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 |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
299605 | nt_gcd_compute_v1_1820931509_796 | Let $a = 635960$ and $b = 1192425$. Compute $\gcd(a, b)$, and let this value be $d$. Find the remainder when $44121 \cdot d$ is divided by $83024$. Determine the value of this remainder. | 50,015 | graphs = [
Graph(
let={
"a": Const(635960),
"b": Const(1192425),
"result": GCD(a=Ref("a"), b=Ref("b")),
"Q": Mod(value=Mul(Const(44121), Ref("result")), modulus=Const(83024)),
},
goal=Ref("Q"),
)
] | NT | null | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM/LIOUVILLE_MINUS_ONE",
"OMEGA_ZERO",
"ONE_PHI_1"
] | c397a6 | nt_gcd_compute_v1 | null | 2 | 0 | [
"LIN_FORM",
"LIOUVILLE_MINUS_ONE",
"OMEGA_ZERO",
"ONE_PHI_1"
] | 4 | 0.034 | 2026-02-08T11:53:09.073889Z | {
"verified": true,
"answer": 50015,
"timestamp": "2026-02-08T11:53:09.107604Z"
} | 3d3e85 | 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": 1253
},
"timestamp": "2026-02-14T20:51:18.983Z",
"answer": 50015
},
... | 1 | [
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "LIOUVILLE_MINUS_ONE",
"status": "ok_later"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "MOD_ADD",
... | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
b9aed5 | comb_catalan_compute_v1_1918700295_4246 | Let $a_1, a_2, a_3$ be positive odd integers. Let $T$ be the set of all integers $t$ such that $5 \leq t \leq 15$ and there exist positive integers $a$ and $b$ with $1 \leq a \leq 3$, $1 \leq b \leq 3$, and $t = 2a + 3b$. Let $s$ be the number of elements in $T$. Suppose $a_1 + a_2 + a_3 = s$. Let $n$ be the number of ... | 93,374 | graphs = [
Graph(
let={
"_m": Const(50069),
"_n": Const(99806),
"n": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x1"), Var("x2"), Var("x3")]), condition=And(IsPositive(arg=Var(name='x1')), IsPositive(arg=Var(name='x2')), IsPositive(arg=Var(name='x3')), IsOdd(ar... | COMB | null | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM/COMB1"
] | 268a62 | comb_catalan_compute_v1 | null | 6 | 0 | [
"COMB1",
"LIN_FORM"
] | 2 | 0.005 | 2026-02-08T09:15:39.830610Z | {
"verified": true,
"answer": 93374,
"timestamp": "2026-02-08T09:15:39.835930Z"
} | 46b7af | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 297,
"completion_tokens": 5389
},
"timestamp": "2026-02-24T10:57:14.136Z",
"answer": 92374
},
{
... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COMB1",
"status": "ok_later"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "V8",
"status": "... | {
"lo": 1.15,
"mid": 4.18,
"hi": 6.61
} | ||
b13d41 | modular_count_residue_v1_1915831931_2035 | Let $n$ be the minimum value of $x + y$ where $x$ and $y$ are positive integers such that $xy = 2500$. Let $m$ be the minimum value of $x_1 + y_1$ where $x_1$ and $y_1$ are positive integers such that $x_1 y_1 = n$. Find the number of positive integers $n$ less than or equal to 77841 such that $n \equiv 2 \pmod{m}$. | 3,892 | 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(2500)))), expr=Sum(Var("x"), Var("y")))),
"upper": Const(77... | NT | null | COUNT | sympy | B3 | [
"B3/B3"
] | 8ffef9 | modular_count_residue_v1 | null | 4 | 0 | [
"B3"
] | 1 | 2.699 | 2026-02-08T16:35:43.109293Z | {
"verified": true,
"answer": 3892,
"timestamp": "2026-02-08T16:35:45.807846Z"
} | 323b8f | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 156,
"completion_tokens": 936
},
"timestamp": "2026-02-17T07:35:22.367Z",
"answer": 3892
},
{
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
},
{
"lemma": "VAL_SUM_EQ",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
572fe4 | antilemma_k2_v1_717093673_4125 | Compute the value of
$$
\sum_{k=1}^{262} \phi(k) \left\lfloor \frac{262}{k} \right\rfloor,
$$
where $\phi(k)$ denotes Euler's totient function. | 34,453 | graphs = [
Graph(
let={
"x": Summation(var="k", start=Const(1), end=Const(262), expr=Mul(EulerPhi(n=Var("k")), Floor(Div(Const(262), Var("k"))))),
},
goal=Ref("x"),
)
] | NT | COMB | COMPUTE | sympy | K13 | [
"K2"
] | 6897ab | antilemma_k2_v1 | null | 4 | 0 | [
"K13",
"K2"
] | 2 | 0.002 | 2026-02-08T18:03:18.721588Z | {
"verified": true,
"answer": 34453,
"timestamp": "2026-02-08T18:03:18.723455Z"
} | 7824bd | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 93,
"completion_tokens": 1870
},
"timestamp": "2026-02-18T13:26:47.436Z",
"answer": 34453
},
{... | 1 | [
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "K2",
"status": "ok"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "VAL_SUM_EQ",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
85b52e | algebra_quadratic_discriminant_v1_1440796553_17 | Let $a = 3$, $b = 1$, and $c = -2$. Let $m$ be the maximum positive integer $d$ such that $1 \leq d \leq 4$ and $d$ divides $44$. Compute $Q = 22801 - (b^2 - m \cdot a \cdot c)$. | 22,776 | graphs = [
Graph(
let={
"_n": Const(2),
"a": Const(3),
"b": Const(1),
"c": Const(-2),
"result": Sub(Pow(Ref("b"), Ref("_n")), Mul(MaxOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Const(1)), Leq(Var("d"), Const(4)), Divides(divi... | NT | null | COMPUTE | sympy | MAX_DIVISOR | [
"MAX_DIVISOR"
] | 51757e | algebra_quadratic_discriminant_v1 | null | 2 | 0 | [
"MAX_DIVISOR"
] | 1 | 0.002 | 2026-02-08T11:12:37.363477Z | {
"verified": true,
"answer": 22776,
"timestamp": "2026-02-08T11:12:37.365854Z"
} | c0825b | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 133,
"completion_tokens": 466
},
"timestamp": "2026-02-16T03:01:02.859Z",
"answer": 22776
},
{
"id": 11,
... | 2 | [
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "MAX_DIVISOR",
"status": "ok"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
},
{
"lemma": "VAL_SUM_EQ",
"status": "no"
}
] | {
"lo": -10,
"mid": -7.71,
"hi": -5.43
} | ||
d7782b | comb_binomial_compute_v1_784195855_5759 | Let $n$ be the number of integers $t$ in the range $9 \leq t \leq 28$ for which there exist integers $a$ and $b$ satisfying $1 \leq a \leq 2$, $1 \leq b \leq 7$, and $t = 7a + 2b$. Let $k = \sum_{k=1}^{3} k$, and let $\binom{n}{k}$ denote the binomial coefficient. Let $Q$ be the remainder when $36071 \cdot \binom{n}{k}... | 9,999 | graphs = [
Graph(
let={
"_n": Const(51018),
"n": CountOverSet(set=SolutionsSet(var=Var("t"), condition=Exists(var=Var(name='a'), condition=Exists(var=Var(name='b'), condition=And(Geq(left=Var(name='a'), right=Const(value=1)), Leq(left=Var(name='a'), right=Const(value=2)), Geq(left=Va... | ALG | COMB | COMPUTE | sympy | SUM_ARITHMETIC | [
"SUM_ARITHMETIC",
"LIN_FORM"
] | 7209d0 | comb_binomial_compute_v1 | null | 5 | 0 | [
"LIN_FORM",
"SUM_ARITHMETIC"
] | 2 | 0.002 | 2026-02-08T08:06:42.345268Z | {
"verified": true,
"answer": 9999,
"timestamp": "2026-02-08T08:06:42.347652Z"
} | 34f454 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 250,
"completion_tokens": 1850
},
"timestamp": "2026-02-24T08:47:52.073Z",
"answer": 9999
},
{
"i... | 1 | [
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "SUM_ARITHMETIC",
"status": "ok"
}
] | {
"lo": -2.35,
"mid": 1.22,
"hi": 4.84
} | ||
aceeca | alg_poly3_min_v1_601307018_5510 | Let $A = \max\{ d \geq 1 : d \mid 141746 \text{ and } d^2 \leq 141746 \}$. Let $B = \min\{ x + y : x, y > 0,\, xy = 34969,\, x \leq y \}$. Find the remainder when
$$
\min\left\{ -27a^3 - 36ab^2 - 54a^2b - 72b^3 : a, b \in \mathbb{Z}^+,\, 1 \leq a \leq A,\, 1 \leq b \leq B \right\}
$$
is divided by $58563$. | 33,480 | graphs = [
Graph(
let={
"_n": Const(58563),
"result": Mod(value=MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("a"), Var("b")]), condition=And(Geq(Var("a"), Const(1)), Leq(Var("a"), MaxOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Const(1)), D... | NT | null | COMPUTE | sympy | B3_CLOSEST | [
"B3_CLOSEST",
"B3"
] | a6b579 | alg_poly3_min_v1 | null | 7 | 0 | [
"B3",
"B3_CLOSEST"
] | 2 | 1.02 | 2026-03-10T06:06:47.563156Z | {
"verified": true,
"answer": 33480,
"timestamp": "2026-03-10T06:06:48.583553Z"
} | 26a477 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 270,
"completion_tokens": 3488
},
"timestamp": "2026-04-19T02:15:25.707Z",
"answer": 33480
},
{
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "B3_CLOSEST",
"status": "ok"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"
... | {
"lo": -3.31,
"mid": 1.32,
"hi": 5.87
} | ||
afa31f | alg_qf_psd_min_v1_1218484723_3867 | Let $M$ be the minimum value of $x + y$ over all positive integers $x, y$ such that $xy = 4494400$. Let $P$ be the minimum value of $x_1 + y_1$ over all positive integers $x_1, y_1$ such that $x_1 y_1 = 9449476$. Find the minimum value of $P a^2 + 848ab + M b^2$ over all positive integers $a, b$ with $1 \leq a, b \leq ... | 11,236 | graphs = [
Graph(
let={
"_m": Const(203),
"_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(4494400)))), expr=Sum(Var("x"), Var("y"))... | ALG | null | COMPUTE | sympy | B3 | [
"B3/B3"
] | 8ffef9 | alg_qf_psd_min_v1 | null | 6 | 0 | [
"B3"
] | 1 | 0.382 | 2026-02-25T05:30:26.713669Z | {
"verified": true,
"answer": 11236,
"timestamp": "2026-02-25T05:30:27.095390Z"
} | 3d0397 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 233,
"completion_tokens": 32768
},
"timestamp": "2026-03-29T12:41:28.649Z",
"answer": null
},
{
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
}
] | {
"lo": -4.26,
"mid": -1.8,
"hi": 1.26
} | ||
498450 | comb_count_partitions_v1_458359167_4217 | Let $n$ be the number of integers $t$ such that $15 \leq t \leq 135$ and there exist positive integers $a$ and $b$ with $1 \leq a \leq 9$, $1 \leq b \leq 9$, and $t = 6a + 9b$. Let $p(n)$ denote the number of integer partitions of $n$. Find the remainder when $47129 \cdot p(n)$ is divided by $55926$. | 38,511 | graphs = [
Graph(
let={
"_n": Const(47129),
"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=9)), Geq(left=Va... | COMB | null | COUNT | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | comb_count_partitions_v1 | null | 5 | 0 | [
"LIN_FORM"
] | 1 | 0.001 | 2026-02-08T11:38:21.896631Z | {
"verified": true,
"answer": 38511,
"timestamp": "2026-02-08T11:38:21.898015Z"
} | 6aaae0 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 220,
"completion_tokens": 5507
},
"timestamp": "2026-02-24T14:23:14.948Z",
"answer": 38511
},
{
"... | 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_SUM",
"status": "no"
... | {
"lo": -2.35,
"mid": 1.22,
"hi": 4.84
} | ||
9a984d | diophantine_fbi2_count_v1_677425708_1000 | Let $a = 38$ and $b$ be the largest integer $k$ such that $11^k$ divides $396!$. Let $d$ be a positive divisor of $\gcd(a, b)$. Define $w = \sum_{d \mid \gcd(a,b)} \mu(d)$, where $\mu$ is the Möbius function. Let $k = 60w$. Determine the number of positive integers $d$ such that $2 \leq d \leq 56$, $d$ divides $k$, $\f... | 4,118 | graphs = [
Graph(
let={
"_n": Const(4),
"a1": Const(38),
"b1": MaxKDivides(target=Factorial(Const(396)), base=Const(11)),
"w": SumOverDivisors(n=GCD(a=Ref(name='a1'), b=Ref(name='b1')), var='d', expr=MoebiusMu(n=Var(name='d'))),
"k": Mul(Const(60),... | NT | null | COUNT | sympy | V1 | [
"V1/MOBIUS_COPRIME",
"LIOUVILLE_ONE"
] | 1b77e2 | diophantine_fbi2_count_v1 | null | 5 | 2 | [
"LIOUVILLE_ONE",
"MOBIUS_COPRIME",
"V1"
] | 3 | 0.007 | 2026-02-08T03:56:47.041534Z | {
"verified": true,
"answer": 4118,
"timestamp": "2026-02-08T03:56:47.048724Z"
} | d4b9e6 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 279,
"completion_tokens": 786
},
"timestamp": "2026-02-09T14:44:07.338Z",
"answer": 4118
},
{
"id... | 1 | [
{
"lemma": "K5",
"status": "same_pattern_wrong"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "LIOUVILLE_ONE",
"status": "ok"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "MOBIUS_COPRIME",
"status":... | {
"lo": -6.5,
"mid": -0.2,
"hi": 6.11
} | ||
ca0118 | comb_sum_binomial_row_v1_1439011603_2481 | Let $n$ be the number of integers $t$ with $5 \leq t \leq 19$ such that there exist positive integers $a \in [1,3]$ and $b \in [1,5]$ satisfying $t = 3a + 2b$. Let $r$ be the number of positive integers $p$ for which there exists a positive integer $q$ such that $pq = 18$, $\gcd(p, q) = 1$, and $p < q$. Let $s = r^n$. ... | 48,267 | graphs = [
Graph(
let={
"_n": Const(57307),
"n": CountOverSet(set=SolutionsSet(var=Var("t"), condition=Exists(var=Var(name='a'), condition=Exists(var=Var(name='b'), condition=And(Geq(left=Var(name='a'), right=Const(value=1)), Leq(left=Var(name='a'), right=Const(value=3)), Geq(left=Va... | NT | null | SUM | sympy | COPRIME_PAIRS | [
"COPRIME_PAIRS",
"LIN_FORM"
] | 67610e | comb_sum_binomial_row_v1 | null | 5 | 0 | [
"COPRIME_PAIRS",
"LIN_FORM"
] | 2 | 0.003 | 2026-02-08T16:49:47.786674Z | {
"verified": true,
"answer": 48267,
"timestamp": "2026-02-08T16:49:47.790088Z"
} | 2e2adf | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 189,
"completion_tokens": 2942
},
"timestamp": "2026-02-17T13:31:08.681Z",
"answer": 48267
},
... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
09a06f | modular_mod_compute_v1_601307018_9971 | Let $m$ be the minimum value of $x + y$ over all ordered pairs $(x, y)$ of positive integers such that $xy = 6350400$. Find the remainder when $-17424$ is divided by $m$. | 2,736 | graphs = [
Graph(
let={
"a": Const(-17424),
"m": MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(Mul(Var("x"), Var("y")), Const(6350400)))), expr=Sum(Var("x"), Var("y")... | NT | null | COMPUTE | sympy | B3 | [
"B3"
] | 0cd20d | modular_mod_compute_v1 | null | 4 | 0 | [
"B3"
] | 1 | 0.002 | 2026-03-10T10:25:06.188347Z | {
"verified": true,
"answer": 2736,
"timestamp": "2026-03-10T10:25:06.190456Z"
} | 755667 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 161,
"completion_tokens": 1202
},
"timestamp": "2026-04-19T12:42:14.387Z",
"answer": 2736
},
{
"... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "V3",
"status": "no"
}
] | {
"lo": -5.34,
"mid": 1.1,
"hi": 7.53
} | ||
941c64 | sequence_count_fib_divisible_v1_1520064083_6710 | Let $U = 820$ and $d = 18$. Compute the number of positive integers $n$ not exceeding $U$ such that the $n$-th Fibonacci number is divisible by $d$. | 68 | graphs = [
Graph(
let={
"upper": Const(820),
"d": Const(18),
"result": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Ref("upper")), Divides(divisor=Ref("d"), dividend=Fibonacci(arg=Var(name='n')))))),
},
g... | NT | null | COUNT | sympy | B3 | [
"V8/MAX_PRIME_BELOW",
"ONE_PHI_2",
"B3"
] | 670fae | sequence_count_fib_divisible_v1 | null | 6 | 0 | [
"B3",
"MAX_PRIME_BELOW",
"ONE_PHI_2",
"V8"
] | 4 | 0.094 | 2026-02-08T08:16:51.707078Z | {
"verified": true,
"answer": 68,
"timestamp": "2026-02-08T08:16:51.801038Z"
} | fbe70e | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 90,
"completion_tokens": 1306
},
"timestamp": "2026-02-13T16:56:43.319Z",
"answer": 68
},
{
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok_later"
},
{
"lemma": "ONE_PHI_2",
"status": "ok"
},
{
"lemma": "V5",
"status"... | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
4416e6 | comb_sum_binomial_row_v1_168721529_834 | Let $d$ be the smallest integer greater than or equal to 2 that divides 71383. Let $x = 2^d$. Compute the remainder when $46003 \cdot x$ is divided by 71698. | 11,888 | graphs = [
Graph(
let={
"n": MinOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Const(2)), Divides(divisor=Var("d"), dividend=Const(71383))))),
"result": Pow(Const(2), Ref("n")),
"_c": Const(46003),
"Q": Mod(value=Mul(Ref("_c"), Ref("result"... | NT | null | SUM | sympy | MIN_PRIME_FACTOR | [
"MIN_PRIME_FACTOR"
] | bc3776 | comb_sum_binomial_row_v1 | null | 3 | 0 | [
"MIN_PRIME_FACTOR"
] | 1 | 0.003 | 2026-02-08T13:19:05.720171Z | {
"verified": true,
"answer": 11888,
"timestamp": "2026-02-08T13:19:05.722829Z"
} | 710db6 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 159,
"completion_tokens": 1650
},
"timestamp": "2026-02-11T07:41:41.428Z",
"answer": 11888
},
{
... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "MIN_PRIME_FACTOR",
"status": "ok"
},
{
"lemma": "V3",
"status": "no... | {
"lo": -1.84,
"mid": 2.85,
"hi": 7.63
} | ||
67ce15 | comb_factorial_compute_v1_865884756_5078 | Let $A$ be the set of all positive integers $n_1$ such that $1 \le n_1 \le 9327$ and $n_1 \equiv \left\lfloor \frac{n_1}{2} \right\rfloor \pmod{11}$. Let $d$ be the smallest integer $d \ge 2$ that divides the number of elements in $A$. Compute $d!$. | 5,040 | graphs = [
Graph(
let={
"_n": Const(2),
"n": MinOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Ref("_n")), Divides(divisor=Var("d"), dividend=CountOverSet(set=SolutionsSet(var=Var("n1"), condition=And(Geq(Var("n1"), Const(1)), Leq(Var("n1"), Const(9327)), Congruen... | NT | null | COMPUTE | sympy | L3C | [
"L3C/MIN_PRIME_FACTOR"
] | eb2a9a | comb_factorial_compute_v1 | null | 6 | 0 | [
"L3C",
"MIN_PRIME_FACTOR"
] | 2 | 0.003 | 2026-02-08T18:22:16.988491Z | {
"verified": true,
"answer": 5040,
"timestamp": "2026-02-08T18:22:16.991049Z"
} | 3671e5 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 137,
"completion_tokens": 1110
},
"timestamp": "2026-02-18T16:33:37.137Z",
"answer": 5040
},
{... | 1 | [
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "L3C",
"status": "ok"
},
{
"lemma": "MIN_PRIME_FACTOR",
"status": "ok_later"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "POLY_PADIC_V... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
9d024f | nt_count_intersection_v1_153355830_291 | Let $N$ be the number of integers $t$ such that $9 \leq t \leq 5020$ and there exist positive integers $a$ and $b$ with $1 \leq a \leq 848$, $1 \leq b \leq 195$, and $t = 5a + 4b$. Determine the value of the number of positive integers $n$ such that $1 \leq n \leq N$, $n$ is divisible by $9$, and $\gcd(n, 14) = 1$. | 238 | 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=848)), Geq(left=Var(name='b'), right=Const(value... | NT | null | COUNT | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | nt_count_intersection_v1 | null | 5 | 0 | [
"LIN_FORM"
] | 1 | 1.743 | 2026-02-08T03:00:20.877547Z | {
"verified": true,
"answer": 238,
"timestamp": "2026-02-08T03:00:22.620294Z"
} | e8d4dc | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 233,
"completion_tokens": 4652
},
"timestamp": "2026-02-10T12:31:25.961Z",
"answer": 238
},
{
"i... | 1 | [
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "V1",
"status": "no"
}
] | {
"lo": -3.45,
"mid": 1.18,
"hi": 5.72
} | ||
ba9fb0 | nt_count_with_divisor_count_v1_151522320_1242 | Let $S$ be the set of all ordered pairs $(x, y)$ of positive integers such that $xy = 14288400$. Define $\sigma$ to be the minimum value of $x + y$ as $(x, y)$ ranges over $S$.
Let $T$ be the set of all integers $t$ with $5 \leq t \leq 12$ that can be written as $t = 2a + 3b$ for some integers $a, b$ satisfying $1 \l... | 24,978 | graphs = [
Graph(
let={
"_m": Const(2),
"_n": Const(84398),
"upper": MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(Mul(Var("x"), Var("y")), Const(14288400... | NT | null | COUNT | sympy | LIN_FORM | [
"LIN_FORM/MAX_PRIME_BELOW",
"B3"
] | 2a7052 | nt_count_with_divisor_count_v1 | null | 7 | 0 | [
"B3",
"LIN_FORM",
"MAX_PRIME_BELOW"
] | 3 | 0.308 | 2026-02-08T03:51:32.845856Z | {
"verified": true,
"answer": 24978,
"timestamp": "2026-02-08T03:51:33.154145Z"
} | 0d5553 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 353,
"completion_tokens": 1038
},
"timestamp": "2026-02-10T15:54:07.547Z",
"answer": 24978
},
{
"... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok_later"
},
{
"lemma": "MOD_FACTORIAL",
"status": "... | {
"lo": -3.53,
"mid": 1.02,
"hi": 5.49
} | ||
b26522 | comb_bell_compute_v1_1915831931_1499 | Let $S$ be the set of all ordered pairs of positive integers $(x, y)$ such that $x + y = 6$. Let $n$ be the maximum value of $xy$ over all such pairs. Let $B_n$ denote the $n$th Bell number, which counts the number of partitions of an $n$-element set. Compute $30276 - B_n$. | 9,129 | graphs = [
Graph(
let={
"n": MaxOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(Sum(Var("x"), Var("y")), Const(6)))), expr=Mul(Var("x"), Var("y")))),
"result": Bell(Ref("n... | COMB | null | COMPUTE | sympy | B1 | [
"B1"
] | 5b950e | comb_bell_compute_v1 | null | 4 | 0 | [
"B1"
] | 1 | 0.002 | 2026-02-08T16:11:19.914306Z | {
"verified": true,
"answer": 9129,
"timestamp": "2026-02-08T16:11:19.916144Z"
} | efadc5 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 193,
"completion_tokens": 394
},
"timestamp": "2026-02-24T20:28:49.024Z",
"answer": 9129
},
{
"i... | 1 | [
{
"lemma": "B1",
"status": "ok"
},
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
... | {
"lo": -5.65,
"mid": -3.17,
"hi": -0.81
} | ||
171cac | modular_sum_quadratic_residues_v1_717093673_586 | Let $n = 329$. Let $p$ be the largest prime number less than or equal to $n$. Compute $\frac{p(p-1)}{4}$. | 25,043 | graphs = [
Graph(
let={
"_n": Const(329),
"p": MaxOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(2)), Leq(Var("n"), Ref("_n")), IsPrime(Var("n"))))),
"result": Div(Mul(Ref("p"), Sub(Ref("p"), Const(1))), Const(4)),
},
goal=Ref("re... | NT | null | SUM | sympy | MAX_PRIME_BELOW | [
"MAX_PRIME_BELOW"
] | dc3ad3 | modular_sum_quadratic_residues_v1 | null | 2 | 0 | [
"MAX_PRIME_BELOW"
] | 1 | 0.002 | 2026-02-08T15:32:18.516765Z | {
"verified": true,
"answer": 25043,
"timestamp": "2026-02-08T15:32:18.518872Z"
} | e2a6c6 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 81,
"completion_tokens": 1134
},
"timestamp": "2026-02-16T08:23:31.863Z",
"answer": 25043
},
{... | 1 | [
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok"
},
{
"lemma": "MOD_FACTORIAL",
"status"... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
e2b29e | nt_sum_over_divisible_v1_898971024_892 | Let $\text{upper} = 16900$. Let $d$ be the number of positive integers $k$ such that $1 \leq k \leq 675$ and $25$ divides $k$. Let $\text{result}$ be the sum of all positive integers $n$ such that $1 \leq n \leq \text{upper}$ and $n \equiv 0 \pmod{d}$. Let $Q$ be the remainder when $79819 \cdot \text{result}$ is divide... | 10,503 | graphs = [
Graph(
let={
"upper": Const(16900),
"divisor": CountOverSet(set=SolutionsSet(var=Var("k"), condition=And(Geq(Var("k"), Const(1)), Leq(Var("k"), Const(675)), Divides(divisor=Const(25), dividend=Var("k"))), domain='positive_integers')),
"result": SumOverSet(set=S... | ALG | NT | SUM | sympy | C2 | [
"C2"
] | 9685eb | nt_sum_over_divisible_v1 | null | 4 | 0 | [
"C2"
] | 1 | 6.205 | 2026-02-08T15:45:59.148737Z | {
"verified": true,
"answer": 10503,
"timestamp": "2026-02-08T15:46:05.353549Z"
} | 736d2d | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 162,
"completion_tokens": 2343
},
"timestamp": "2026-02-16T13:10:32.585Z",
"answer": 10503
},
... | 1 | [
{
"lemma": "C2",
"status": "ok"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "VAL_SUM_EQ",
"status": "no"
... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
fccda7 | comb_factorial_compute_v1_1218484723_6954 | Let $n$ be the number of positive integers $v$ with $5 \le v \le X$ such that there exist integers $a, b$ with $1 \le a, b \le 8$ satisfying $5b^2 = v$, where $$X = \left|\left\{ (a, b) : 1 \le a \le 25,\ 1 \le b \le 25,\ a \le b,\ 2a^2 - 4ab + 2b^2 = 50 \right\}\right| \cdot \max\left\{ b \le 20 : \text{for some } a,\... | 40,320 | graphs = [
Graph(
let={
"_c": Const(20),
"_m": Const(2),
"_n": Const(5),
"n": CountOverSet(set=SolutionsSet(var=Var("v"), condition=And(Geq(Var("v"), Ref("_n")), Leq(Var("v"), CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("a"), Var("b")]), condition=An... | COMB | null | COMPUTE | sympy | QF_PSD_ORBIT | [
"QF_PSD_ORBIT/QF_PSD_COUNT_LEQ/QF_PSD_DISTINCT"
] | 8f6402 | comb_factorial_compute_v1 | null | 6 | 0 | [
"QF_PSD_COUNT_LEQ",
"QF_PSD_DISTINCT",
"QF_PSD_ORBIT"
] | 3 | 0.007 | 2026-02-25T08:23:02.381111Z | {
"verified": true,
"answer": 40320,
"timestamp": "2026-02-25T08:23:02.388310Z"
} | 4346a7 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 283,
"completion_tokens": 1478
},
"timestamp": "2026-03-30T03:23:36.906Z",
"answer": 40320
},
{
"... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "QF_PSD_COUNT_LEQ",
"status": "ok_later"
},
{
"lemma": "Q... | {
"lo": -6.2,
"mid": -2.87,
"hi": 0.44
} | ||
21b6ec_l | algebra_vieta_sum_v1_1742523217_4274 | Let $C=581$. Let $K$ be the number of nonnegative integers $j$ with $0\le j\le C$ such that
$$\binom{C}{j}\equiv 1\pmod{2}.$$
Let
$$M = K+9.$$
Consider all ordered pairs $(x,y)$ of positive integers such that $xy=M$, and let $S$ be the set of all possible values of $x+y$ for these pairs. Let $s_0$ be the smallest elem... | 0 | ALG | COMB | COMPUTE | sympy | B3 | [
"V8/B3/B1"
] | b2115a | algebra_vieta_sum_v1 | null | 8 | 0 | [
"B1",
"B3",
"V8"
] | 3 | 0.076 | 2026-02-08T07:09:26.348732Z | {
"verified": false,
"answer": 25,
"timestamp": "2026-02-08T07:09:26.425183Z"
} | eb3a7a | 21b6ec | legacy_text | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 318,
"completion_tokens": 905
},
"timestamp": "2026-02-24T07:41:35.221Z",
"answer": 25
},
{
"id":... | 1 | [
{
"lemma": "B1",
"status": "ok_later"
},
{
"lemma": "B3",
"status": "ok_later"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "V1",
"status": "no"
},
{
"lemma": "V3"... | {
"lo": -2.35,
"mid": 1.22,
"hi": 4.84
} | |
0b9490 | lin_form_endings_v1_1520064083_8119 | Let $d$ be the number of integers $t$ such that $72 \leq t \leq 2000$ and there exist positive integers $a$ and $b$ with $1 \leq a \leq 27$, $1 \leq b \leq 28$, and $t = 16a + 56b$. Compute the remainder when $5299d$ is divided by $75238$. | 46,756 | graphs = [
Graph(
let={
"_inner_result": 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=27)), Geq(left=Var(name='b'), right=... | COMB | null | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | lin_form_endings_v1 | null | 4 | null | [
"LIN_FORM"
] | 1 | 0.002 | 2026-02-08T10:01:29.781747Z | {
"verified": true,
"answer": 46756,
"timestamp": "2026-02-08T10:01:29.783723Z"
} | fa9f66 | 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": 4772
},
"timestamp": "2026-02-24T11:46:11.502Z",
"answer": 46756
},
{
"... | 1 | [
{
"lemma": "COUNT_CARTESIAN",
"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_SUM",
"st... | {
"lo": -2.35,
"mid": 1.22,
"hi": 4.84
} | ||
06b721 | nt_min_with_divisor_count_v1_1520064083_7620 | Let $T$ be the set of all integers $t$ such that $9 \leq t \leq 2043$ and there exist integers $a$ and $b$ with $1 \leq a \leq 62$, $1 \leq b \leq 359$, and $t = 4a + 5b$. Let $u$ be the number of elements in $T$. Let $n$ be the smallest positive integer such that $1 \leq n \leq u$ and $n$ has exactly 6 positive diviso... | 33,551 | graphs = [
Graph(
let={
"upper": CountOverSet(set=SolutionsSet(var=Var("t"), condition=Exists(var=Var(name='a'), condition=Exists(var=Var(name='b'), condition=And(Geq(left=Var(name='a'), right=Const(value=1)), Leq(left=Var(name='a'), right=Const(value=62)), Geq(left=Var(name='b'), right=Const(va... | NT | null | EXTREMUM | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | nt_min_with_divisor_count_v1 | null | 5 | 0 | [
"LIN_FORM"
] | 1 | 0.083 | 2026-02-08T09:12:50.008724Z | {
"verified": true,
"answer": 33551,
"timestamp": "2026-02-08T09:12:50.091696Z"
} | e8d409 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 179,
"completion_tokens": 6813
},
"timestamp": "2026-02-14T01:36:53.528Z",
"answer": 33551
},
... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
}
] | {
"lo": -5.49,
"mid": 0.22,
"hi": 6.51
} | ||
a19706 | nt_num_divisors_compute_v1_1520064083_1056 | Let $N_0 = 74892$. Let $n$ be the number of integers $k$ with $1 \le k \le N_0$ such that $12$ divides the $k$th Fibonacci number $F_k$.
Let $d(n)$ denote the number of positive divisors of $n$, and let $\varphi$ denote Euler's totient function. Define
$$Q = d(n) + \varphi\big(|d(n)| + 1\big) + d\big(|d(n)| + 1\big).$$... | 8 | graphs = [
Graph(
let={
"_n": Const(74892),
"n": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Ref("_n")), Divides(divisor=Const(12), dividend=Fibonacci(arg=Var(name='n')))))),
"result": NumDivisors(n=Ref("n")),
... | NT | null | COMPUTE | sympy | L3C | [
"COUNT_FIB_DIVISIBLE"
] | 66de3c | nt_num_divisors_compute_v1 | null | 8 | 0 | [
"COUNT_FIB_DIVISIBLE",
"L3C"
] | 2 | 0.018 | 2026-02-08T03:45:25.905872Z | {
"verified": true,
"answer": 8,
"timestamp": "2026-02-08T03:45:25.923631Z"
} | 78d202 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 238,
"completion_tokens": 1845
},
"timestamp": "2026-02-10T15:38:31.663Z",
"answer": 8
},
{
"id":... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "ok"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "V3",
"status": "n... | {
"lo": 1.15,
"mid": 3.18,
"hi": 4.97
} | ||
308f08 | nt_sum_divisors_mod_v1_1439011603_336 | Let $n$ be the number of positive integers at most $3674$ that are even and relatively prime to $35$. Let $\sigma$ be the sum of all positive divisors of $n$. Compute the remainder when $26279\sigma$ is divided by $93949$. | 74,943 | graphs = [
Graph(
let={
"_n": Const(35),
"n": CountOverSet(set=SolutionsSet(var=Var("n1"), condition=And(Geq(Var("n1"), Const(1)), Leq(Var("n1"), Const(3674)), Divides(divisor=Const(2), dividend=Var("n1")), Eq(GCD(a=Var("n1"), b=Ref("_n")), Const(1))))),
"M": Const(11813)... | NT | null | COMPUTE | sympy | C5 | [
"C5"
] | 1d9668 | nt_sum_divisors_mod_v1 | null | 5 | 0 | [
"C5"
] | 1 | 0.004 | 2026-02-08T15:25:06.228252Z | {
"verified": true,
"answer": 74943,
"timestamp": "2026-02-08T15:25:06.232172Z"
} | 48bf92 | 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": 2850
},
"timestamp": "2026-02-16T06:29:57.085Z",
"answer": 74943
},
... | 1 | [
{
"lemma": "C5",
"status": "ok"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "V1",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
11fc53 | algebra_poly_eval_v1_971394319_617 | Let $k = 11$. Define $S$ as the set of all positive integers $n$ such that $1 \le n \le m$, where $m$ is the minimum value of $x + y$ over all ordered pairs $(x, y)$ of positive integers satisfying $xy = 3189796$, and the sum of the decimal digits of $n$ is even. Compute the value of $$\frac{160k^4 - 168k^3 - 48k^2 - 1... | 25,709 | graphs = [
Graph(
let={
"_n": Const(2),
"k": Const(11),
"result": Div(Sum(Mul(Const(160), Pow(Ref("k"), Const(4))), Mul(Const(-168), Pow(Ref("k"), Const(3))), Mul(Const(-48), Pow(Ref("k"), Ref("_n"))), Mul(Const(-18), Ref("k")), Const(-108)), CountOverSet(set=SolutionsSet... | NT | null | COMPUTE | sympy | B3 | [
"B3/L3B"
] | aaa20b | algebra_poly_eval_v1 | null | 6 | 0 | [
"B3",
"L3B"
] | 2 | 0.006 | 2026-02-08T13:13:30.270902Z | {
"verified": true,
"answer": 25709,
"timestamp": "2026-02-08T13:13:30.276895Z"
} | 2842e2 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 185,
"completion_tokens": 4892
},
"timestamp": "2026-02-15T10:53:00.718Z",
"answer": 25709
},
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "L3B",
"status": "ok_later"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
... | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
045293 | antilemma_sum_equals_v1_1439011603_2443 | Let $n = 90$. Compute the number of ordered pairs $(i,j)$ of positive integers such that $i + j = n$, $1 \leq i \leq 89$, and $1 \leq j \leq 90$. | 89 | graphs = [
Graph(
let={
"_n": Const(90),
"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(89)), right=IntegerRange(start=Const(1), end=Con... | COMB | GEOM | COMPUTE | sympy | LIN_FORM | [
"COUNT_SUM_EQUALS"
] | 75ab0f | antilemma_sum_equals_v1 | null | 2 | 0 | [
"COUNT_SUM_EQUALS",
"LIN_FORM"
] | 2 | 0.123 | 2026-02-08T16:47:01.092015Z | {
"verified": true,
"answer": 89,
"timestamp": "2026-02-08T16:47:01.215202Z"
} | 174076 | 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": 1207
},
"timestamp": "2026-02-24T21:51:30.161Z",
"answer": 89
},
{
... | 2 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "ok"
},
{
"lemma": "V8",
"status": "no"
},
{
"lemma": "V8_SUM",
"status"... | {
"lo": -10,
"mid": -7.42,
"hi": -4.85
} | ||
c6475b | algebra_poly_eval_v1_784195855_8094 | Let $x$ and $y$ be positive integers such that $xy = 144$. Let $t$ be the minimum possible value of $x + y$ over all such pairs. Define the quantity
$$
\text{result} = 10t^2 - 3t + 5.
$$
Let $Q$ be the remainder when $22293 \cdot \text{result}$ is divided by $55126$. Compute $Q$. | 13,997 | graphs = [
Graph(
let={
"_n": Const(55126),
"t": 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(144)))), expr=Sum(Var("x"), Var("y")))),... | NT | null | COMPUTE | sympy | B3 | [
"B3"
] | 0cd20d | algebra_poly_eval_v1 | null | 3 | 0 | [
"B3"
] | 1 | 0.002 | 2026-02-08T10:48:08.081719Z | {
"verified": true,
"answer": 13997,
"timestamp": "2026-02-08T10:48:08.083847Z"
} | 00d531 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 139,
"completion_tokens": 675
},
"timestamp": "2026-02-16T16:05:45.931Z",
"answer": 13997
},
{... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "V1",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
9729e8 | nt_count_gcd_equals_v1_124444284_3685 | Let $ k = 270 $, $ d = 10 $, and $ U = 6000 $. Let $ C $ be the number of positive integers $ n \le U $ such that $ \gcd(n, k) = d $. Let $ S = \sum_{i=1}^{89} i $. Compute the remainder when $ C^2 + 24 \cdot C + S $ is divided by $ 73893 $. Find the value of this remainder. | 25,819 | graphs = [
Graph(
let={
"_n": Const(24),
"upper": Const(6000),
"k": Const(270),
"d": Const(10),
"result": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Ref("upper")), Eq(GCD(a=Var("n"), b=Ref("k"))... | NT | null | COUNT | sympy | SUM_ARITHMETIC | [
"SUM_ARITHMETIC"
] | 609463 | nt_count_gcd_equals_v1 | quadratic_mod | 4 | 0 | [
"SUM_ARITHMETIC"
] | 1 | 0.489 | 2026-02-08T05:32:39.618043Z | {
"verified": true,
"answer": 25819,
"timestamp": "2026-02-08T05:32:40.106980Z"
} | e3d744 | 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": 745
},
"timestamp": "2026-02-12T10:27:25.390Z",
"answer": 25819
},
{... | 1 | [
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "SUM_ARITHMETIC",
"status": "ok"
},
{
"lemma": "V5",
"status": "no"
},
{
"lemma": "V8",
"status": "no"... | {
"lo": -3.51,
"mid": 1.33,
"hi": 6.56
} | ||
a0f385 | geo_count_lattice_rect_v1_1439011603_1270 | Compute the number of lattice points in the rectangle $ [0, 50] \times [0, 172] $, including the boundary. | 8,823 | graphs = [
Graph(
let={
"a": Const(50),
"b": Const(172),
"result": LatticePointsRect(a=Ref(name='a'), b=Ref(name='b')),
},
goal=Ref("result"),
)
] | GEOM | null | COUNT | sympy | [] | geo_count_lattice_rect_v1 | null | 3 | 0 | null | null | 0.003 | 2026-02-08T16:00:19.423829Z | {
"verified": true,
"answer": 8823,
"timestamp": "2026-02-08T16:00:19.426992Z"
} | 3799ea | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 139,
"completion_tokens": 222
},
"timestamp": "2026-02-24T19:26:42.949Z",
"answer": 8823
},
{
"i... | 1 | [] | {
"lo": -8.52,
"mid": -5.43,
"hi": -3.2
} | ||||
e05fb6 | antilemma_v8_lucas_1116507919_12 | Let $m$ be the number of integers $n$ with $1\le n\le 56$ such that the sum of the decimal digits of $n$ is odd.
Let
$$L=\sum_{d\mid m}\mu(d).$$
Let $c$ be the number of positive integers $p$ for which there exists a positive integer $q$ such that
$$pq=24,\quad \gcd(p,q)=1,\quad p<q.$$
Let $x$ be the number of nonne... | 47,977 | graphs = [
Graph(
let={
"_m": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Const(56)), Eq(Mod(value=DigitSum(Var("n")), modulus=Const(2)), Const(1))))),
"_n": Const(93439),
"x": CountOverSet(set=SolutionsSet(var=Var("j")... | NT | null | COMPUTE | sympy | L3B | [
"L3B/COPRIME_PAIRS/MOBIUS_SUM/V8",
"COPRIME_PAIRS/V8",
"V8"
] | f4cbf3 | antilemma_v8_lucas | null | 7 | 0 | [
"COPRIME_PAIRS",
"L3B",
"MOBIUS_SUM",
"V8"
] | 4 | 0.003 | 2026-02-08T02:23:14.781000Z | {
"verified": true,
"answer": 47977,
"timestamp": "2026-02-08T02:23:14.784479Z"
} | d3d61c | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 280,
"completion_tokens": 1771
},
"timestamp": "2026-02-08T18:28:35.253Z",
"answer": 47977
},
{
"... | 1 | [
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "L3B",
"status": "ok"
},
{
"lemma": "MOBIUS_SUM",
"status": "ok_later"
},
{
"lemma": "V3",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
},
{
"... | {
"lo": -4.6,
"mid": 0.19,
"hi": 4.77
} | ||
36799d | diophantine_fbi2_count_v1_168721529_987 | Let $k$ be the minimum value of $x + y$ over all pairs of positive integers $(x, y)$ such that $xy = 129600$. Let $r$ be the number of positive integers $d$ such that $5 \le d \le 124$, $d$ divides $k$, and $5 \le \frac{k}{d} \le 124$. Compute $r + \phi(|r| + 1) + \tau(|r| + 1)$, where $\phi(n)$ is Euler's totient func... | 36 | 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")), Const(129600)))), expr=Sum(Var("x"), Var("y")))),
"result": CountO... | NT | null | COUNT | sympy | VIETA_SUM | [
"B3"
] | 0cd20d | diophantine_fbi2_count_v1 | null | 6 | 0 | [
"B3",
"VIETA_SUM"
] | 2 | 0.254 | 2026-02-08T13:23:24.168398Z | {
"verified": true,
"answer": 36,
"timestamp": "2026-02-08T13:23:24.422668Z"
} | 8000a8 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 247,
"completion_tokens": 2896
},
"timestamp": "2026-02-09T11:35:05.952Z",
"answer": 36
},
{
"id"... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"... | {
"lo": -5.65,
"mid": -2.15,
"hi": 1.88
} | ||
1c14d8 | modular_sum_quadratic_residues_v1_1125832087_242 | Let $p = 353$. Compute the value of $\frac{p(p-1)}{4}$. | 31,064 | graphs = [
Graph(
let={
"p": Const(353),
"result": Div(Mul(Ref("p"), Sub(Ref("p"), Const(1))), Const(4)),
},
goal=Ref("result"),
)
] | NT | null | SUM | sympy | B1 | [
"B1/LIN_FORM"
] | 7f6ba8 | modular_sum_quadratic_residues_v1 | null | 2 | 0 | [
"B1",
"LIN_FORM"
] | 2 | 0.003 | 2026-02-08T02:58:45.751042Z | {
"verified": true,
"answer": 31064,
"timestamp": "2026-02-08T02:58:45.754194Z"
} | 598a6c | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 133,
"completion_tokens": 155
},
"timestamp": "2026-02-10T12:22:39.164Z",
"answer": 31064
},
{
"i... | 1 | [
{
"lemma": "B1",
"status": "ok"
},
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok_later"
},
{
"lem... | {
"lo": -5.55,
"mid": -3.02,
"hi": 0.3
} | ||
2bc3ee | nt_sum_gcd_range_mod_v1_1874849503_765 | Let $N$ be the number of nonnegative integers $j$ such that $0 \leq j \leq 95823$ and $\binom{95823}{j}$ is odd. Let $k = 60$ and $M = 10333$. Define
$$
S = \sum_{n=1}^{N} \gcd(n, 60).
$$
Let $r = S \mod 10333$. Compute the value of
$$
Q = (44121 \cdot r) \mod 93922.
$$ | 4,717 | graphs = [
Graph(
let={
"_n": Const(2),
"N": CountOverSet(set=SolutionsSet(var=Var("j"), condition=And(Geq(Var("j"), Const(0)), Leq(Var("j"), Const(95823)), Eq(Mod(value=Binom(n=Const(95823), k=Var("j")), modulus=Ref("_n")), Const(1))), domain='nonnegative_integers')),
"k... | NT | null | COMPUTE | sympy | V8 | [
"V8"
] | 86348e | nt_sum_gcd_range_mod_v1 | null | 7 | 0 | [
"V8"
] | 1 | 0.251 | 2026-02-08T13:18:15.043878Z | {
"verified": true,
"answer": 4717,
"timestamp": "2026-02-08T13:18:15.294621Z"
} | f8fd46 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 227,
"completion_tokens": 2143
},
"timestamp": "2026-02-09T20:40:36.686Z",
"answer": 4717
},
{
"i... | 1 | [
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "V8",
"status": "ok"
}
] | {
"lo": -5.15,
"mid": 0.12,
"hi": 6.12
} | ||
c8f54a | nt_min_with_divisor_count_v1_655260480_2600 | Let $S$ be the set of all positive integers $n$ such that $1 \leq n \leq 23716$ and $n$ has exactly $12$ positive divisors. Determine the value of the smallest element of $S$. | 60 | graphs = [
Graph(
let={
"upper": Const(23716),
"div_count": Const(12),
"result": MinOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Ref("upper")), Eq(NumDivisors(n=Var("n")), Ref("div_count"))))),
},
goal=Ref("re... | NT | null | EXTREMUM | sympy | SUM_DIVISIBLE | [
"SUM_DIVISIBLE",
"B3"
] | 26d1a5 | nt_min_with_divisor_count_v1 | null | 4 | 0 | [
"B3",
"SUM_DIVISIBLE"
] | 2 | 2.023 | 2026-02-08T16:51:34.129551Z | {
"verified": true,
"answer": 60,
"timestamp": "2026-02-08T16:51:36.152792Z"
} | 8ec300 | 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": 1273
},
"timestamp": "2026-02-17T13:26:27.818Z",
"answer": 60
},
{
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "SUM_DIVISIBLE",
"status": "ok"
... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
9f2041 | nt_count_with_divisor_count_v1_677425708_1115 | Let $\_m = 146$ and $\_n = 9$. Define $\text{upper}$ to be the maximum value of $x \cdot y$ over all pairs of positive integers $(x, y)$ such that $x + y = \_m$. Let $\text{div\_count}$ be the largest prime number less than or equal to $\_n$. Compute the number of positive integers $n$ such that $1 \leq n \leq \text{up... | 3 | graphs = [
Graph(
let={
"_m": Const(146),
"_n": Const(9),
"upper": MaxOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(Sum(Var("x"), Var("y")), Ref("_m")))), ex... | NT | null | COUNT | sympy | MAX_PRIME_BELOW | [
"MAX_PRIME_BELOW",
"B1"
] | 7086d0 | nt_count_with_divisor_count_v1 | null | 7 | 0 | [
"B1",
"MAX_PRIME_BELOW"
] | 2 | 0.316 | 2026-02-08T04:00:14.495303Z | {
"verified": true,
"answer": 3,
"timestamp": "2026-02-08T04:00:14.811531Z"
} | 4515b6 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 270,
"completion_tokens": 620
},
"timestamp": "2026-02-09T15:50:14.748Z",
"answer": 3
},
{
"id": ... | 1 | [
{
"lemma": "B1",
"status": "ok"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
... | {
"lo": -6.5,
"mid": -0.2,
"hi": 6.11
} | ||
53766f | comb_factorial_compute_v1_458359167_3054 | Let $m = 644$. Determine the number of positive integers $n$ with $1 \leq n \leq 4508$ such that $n \equiv \left\lfloor \frac{n}{2} \right\rfloor \pmod{7}$. Denote this number by $N$. Now consider the set of all nonnegative integers $j$ such that $0 \leq j \leq m$ and $\binom{N}{j}$ is odd. Let $k$ be the number of suc... | 40,320 | graphs = [
Graph(
let={
"_m": Const(644),
"_n": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Const(4508)), Congruent(a=Var(name='n'), b=Floor(arg=Div(left=Var(name='n'), right=Const(value=2))), modulus=Const(value=7))))),
... | NT | null | COMPUTE | sympy | L3C | [
"L3C/V8"
] | 2a9f26 | comb_factorial_compute_v1 | null | 7 | 0 | [
"L3C",
"V8"
] | 2 | 0.002 | 2026-02-08T06:54:46.065795Z | {
"verified": true,
"answer": 40320,
"timestamp": "2026-02-08T06:54:46.067602Z"
} | dd2df8 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 160,
"completion_tokens": 1773
},
"timestamp": "2026-02-13T05:57:59.622Z",
"answer": 2092278988... | 1 | [
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "L3C",
"status": "ok"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "V7",
"status": "... | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
a389a4 | comb_catalan_compute_v1_1419126231_1659 | Let $C_n$ denote the $n$-th Catalan number. Find the number of ordered pairs $(x_1, x_2)$ of positive integers such that $x_1 + x_2 = 22$ and both $x_1$ and $x_2$ are odd. Let $n$ be this number, and let $M = C_n$. Compute the remainder when $69500M$ is divided by $54671$. | 8,499 | graphs = [
Graph(
let={
"_n": Const(54671),
"n": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x1"), Var("x2")]), condition=And(IsPositive(arg=Var(name='x1')), IsPositive(arg=Var(name='x2')), IsOdd(arg=Var(name='x1')), IsOdd(arg=Var(name='x2')), Eq(Sum(Var("x1"), Var("x2")),... | COMB | null | COMPUTE | sympy | COMB1 | [
"COMB1"
] | 567f58 | comb_catalan_compute_v1 | null | 3 | 0 | [
"COMB1"
] | 1 | 0.001 | 2026-02-25T11:12:44.946295Z | {
"verified": true,
"answer": 8499,
"timestamp": "2026-02-25T11:12:44.947601Z"
} | d7a793 | 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": 4345
},
"timestamp": "2026-03-30T13:26:06.187Z",
"answer": 8499
},
{
"i... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COMB1",
"status": "ok"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
}
] | {
"lo": -5.37,
"mid": 0.23,
"hi": 5.22
} | ||
724172 | algebra_vieta_sum_v1_809748730_70 | Let $p$ and $q$ be positive integers such that $pq = 2250$, $p < q$, and $\gcd(p, q) = 1$. Define $n$ to be the number of such integers $p$. Let $\text{result}$ be the sum of all real solutions $x$ to the equation
$$
x^n + 7x^3 - 46x^2 - 172x - 120 = 0.
$$
Find the remainder when $65893 \cdot \text{result}$ is divided ... | 18,299 | graphs = [
Graph(
let={
"_n": Const(95910),
"result": SumOverSet(set=SolutionsSet(var=Var("x"), condition=Eq(Sum(Pow(Var("x"), 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 | COMPUTE | sympy | BINOMIAL_ALTERNATING | [
"COPRIME_PAIRS"
] | 2bb3aa | algebra_vieta_sum_v1 | null | 5 | 0 | [
"BINOMIAL_ALTERNATING",
"COPRIME_PAIRS"
] | 2 | 0.124 | 2026-02-08T11:18:54.490731Z | {
"verified": true,
"answer": 18299,
"timestamp": "2026-02-08T11:18:54.615003Z"
} | 2ba3b5 | 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": 1919
},
"timestamp": "2026-02-14T11:38:27.560Z",
"answer": 18299
},
... | 1 | [
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
}
] | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
bc3569 | geo_count_lattice_triangle_v1_601307018_5637 | Let $N = \left|222 \cdot 196 + 256 \cdot (-120)\right|$, \[ M = \gcd(222, 120) + \gcd(|256 - 222|, |196 - 120|) + \gcd(256, 196), \] and \[ R = \frac{N + 2 - M}{2}. \] Compute $|R|$. | 6,391 | graphs = [
Graph(
let={
"area_2x": Abs(arg=Sum(Mul(Const(value=222), Const(value=196)), Mul(Const(value=256), Sub(left=Const(value=0), right=Const(value=120))))),
"boundary": Sum(GCD(a=Abs(arg=Const(value=222)), b=Abs(arg=Const(value=120))), GCD(a=Abs(arg=Sub(left=Const(value=256), r... | GEOM | NT | COUNT | sympy | POLY_ORBIT_COUNT | [
"POLY_ORBIT_COUNT",
"POLY3_MIN"
] | 075bb3 | geo_count_lattice_triangle_v1 | null | 4 | 0 | [
"POLY3_MIN",
"POLY_ORBIT_COUNT"
] | 2 | 0.237 | 2026-03-10T06:13:10.394746Z | {
"verified": true,
"answer": 6391,
"timestamp": "2026-03-10T06:13:10.631666Z"
} | 40bad5 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 203,
"completion_tokens": 726
},
"timestamp": "2026-04-19T02:35:46.318Z",
"answer": 6391
},
{
"i... | 1 | [
{
"lemma": "POLY3_MIN",
"status": "ok"
},
{
"lemma": "POLY_ORBIT_COUNT",
"status": "ok"
}
] | {
"lo": -5.35,
"mid": 0.52,
"hi": 5.84
} | ||
50cfbe | nt_min_crt_v1_1520064083_4559 | Let $S$ be the set of all ordered pairs $(x, y)$ of positive integers such that $xy = 1936$. Let $u$ be the minimum value of $x + y$ as $(x, y)$ ranges over $S$. Determine the smallest positive integer $n$ such that $n \leq u$, $n \equiv 5 \pmod{8}$, and $n \equiv 10 \pmod{11}$. Let $r$ be this integer. Compute the rem... | 44,271 | graphs = [
Graph(
let={
"_n": Const(1936),
"m": Const(8),
"k": Const(11),
"a": Const(5),
"b": Const(10),
"upper": MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name... | NT | null | EXTREMUM | sympy | B3 | [
"B3"
] | 0cd20d | nt_min_crt_v1 | null | 6 | 0 | [
"B3"
] | 1 | 0.014 | 2026-02-08T06:19:41.030668Z | {
"verified": true,
"answer": 44271,
"timestamp": "2026-02-08T06:19:41.044441Z"
} | 9cba14 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 167,
"completion_tokens": 1138
},
"timestamp": "2026-02-12T22:49:17.239Z",
"answer": 44271
},
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
},
{
"lemma": "VAL_SUM_EQ",
"status": "no"
}
] | {
"lo": -5.49,
"mid": 0.22,
"hi": 6.51
} | ||
e23565 | alg_qf_psd_count_leq_v1_601307018_8866 | Let $S = \left|\{ v : v \geq 4,\ v \leq 1481,\ \text{there exist integers } a, b \text{ with } 1 \leq a, b \leq 8 \text{ such that } 25b^2 + 29a^2 - 50ab = v \}\right|$. Find the number of ordered pairs $(a, b)$ of positive integers with $1 \leq a, b \leq 151$ such that $-68ab + S \cdot a^2 + 26b^2 \leq 44100$. | 4,308 | graphs = [
Graph(
let={
"_n": Const(2),
"result": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("a"), Var("b")]), condition=And(Geq(Var("a"), Const(1)), Leq(Var("a"), Const(151)), Geq(Var("b"), Const(1)), Leq(Var("b"), Const(151)), Leq(Sum(Mul(Const(-68), Var("a"), Var("b")),... | ALG | null | COUNT | sympy | QF_PSD_DISTINCT | [
"QF_PSD_DISTINCT"
] | a8f9cb | alg_qf_psd_count_leq_v1 | null | 7 | 0 | [
"QF_PSD_DISTINCT"
] | 1 | 0.07 | 2026-03-10T09:18:48.618482Z | {
"verified": true,
"answer": 4308,
"timestamp": "2026-03-10T09:18:48.688316Z"
} | 499cfd | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 247,
"completion_tokens": 24354
},
"timestamp": "2026-04-19T10:04:19.940Z",
"answer": 4308
},
{
... | 1 | [
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "QF_PSD_DISTINCT",
"status": "ok"
}
] | {
"lo": -5.34,
"mid": 1.1,
"hi": 7.53
} | ||
75469b | comb_count_derangements_v1_1918700295_2005 | Let $n_0$ be the maximum value of $xy$ over all pairs of positive integers $(x,y)$ such that $x + y = 6$. Let $t$ be the number of positive integers $p$ for which there exists a positive integer $q$ such that $pq = 6$, $\gcd(p,q) = 1$, and $p < q$. Let $n$ be the largest prime number satisfying $t \leq n \leq n_0$. Com... | 7,834 | graphs = [
Graph(
let={
"_c": Const(65434),
"_m": Const(44121),
"_n": MaxOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(Sum(Var("x"), Var("y")), Const(6)))), ... | NT | COMB | COUNT | sympy | COPRIME_PAIRS | [
"COPRIME_PAIRS/MAX_PRIME_BELOW",
"B1/MAX_PRIME_BELOW"
] | efa041 | comb_count_derangements_v1 | null | 5 | 0 | [
"B1",
"COPRIME_PAIRS",
"MAX_PRIME_BELOW"
] | 3 | 0.007 | 2026-02-08T07:36:45.364900Z | {
"verified": true,
"answer": 7834,
"timestamp": "2026-02-08T07:36:45.371662Z"
} | f828fd | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 178,
"completion_tokens": 1237
},
"timestamp": "2026-02-13T11:27:22.961Z",
"answer": 7834
},
{... | 1 | [
{
"lemma": "B1",
"status": "ok"
},
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok_later"... | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
cc96c4 | nt_count_intersection_v1_124444284_2355 | Let $x$ and $y$ be positive integers such that $x + y = 200$. Consider the set of all such ordered pairs $(x, y)$, and let $P$ be the set of values of $xy$ corresponding to these pairs. Let $N$ be the maximum value in $P$. Determine the number of positive integers $n \leq N$ such that $n$ is divisible by $5$ and $\gcd(... | 47,839 | graphs = [
Graph(
let={
"N": MaxOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(Sum(Var("x"), Var("y")), Const(200)))), expr=Mul(Var("x"), Var("y")))),
"a": Const(5),
... | NT | null | COUNT | sympy | B1 | [
"B1"
] | 5b950e | nt_count_intersection_v1 | null | 4 | 0 | [
"B1"
] | 1 | 1.096 | 2026-02-08T04:36:16.383365Z | {
"verified": true,
"answer": 47839,
"timestamp": "2026-02-08T04:36:17.479568Z"
} | 4a6685 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 231,
"completion_tokens": 1985
},
"timestamp": "2026-02-10T17:16:24.377Z",
"answer": 47839
},
{
... | 1 | [
{
"lemma": "B1",
"status": "ok"
},
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
}
] | {
"lo": -3.42,
"mid": 1.86,
"hi": 7.55
} | ||
ce5c55 | alg_poly_orbit_hensel_v1_1218484723_2717 | For a non-negative integer $a$, define a sequence by $N = 2a^3 + a^2 + a + 1 \bmod 1331$, $M = 2N^3 + N^2 + N + 1 \bmod 1331$, $R = 2M^3 + M^2 + M + 1 \bmod 1331$, $S = 2R^3 + R^2 + R + 1 \bmod 1331$, and $T = 2S^3 + S^2 + S + 1 \bmod 1331$. Find the number of integers $a$ with $0 \le a \le 1220526$ such that $T = a$, ... | 18,340 | graphs = [
Graph(
let={
"p1": Mod(value=Sum(Mul(Const(2), Pow(Var("a"), Const(3))), Pow(Var("a"), Const(2)), Var("a"), Const(1)), modulus=Const(1331)),
"p2": Mod(value=Sum(Mul(Const(2), Pow(Ref("p1"), Const(3))), Pow(Ref("p1"), Const(2)), Ref("p1"), Const(1)), modulus=Const(1331)),
... | ALG | null | COUNT | sympy | POLY_ORBIT_COUNT | [
"POLY_ORBIT_COUNT"
] | 4ad965 | alg_poly_orbit_hensel_v1 | null | 6 | null | [
"POLY_ORBIT_COUNT"
] | 1 | 0.103 | 2026-02-25T04:26:41.684511Z | {
"verified": true,
"answer": 18340,
"timestamp": "2026-02-25T04:26:41.787952Z"
} | 9f7204 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 296,
"completion_tokens": 8011
},
"timestamp": "2026-03-29T06:11:13.315Z",
"answer": 20
},
{
"... | 1 | [
{
"lemma": "POLY_ORBIT_COUNT",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
}
] | {
"lo": 3.81,
"mid": 6.33,
"hi": 9.49
} | ||
c0093a | antilemma_k3_v1_1874849503_1136 | Let $n = 81792$. Compute $\sum_{d \mid n} \phi(d)$. | 81,792 | graphs = [
Graph(
let={
"_n": Const(81792),
"x": SumOverDivisors(n=Ref(name='_n'), var='d', expr=EulerPhi(n=Var(name='d'))),
},
goal=Ref("x"),
)
] | NT | COMB | COMPUTE | sympy | K3 | [
"K3"
] | 54c41e | antilemma_k3_v1 | null | 2 | 0 | [
"K3"
] | 1 | 0 | 2026-02-08T13:38:41.898118Z | {
"verified": true,
"answer": 81792,
"timestamp": "2026-02-08T13:38:41.898479Z"
} | b4a25e | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 132,
"completion_tokens": 243
},
"timestamp": "2026-02-10T01:32:15.073Z",
"answer": 81792
},
{
"i... | 1 | [
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "K3",
"status": "ok"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "VAL_SUM_EQ",
"status": "no"
}
] | {
"lo": -5.49,
"mid": 0.03,
"hi": 6.12
} | ||
38a774 | comb_bell_compute_v1_458359167_2871 | Let $S$ be the set of all ordered pairs $(i,j)$ of positive integers such that $1 \le i \le 3$, $1 \le j \le 4$, and $\gcd(i,j) = 1$. Let $n$ be the number of elements in $S$. Compute the Bell number $B_n$. | 21,147 | 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(4))))),
"res... | NT | COMB | COMPUTE | sympy | COUNT_COPRIME_GRID | [
"COUNT_COPRIME_GRID"
] | 20ec03 | comb_bell_compute_v1 | null | 3 | 0 | [
"COUNT_COPRIME_GRID"
] | 1 | 0.002 | 2026-02-08T06:49:14.428181Z | {
"verified": true,
"answer": 21147,
"timestamp": "2026-02-08T06:49:14.430037Z"
} | 4b466d | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 118,
"completion_tokens": 577
},
"timestamp": "2026-02-13T04:49:51.756Z",
"answer": 21147
},
{... | 1 | [
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "ok"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "MAX_VAL",... | {
"lo": -5.55,
"mid": -3.01,
"hi": 0.32
} | ||
566183_l | algebra_poly_eval_v1_809748730_789 | Let $x$ be the maximum value of $xy$ over all ordered pairs $(x,y)$ of positive integers such that $x + y = 10$. Compute $4x^2 + 10x - 10$. | 140 | NT | ALG | COMPUTE | sympy | B1 | [
"B1"
] | 5b950e | algebra_poly_eval_v1 | null | 3 | 0 | [
"B1"
] | 1 | 0.002 | 2026-02-08T11:45:36.437990Z | {
"verified": false,
"answer": 2740,
"timestamp": "2026-02-08T11:45:36.439572Z"
} | 5dbba8 | 566183 | 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": 94,
"completion_tokens": 625
},
"timestamp": "2026-02-14T18:27:10.889Z",
"answer": 2740
},
{
... | 1 | [
{
"lemma": "B1",
"status": "ok"
},
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
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"status": "no"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "VAL_SUM_EQ",
"status": "no"
}
] | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | |
034c09 | geo_count_lattice_triangle_v1_349078426_1949 | Let
$$
\text{area}_{2x} = \left| 128 \cdot 120 + 3 \cdot (0 - 9) \right|.
$$
Let
$$
\text{boundary} = \gcd(|128|, |9|) + \gcd(|3 - 128|, |120 - 9|) + \gcd(|0 - 3|, |0 - 120|).
$$
Let $S$ be the set of all positive integers $p$ such that there exists a positive integer $q$ satisfying $p \cdot q = 6$, $\gcd(p, q) = 1$, a... | 68,471 | graphs = [
Graph(
let={
"_n": Const(120),
"area_2x": Abs(arg=Sum(Mul(Const(value=128), Const(value=120)), Mul(Const(value=3), Sub(left=Const(value=0), right=Const(value=9))))),
"boundary": Sum(GCD(a=Abs(arg=Const(value=128)), b=Abs(arg=Const(value=9))), GCD(a=Abs(arg=Sub(... | NT | null | COUNT | sympy | COPRIME_PAIRS | [
"COPRIME_PAIRS"
] | 2bb3aa | geo_count_lattice_triangle_v1 | null | 6 | 0 | [
"COPRIME_PAIRS"
] | 1 | 0.01 | 2026-02-08T14:02:00.023794Z | {
"verified": true,
"answer": 68471,
"timestamp": "2026-02-08T14:02:00.034096Z"
} | 9d7142 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 245,
"completion_tokens": 888
},
"timestamp": "2026-02-15T23:12:49.156Z",
"answer": 68471
},
{... | 1 | [
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
... | {
"lo": -5.49,
"mid": 0.22,
"hi": 6.51
} | ||
7c421b | sequence_count_fib_divisible_v1_2051736721_3118 | Let $n$ be an integer. Define $\text{upper}$ to be the largest prime number $n$ such that $2 \leq n \leq 346$. Let $d = 6$. Define $\text{result}$ to be the number of positive integers $n_1$ with $1 \leq n_1 \leq \text{upper}$ such that $d$ divides the $n_1$-th Fibonacci number. Let $Q$ be the remainder when $44121 \cd... | 24,468 | graphs = [
Graph(
let={
"_n": Const(44121),
"upper": MaxOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(2)), Leq(Var("n"), Const(346)), IsPrime(Var("n"))))),
"d": Const(6),
"result": CountOverSet(set=SolutionsSet(var=Var("n1"), conditi... | NT | null | COUNT | sympy | MAX_PRIME_BELOW | [
"MAX_PRIME_BELOW"
] | dc3ad3 | sequence_count_fib_divisible_v1 | null | 5 | 0 | [
"MAX_PRIME_BELOW"
] | 1 | 0.017 | 2026-02-08T17:07:09.041950Z | {
"verified": true,
"answer": 24468,
"timestamp": "2026-02-08T17:07:09.059056Z"
} | a79bec | 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": 1391
},
"timestamp": "2026-02-17T19:09:10.615Z",
"answer": 24468
},
... | 1 | [
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "V3",
"status": "no"
},
{
"lemma": "VAL_SUM_EQ",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
2b1763 | nt_count_divisors_in_range_v1_677425708_204 | Let $n_2 = 1139$ and define $u = \sum_{d \mid n_2} \phi(d) - n_2$. Let $p = 19$ and let $q$ be the smallest integer greater than or equal to 2 that divides 1517. Define $n_1 = p \cdot q$ and $m = \mu(n_1)^2$. Let $n = 7560 + u$, $a = 23$, and $b = 1898 \cdot m$. Determine the value of $Q$, where $Q$ is the remainder wh... | 98,023 | graphs = [
Graph(
let={
"n2": Const(1139),
"u": Sub(SumOverDivisors(n=Ref(name='n2'), var='d', expr=EulerPhi(n=Var(name='d'))), Ref("n2")),
"p": Const(19),
"q": MinOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Const(2)), Divides(divisor=Va... | NT | null | COUNT | sympy | MIN_PRIME_FACTOR | [
"MIN_PRIME_FACTOR/MOBIUS_SQUAREFREE",
"EULER_TOTIENT_SUM"
] | 0bb18f | nt_count_divisors_in_range_v1 | null | 7 | 2 | [
"EULER_TOTIENT_SUM",
"MIN_PRIME_FACTOR",
"MOBIUS_SQUAREFREE"
] | 3 | 0.025 | 2026-02-08T03:07:41.851062Z | {
"verified": true,
"answer": 98023,
"timestamp": "2026-02-08T03:07:41.876459Z"
} | c5671c | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 277,
"completion_tokens": 3348
},
"timestamp": "2026-02-10T00:29:45.305Z",
"answer": 98023
},
{
... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "EULER_TOTIENT_SUM",
"status": "ok"
},
{
"lemma": "MIN_PRIME_FACTOR",
"status": "ok"
},
{
"lemma": "MOBIUS_SQ... | {
"lo": -6.5,
"mid": -0.15,
"hi": 5.67
} | ||
3064ea | alg_linear_system_2x2_v1_1218484723_1644 | Let $\det = 7 \cdot (-18) - 15 \cdot 3$, $M = 416345 \cdot (-18) - 887844 \cdot 3$, and $R = 7 \cdot 887844 - \sum_{k=0}^{3} 2^k \cdot 416345$. Define $S = \frac{M}{\det} + \frac{R}{\det}$. Find the remainder when $44631S$ is divided by $66143$. | 55,606 | graphs = [
Graph(
let={
"_n": Const(15),
"num_x": Sub(Mul(Const(416345), Const(-18)), Mul(Const(887844), Const(3))),
"num_y": Sub(Mul(Const(7), Const(887844)), Mul(Summation(var="k", start=Const(0), end=Const(3), expr=Pow(Const(2), Var("k"))), Const(416345))),
... | ALG | null | COMPUTE | sympy | SUM_GEOM | [
"SUM_GEOM"
] | 04214c | alg_linear_system_2x2_v1 | null | 4 | 0 | [
"SUM_GEOM"
] | 1 | 0.003 | 2026-02-25T03:20:40.886889Z | {
"verified": true,
"answer": 55606,
"timestamp": "2026-02-25T03:20:40.889608Z"
} | 8f34f8 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 224,
"completion_tokens": 1846
},
"timestamp": "2026-03-29T00:39:49.850Z",
"answer": 55606
},
{
"... | 1 | [
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "SUM_GEOM",
"status": "ok"
}
] | {
"lo": -2.47,
"mid": 1.2,
"hi": 4.81
} | ||
c44e67 | nt_min_coprime_above_v1_784195855_3740 | Let $ m $ be the number of integers $ t $ with $ 10 \leq t \leq 346 $ for which there exist integers $ a $ and $ b $ such that $ 1 \leq a \leq 11 $, $ 1 \leq b \leq 70 $, and $ t = 6a + 4b $. Determine the value of the smallest integer $ n $ such that $ 1811 < n \leq 1988 $ and $ \gcd(n, m) = 1 $. | 1,812 | graphs = [
Graph(
let={
"start": Const(1811),
"upper": Const(1988),
"modulus": CountOverSet(set=SolutionsSet(var=Var("t"), condition=Exists(var=Var(name='a'), condition=Exists(var=Var(name='b'), condition=And(Geq(left=Var(name='a'), right=Const(value=1)), Leq(left=Var(nam... | NT | null | EXTREMUM | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | nt_min_coprime_above_v1 | null | 4 | 0 | [
"LIN_FORM"
] | 1 | 0.019 | 2026-02-08T06:36:01.873364Z | {
"verified": true,
"answer": 1812,
"timestamp": "2026-02-08T06:36:01.892538Z"
} | 6fd2c7 | 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": 3559
},
"timestamp": "2026-02-13T02:44:14.993Z",
"answer": 1812
},
{... | 1 | [
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "V1",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
}
] | {
"lo": -5.55,
"mid": -3.01,
"hi": 0.32
} | ||
037f6b | diophantine_sum_product_min_v1_397696148_944 | Let $n$ be a positive integer. Define $S$ to be the number of positive integers $n$ such that $1 \leq n \leq 226$, $n$ is even, and $\gcd(n, 21) = 1$. Let $P = 1054$. Determine the value of the smallest positive integer $x$ such that $1 \leq x \leq 64$ and $x(S - x) = P$. | 31 | graphs = [
Graph(
let={
"_n": Const(21),
"S": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Const(226)), Divides(divisor=Const(2), dividend=Var("n")), Eq(GCD(a=Var("n"), b=Ref("_n")), Const(1))))),
"P": Const(1054),
... | NT | null | EXTREMUM | sympy | C2 | [
"C5"
] | 1d9668 | diophantine_sum_product_min_v1 | null | 6 | 0 | [
"C2",
"C5"
] | 2 | 0.43 | 2026-02-08T11:57:50.663462Z | {
"verified": true,
"answer": 31,
"timestamp": "2026-02-08T11:57:51.093694Z"
} | 0db79a | 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": 1137
},
"timestamp": "2026-02-14T21:09:28.416Z",
"answer": 31
},
{
... | 1 | [
{
"lemma": "C5",
"status": "ok"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
},
{
"lemma": "VAL_SUM_EQ",
"status": "no"
}
] | {
"lo": -6.96,
"mid": -4.56,
"hi": -1.46
} | ||
c5b2d8 | diophantine_fbi2_min_v1_1116507919_42 | Let $k = 6$ and let $\text{upper} = 16$. Define $D$ as the set of all integers $d$ such that $d \geq 3$, $d \leq 16$, $d$ divides $k$, and $\frac{k}{d} \geq 2$. Let $m$ be the minimum element of $D$. Compute $\sum_{n=1}^{|m|} \tau(n)$, where $\tau(n)$ denotes the number of positive divisors of $n$. | 5 | graphs = [
Graph(
let={
"k": Const(6),
"upper": Const(16),
"result": MinOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Const(3)), Leq(Var("d"), Ref("upper")), Divides(divisor=Var("d"), dividend=Ref("k")), Geq(Div(Ref("k"), Var("d")), Const(2))))),
... | NT | null | EXTREMUM | sympy | SUM_ARITHMETIC | [
"COPRIME_PAIRS"
] | 2bb3aa | diophantine_fbi2_min_v1 | null | 4 | 0 | [
"COPRIME_PAIRS",
"SUM_ARITHMETIC"
] | 2 | 0.056 | 2026-02-08T02:24:01.866888Z | {
"verified": true,
"answer": 5,
"timestamp": "2026-02-08T02:24:01.922769Z"
} | 0b25d9 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 228,
"completion_tokens": 288
},
"timestamp": "2026-02-08T18:31:52.833Z",
"answer": 5
},
{
"id": ... | 1 | [
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma... | {
"lo": -4.74,
"mid": -2.92,
"hi": -1.07
} | ||
3e8c1c | modular_count_residue_v1_677425708_3696 | Let $M$ be the minimum value of $x+y$ over all ordered pairs $(x,y)$ of positive integers such that $xy=104976$.
Let $A$ be the set of all ordered pairs $(x_1,x_2)$ of positive integers such that $x_1$ and $x_2$ are both odd and
$$x_1 + x_2 = M.$$
Let $N$ be the number of elements in $A$.
For each positive integer $n... | 1,114 | graphs = [
Graph(
let={
"_n": Const(16),
"upper": Const(30091),
"m": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x1"), Var("x2")]), condition=And(IsPositive(arg=Var... | NT | null | COUNT | sympy | B3 | [
"B3/COMB1/COUNT_FIB_DIVISIBLE"
] | e02802 | modular_count_residue_v1 | null | 8 | 0 | [
"B3",
"COMB1",
"COUNT_FIB_DIVISIBLE"
] | 3 | 0.994 | 2026-02-08T05:53:42.787250Z | {
"verified": true,
"answer": 1114,
"timestamp": "2026-02-08T05:53:43.781086Z"
} | b458b3 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 258,
"completion_tokens": 2828
},
"timestamp": "2026-02-12T16:00:03.844Z",
"answer": 1114
},
{... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "COMB1",
"status": "ok_later"
},
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "ok_later"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "L3b",
"stat... | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
1ac28e | nt_count_digit_sum_v1_124444284_6052 | Let $t$ be the number of nonnegative integers $j \leq 32842$ such that $\binom{32842}{j}$ is odd. Let $s = t + 7$. Compute the number of positive integers $n \leq 99999$ such that the sum of the digits of $n$ is equal to $s$. Subtract this number from $23409$ and report the result. | 17,409 | graphs = [
Graph(
let={
"_n": Const(7),
"upper": Const(99999),
"target_sum": Sum(CountOverSet(set=SolutionsSet(var=Var("j"), condition=And(Geq(Var("j"), Const(0)), Leq(Var("j"), Const(32842)), Eq(Mod(value=Binom(n=Const(32842), k=Var("j")), modulus=Const(2)), Const(1))), ... | ALG | COMB | COUNT | sympy | V8 | [
"V8"
] | 86348e | nt_count_digit_sum_v1 | null | 6 | 0 | [
"V8"
] | 1 | 4.2 | 2026-02-08T08:05:58.592394Z | {
"verified": true,
"answer": 17409,
"timestamp": "2026-02-08T08:06:02.791897Z"
} | 2f7418 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 199,
"completion_tokens": 2334
},
"timestamp": "2026-02-24T08:51:20.948Z",
"answer": 17409
},
{
"... | 1 | [
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "V8",
"status": "ok"
},
{
"lemma": "VAL_SUM_EQ",
"status": "no"
}
] | {
"lo": -2.35,
"mid": 1.22,
"hi": 4.84
} | ||
e374e5 | diophantine_fbi2_count_v1_2051736721_5919 | Let $k = 1260$. Let $S$ be the set of all integers $d$ such that $d \geq 2$, $d \leq D$, $d$ divides $k$, $k/d \geq 5$, and $k/d \leq 64$, where $D$ is the maximum integer $d_1$ satisfying $1 \leq d_1 \leq 61$ and $d_1$ divides 4331. Compute the number of elements in $S$. | 9 | graphs = [
Graph(
let={
"k": Const(1260),
"result": CountOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Const(2)), Leq(Var("d"), MaxOverSet(set=SolutionsSet(var=Var("d1"), condition=And(Geq(Var("d1"), Const(1)), Leq(Var("d1"), Const(61)), Divides(divisor=Var("d1")... | NT | null | COUNT | sympy | MAX_DIVISOR | [
"MAX_DIVISOR"
] | 51757e | diophantine_fbi2_count_v1 | null | 4 | 0 | [
"MAX_DIVISOR"
] | 1 | 0.013 | 2026-02-08T18:51:55.371026Z | {
"verified": true,
"answer": 9,
"timestamp": "2026-02-08T18:51:55.384035Z"
} | bf647d | 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": 1694
},
"timestamp": "2026-02-18T19:58:43.783Z",
"answer": 9
},
{
... | 1 | [
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "MAX_DIVISOR",
"status": "ok"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
f04bbf | nt_count_gcd_equals_v1_1978505735_3540 | Let $S$ be the set of all ordered pairs $(x,y)$ of positive integers such that $x + y = 162$. Define $P$ to be the maximum value of $xy$ over all pairs $(x,y) \in S$. Let $k = 70$ and $d = 5$. Compute the number of positive integers $n$ such that $1 \leq n \leq P$ and $\gcd(n, k) = d$. | 562 | graphs = [
Graph(
let={
"upper": MaxOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(Sum(Var("x"), Var("y")), Const(162)))), expr=Mul(Var("x"), Var("y")))),
"k": Const(70),... | NT | null | COUNT | sympy | B1 | [
"B1"
] | 5b950e | nt_count_gcd_equals_v1 | null | 4 | 0 | [
"B1"
] | 1 | 0.526 | 2026-02-08T17:42:44.773903Z | {
"verified": true,
"answer": 562,
"timestamp": "2026-02-08T17:42:45.300187Z"
} | 067799 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 143,
"completion_tokens": 862
},
"timestamp": "2026-02-18T07:20:57.983Z",
"answer": 562
},
{
... | 1 | [
{
"lemma": "B1",
"status": "ok"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "V1",
"status": "no"
},
{
"lemma": "VAL_SUM_EQ",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
95fc63 | geo_count_lattice_triangle_v1_1218484723_2603 | Let $R = \left|120 \cdot 225 + 88 \cdot \left(0 - \left|\{ (a, b) : 1 \le a, b \le 25,\ 10a^2 - 18ab + 25b^2 \leq \min \{ d : d \geq 2,\ d \mid 6380651 \} \right|\right)\right|$. Let $S = \gcd(120, 200) + \gcd(|88 - 120|, |225 - 200|) + \gcd(|0 - 88|, |0 - 225|)$. Compute $\frac{R + 2 - S}{2}$. | 4,680 | graphs = [
Graph(
let={
"_m": Const(88),
"_n": Const(120),
"area_2x": Abs(arg=Sum(Mul(Const(value=120), Const(value=225)), Mul(Const(value=88), Sub(left=Const(value=0), right=CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var(name='a'), Var(name='b')]), condition=And(G... | GEOM | NT | COUNT | sympy | MIN_PRIME_FACTOR | [
"MIN_PRIME_FACTOR/QF_PSD_COUNT_LEQ",
"TELESCOPE"
] | 3dcccd | geo_count_lattice_triangle_v1 | null | 5 | 0 | [
"MIN_PRIME_FACTOR",
"QF_PSD_COUNT_LEQ",
"TELESCOPE"
] | 3 | 0.019 | 2026-02-25T04:21:38.248085Z | {
"verified": true,
"answer": 4680,
"timestamp": "2026-02-25T04:21:38.267482Z"
} | dfdbae | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 1,
"correct": {
"strict": false,
"boxed": false,
"relaxed": true
},
"usage": {
"prompt_tokens": 268,
"completion_tokens": 32768
},
"timestamp": "2026-03-29T05:40:20.727Z",
"answer": null
},
{
... | 1 | [
{
"lemma": "MIN_PRIME_FACTOR",
"status": "ok"
},
{
"lemma": "QF_PSD_COUNT_LEQ",
"status": "ok_later"
},
{
"lemma": "TELESCOPE",
"status": "ok"
}
] | {
"lo": 3.81,
"mid": 6.33,
"hi": 9.49
} | ||
0c9363 | algebra_quadratic_discriminant_v1_48377204_608 | Let $a = 1$, $b = 7$, and $c = \sum_{k=1}^{4} \phi(k) \left\lfloor \frac{4}{k} \right\rfloor$, where $\phi$ denotes Euler's totient function. Compute $b^2 - 4ac$. | 9 | graphs = [
Graph(
let={
"a": Const(1),
"b": Const(7),
"c": Summation(var="k", start=Const(1), end=Const(4), expr=Mul(EulerPhi(n=Var("k")), Floor(Div(Const(4), Var("k"))))),
"result": Sub(Pow(Ref("b"), Const(2)), Mul(Const(4), Ref("a"), Ref("c"))),
},
... | NT | null | COMPUTE | sympy | K2 | [
"K2"
] | 6897ab | algebra_quadratic_discriminant_v1 | null | 4 | 0 | [
"K2"
] | 1 | 0.002 | 2026-02-08T15:36:50.759252Z | {
"verified": true,
"answer": 9,
"timestamp": "2026-02-08T15:36:50.761152Z"
} | ecba00 | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 127,
"completion_tokens": 336
},
"timestamp": "2026-02-16T06:10:38.630Z",
"answer": 9
},
{
"id": 11,
"... | 2 | [
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K2",
"status": "ok"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
}
] | {
"lo": -10,
"mid": -7.27,
"hi": -4.54
} | ||
6cb06b | geo_count_lattice_triangle_v1_1218484723_3175 | Let $M = \left|120 \cdot 111 + 81 \cdot (0 - 200)\right|$,
$$
R = \gcd(120, 200) + \gcd\left(\left|81 - \left|\{ v \in [41, 4961] : \exists a,b \in [1,11] \text{ such that } 8ab + 32b^2 + a^2 = v \}\right|\right|, |111 - 200|\right) + \gcd(|0 - 81|, |0 - 111|).
$$
Compute $\frac{M + 2 - R}{2}$. | 1,419 | graphs = [
Graph(
let={
"_n": Const(81),
"area_2x": Abs(arg=Sum(Mul(Const(value=120), Const(value=111)), Mul(Const(value=81), Sub(left=Const(value=0), right=Const(value=200))))),
"boundary": Sum(GCD(a=Abs(arg=Const(value=120)), b=Abs(arg=Const(value=200))), GCD(a=Abs(arg=... | GEOM | NT | COUNT | sympy | B3 | [
"QF_PSD_DISTINCT"
] | a8f9cb | geo_count_lattice_triangle_v1 | null | 5 | 0 | [
"B3",
"QF_PSD_DISTINCT"
] | 2 | 0.161 | 2026-02-25T04:53:46.677515Z | {
"verified": true,
"answer": 1419,
"timestamp": "2026-02-25T04:53:46.838590Z"
} | 550502 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 259,
"completion_tokens": 9985
},
"timestamp": "2026-03-29T08:50:09.145Z",
"answer": 1419
},
{
"i... | 1 | [
{
"lemma": "QF_PSD_DISTINCT",
"status": "ok"
}
] | {
"lo": -2.45,
"mid": 1.37,
"hi": 5.29
} | ||
a249da | alg_qf_psd_orbit_v1_601307018_4656 | Find the number of ordered triples $(a, b, c)$ of positive integers such that $1 \le a \le b \le c \le 53$ and
$$
27a^2 + 27b^2 + 27c^2 - 2ab - 2ac - 2bc = 81332.
$$ | 5 | graphs = [
Graph(
let={
"result": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("a"), Var("b"), Var("c")]), condition=And(Geq(Var("a"), Const(1)), Leq(Var("a"), Const(53)), Geq(Var("b"), Const(1)), Leq(Var("b"), Const(53)), Geq(Var("c"), Const(1)), Leq(Var("c"), Const(53)), Leq(Var("a"),... | ALG | null | COUNT | sympy | POLY4_COUNT | [
"QF_PSD_COUNT"
] | 09ce67 | alg_qf_psd_orbit_v1 | null | 7 | null | [
"POLY4_COUNT",
"QF_PSD_COUNT"
] | 2 | 2.69 | 2026-03-10T05:19:38.696618Z | {
"verified": true,
"answer": 5,
"timestamp": "2026-03-10T05:19:41.386208Z"
} | 6e5935 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 1,
"correct": {
"strict": false,
"boxed": false,
"relaxed": true
},
"usage": {
"prompt_tokens": 182,
"completion_tokens": 32768
},
"timestamp": "2026-03-29T13:01:59.816Z",
"answer": null
},
{
... | 1 | [
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "QF_PSD_COUNT",
"status": "ok"
}
] | {
"lo": 3.34,
"mid": 5.77,
"hi": 8.89
} | ||
3ab219 | comb_factorial_compute_v1_124444284_10226 | Let $n$ be the number of integers $t$ such that $10 \leq t \leq 28$ and there exist integers $a$ and $b$ with $1 \leq a \leq 2$, $1 \leq b \leq 4$, and $t = 6a + 4b$. Compute $n!$. | 40,320 | 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=2)), Geq(left=Var(name='b'), right=Const(value=1... | ALG | COMB | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | comb_factorial_compute_v1 | null | 4 | 0 | [
"LIN_FORM"
] | 1 | 0.002 | 2026-02-08T12:54:09.235520Z | {
"verified": true,
"answer": 40320,
"timestamp": "2026-02-08T12:54:09.237942Z"
} | 9840fd | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 189,
"completion_tokens": 440
},
"timestamp": "2026-02-24T16:46:32.338Z",
"answer": 40320
},
{
"i... | 2 | [
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
}
] | {
"lo": -9.23,
"mid": -6.18,
"hi": -4.06
} | ||
496330 | modular_min_linear_v1_1248542787_118 | Let $n$ be the minimum value of $x + y$ over all ordered pairs $(x, y)$ of positive integers such that $xy = 6340324$. Let $a = \sum_{d \mid n} \phi(d)$, where $\phi$ denotes Euler's totient function. Let $m = 14157$ and $b = 14064$. Determine the smallest positive integer $x \leq m$ such that
$$
ax \equiv b \pmod{m}.
... | 4,287 | 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(6340324)))), expr=Sum(Var("x"), Var("y")))),
"a": SumOverDi... | NT | null | EXTREMUM | sympy | B3 | [
"B3/K3"
] | 4a4ef2 | modular_min_linear_v1 | null | 6 | 0 | [
"B3",
"K3"
] | 2 | 0.566 | 2026-02-08T02:57:54.185697Z | {
"verified": true,
"answer": 4287,
"timestamp": "2026-02-08T02:57:54.751563Z"
} | 28c877 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 227,
"completion_tokens": 32768
},
"timestamp": "2026-02-23T21:13:25.287Z",
"answer": null
},
{
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "K3",
"status": "ok_later"
},
{
"lemma": "V7",
"status": "no"
},
{
"le... | {
"lo": 3.28,
"mid": 4.87,
"hi": 6.6
} | ||
be69f6 | nt_num_divisors_compute_v1_677425708_1747 | Let $n$ be the number of integers $t$ such that $8 \leq t \leq 237$ and there exist positive integers $a$ and $b$ with $1 \leq a \leq 42$, $1 \leq b \leq 9$, and $t = 5a + 3b$. Let $d$ be the number of positive divisors of $n$. Compute the remainder when $65381 \cdot d$ is divided by $69056$. | 39,656 | 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=42)), Geq(left=Var(name='b'), right=Const(value=... | NT | null | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | nt_num_divisors_compute_v1 | null | 4 | 0 | [
"LIN_FORM"
] | 1 | 0.004 | 2026-02-08T04:24:47.397444Z | {
"verified": true,
"answer": 39656,
"timestamp": "2026-02-08T04:24:47.401152Z"
} | 37854d | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 219,
"completion_tokens": 3836
},
"timestamp": "2026-02-10T00:25:10.952Z",
"answer": 39756
},
{
... | 1 | [
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
}
] | {
"lo": 1.71,
"mid": 5.04,
"hi": 8.38
} | ||
a917fc | antilemma_k3_v1_784195855_1652 | Let $m = 307$ and $n = 72290$. Define
$$
x = \sum_{d \mid n} \phi(d),
$$
where $\phi$ denotes Euler's totient function. Let
$$
c = \sum_{d \mid 7001} \phi(d).
$$
Compute
$$
(x \bmod m) + c \cdot (x \bmod 317).
$$ | 98,159 | graphs = [
Graph(
let={
"_m": Const(307),
"_n": Const(72290),
"x": SumOverDivisors(n=Ref(name='_n'), var='d', expr=EulerPhi(n=Var(name='d'))),
"_c": SumOverDivisors(n=Const(value=7001), var='d', expr=EulerPhi(n=Var(name='d'))),
"Q": Sum(Mod(value=R... | NT | COMB | COMPUTE | sympy | K3 | [
"K3",
"K3"
] | d06fb8 | antilemma_k3_v1 | two_moduli | 4 | 0 | [
"K3"
] | 1 | 0.003 | 2026-02-08T05:12:07.512015Z | {
"verified": true,
"answer": 98159,
"timestamp": "2026-02-08T05:12:07.514528Z"
} | 7e1980 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 202,
"completion_tokens": 578
},
"timestamp": "2026-02-11T23:03:02.117Z",
"answer": 98159
},
{
"... | 1 | [
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K3",
"status": "ok"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
}
] | {
"lo": -3.42,
"mid": 1.86,
"hi": 7.55
} | ||
b5d274 | nt_num_divisors_compute_v1_2051736721_3846 | Let $p$ and $q$ be positive integers such that $pq = 24$, $\gcd(p, q) = 1$, and $p < q$. Let $\_n$ be the number of such values of $p$. Compute the number of prime numbers $n_1$ such that $\_n \leq n_1 \leq 104723$. Then determine the number of positive divisors of this count. | 12 | 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=24)), Eq(left=GCD(a=Var(name='p'), b=Var(name='q')), right=Const(value=1)), ... | NT | null | COMPUTE | sympy | COPRIME_PAIRS | [
"COPRIME_PAIRS/COUNT_PRIMES"
] | c35fa2 | nt_num_divisors_compute_v1 | null | 4 | 0 | [
"COPRIME_PAIRS",
"COUNT_PRIMES"
] | 2 | 0.006 | 2026-02-08T17:36:15.414397Z | {
"verified": true,
"answer": 12,
"timestamp": "2026-02-08T17:36:15.420834Z"
} | d0943c | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 135,
"completion_tokens": 1519
},
"timestamp": "2026-02-18T04:28:19.269Z",
"answer": 12
},
{
... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "COUNT_PRIMES",
"status": "ok_later"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
}... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
30658c | alg_sym_quad_system_v1_601307018_3616 | Let $M$ be the sum of $a^3 + b^3 + c^3$ over all positive integers $a, b, c$ satisfying $a^2 + b^2 + c^2 = ab + bc + ca$ and $5a + b + 4c = \min\{x + y : x, y > 0,\, xy = 680625\}$, taken modulo $2797$. Find the remainder when $44121M$ is divided by $82210$. | 19,609 | graphs = [
Graph(
let={
"_n": Const(3),
"result": Mod(value=SumOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("a"), Var("b"), Var("c")]), condition=And(Eq(Sum(Pow(Var("a"), Const(2)), Pow(Var("b"), Const(2)), Pow(Var("c"), Const(2))), Sum(Mul(Var("a"), Var("b")), Mul... | ALG | null | COMPUTE | sympy | B3 | [
"B3"
] | 0cd20d | alg_sym_quad_system_v1 | null | 6 | 0 | [
"B3"
] | 1 | 0.044 | 2026-03-10T04:14:46.835516Z | {
"verified": true,
"answer": 19609,
"timestamp": "2026-03-10T04:14:46.879390Z"
} | 072da4 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 219,
"completion_tokens": 2861
},
"timestamp": "2026-03-29T09:16:57.271Z",
"answer": 81895
},
{
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
}
] | {
"lo": 1.23,
"mid": 4.27,
"hi": 6.7
} | ||
b18b82 | algebra_quadratic_discriminant_v1_1978505735_6564 | Let $s$ be the minimum value of $x + y$ over all pairs of positive integers $(x, y)$ such that $xy = 4$. Compute $(-6)^2 - s \cdot (-2) \cdot 140$. | 1,156 | graphs = [
Graph(
let={
"a": Const(-2),
"b": Const(-6),
"c": Const(140),
"result": Sub(Pow(Ref("b"), Const(2)), Mul(MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg... | NT | null | COMPUTE | sympy | B3 | [
"B3"
] | 0cd20d | algebra_quadratic_discriminant_v1 | null | 3 | 0 | [
"B3"
] | 1 | 0.002 | 2026-02-08T19:39:59.754419Z | {
"verified": true,
"answer": 1156,
"timestamp": "2026-02-08T19:39:59.755941Z"
} | fb6070 | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 109,
"completion_tokens": 214
},
"timestamp": "2026-02-16T18:43:42.622Z",
"answer": 1156
},
{
"id": 11,
... | 2 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "V1",
"status": "no"
}
] | {
"lo": -10,
"mid": -7.27,
"hi": -4.54
} | ||
b9f93d | nt_euler_phi_compute_v1_1248542787_538 | Let $f = \omega(1)$, where $\omega(n)$ denotes the number of distinct prime factors of $n$. Let $p = 3 + f$. Let $k$ be the number of positive integers $p$ such that there exists a positive integer $q$ with $p < q$, $pq = 108$, and $\gcd(p, q) = 1$. Define $n_1 = p^k$. Let $h = \lambda(n_1)$, where $\lambda$ is the Lio... | 26,532 | graphs = [
Graph(
let={
"_n": Const(3),
"n2": Const(1),
"f": SmallOmega(n=Ref(name='n2')),
"p": Sum(Ref("_n"), Ref("f")),
"n1": Pow(Ref("p"), CountOverSet(set=SolutionsSet(var=Var("p"), condition=And(IsPositive(arg=Var(name='p')), Exists(var=Var(na... | NT | null | COMPUTE | sympy | COPRIME_PAIRS | [
"COPRIME_PAIRS/LIOUVILLE_ONE",
"OMEGA_ZERO"
] | ed34fb | nt_euler_phi_compute_v1 | null | 6 | 2 | [
"COPRIME_PAIRS",
"LIOUVILLE_ONE",
"OMEGA_ZERO"
] | 3 | 0.005 | 2026-02-08T03:12:18.787364Z | {
"verified": true,
"answer": 26532,
"timestamp": "2026-02-08T03:12:18.792543Z"
} | ea445e | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 250,
"completion_tokens": 1296
},
"timestamp": "2026-02-09T05:19:09.470Z",
"answer": 26532
},
{
"... | 1 | [
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "LIOUVILLE_ONE",
"status": "ok_later"
},
{
"lemma": "LTE_SUM",
"status": "n... | {
"lo": -6.51,
"mid": -0.31,
"hi": 5.43
} | ||
5ebb73 | diophantine_fbi2_min_v1_1440796553_847 | Let $k$ be the number of positive integers $n \leq 66$ such that $n \equiv \left\lfloor \frac{n}{2} \right\rfloor \pmod{3}$. Let $d$ be the smallest integer $d$ such that $2 \leq d \leq 32$, $d$ divides $k$, and $\frac{k}{d} \geq 7$. Compute the value of $d$. | 2 | graphs = [
Graph(
let={
"_n": Const(7),
"k": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Const(66)), Congruent(a=Var(name='n'), b=Floor(arg=Div(left=Var(name='n'), right=Const(value=2))), modulus=Const(value=3))))),
"up... | NT | null | EXTREMUM | sympy | B1 | [
"LIN_FORM",
"L3C"
] | ecf77f | diophantine_fbi2_min_v1 | null | 6 | 0 | [
"B1",
"L3C",
"LIN_FORM"
] | 3 | 0.088 | 2026-02-08T12:01:25.539999Z | {
"verified": true,
"answer": 2,
"timestamp": "2026-02-08T12:01:25.627644Z"
} | 149bf5 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 139,
"completion_tokens": 894
},
"timestamp": "2026-02-14T21:43:53.571Z",
"answer": 2
},
{
... | 1 | [
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "L3C",
"status": "ok"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "MOD_ADD",
"status": ... | {
"lo": -6.96,
"mid": -4.56,
"hi": -1.46
} | ||
d13509 | comb_count_permutations_fixed_v1_865884756_3499 | Let $n = 6$ and $N = 525$. Let $k$ be the smallest divisor of $N$ that is at least 2. Compute the value of $\binom{n}{k} \cdot !(n - k)$, where $!m$ denotes the number of derangements of $m$ elements. Then find the remainder when $24261$ times this result is divided by $83126$. | 56,054 | graphs = [
Graph(
let={
"_n": Const(525),
"n": Const(6),
"k": MinOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Const(2)), Divides(divisor=Var("d"), dividend=Ref("_n"))))),
"result": Mul(Binom(n=Ref("n"), k=Ref("k")), Subfactorial(arg=Sub(l... | NT | COMB | COUNT | sympy | MIN_PRIME_FACTOR | [
"MIN_PRIME_FACTOR"
] | bc3776 | comb_count_permutations_fixed_v1 | null | 4 | 0 | [
"MIN_PRIME_FACTOR"
] | 1 | 0.002 | 2026-02-08T17:29:07.819505Z | {
"verified": true,
"answer": 56054,
"timestamp": "2026-02-08T17:29:07.821816Z"
} | d1b44f | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 134,
"completion_tokens": 842
},
"timestamp": "2026-02-18T02:40:37.233Z",
"answer": 56054
},
{... | 1 | [
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "MIN_PRIME_FACTOR",
"status": "ok"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "V1",
"status": "no"
... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
ed2718 | modular_min_linear_v1_677425708_422 | Let $x$ be the smallest positive integer solution to the congruence $16567x \equiv 10047 \pmod{23808}$ with $1 \le x \le 23808$. Let $c$ be the number of positive integers $n$ such that $n \le 729$, $\gcd(n, 14) = 1$, and $n \ge \sum_{d \mid \gcd(3,5)} \mu(d)$. Compute the remainder when $ (x \bmod 317) + 1009 \cdot (x... | 1,224 | graphs = [
Graph(
let={
"a": Const(16567),
"b": Const(10047),
"m": Const(23808),
"result": MinOverSet(set=SolutionsSet(var=Var("x"), condition=And(Geq(Var("x"), Const(1)), Leq(Var("x"), Ref("m")), Eq(Mod(value=Mul(Ref("a"), Var("x")), modulus=Ref("m")), Ref("b... | NT | null | EXTREMUM | sympy | C4 | [
"C4",
"MOBIUS_COPRIME"
] | 00c72f | modular_min_linear_v1 | two_moduli | 6 | 0 | [
"C4",
"MOBIUS_COPRIME"
] | 2 | 1.029 | 2026-02-08T03:32:32.641569Z | {
"verified": true,
"answer": 1224,
"timestamp": "2026-02-08T03:32:33.670147Z"
} | 599df5 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 251,
"completion_tokens": 2712
},
"timestamp": "2026-02-08T20:33:54.935Z",
"answer": 1224
},
{
"i... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "C4",
"status": "ok"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "MOBIUS_COPRIME",
"status": "ok"... | {
"lo": -6.51,
"mid": -0.31,
"hi": 5.43
} | ||
c7fcee | nt_max_prime_below_v1_784195855_6880 | Let $S$ be the set of all positive integers $p$ such that there exists a positive integer $q$ satisfying $pq = 36$, $\gcd(p, q) = 1$, and $p < q$. Let $m$ be the number of elements in $S$. Let $T$ be the set of all prime numbers $n$ such that $m \leq n \leq 11111$. Let $r$ be the largest element of $T$. Compute the rem... | 41,775 | graphs = [
Graph(
let={
"_n": Const(65056),
"upper": Const(11111),
"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 | 0.258 | 2026-02-08T08:56:17.352997Z | {
"verified": true,
"answer": 41775,
"timestamp": "2026-02-08T08:56:17.611374Z"
} | d67884 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 164,
"completion_tokens": 3755
},
"timestamp": "2026-02-13T23:01:01.695Z",
"answer": 41775
},
... | 1 | [
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "V8",
"stat... | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
edcd10 | sequence_lucas_compute_v1_124444284_2851 | Let $T$ be the set of all integers $t$ such that $16 \leq t \leq 70$ and $t = 10a + 6b$ for some integers $a$ and $b$ with $1 \leq a \leq 4$ and $1 \leq b \leq 5$. Let $n = |T|$. Define $L_n$ to be the $n$th Lucas number, where $L_1 = 1$, $L_2 = 3$, and $L_k = L_{k-1} + L_{k-2}$ for $k \geq 3$. Compute the remainder wh... | 15,127 | graphs = [
Graph(
let={
"_n": Const(63100),
"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=Va... | NT | null | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | sequence_lucas_compute_v1 | null | 4 | 0 | [
"LIN_FORM"
] | 1 | 0.001 | 2026-02-08T05:02:40.835162Z | {
"verified": true,
"answer": 15127,
"timestamp": "2026-02-08T05:02:40.836623Z"
} | ffbe3f | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 269,
"completion_tokens": 1356
},
"timestamp": "2026-02-11T22:47:23.377Z",
"answer": 15127
},
{
... | 1 | [
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "V3",
"statu... | {
"lo": -3.42,
"mid": 1.86,
"hi": 7.55
} | ||
bddd87 | nt_count_digit_sum_v1_124444284_637 | Let $n$ be a positive integer such that $1 \leq n \leq 1341$ and $n \equiv \left\lfloor \frac{n}{2} \right\rfloor \pmod{11}$. Let $S$ be the set of all such $n$. Let $T$ be the set of all ordered pairs $(x, y)$ of positive integers such that $xy = |S|$. Define $\sigma$ to be the minimum value of $x + y$ over all pairs ... | 1,368 | graphs = [
Graph(
let={
"_n": Const(1341),
"upper": Const(24649),
"target_sum": MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(Mul(Var("x"), Var("y")), Cou... | NT | null | COUNT | sympy | L3C | [
"L3C/B3"
] | 4d8a41 | nt_count_digit_sum_v1 | null | 7 | 0 | [
"B3",
"L3C"
] | 2 | 1.227 | 2026-02-08T03:25:45.197308Z | {
"verified": true,
"answer": 1368,
"timestamp": "2026-02-08T03:25:46.424218Z"
} | 25f3ac | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 275,
"completion_tokens": 5392
},
"timestamp": "2026-02-09T04:16:14.556Z",
"answer": 1368
},
{
"... | 1 | [
{
"lemma": "B3",
"status": "ok_later"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "L3C",
"status": "ok"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
... | {
"lo": -3.42,
"mid": 1.86,
"hi": 7.55
} | ||
6d8c1e | antilemma_cartesian_v1_168721529_948 | Compute the number of lattice points $ (x, y) $ such that $ 1 \le x \le 16 $ and $ 1 \le y \le 19 $. Let $ Q $ be the remainder when 44121 times this number is divided by 98102. Find $ Q $. | 70,912 | graphs = [
Graph(
let={
"x": CountOverSet(set=CartesianProduct(left=IntegerRange(start=Const(1), end=Const(16)), right=IntegerRange(start=Const(1), end=Const(19)))),
"Q": Mod(value=Mul(Const(44121), Ref("x")), modulus=Const(98102)),
},
goal=Ref("Q"),
)
] | COMB | GEOM | COMPUTE | sympy | COUNT_CARTESIAN | [
"COUNT_CARTESIAN"
] | 409d7d | antilemma_cartesian_v1 | null | 2 | 0 | [
"COUNT_CARTESIAN"
] | 1 | 0.001 | 2026-02-08T13:21:11.925739Z | {
"verified": true,
"answer": 70912,
"timestamp": "2026-02-08T13:21:11.926419Z"
} | 188a03 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 177,
"completion_tokens": 753
},
"timestamp": "2026-02-09T11:07:46.299Z",
"answer": 70912
},
{
"i... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "ok"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "V8",
... | {
"lo": -1.2,
"mid": 1.93,
"hi": 4.95
} | ||
8e221d | nt_sum_totient_over_divisors_v1_784195855_1217 | Let $T$ be the number of integers $n$ such that $1\le n\le19326$, $6$ divides $n$, and $\gcd(n,35)=1$. Let $E=T^{34}$, and let $K$ be the greatest integer $k$ such that $47^k$ divides $E$.
Let $p$ be the largest prime number $q$ such that $2\le q\le K$. (Assume this set is nonempty.) Define
\[
n_2 = p^2\cdot11\cdot83.... | 92,227 | graphs = [
Graph(
let={
"p": MaxOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(2)), Leq(Var("n"), MaxKDivides(target=Pow(CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Const(19326)), Divides(divisor=Const(6), dividend=Va... | NT | null | COMPUTE | sympy | C5 | [
"C5/K14/MAX_PRIME_BELOW/MOBIUS_SQUAREFREE",
"OMEGA_ZERO"
] | 6ffc62 | nt_sum_totient_over_divisors_v1 | null | 8 | 2 | [
"C5",
"K14",
"MAX_PRIME_BELOW",
"MOBIUS_SQUAREFREE",
"OMEGA_ZERO"
] | 5 | 0.004 | 2026-02-08T04:54:31.132149Z | {
"verified": true,
"answer": 92227,
"timestamp": "2026-02-08T04:54:31.136590Z"
} | cdcabe | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 335,
"completion_tokens": 736
},
"timestamp": "2026-02-18T14:39:15.697Z",
"answer": 92227
}
] | 2 | [
{
"lemma": "C5",
"status": "ok"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "K14",
"status": "ok_later"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok_late... | {
"lo": -10,
"mid": -6.47,
"hi": -2.95
} | ||
3641b2 | nt_count_digit_sum_v1_784195855_6922 | Let $A$ be the number of positive integers $n$ such that $1 \le n \le 9999$ and the sum of the decimal digits of $n$ is 24. Let $B$ be the number of ordered pairs $(p, q)$ of positive integers such that $p < q$, $\gcd(p, q) = 1$, and $p \cdot q = 6$. Compute the remainder when
$$
A^B + 5A + \sum_{k=1}^{19} k
$$
is divi... | 83,684 | graphs = [
Graph(
let={
"_n": Const(5),
"upper": Const(9999),
"target_sum": Const(24),
"result": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Ref("upper")), Eq(DigitSum(Var("n")), Ref("target_sum"))))),
... | NT | null | COUNT | sympy | SUM_ARITHMETIC | [
"SUM_ARITHMETIC",
"COPRIME_PAIRS"
] | 26b550 | nt_count_digit_sum_v1 | quadratic_mod | 5 | 0 | [
"COPRIME_PAIRS",
"SUM_ARITHMETIC"
] | 2 | 0.735 | 2026-02-08T09:00:33.022765Z | {
"verified": true,
"answer": 83684,
"timestamp": "2026-02-08T09:00:33.757869Z"
} | daf2c4 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 166,
"completion_tokens": 1711
},
"timestamp": "2026-02-13T23:02:55.336Z",
"answer": 83684
},
... | 1 | [
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
... | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
e818da | nt_num_divisors_compute_v1_124444284_6352 | Compute the number of positive integer divisors of $48400$. | 45 | graphs = [
Graph(
let={
"n": Const(48400),
"result": NumDivisors(n=Ref("n")),
},
goal=Ref("result"),
)
] | NT | null | COMPUTE | sympy | LIN_FORM | [
"K13"
] | 8d970a | nt_num_divisors_compute_v1 | null | 2 | 0 | [
"K13",
"LIN_FORM"
] | 2 | 0.073 | 2026-02-08T08:18:27.005722Z | {
"verified": true,
"answer": 45,
"timestamp": "2026-02-08T08:18:27.079020Z"
} | 069b8f | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 71,
"completion_tokens": 376
},
"timestamp": "2026-02-15T20:12:19.862Z",
"answer": 36
},
{
"id": 11,
... | 1 | [
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K13",
"status": "ok"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
}... | {
"lo": -9.14,
"mid": -6.05,
"hi": -3.73
} | ||
056bb9 | nt_count_divisible_v1_1742523217_282 | Let $\delta$ be the sum over all positive divisors $d$ of $\gcd(7, 11)$ of the Möbius function $\mu(d)$. Let $d_{\max}$ be the largest prime number $n$ such that $2 \leq n \leq 25$. Determine the number of positive integers $n$ such that $\delta \leq n \leq 80656$ and $n$ is divisible by $d_{\max}$. | 3,506 | graphs = [
Graph(
let={
"_n": Const(7),
"upper": Const(80656),
"divisor": MaxOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(2)), Leq(Var("n"), Const(25)), IsPrime(Var("n"))))),
"result": CountOverSet(set=SolutionsSet(var=Var("n"), con... | NT | null | COUNT | sympy | MOBIUS_COPRIME | [
"MOBIUS_COPRIME",
"MAX_PRIME_BELOW"
] | f86db3 | nt_count_divisible_v1 | null | 4 | 0 | [
"MAX_PRIME_BELOW",
"MOBIUS_COPRIME"
] | 2 | 4.143 | 2026-02-08T02:57:36.722170Z | {
"verified": true,
"answer": 3506,
"timestamp": "2026-02-08T02:57:40.865244Z"
} | adcc7d | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 211,
"completion_tokens": 734
},
"timestamp": "2026-02-09T15:55:42.394Z",
"answer": 3506
},
{
"id... | 2 | [
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok"
},
{
"lemma": "MOBIUS_COPRIME",
"status": "ok"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "n... | {
"lo": -10,
"mid": -6.47,
"hi": -2.95
} | ||
d310a9 | sequence_fibonacci_compute_v1_153355830_865 | Let $ n $ be the number of positive integers at most 41 that are relatively prime to 15. Compute the $ n $-th Fibonacci number. | 17,711 | graphs = [
Graph(
let={
"_n": Const(41),
"n": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Ref("_n")), Eq(GCD(a=Var("n"), b=Const(15)), Const(1))))),
"result": Fibonacci(arg=Ref(name='n')),
},
goal=Ref("r... | NT | null | COMPUTE | sympy | C4 | [
"C4"
] | 08d162 | sequence_fibonacci_compute_v1 | null | 4 | 0 | [
"C4"
] | 1 | 0.001 | 2026-02-08T04:12:36.424426Z | {
"verified": true,
"answer": 17711,
"timestamp": "2026-02-08T04:12:36.425081Z"
} | c1b91c | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 142,
"completion_tokens": 912
},
"timestamp": "2026-02-10T16:06:23.185Z",
"answer": 17711
},
{
"... | 1 | [
{
"lemma": "C4",
"status": "ok"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
}
] | {
"lo": -5.55,
"mid": -3.01,
"hi": 0.33
} | ||
9adba4 | nt_count_intersection_v1_1439011603_2202 | Let $N = 100000$, $a = 11$, and $b = 10$. Define $r$ to be the number of positive integers $n \leq N$ such that $11$ divides $n$ and $\gcd(n, 10) = 1$.
Let $S$ be the set of all ordered pairs $(x, y)$ of positive integers such that $xy = 19749136$. Define $s$ to be the minimum value of $x + y$ as $(x, y)$ ranges over ... | 20,744 | graphs = [
Graph(
let={
"_n": Const(78796),
"N": Const(100000),
"a": Const(11),
"b": Const(10),
"result": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Ref("N")), Divides(divisor=Ref("a"), dividend... | NT | null | COUNT | sympy | B3 | [
"B3"
] | d720b5 | nt_count_intersection_v1 | quadratic_mod | 6 | 0 | [
"B3"
] | 1 | 6.013 | 2026-02-08T16:35:40.310732Z | {
"verified": true,
"answer": 20744,
"timestamp": "2026-02-08T16:35:46.323921Z"
} | c0c500 | 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": 1949
},
"timestamp": "2026-02-17T08:08:50.574Z",
"answer": 20744
},
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "V3",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
e45e80 | antilemma_k3_v1_124444284_6605 | Let $x = \sum_{d \mid 78650} \phi(d)$, where $\phi$ denotes Euler's totient function. Find the remainder when $68845x$ is divided by $64907$. | 52,403 | graphs = [
Graph(
let={
"x": SumOverDivisors(n=Const(value=78650), var='d', expr=EulerPhi(n=Var(name='d'))),
"Q": Mod(value=Mul(Const(68845), Ref("x")), modulus=Const(64907)),
},
goal=Ref("Q"),
)
] | NT | COMB | COMPUTE | sympy | K3 | [
"K3"
] | 54c41e | antilemma_k3_v1 | null | 3 | 0 | [
"K3"
] | 1 | 0 | 2026-02-08T08:33:08.319438Z | {
"verified": true,
"answer": 52403,
"timestamp": "2026-02-08T08:33:08.319715Z"
} | 7ffdbd | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 91,
"completion_tokens": 1166
},
"timestamp": "2026-02-13T19:21:42.829Z",
"answer": 52403
},
{... | 1 | [
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K3",
"status": "ok"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
}
] | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
b761f8 | nt_sum_totient_over_divisors_v1_1526740231_104 | Let $S$ be the set of all ordered pairs $(x, y)$ of positive integers such that $xy = 1411344$. Let $n$ be the minimum value of $x + y$ as $(x, y)$ ranges over $S$. Compute the sum of $\phi(d)$ over all positive divisors $d$ of $n$, where $\phi$ denotes Euler's totient function. | 2,376 | 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(1411344)))), expr=Sum(Var("x"), Var("y")))),
"result": SumOv... | NT | null | COMPUTE | sympy | B3 | [
"B3"
] | 0cd20d | nt_sum_totient_over_divisors_v1 | null | 6 | 0 | [
"B3"
] | 1 | 0.004 | 2026-02-08T11:21:00.018023Z | {
"verified": true,
"answer": 2376,
"timestamp": "2026-02-08T11:21:00.021726Z"
} | 5ab406 | 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": 1397
},
"timestamp": "2026-02-14T11:57:15.133Z",
"answer": 2376
},
{... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "V1",
"status": "no"
}
] | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
f548d5 | antilemma_product_of_sums_v1_1248542787_557 | Let $S_1$ be the sum of $k$ over all pairs $(k, j)$ with $1 \leq k \leq 14$ and $1 \leq j \leq 8$. Let $S_2 = \sum_{k=1}^{14} k$. Let $x = S_1 \cdot S_2$. Find the multiplicative order of $2$ modulo $2|x| + 3$. | 462 | graphs = [
Graph(
let={
"S1": SumOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("k"), Var("_j")]), condition=Const(1), domain=CartesianProduct(left=IntegerRange(start=Const(1), end=Const(14)), right=IntegerRange(start=Const(1), end=Const(8)))), expr=Var("k"))),
"S2":... | NT | null | COMPUTE | sympy | PRODUCT_OF_SUMS | [
"PRODUCT_OF_SUMS"
] | f2b2b0 | antilemma_product_of_sums_v1 | null | 4 | 0 | [
"PRODUCT_OF_SUMS"
] | 1 | 0.001 | 2026-02-08T03:13:10.371575Z | {
"verified": true,
"answer": 462,
"timestamp": "2026-02-08T03:13:10.372104Z"
} | b1afc2 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 207,
"completion_tokens": 3805
},
"timestamp": "2026-02-09T18:22:17.002Z",
"answer": 462
},
{
"i... | 1 | [
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "PRODUCT_OF_SUMS",
"status": "ok"
},
{
"lemma": "V8_SUM",
"status": "no"
}
] | {
"lo": -6.49,
"mid": 0.51,
"hi": 7.52
} | ||
846c4f | comb_count_partitions_v1_1520064083_6715 | Let $n$ be the largest prime number such that $2 \leq n \leq 44$. Define $p(n)$ to be the number of integer partitions of $n$. Compute the remainder when $66181 \cdot p(n)$ is divided by $80836$. Determine the value of this remainder. | 18,129 | graphs = [
Graph(
let={
"_n": Const(2),
"n": MaxOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Ref("_n")), Leq(Var("n"), Const(44)), IsPrime(Var("n"))))),
"result": Partition(arg=Ref(name='n')),
"_c": Const(66181),
"Q": Mod(valu... | NT | COMB | COUNT | sympy | MAX_PRIME_BELOW | [
"MAX_PRIME_BELOW"
] | dc3ad3 | comb_count_partitions_v1 | null | 5 | 0 | [
"MAX_PRIME_BELOW"
] | 1 | 0.001 | 2026-02-08T08:16:53.589876Z | {
"verified": true,
"answer": 18129,
"timestamp": "2026-02-08T08:16:53.591330Z"
} | d9d4b9 | 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": 3204
},
"timestamp": "2026-02-13T16:55:57.601Z",
"answer": 18129
},
... | 1 | [
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "VAL_SUM_EQ",
... | {
"lo": -3.51,
"mid": 1.33,
"hi": 6.56
} | ||
2e921f | modular_mod_compute_v1_655260480_963 | Let $a$ be the minimum value of $x + y$ over all ordered pairs $(x, y)$ of positive integers such that $xy = 16000000$. Compute the remainder when $a$ is divided by $88888$. | 8,000 | graphs = [
Graph(
let={
"a": MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(Mul(Var("x"), Var("y")), Const(16000000)))), expr=Sum(Var("x"), Var("y")))),
"m": Const(888... | NT | null | COMPUTE | sympy | B3 | [
"B3"
] | 0cd20d | modular_mod_compute_v1 | null | 3 | 0 | [
"B3"
] | 1 | 0.003 | 2026-02-08T15:48:16.747809Z | {
"verified": true,
"answer": 8000,
"timestamp": "2026-02-08T15:48:16.750878Z"
} | ee4df8 | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 114,
"completion_tokens": 246
},
"timestamp": "2026-02-16T06:34:26.539Z",
"answer": 2400
},
{
"id": 11,... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
}
] | {
"lo": -8.26,
"mid": -5.01,
"hi": -1.76
} | ||
9da6cf | comb_count_surjections_v1_655260480_3121 | Let $n$ be the number of ordered pairs $(x_1, x_2)$ of positive odd integers such that $x_1 + x_2 = 14$. Let $k = 5$. Define $r = k! \cdot S(n, k)$, where $S(n, k)$ denotes the number of ways to partition a set of $n$ elements into $k$ nonempty unlabeled subsets.
Compute the remainder when $44121 \cdot r$ is divided b... | 29,757 | graphs = [
Graph(
let={
"_n": Const(44121),
"n": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x1"), Var("x2")]), condition=And(IsPositive(arg=Var(name='x1')), IsPositive(arg=Var(name='x2')), IsOdd(arg=Var(name='x1')), IsOdd(arg=Var(name='x2')), Eq(Sum(Var("x1"), Var("x2")),... | COMB | null | COUNT | sympy | COMB1 | [
"COMB1"
] | 567f58 | comb_count_surjections_v1 | null | 4 | 0 | [
"COMB1"
] | 1 | 0.003 | 2026-02-08T17:11:54.857380Z | {
"verified": true,
"answer": 29757,
"timestamp": "2026-02-08T17:11:54.859963Z"
} | 547a16 | 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": 1752
},
"timestamp": "2026-02-17T21:06:40.504Z",
"answer": 29757
},
... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COMB1",
"status": "ok"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
}
] | {
"lo": -2.38,
"mid": 1.74,
"hi": 6.59
} | ||
c06210 | nt_lcm_compute_v1_809748730_1432 | Let $a$ be the number of integers $t$ such that $21 \leq t \leq 6597$ and there exist positive integers $a'$ and $b'$ with $1 \leq a' \leq 527$, $1 \leq b' \leq 229$, and $t = 6a' + 15b'$. Let $b$ be the minimum value of $x + y$ over all ordered pairs $(x,y)$ of positive integers such that $xy = 990025$. Compute the le... | 21,890 | graphs = [
Graph(
let={
"a": CountOverSet(set=SolutionsSet(var=Var("t"), condition=Exists(var=Var(name='a'), condition=Exists(var=Var(name='b'), condition=And(Geq(left=Var(name='a'), right=Const(value=1)), Leq(left=Var(name='a'), right=Const(value=527)), Geq(left=Var(name='b'), right=Const(value... | NT | null | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM",
"B3"
] | 688dbe | nt_lcm_compute_v1 | null | 6 | 0 | [
"B3",
"LIN_FORM"
] | 2 | 0.005 | 2026-02-08T12:25:38.525197Z | {
"verified": true,
"answer": 21890,
"timestamp": "2026-02-08T12:25:38.529722Z"
} | e22c71 | 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": 3748
},
"timestamp": "2026-02-15T01:17:34.087Z",
"answer": 21890
},
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no... | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
f38e63 | nt_count_digit_sum_v1_865884756_1689 | Let $S$ be the set of all positive integers $n$ such that $1 \le n \le 99999$ and the sum of the digits of $n$ is $16$. Let $k$ be the number of elements in $S$. Let $p$ be a positive integer, and suppose there exist positive integers $p$ and $q$ such that $p \cdot q = 216$, $\gcd(p, q) = 1$, and $p < q$. Let $r$ be th... | 52,136 | graphs = [
Graph(
let={
"upper": Const(99999),
"target_sum": Const(16),
"result": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Ref("upper")), Eq(DigitSum(Var("n")), Ref("target_sum"))))),
"_c": Const(51984),
... | NT | null | COUNT | sympy | COPRIME_PAIRS | [
"COPRIME_PAIRS"
] | a9a663 | nt_count_digit_sum_v1 | digits_weighted_mod | 5 | 0 | [
"COPRIME_PAIRS"
] | 1 | 3.751 | 2026-02-08T16:13:20.509130Z | {
"verified": true,
"answer": 52136,
"timestamp": "2026-02-08T16:13:24.259923Z"
} | 8d7b36 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 244,
"completion_tokens": 1958
},
"timestamp": "2026-02-16T23:09:24.904Z",
"answer": 52136
},
... | 1 | [
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
},
{
"lemma": "VAL_SUM_EQ",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
e6dcb9 | algebra_quadratic_discriminant_v1_865884756_6814 | Let $a$ be the largest prime number $n$ such that $2 \leq n \leq 3$. Let $b = -2$ and $c = -10$. Let $n$ be the number of positive integers $p$ such that there exists a positive integer $q$ with $p < q$, $\gcd(p, q) = 1$, and $pq = 180$. Compute $b^2 - n \cdot a \cdot c$. | 124 | graphs = [
Graph(
let={
"_n": Const(2),
"a": MaxOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(2)), Leq(Var("n"), Const(3)), IsPrime(Var("n"))))),
"b": Const(-2),
"c": Const(-10),
"result": Sub(Pow(Ref("b"), Ref("_n")), Mu... | NT | null | COMPUTE | sympy | MAX_PRIME_BELOW | [
"MAX_PRIME_BELOW",
"COPRIME_PAIRS"
] | 05d703 | algebra_quadratic_discriminant_v1 | null | 5 | 0 | [
"COPRIME_PAIRS",
"MAX_PRIME_BELOW"
] | 2 | 0.003 | 2026-02-08T19:24:30.079655Z | {
"verified": true,
"answer": 124,
"timestamp": "2026-02-08T19:24:30.082475Z"
} | 308ab6 | 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": 2132
},
"timestamp": "2026-02-18T22:16:54.706Z",
"answer": 124
},
{
... | 1 | [
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok"
},
{... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
4b8456 | comb_binomial_compute_v1_1218484723_4775 | Let $n$ be the number of ordered pairs $(a, b)$ of positive integers with $1 \le a \le 35$ and $1 \le b \le B$, where $B$ is the number of ordered pairs $(a_1, b_1)$ with $1 \le a_1, b_1 \le 35$ satisfying $-189a_1^3 = -23625$, such that $b^2 + 16a^2 - 8ab = 25$. Let $R = \binom{n}{9}$. Find the remainder when $32411R$... | 88,715 | graphs = [
Graph(
let={
"_m": Const(2),
"_n": Const(89865),
"n": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("a"), Var("b")]), condition=And(Geq(Var("a"), Const(1)), Leq(Var("a"), Const(35)), Geq(Var("b"), Const(1)), Leq(Var("b"), CountOverSet(set=SolutionsSet(v... | COMB | null | COMPUTE | sympy | POLY3_COUNT | [
"POLY3_COUNT/QF_PSD_COUNT"
] | 682a6e | comb_binomial_compute_v1 | null | 5 | 0 | [
"POLY3_COUNT",
"QF_PSD_COUNT"
] | 2 | 0.005 | 2026-02-25T06:26:12.200758Z | {
"verified": true,
"answer": 88715,
"timestamp": "2026-02-25T06:26:12.205984Z"
} | 34cd45 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 248,
"completion_tokens": 2840
},
"timestamp": "2026-03-29T17:34:05.047Z",
"answer": 88715
},
{
"... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "POLY3_COUNT",
"status": "ok"
},
{
"lemma": "QF_PSD_COUNT",
"status": "ok_later"
},
{
"lemma": "V7",
... | {
"lo": -3.33,
"mid": 1.03,
"hi": 5.26
} | ||
553d26 | nt_count_divisors_in_range_v1_1918700295_1355 | Let $n = 10080$, $a = 16$, and let $b$ be the smallest divisor of $180355361$ that is at least $2$. Compute the number of positive divisors $d$ of $n$ such that $a \leq d \leq b$. | 45 | graphs = [
Graph(
let={
"n": Const(10080),
"a": Const(16),
"b": MinOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Const(2)), Divides(divisor=Var("d"), dividend=Const(180355361))))),
"result": CountOverSet(set=SolutionsSet(var=Var("d"), cond... | NT | null | COUNT | sympy | MIN_PRIME_FACTOR | [
"MIN_PRIME_FACTOR"
] | bc3776 | nt_count_divisors_in_range_v1 | null | 4 | 0 | [
"MIN_PRIME_FACTOR"
] | 1 | 0.031 | 2026-02-08T05:47:52.972929Z | {
"verified": true,
"answer": 45,
"timestamp": "2026-02-08T05:47:53.003776Z"
} | 8e15a3 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 107,
"completion_tokens": 4378
},
"timestamp": "2026-02-12T14:16:54.446Z",
"answer": 45
},
{
... | 1 | [
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "MIN_PRIME_FACTOR",
"status": "ok"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "V5",
"status": "... | {
"lo": -3.51,
"mid": 1.33,
"hi": 6.56
} | ||
5b6b49 | algebra_quadratic_discriminant_v1_1440796553_1450 | Let $a = 1$, $b = \sum_{k=1}^{2} \phi(k) \left\lfloor \frac{2}{k} \right\rfloor$, and $c = -40$. Compute $b^2 - 4ac$. | 169 | graphs = [
Graph(
let={
"_n": Const(4),
"a": Const(1),
"b": Summation(var="k", start=Const(1), end=Const(2), expr=Mul(EulerPhi(n=Var("k")), Floor(Div(Const(2), Var("k"))))),
"c": Const(-40),
"result": Sub(Pow(Ref("b"), Const(2)), Mul(Ref("_n"), Ref... | NT | null | COMPUTE | sympy | K2 | [
"K2"
] | 6897ab | algebra_quadratic_discriminant_v1 | null | 3 | 0 | [
"K2"
] | 1 | 0.002 | 2026-02-08T14:00:46.863429Z | {
"verified": true,
"answer": 169,
"timestamp": "2026-02-08T14:00:46.865220Z"
} | 509aaa | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 115,
"completion_tokens": 402
},
"timestamp": "2026-02-16T05:11:59.188Z",
"answer": 169
},
{
"id": 11,
... | 2 | [
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "K2",
"status": "ok"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "V3",
"status": "no"
}
] | {
"lo": -10,
"mid": -7.27,
"hi": -4.54
} | ||
66ae37 | antilemma_sum_equals_v1_1520064083_4073 | Let $ m = 14 $. Determine the number of ordered pairs $ (i,j) $ of integers such that $ 1 \le i \le 12 $, $ 1 \le j \le 13 $, and $ i + j = m $. Call this number $ n $. Now determine the number of ordered pairs $ (i,j) $ of integers such that $ 1 \le i \le 11 $, $ 1 \le j \le 12 $, and $ i + j = n $. Compute this numbe... | 11 | graphs = [
Graph(
let={
"_m": Const(14),
"_n": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("i"), Var("j")]), condition=Eq(Sum(Var("i"), Var("j")), Ref("_m")), domain=CartesianProduct(left=IntegerRange(start=Const(1), end=Const(12)), right=IntegerRange(start=Const(1), end=Co... | COMB | GEOM | COMPUTE | sympy | COUNT_SUM_EQUALS | [
"COUNT_SUM_EQUALS/COUNT_SUM_EQUALS",
"COUNT_SUM_EQUALS"
] | ae9919 | antilemma_sum_equals_v1 | null | 3 | 0 | [
"COUNT_SUM_EQUALS"
] | 1 | 0.025 | 2026-02-08T06:03:19.416384Z | {
"verified": true,
"answer": 11,
"timestamp": "2026-02-08T06:03:19.441226Z"
} | cc4b6b | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 220,
"completion_tokens": 1093
},
"timestamp": "2026-02-24T05:18:31.950Z",
"answer": 11
},
{
"id"... | 2 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "ok"
},
{
"lemma": "V8",
... | {
"lo": -10,
"mid": -7.79,
"hi": -5.57
} | ||
322c57 | modular_sum_quadratic_residues_v1_601307018_1302 | Let $p$ be the number of ordered pairs $(a, b)$ of positive integers with $1 \le a, b \le 40$ such that $$\left|\left\{ (a_1, b_1) : a_1, b_1 \geq 1,\ a_1 \leq 35,\ b_1 \leq 35,\ a_1 \leq b_1,\ 2b_1^2 - 4a_1b_1 + 2a_1^2 = 968 \right\}\right| \cdot a^2 + 2b^2 - 2ab \leq \min\{ x + y : x, y > 0,\ xy = 810000,\ x \leq y \... | 21,389 | graphs = [
Graph(
let={
"_c": Const(4),
"_m": Const(2),
"_n": Const(2),
"p": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("a"), Var("b")]), condition=And(Geq(Var("a"), Const(1)), Leq(Var("a"), Const(40)), Geq(Var("b"), Const(1)), Leq(Var("b"), Const(4... | NT | null | SUM | sympy | B3_DIFF | [
"QF_PSD_ORBIT/QF_PSD_COUNT_LEQ",
"B3/QF_PSD_COUNT_LEQ"
] | f9e3be | modular_sum_quadratic_residues_v1 | null | 7 | 0 | [
"B3",
"B3_DIFF",
"QF_PSD_COUNT_LEQ",
"QF_PSD_ORBIT"
] | 4 | 0.022 | 2026-03-10T01:58:48.040358Z | {
"verified": true,
"answer": 21389,
"timestamp": "2026-03-10T01:58:48.062207Z"
} | 464931 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 296,
"completion_tokens": 32768
},
"timestamp": "2026-03-29T01:50:46.386Z",
"answer": null
},
{
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "QF_PSD_COUNT_LEQ",
"status": "ok_later"
},
{
"lemma": "QF_PSD_ORBIT",
"status": "ok"
},
{
"lemma": "V3",
"status": "no"
},
... | {
"lo": 2.84,
"mid": 4.95,
"hi": 7.12
} | ||
56a187 | antilemma_k3_v1_677425708_977 | Let $n = 11348$. Define $x$ to be the sum of $\phi(d)$ over all positive divisors $d$ of $n$, where $\phi$ denotes Euler's totient function. Let $Q$ be the remainder when $89905 \cdot x$ is divided by $98834$. Find the value of $Q$. | 77,392 | graphs = [
Graph(
let={
"_n": Const(11348),
"x": SumOverDivisors(n=Ref(name='_n'), var='d', expr=EulerPhi(n=Var(name='d'))),
"Q": Mod(value=Mul(Const(89905), Ref("x")), modulus=Const(98834)),
},
goal=Ref("Q"),
)
] | NT | COMB | COMPUTE | sympy | K3 | [
"K3"
] | 54c41e | antilemma_k3_v1 | null | 4 | 0 | [
"K3"
] | 1 | 0 | 2026-02-08T03:54:44.552672Z | {
"verified": true,
"answer": 77392,
"timestamp": "2026-02-08T03:54:44.552989Z"
} | f8a88e | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 188,
"completion_tokens": 1810
},
"timestamp": "2026-02-09T14:32:13.843Z",
"answer": 77392
},
{
"... | 1 | [
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K3",
"status": "ok"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "V1",
"status": "no"
},
{
"lemma": "VAL_SUM_EQ",
"status": "no"
}
] | {
"lo": -3.53,
"mid": 1.02,
"hi": 5.49
} |
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