such that $7$ divides $n$ and $\gcd(n, 15) = 1$. Compute the value of $9298... | 64,097 | graphs = [
Graph(
let={
"N": CountOverSet(set=SolutionsSet(var=Var("t"), condition=Exists(var=Var(name='a'), condition=Exists(var=Var(name='b'), condition=And(Geq(left=Var(name='a'), right=Const(value=1)), Leq(left=Var(name='a'), right=Const(value=1382)), Geq(left=Var(name='b'), right=Const(valu... | NT | null | COUNT | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | nt_count_intersection_v1 | null | 5 | 0 | [
"LIN_FORM"
] | 1 | 0.179 | 2026-02-08T15:35:07.698828Z | {
"verified": true,
"answer": 64097,
"timestamp": "2026-02-08T15:35:07.877866Z"
} | c3e6a7 | 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": 3609
},
"timestamp": "2026-02-16T08:49:42.732Z",
"answer": 64097
},
... | 1 | [
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "V3",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
b2ef38 | alg_poly4_count_v1_601307018_8997 | Find the number of ordered pairs $(a, b)$ of positive integers with $1 \leq a, b \leq 329$ such that $97b^4 = 118614603217$. | 329 | graphs = [
Graph(
let={
"result": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("a"), Var("b")]), condition=And(Geq(Var("a"), Const(1)), Leq(Var("a"), Const(329)), Geq(Var("b"), Const(1)), Leq(Var("b"), Const(329)), Eq(Mul(Const(97), Pow(Var("b"), Const(4))), Const(118614603217))))),
... | ALG | null | COUNT | sympy | TELESCOPE | [
"TELESCOPE/POLY_ORBIT_HENSEL"
] | 499335 | alg_poly4_count_v1 | null | 3 | null | [
"POLY_ORBIT_HENSEL",
"TELESCOPE"
] | 2 | 3.527 | 2026-03-10T09:25:47.208547Z | {
"verified": true,
"answer": 329,
"timestamp": "2026-03-10T09:25:50.735890Z"
} | 391c40 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 153,
"completion_tokens": 2086
},
"timestamp": "2026-04-19T10:21:54.543Z",
"answer": 329
},
{
"i... | 2 | [
{
"lemma": "POLY_ORBIT_HENSEL",
"status": "ok_later"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "TELESCOPE",
"status": "ok"
}
] | {
"lo": -10,
"mid": -5.89,
"hi": -1.79
} | ||
8ecaa0 | antilemma_k2_v1_458359167_413 | Let $x = \sum_{k=1}^{367} \phi(k) \left\lfloor \frac{s_k}{k} \right\rfloor$, where $\phi(k)$ is Euler's totient function and $s_k$ is the sum of all real solutions $x$ to the equation $x^2 - 367x + 22752 = 0$. Compute $x$. | 67,528 | graphs = [
Graph(
let={
"_n": Const(2),
"x": Summation(var="k", start=Const(1), end=Const(367), expr=Mul(EulerPhi(n=Var("k")), Floor(Div(SumOverSet(set=SolutionsSet(var=Var("x"), condition=Eq(Sum(Pow(Var("x"), Ref("_n")), Mul(Const(-367), Var("x")), Const(22752)), Const(0)))), Var("k... | NT | COMB | COMPUTE | sympy | K13 | [
"VIETA_SUM/K2",
"IDENTITY_POW_ZERO",
"K2"
] | 9ac93e | antilemma_k2_v1 | null | 7 | 0 | [
"IDENTITY_POW_ZERO",
"K13",
"K2",
"VIETA_SUM"
] | 4 | 0.003 | 2026-02-08T03:16:57.889707Z | {
"verified": true,
"answer": 67528,
"timestamp": "2026-02-08T03:16:57.892953Z"
} | b455e6 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 194,
"completion_tokens": 1663
},
"timestamp": "2026-02-10T13:41:53.890Z",
"answer": 67528
},
{
"... | 1 | [
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "IDENTITY_POW_ZERO",
"status": "ok"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "K2",
"status": "ok"
},
{
"lemma": "MAX_VAL",
"status": "no"
... | {
"lo": -3.46,
"mid": 1.03,
"hi": 5.49
} | ||
68cabd | nt_count_digit_sum_v1_153355830_333 | Let $ S $ be the set of all integers $ t $ with $ 10 \leq t \leq 190 $ for which there exist positive integers $ a $ and $ b $, with $ 1 \leq a \leq 40 $ and $ 1 \leq b \leq 10 $, such that $ t = 3a + 7b $. Let $ N = |S| $. Let $ T $ be the set of all ordered pairs of positive integers $ (x, y) $ such that $ xy = N $. ... | 5,280 | graphs = [
Graph(
let={
"_n": CountOverSet(set=SolutionsSet(var=Var("t"), condition=Exists(var=Var(name='a'), condition=Exists(var=Var(name='b'), condition=And(Geq(left=Var(name='a'), right=Const(value=1)), Leq(left=Var(name='a'), right=Const(value=40)), Geq(left=Var(name='b'), right=Const(value... | NT | null | COUNT | sympy | COPRIME_PAIRS | [
"LIN_FORM/B3"
] | 05313e | nt_count_digit_sum_v1 | null | 7 | 0 | [
"B3",
"COPRIME_PAIRS",
"LIN_FORM"
] | 3 | 8.758 | 2026-02-08T03:02:34.846721Z | {
"verified": true,
"answer": 5280,
"timestamp": "2026-02-08T03:02:43.604448Z"
} | 46f37f | 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": 3155
},
"timestamp": "2026-02-10T12:38:35.738Z",
"answer": 4840
},
{
... | 1 | [
{
"lemma": "B3",
"status": "ok_later"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "V1",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
},
{
... | {
"lo": 3.24,
"mid": 5.68,
"hi": 8.81
} | ||
5e0165 | diophantine_fbi2_min_v1_349078426_219 | Let $k = 64$. Let $S$ be the set of real solutions to the equation $x^2 - 74x - 12555 = 0$. Define $u$ to be the sum of all elements in $S$. Let $d$ be a positive integer such that $7 \leq d \leq u$, $d$ divides $k$, and $\frac{k}{d} \geq 3$. Determine the smallest possible value of such $d$. Compute this value. | 8 | graphs = [
Graph(
let={
"k": Const(64),
"upper": SumOverSet(set=SolutionsSet(var=Var("x"), condition=Eq(Sum(Pow(Var("x"), Const(2)), Mul(Const(-74), Var("x")), Const(-12555)), Const(0)))),
"result": MinOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Con... | NT | null | EXTREMUM | sympy | B3 | [
"VIETA_SUM"
] | b33a7a | diophantine_fbi2_min_v1 | null | 4 | 0 | [
"B3",
"VIETA_SUM"
] | 2 | 0.017 | 2026-02-08T12:52:52.216629Z | {
"verified": true,
"answer": 8,
"timestamp": "2026-02-08T12:52:52.233895Z"
} | dd89d5 | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 1,
"correct": {
"strict": false,
"boxed": false,
"relaxed": true
},
"usage": {
"prompt_tokens": 166,
"completion_tokens": 614
},
"timestamp": "2026-02-16T04:08:33.826Z",
"answer": 2
},
{
"id": 11,
... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
},
{
"lemma": "VIETA_SUM",
"status": "ok"
}
] | {
"lo": -9.12,
"mid": -6.02,
"hi": -3.62
} |
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