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 |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
2eb9d5 | nt_count_intersection_v1_53965629_55 | Let $d_0$ be the smallest integer greater than or equal to 2 that divides 1037153. Let $N$ be the number of positive integers $n$ such that $1 \leq n \leq 35000$ and $d_0$ divides the $n$-th Fibonacci number. Let $T$ be the set of positive integers $n$ such that $1 \leq n \leq N$, $7$ divides $n$, and $\gcd(n, 15) = 1$... | 8,573 | graphs = [
Graph(
let={
"_n": Const(58718),
"N": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Const(35000)), Divides(divisor=MinOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Const(2)), Divides(divisor=Var("d"), ... | NT | null | COUNT | sympy | MIN_PRIME_FACTOR | [
"MIN_PRIME_FACTOR/COUNT_FIB_DIVISIBLE"
] | f5c873 | nt_count_intersection_v1 | null | 7 | 0 | [
"COUNT_FIB_DIVISIBLE",
"MIN_PRIME_FACTOR"
] | 2 | 0.372 | 2026-02-08T11:15:45.364677Z | {
"verified": true,
"answer": 8573,
"timestamp": "2026-02-08T11:15:45.737062Z"
} | 3fc112 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 263,
"completion_tokens": 4273
},
"timestamp": "2026-02-09T11:23:53.385Z",
"answer": 8573
},
{
"i... | 1 | [
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "ok_later"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MIN_PRIME_FACTOR",
"status": "ok"
},
{
"lemma": "MOD_FACTORIAL",
"... | {
"lo": -5.5,
"mid": -0.08,
"hi": 5.44
} | ||
2dd81d | antilemma_k3_v1_1470522791_158 | Let $n = 40162$. Define $x$ to be the sum of $\phi(d)$ over all positive divisors $d$ of $n$, where $\phi$ denotes Euler's totient function. Let $c = 64327$. Compute the remainder when $c \cdot x$ is divided by $90243$. | 24,370 | graphs = [
Graph(
let={
"_n": Const(40162),
"x": SumOverDivisors(n=Ref(name='_n'), var='d', expr=EulerPhi(n=Var(name='d'))),
"_c": Const(64327),
"Q": Mod(value=Mul(Ref("_c"), Ref("x")), modulus=Const(90243)),
},
goal=Ref("Q"),
)
] | NT | COMB | COMPUTE | sympy | K3 | [
"K3"
] | 54c41e | antilemma_k3_v1 | null | 3 | 0 | [
"K3"
] | 1 | 0.001 | 2026-02-08T12:51:13.863480Z | {
"verified": true,
"answer": 24370,
"timestamp": "2026-02-08T12:51:13.864300Z"
} | 304d77 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 114,
"completion_tokens": 2940
},
"timestamp": "2026-02-15T07:08:22.073Z",
"answer": 24370
},
... | 1 | [
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "K3",
"status": "ok"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
... | {
"lo": -5.49,
"mid": 0.22,
"hi": 6.51
} | ||
60fbe2 | comb_count_permutations_fixed_v1_809748730_1446 | Let $m = 15880$. Let $\ell$ be the largest prime number such that $2 \leq \ell \leq 9$. Let $k$ be the largest positive integer such that $\ell^k \leq m$. Define $n = 8$. Compute the value of $\binom{n}{k} \cdot !(n - k)$, where $!r$ denotes the number of derangements of $r$ elements. | 630 | graphs = [
Graph(
let={
"_m": Const(15880),
"_n": MaxOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(2)), Leq(Var("n"), Const(9)), IsPrime(Var("n"))))),
"n": Const(8),
"k": MaxOverSet(set=SolutionsSet(var=Var("k"), condition=Leq(Pow(Re... | NT | COMB | COUNT | sympy | LIN_FORM | [
"MAX_PRIME_BELOW/MAX_VAL"
] | b2f06b | comb_count_permutations_fixed_v1 | null | 5 | 0 | [
"LIN_FORM",
"MAX_PRIME_BELOW",
"MAX_VAL"
] | 3 | 0.018 | 2026-02-08T12:25:40.869813Z | {
"verified": true,
"answer": 630,
"timestamp": "2026-02-08T12:25:40.887397Z"
} | b8fb71 | 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": 796
},
"timestamp": "2026-02-15T01:18:14.329Z",
"answer": 630
},
{
... | 1 | [
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok"
},
{
"lemma": "MAX_VAL",
"status": "ok_later"
},
{
... | {
"lo": -9.12,
"mid": -6.02,
"hi": -3.62
} | ||
f0c4f3 | diophantine_fbi2_min_v1_151522320_424 | Let $k = 360$. Consider the set of all ordered pairs $(x, y)$ of positive integers such that $xy = 9$. For each such pair, compute the sum $x + y$. Let $m$ be the minimum value of these sums.
Now, let $D$ be the set of all integers $d$ such that $4 \leq d \leq 370$, $d$ divides $k$, and $\frac{k}{d} \geq m$. Let $d_{\... | 51,322 | graphs = [
Graph(
let={
"_n": Const(44121),
"k": Const(360),
"upper": Const(370),
"result": MinOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Const(4)), Leq(Var("d"), Ref("upper")), Divides(divisor=Var("d"), dividend=Ref("k")), Geq(Div(Ref(... | NT | null | EXTREMUM | sympy | B3 | [
"B3"
] | 0cd20d | diophantine_fbi2_min_v1 | null | 4 | 0 | [
"B3"
] | 1 | 0.019 | 2026-02-08T03:14:42.244840Z | {
"verified": true,
"answer": 51322,
"timestamp": "2026-02-08T03:14:42.263882Z"
} | b5e705 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 262,
"completion_tokens": 794
},
"timestamp": "2026-02-10T13:28:53.985Z",
"answer": 51222
},
{
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "V3",
"status": "no"
},
{
"lemma": "VAL_SUM_EQ",
"status": "no"
}
] | {
"lo": -3.46,
"mid": 1.03,
"hi": 5.49
} | ||
03a8c1 | lin_form_endings_v1_1918700295_4466 | Let $a = 42$ and $b = 56$. Compute $\text{lcm}(a, b)$, and define $s = 3 \cdot \text{lcm}(a, b) + a + b$. Multiply $s$ by $13297$, and let $x$ be the remainder when this product is divided by $95986$. Compute $x$. | 37,956 | graphs = [
Graph(
let={
"a_coeff": Const(42),
"b_coeff": Const(56),
"k_val": Const(3),
"lcm_node": LCM(a=Ref("a_coeff"), b=Ref("b_coeff")),
"_inner_result": Sum(Mul(Ref("k_val"), Ref("lcm_node")), Ref("a_coeff"), Ref("b_coeff")),
"_scal... | COMB | NT | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | lin_form_endings_v1 | null | 2 | null | [
"LIN_FORM"
] | 1 | 0.001 | 2026-02-08T09:23:43.254837Z | {
"verified": true,
"answer": 37956,
"timestamp": "2026-02-08T09:23:43.255887Z"
} | b55566 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 125,
"completion_tokens": 533
},
"timestamp": "2026-02-14T04:01:48.076Z",
"answer": 37956
},
{... | 1 | [
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "V8",
"status": "no"
},
{
"lemma": "V8_SUM",
... | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
d21577 | diophantine_product_count_v1_124444284_6005 | Let $k = 60$ and $u = 54$. Compute the number of positive integers $x$ such that $1 \leq x \leq u$, $x$ divides $k$, and $\frac{k}{x} \leq u$. | 10 | graphs = [
Graph(
let={
"k": Const(60),
"upper": Const(54),
"result": CountOverSet(set=SolutionsSet(var=Var("x"), condition=And(Geq(Var("x"), Const(1)), Leq(Var("x"), Ref("upper")), Divides(divisor=Var("x"), dividend=Ref("k")), Leq(Div(Ref("k"), Var("x")), Ref("upper"))))... | NT | null | COUNT | sympy | B3 | [
"B3"
] | 0cd20d | diophantine_product_count_v1 | null | 3 | 0 | [
"B3"
] | 1 | 0.044 | 2026-02-08T06:58:26.868513Z | {
"verified": true,
"answer": 10,
"timestamp": "2026-02-08T06:58:26.912435Z"
} | 21424f | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 99,
"completion_tokens": 1117
},
"timestamp": "2026-02-13T06:24:43.952Z",
"answer": 10
},
{
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
},
{
"lemma": "VAL_SUM_EQ",
"status": "no"
}
] | {
"lo": -5.55,
"mid": -3.01,
"hi": 0.32
} | ||
0fc793 | alg_qf_psd_orbit_v1_1419126231_828 | Find the number of ordered pairs $(a, b)$ of positive integers with $1 \leq a \leq b \leq 465$ such that
$$
34a^2 + 34b^2 - 60ab = 1064200.
$$ | 5 | graphs = [
Graph(
let={
"result": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("a"), Var("b")]), condition=And(Geq(Var("a"), Const(1)), Leq(Var("a"), Const(465)), Geq(Var("b"), Const(1)), Leq(Var("b"), Const(465)), Leq(Var("a"), Var("b")), Eq(Sum(Mul(Const(34), Pow(Var("b"), Const(2))),... | ALG | null | COUNT | sympy | QF_PSD_ORBIT | [
"QF_PSD_DISTINCT/QF_PSD_DISTINCT",
"B3/QF_PSD_DISTINCT"
] | fa89e7 | alg_qf_psd_orbit_v1 | null | 3 | null | [
"B3",
"QF_PSD_DISTINCT",
"QF_PSD_ORBIT"
] | 3 | 1.417 | 2026-02-25T10:18:30.060991Z | {
"verified": true,
"answer": 5,
"timestamp": "2026-02-25T10:18:31.478442Z"
} | a5aafe | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 167,
"completion_tokens": 10509
},
"timestamp": "2026-03-30T10:08:08.004Z",
"answer": 5
},
{
"id"... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "QF_PSD_DISTINCT",
"status": "ok"
}
] | {
"lo": 1.5,
"mid": 4.69,
"hi": 7.23
} | ||
34e881 | diophantine_fbi2_count_v1_677425708_1758 | Let $n = 2$ and $k = 840$. Consider the set of all integers $d$ such that $d \geq n$, $d \leq 90$, $d$ divides $k$, $\frac{k}{d} \geq 2$, and $\frac{k}{d} \leq 90$. Compute the number of elements in this set. | 16 | graphs = [
Graph(
let={
"_n": Const(2),
"k": Const(840),
"result": CountOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Ref("_n")), Leq(Var("d"), Const(90)), Divides(divisor=Var("d"), dividend=Ref("k")), Geq(Div(Ref("k"), Var("d")), Const(2)), Leq(Div(R... | NT | null | COUNT | sympy | C4 | [
"MIN_PRIME_FACTOR"
] | bc3776 | diophantine_fbi2_count_v1 | null | 3 | 0 | [
"C4",
"MIN_PRIME_FACTOR"
] | 2 | 0.03 | 2026-02-08T04:26:15.270274Z | {
"verified": true,
"answer": 16,
"timestamp": "2026-02-08T04:26:15.300177Z"
} | 6492a1 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 191,
"completion_tokens": 3538
},
"timestamp": "2026-02-10T00:32:29.973Z",
"answer": 16
},
{
"id"... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "MIN_PRIME_FACTOR",
"status": "ok"
},
{
"lemma": "MOD_SUB",
"status": "no"
}... | {
"lo": -7.01,
"mid": -4.68,
"hi": -2.15
} | ||
fe1b00 | diophantine_fbi2_count_v1_1742523217_846 | Let $k$ be the number of integers $t$ such that $5 \leq t \leq 486$ and there exist positive integers $a$ and $b$ with $1 \leq a \leq 207$, $1 \leq b \leq 24$, and $t = 2a + 3b$. Let $r$ be the number of positive integers $d$ such that $4 \leq d \leq 81$, $d$ divides $k$, and the quotient $k/d$ satisfies $6 \leq k/d \l... | 14 | graphs = [
Graph(
let={
"k": CountOverSet(set=SolutionsSet(var=Var("t"), condition=Exists(var=Var(name='a'), condition=Exists(var=Var(name='b'), condition=And(Geq(left=Var(name='a'), right=Const(value=1)), Leq(left=Var(name='a'), right=Const(value=207)), Geq(left=Var(name='b'), right=Const(value... | NT | null | COUNT | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | diophantine_fbi2_count_v1 | null | 7 | 0 | [
"LIN_FORM"
] | 1 | 0.007 | 2026-02-08T03:17:44.557495Z | {
"verified": true,
"answer": 14,
"timestamp": "2026-02-08T03:17:44.564933Z"
} | c9718c | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 251,
"completion_tokens": 3516
},
"timestamp": "2026-02-09T07:48:09.370Z",
"answer": 14
},
{
"id... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
}
] | {
"lo": -3.49,
"mid": 1.84,
"hi": 7.55
} | ||
4f5155 | diophantine_product_count_v1_168721529_1543 | Let $k = 840$. Let $u$ be the number of positive integers $n \leq 1116$ such that $8$ divides the $n$-th Fibonacci number. Let $S$ be the set of positive integers $x \leq u$ such that $x$ divides $k$ and $\frac{k}{x} \leq u$. Compute the number of elements in $S$. | 24 | graphs = [
Graph(
let={
"_n": Const(8),
"k": Const(840),
"upper": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Const(1116)), Divides(divisor=Ref("_n"), dividend=Fibonacci(arg=Var(name='n')))))),
"result": Cou... | NT | null | COUNT | sympy | COUNT_FIB_DIVISIBLE | [
"COUNT_FIB_DIVISIBLE"
] | 66de3c | diophantine_product_count_v1 | null | 6 | 0 | [
"COUNT_FIB_DIVISIBLE"
] | 1 | 0.017 | 2026-02-08T13:45:49.718396Z | {
"verified": true,
"answer": 24,
"timestamp": "2026-02-08T13:45:49.734999Z"
} | 7b6ed3 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 198,
"completion_tokens": 2475
},
"timestamp": "2026-02-11T07:58:10.066Z",
"answer": 24
},
{
"id... | 1 | [
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "ok"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "V1",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
}
] | {
"lo": -8.26,
"mid": -5.01,
"hi": -1.76
} | ||
cf1e53 | nt_sum_totient_over_divisors_v1_1520064083_9431 | Let $n = 65134$. Consider the sum
\[S = \sum_{d \mid n} \varphi(d),\]
where the sum is taken over all positive divisors $d$ of $n$, and $\varphi(d)$ denotes the number of positive integers less than or equal to $d$ that are relatively prime to $d$.
Compute $S$. | 65,134 | graphs = [
Graph(
let={
"n": Const(65134),
"result": SumOverDivisors(n=Ref(name='n'), var='d', expr=EulerPhi(n=Var(name='d'))),
},
goal=Ref("result"),
)
] | NT | null | COMPUTE | sympy | COUNT_SUM_EQUALS | [
"COUNT_SUM_EQUALS/COUNT_SUM_EQUALS/BINOMIAL_ALTERNATING/VIETA_SUM/MAX_DIVISOR",
"COUNT_SUM_EQUALS/VIETA_SUM/MAX_DIVISOR"
] | ca2545 | nt_sum_totient_over_divisors_v1 | null | 3 | 0 | [
"BINOMIAL_ALTERNATING",
"COUNT_SUM_EQUALS",
"MAX_DIVISOR",
"VIETA_SUM"
] | 4 | 0.042 | 2026-02-08T10:45:25.984727Z | {
"verified": true,
"answer": 65134,
"timestamp": "2026-02-08T10:45:26.026962Z"
} | 354d0e | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 1,
"correct": {
"strict": false,
"boxed": false,
"relaxed": true
},
"usage": {
"prompt_tokens": 139,
"completion_tokens": 789
},
"timestamp": "2026-02-15T21:03:13.434Z",
"answer": 30000
},
{
"id": 11,... | 1 | [
{
"lemma": "BINOMIAL_ALTERNATING",
"status": "ok_later"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "ok"
},
{
"lemma": "MAX_DIVISOR",
"status": "ok_later"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"... | {
"lo": -6.96,
"mid": -4.56,
"hi": -1.46
} | ||
452784 | nt_count_intersection_v1_784195855_2335 | Let $N$ be the minimum value of $x + y$ over all ordered pairs $(x, y)$ of positive integers such that $xy = 25000000$. Let $a$ be the smallest integer $d \geq 2$ that divides 2695. Compute the number of positive integers $n \leq N$ such that $a$ divides $n$ and $\gcd(n, 6) = 1$. Let this count be $C$. Find the remaind... | 14,146 | graphs = [
Graph(
let={
"_n": Const(22039),
"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(25000000)))), expr=Sum(Var("x"), Var("y"... | NT | null | COUNT | sympy | MIN_PRIME_FACTOR | [
"MIN_PRIME_FACTOR",
"B3"
] | 6c6c26 | nt_count_intersection_v1 | null | 4 | 0 | [
"B3",
"MIN_PRIME_FACTOR"
] | 2 | 0.391 | 2026-02-08T05:41:41.008807Z | {
"verified": true,
"answer": 14146,
"timestamp": "2026-02-08T05:41:41.399648Z"
} | 3a517b | 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": 1941
},
"timestamp": "2026-02-12T13:07:12.401Z",
"answer": 14146
},
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "MIN_PRIME_FACTOR",
"status": "ok"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
... | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
a9a230 | comb_count_surjections_v1_1520064083_3456 | Let $n$ be the number of ordered triples $(x_1, x_2, x_3)$ of positive odd integers such that $x_1 + x_2 + x_3 = 7$. Let $k = 6$. Define $\text{result} = k! \cdot S(n, k)$, where $S(n, k)$ denotes the Stirling number of the second kind. Compute the remainder when $44121 \cdot \text{result}$ is divided by $56911$. | 10,782 | graphs = [
Graph(
let={
"_n": Const(56911),
"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(arg=Var(name='x1')), IsOdd(arg=Var... | COMB | null | COUNT | sympy | COMB1 | [
"COMB1"
] | 567f58 | comb_count_surjections_v1 | null | 6 | 0 | [
"COMB1"
] | 1 | 0.002 | 2026-02-08T05:41:28.394436Z | {
"verified": true,
"answer": 10782,
"timestamp": "2026-02-08T05:41:28.396021Z"
} | 0fa4d8 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 219,
"completion_tokens": 1258
},
"timestamp": "2026-02-24T04:18:11.755Z",
"answer": 10782
},
{
"... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COMB1",
"status": "ok"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "V8",
"status":... | {
"lo": -2.46,
"mid": 0.47,
"hi": 3.59
} | ||
88bf31 | antilemma_k3_v1_784195855_9165 | Let $n = 89148$. Define $x = \sum_{d \mid n} \phi(d)$, where the sum is taken over all positive divisors $d$ of $n$, and $\phi$ denotes Euler's totient function.
Compute the remainder when $17030x$ is divided by $61257$. | 58,209 | graphs = [
Graph(
let={
"_n": Const(89148),
"x": SumOverDivisors(n=Ref(name='_n'), var='d', expr=EulerPhi(n=Var(name='d'))),
"Q": Mod(value=Mul(Const(17030), Ref("x")), modulus=Const(61257)),
},
goal=Ref("Q"),
)
] | NT | COMB | COMPUTE | sympy | K3 | [
"K3"
] | 54c41e | antilemma_k3_v1 | null | 3 | 0 | [
"K3"
] | 1 | 0 | 2026-02-08T16:34:30.740348Z | {
"verified": true,
"answer": 58209,
"timestamp": "2026-02-08T16:34:30.740769Z"
} | aae745 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 113,
"completion_tokens": 3060
},
"timestamp": "2026-02-17T07:31:58.303Z",
"answer": 58209
},
... | 1 | [
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "K3",
"status": "ok"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
}... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
e63749 | modular_mod_compute_v1_1978505735_2818 | Let $a = 37$. Let $T$ be the set of all integers $t$ such that there exist positive integers $a$ and $b$ satisfying $1 \le a \le 124$, $1 \le b \le 248$, $34 \le t \le 4846$, and $t = 9a + 15b + 10$. Let $m = |T|$, and let $r$ be the remainder when $a$ is divided by $m$. Compute the remainder when $93170 \cdot r$ is di... | 34,319 | graphs = [
Graph(
let={
"_n": Const(66921),
"a": Const(37),
"m": CountOverSet(set=SolutionsSet(var=Var("t"), condition=Exists(var=Var(name='a'), condition=Exists(var=Var(name='b'), condition=And(Geq(left=Var(name='a'), right=Const(value=1)), Leq(left=Var(name='a'), right=... | NT | null | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | modular_mod_compute_v1 | null | 4 | 0 | [
"LIN_FORM"
] | 1 | 0.002 | 2026-02-08T17:11:26.984862Z | {
"verified": true,
"answer": 34319,
"timestamp": "2026-02-08T17:11:26.987197Z"
} | 325a81 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 171,
"completion_tokens": 5660
},
"timestamp": "2026-02-17T21:33:57.247Z",
"answer": 34319
},
... | 1 | [
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "V1",
"status": "no"... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
a90c91 | antilemma_coprime_grid_v1_1456120455_87 | Let $S$ be the set of all ordered pairs $(i, j)$ of positive integers with $1 \le i \le 41$ and $1 \le j \le 165$ such that $\gcd(i, j) = 1$. Let $x$ be the number of elements in $S$. Find the remainder when $44121x$ is divided by $89483$. | 35,510 | graphs = [
Graph(
let={
"x": 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(41)), right=IntegerRange(start=Const(1), end=Const(165))))),
"... | NT | COMB | COMPUTE | sympy | COUNT_COPRIME_GRID | [
"COUNT_COPRIME_GRID"
] | 20ec03 | antilemma_coprime_grid_v1 | null | 5 | 0 | [
"COUNT_COPRIME_GRID"
] | 1 | 0.001 | 2026-02-08T02:53:26.307823Z | {
"verified": true,
"answer": 35510,
"timestamp": "2026-02-08T02:53:26.308365Z"
} | 337478 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 197,
"completion_tokens": 6881
},
"timestamp": "2026-02-08T20:02:39.059Z",
"answer": 35510
},
{
"... | 1 | [
{
"lemma": "COUNT_COPRIME_GRID",
"status": "ok"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
}... | {
"lo": -6.51,
"mid": -0.53,
"hi": 4.75
} | ||
bfe187 | nt_count_gcd_equals_v1_898971024_1035 | Let $k_1$ range over the positive integers from 1 to the minimum value of $x + y$ over all ordered pairs $(x, y)$ of positive integers such that $xy = 144$. Compute
$$
\sum_{k_1=1}^{\min(x+y)} \phi(k_1) \left\lfloor \frac{24}{k_1} \right\rfloor,
$$
where $\phi$ denotes Euler's totient function. Call this sum $k$. Deter... | 101 | graphs = [
Graph(
let={
"_n": Const(144),
"upper": Const(15120),
"k": Summation(var="k1", start=Const(1), end=MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), E... | NT | null | COUNT | sympy | B3 | [
"B3/K2"
] | 9f3175 | nt_count_gcd_equals_v1 | null | 6 | 0 | [
"B3",
"K2"
] | 2 | 1.332 | 2026-02-08T15:53:05.365726Z | {
"verified": true,
"answer": 101,
"timestamp": "2026-02-08T15:53:06.697459Z"
} | 290cdd | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 180,
"completion_tokens": 2614
},
"timestamp": "2026-02-16T15:53:10.445Z",
"answer": 101
},
{
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K2",
"status": "ok_later"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
4ec34f | nt_gcd_compute_v1_1742523217_3304 | Let $a = 323036$ and $b = 726831$. Let $d$ be the greatest common divisor of $a$ and $b$. Consider the set of all integers $t$ such that there exist integers $a'$ and $b'$ satisfying the following conditions:
- $1 \leq a' \leq 3$,
- $1 \leq b' \leq 11$,
- $23 \leq t \leq 67$,
- $t = 7a' + 3b' + 13$.
Let $N$ be the nu... | 67,276 | graphs = [
Graph(
let={
"_n": Const(74001),
"a": Const(323036),
"b": Const(726831),
"result": GCD(a=Ref("a"), b=Ref("b")),
"Q": Mod(value=Sub(CountOverSet(set=SolutionsSet(var=Var("t"), condition=Exists(var=Var(name='a'), condition=Exists(var=Var(n... | NT | null | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM"
] | 324ba4 | nt_gcd_compute_v1 | negation_mod | 3 | 0 | [
"LIN_FORM"
] | 1 | 0.005 | 2026-02-08T05:46:23.955115Z | {
"verified": true,
"answer": 67276,
"timestamp": "2026-02-08T05:46:23.960036Z"
} | f09daf | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 192,
"completion_tokens": 2084
},
"timestamp": "2026-02-12T13:42:38.943Z",
"answer": 67276
},
... | 1 | [
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
}
] | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
0df897_n | alg_sum_powers_v1_1218484723_4021 | A music composer assigns pitches based on integer values from 1 to 304. Each pitch $i$ is played with intensity $i^k$, where $k$ is the number of distinct note pairs $(a,b)$ with $1 \leq a \leq b \leq 15$ such that $5a^2 - 8ab + 5b^2 = 425$. The total volume is the sum of all intensities. This sum is transmitted in blo... | 7,225 | ALG | null | COMPUTE | sympy | QF_PSD_ORBIT | [
"QF_PSD_ORBIT",
"LIN_FORM"
] | 7e2c84 | alg_sum_powers_v1 | null | 5 | null | [
"LIN_FORM",
"QF_PSD_ORBIT"
] | 2 | 0.012 | 2026-02-25T05:37:48.074069Z | null | a8ba55 | 0df897 | narrative | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 293,
"completion_tokens": 32768
},
"timestamp": "2026-03-30T21:02:12.708Z",
"answer": 7225
},
{
"... | 1 | [
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "QF_PSD_ORBIT",
"status": "ok"
}
] | {
"lo": 1.5,
"mid": 4.69,
"hi": 7.23
} | |
2a571a | alg_poly_orbit_count_v1_1218484723_7672 | Work in arithmetic modulo $61$. Define
\[N = 3a^{3} - 5a^{2} - 3a - 4 \bmod 61,\]
\[M = 3N^{3} - 5N^{2} - 3N - 4 \bmod 61,\]
\[R = 3M^{3} - 5M^{2} - 3M - 4 \bmod 61,\]
\[S = 3R^{3} - 5R^{2} - 3R - 4 \bmod 61,\]
\[T = 3S^{3} - 5S^{2} - 3S - 4 \bmod 61,\]
\[K = 3T^{3} - 5T^{2} - 3T - 4 \bmod 61.\]
Let $Q$ be the number o... | 1,500 | graphs = [
Graph(
let={
"p1": Mod(value=Sum(Mul(Const(3), Pow(Var("a"), Const(3))), Mul(Const(-5), Pow(Var("a"), Const(2))), Mul(Const(-3), Var("a")), Const(-4)), modulus=Const(61)),
"p2": Mod(value=Sum(Mul(Const(3), Pow(Ref("p1"), Const(3))), Mul(Const(-5), Pow(Ref("p1"), Const(2)))... | ALG | null | COUNT | sympy | POLY_ORBIT_COUNT | [
"POLY_ORBIT_COUNT"
] | 4ad965 | alg_poly_orbit_count_v1 | null | 7 | null | [
"POLY_ORBIT_COUNT"
] | 1 | 0.146 | 2026-02-25T09:08:57.642539Z | {
"verified": true,
"answer": 1500,
"timestamp": "2026-02-25T09:08:57.788921Z"
} | d0426b | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 371,
"completion_tokens": 21290
},
"timestamp": "2026-03-30T05:51:10.160Z",
"answer": 1500
},
{
"... | 1 | [
{
"lemma": "POLY_ORBIT_COUNT",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
}
] | {
"lo": 3.81,
"mid": 6.33,
"hi": 9.49
} | ||
942748 | comb_count_partitions_v1_655260480_303 | Let $u = 5$ and $n_2 = u + 1$. Define
$$
f = \sum_{k=0}^{n_2} (-1)^k \binom{n_2}{k}.
$$
Let $n_1 = u + 1 + f$, and define
$$
v = \sum_{k_1=0}^{n_1} (-1)^{k_1} \binom{n_1}{k_1}.
$$
Let $n = 44 + v$. Compute the number of integer partitions of $n$. | 75,175 | graphs = [
Graph(
let={
"u1": Const(5),
"n2": Sum(Ref("u1"), Const(1)),
"f": Summation(var="k", start=Const(0), end=Ref("n2"), expr=Mul(Pow(Const(-1), Var("k")), Binom(n=Ref("n2"), k=Var("k")))),
"u": Const(5),
"n1": Sum(Ref("u"), Const(1), Ref("f"... | COMB | null | COUNT | sympy | BINOMIAL_ALTERNATING | [
"BINOMIAL_ALTERNATING"
] | c21569 | comb_count_partitions_v1 | null | 4 | 2 | [
"BINOMIAL_ALTERNATING"
] | 1 | 0.002 | 2026-02-08T15:20:23.708380Z | {
"verified": true,
"answer": 75175,
"timestamp": "2026-02-08T15:20:23.710089Z"
} | af0e48 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 235,
"completion_tokens": 879
},
"timestamp": "2026-02-24T20:27:36.763Z",
"answer": 75175
},
{
"i... | 1 | [
{
"lemma": "BINOMIAL_ALTERNATING",
"status": "ok"
},
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "V8"... | {
"lo": -2.43,
"mid": 1.2,
"hi": 4.84
} | ||
df0c2b | modular_sum_quadratic_residues_v1_48377204_272 | Let $ p = 433 $ and $ n = 317 $. Let $ r = \frac{p(p-1)}{4} $. Let $ c $ be the largest prime number less than or equal to 7008. Compute the remainder when $ (r \bmod n) + c \cdot (r \bmod 313) $ is divided by 72343. | 21,176 | graphs = [
Graph(
let={
"_n": Const(317),
"p": Const(433),
"result": Div(Mul(Ref("p"), Sub(Ref("p"), Const(1))), Const(4)),
"_c": MaxOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(2)), Leq(Var("n"), Const(7008)), IsPrime(Var("n"))))),... | NT | null | SUM | sympy | MAX_PRIME_BELOW | [
"MAX_PRIME_BELOW"
] | 08a653 | modular_sum_quadratic_residues_v1 | two_moduli | 4 | 0 | [
"MAX_PRIME_BELOW"
] | 1 | 0.003 | 2026-02-08T15:19:51.494579Z | {
"verified": true,
"answer": 21176,
"timestamp": "2026-02-08T15:19:51.497210Z"
} | b8aba7 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 125,
"completion_tokens": 1754
},
"timestamp": "2026-02-16T03:07:26.101Z",
"answer": 21176
},
... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
bf470d | algebra_quadratic_discriminant_v1_717093673_938 | Let $a = -1$, $b = 0$, and $n = 4$. Let $c$ be the maximum value of $xy$ over all ordered pairs $(x, y)$ of positive integers satisfying $x + y = 14$. Compute $b^2 - nac$. | 196 | graphs = [
Graph(
let={
"_n": Const(4),
"a": Const(-1),
"b": Const(0),
"c": MaxOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(Sum(Var("x"), Var("y... | NT | null | COMPUTE | sympy | B1 | [
"B1"
] | 5b950e | algebra_quadratic_discriminant_v1 | null | 3 | 0 | [
"B1"
] | 1 | 0.002 | 2026-02-08T15:45:45.401186Z | {
"verified": true,
"answer": 196,
"timestamp": "2026-02-08T15:45:45.403463Z"
} | 77f6ba | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 119,
"completion_tokens": 346
},
"timestamp": "2026-02-16T06:17:13.328Z",
"answer": 196
},
{
"id": 11,
... | 2 | [
{
"lemma": "B1",
"status": "ok"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
},
{
"lemma": "VAL_SUM_EQ",
"status": "no"
}
] | {
"lo": -10,
"mid": -7.27,
"hi": -4.54
} | ||
2a78bc | alg_poly4_min_v1_1218484723_6944 | Find the minimum value of $702270a^2b^2 - 530604a^3b + 252297a^4 - 593028ab^{\sum_{k=1}^{2} \varphi(k) \cdot \lfloor 2/k \rfloor} + 213282b^4$ over all ordered pairs $(a, b)$ of positive integers with $1 \le a, b \le 72$. | 44,217 | graphs = [
Graph(
let={
"_n": Const(4),
"result": MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("a"), Var("b")]), condition=And(Geq(Var("a"), Const(1)), Leq(Var("a"), Const(72)), Geq(Var("b"), Const(1)), Leq(Var("b"), Const(72)))), expr=Sum(Mul(Const(702270), Pow... | NT | null | COMPUTE | sympy | K2 | [
"K2"
] | 6897ab | alg_poly4_min_v1 | null | 5 | 0 | [
"K2"
] | 1 | 0.023 | 2026-02-25T08:22:58.883883Z | {
"verified": true,
"answer": 44217,
"timestamp": "2026-02-25T08:22:58.906690Z"
} | a50659 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 205,
"completion_tokens": 7212
},
"timestamp": "2026-03-30T03:19:47.401Z",
"answer": 44217
},
{
"... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "K2",
"status": "ok"
},
{
"lemma": "V5",
"status": "no"
}
] | {
"lo": -3.33,
"mid": 1.03,
"hi": 5.26
} | ||
249aa5 | modular_count_residue_v1_349078426_257 | Let $n = 18$ and $m = 19$. Let $r$ be the largest prime number such that $2 \leq r \leq n$. Compute the number of positive integers $n$ such that $1 \leq n \leq 33124$ and $n \equiv r \pmod{19}$. | 1,743 | graphs = [
Graph(
let={
"_n": Const(18),
"upper": Const(33124),
"m": Const(19),
"r": MaxOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(2)), Leq(Var("n"), Ref("_n")), IsPrime(Var("n"))))),
"result": CountOverSet(set=Solutio... | NT | null | COUNT | sympy | MAX_PRIME_BELOW | [
"MAX_PRIME_BELOW"
] | dc3ad3 | modular_count_residue_v1 | null | 3 | 0 | [
"MAX_PRIME_BELOW"
] | 1 | 1.119 | 2026-02-08T12:54:04.241346Z | {
"verified": true,
"answer": 1743,
"timestamp": "2026-02-08T12:54:05.360162Z"
} | dac5e4 | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 130,
"completion_tokens": 662
},
"timestamp": "2026-02-16T04:09:05.237Z",
"answer": 1743
},
{
"id": 11,
... | 2 | [
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "V3",
"stat... | {
"lo": -9.12,
"mid": -6.02,
"hi": -3.62
} | ||
7d13c0 | nt_min_crt_v1_1918700295_4592 | Let $m = 4$, $k = 9$, $a = 1$, and $b = 3$. Let the upper bound be $36$. Consider the set of all positive integers $n$ such that $1 \leq n \leq 36$, $n \equiv a \pmod{m}$, and $n \equiv b \pmod{k}$. Let $r$ be the minimum element of this set. Compute the Bell number $B_s$, where $s = |r| \bmod{11}$, and then find the r... | 36,067 | graphs = [
Graph(
let={
"m": Const(4),
"k": Const(9),
"a": Const(1),
"b": Const(3),
"upper": Const(36),
"result": MinOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Ref("upper")), Eq(Mod(value... | COMB | null | EXTREMUM | sympy | MIN_PRIME_FACTOR | [
"MIN_PRIME_FACTOR"
] | 58d7e9 | nt_min_crt_v1 | bell_mod | 4 | 0 | [
"MIN_PRIME_FACTOR"
] | 1 | 0.059 | 2026-02-08T09:28:36.160331Z | {
"verified": true,
"answer": 36067,
"timestamp": "2026-02-08T09:28:36.219817Z"
} | 91baca | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 252,
"completion_tokens": 1209
},
"timestamp": "2026-02-24T11:22:39.757Z",
"answer": 36067
},
{
"... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "MIN_PRIME_FACTOR",
"status": "ok"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8_SUM",
"stat... | {
"lo": -4.92,
"mid": -2.91,
"hi": -0.68
} | ||
ee4765 | geo_visible_lattice_v1_655260480_4682 | Let $n = 66$. Define $L$ to be the number of ordered pairs $(x, y)$ of positive integers such that $1 \leq x, y \leq n$ and $\gcd(x, y) = 1$. Compute the remainder when $44121 \cdot L$ is divided by $86960$. | 6,135 | graphs = [
Graph(
let={
"n": Const(66),
"result": VisibleLatticePoints(n=Ref(name='n')),
"Q": Mod(value=Mul(Const(44121), Ref("result")), modulus=Const(86960)),
},
goal=Ref("Q"),
)
] | GEOM | null | COUNT | sympy | [] | geo_visible_lattice_v1 | null | 4 | 0 | null | null | 0.1 | 2026-02-08T18:03:13.074631Z | {
"verified": true,
"answer": 6135,
"timestamp": "2026-02-08T18:03:13.174950Z"
} | 1941f3 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 115,
"completion_tokens": 3387
},
"timestamp": "2026-02-18T12:44:26.009Z",
"answer": 6135
},
{... | 1 | [] | {
"lo": -2.38,
"mid": 1.74,
"hi": 6.59
} | ||||
99f623 | modular_modexp_compute_v1_1742523217_906 | Let $m=5$ and $n=14$. Let $a=3$.
Consider all ordered pairs $(x,y)$ of positive integers such that
$$xy=1018081.$$
For each such pair, form the sum $x+y$. Let $e$ be the minimum possible value of $x+y$ over all such pairs.
Let $M=32768$. Define
$$r\equiv 3^e \pmod{32768},\qquad 0\le r<32768.$$
Let $U$ be the set of ... | 4,140 | graphs = [
Graph(
let={
"_m": Const(5),
"_n": Const(14),
"a": Const(3),
"e": 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("... | NT | COMB | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM/C5",
"B3"
] | 09cda8 | modular_modexp_compute_v1 | bell_mod | 9 | 0 | [
"B3",
"C5",
"LIN_FORM"
] | 3 | 0.004 | 2026-02-08T03:21:13.782161Z | {
"verified": true,
"answer": 4140,
"timestamp": "2026-02-08T03:21:13.786661Z"
} | be23a7 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 406,
"completion_tokens": 7496
},
"timestamp": "2026-02-09T08:27:06.631Z",
"answer": 4140
},
{
"... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "C5",
"status": "ok_later"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "LTE_D... | {
"lo": 2.58,
"mid": 5.33,
"hi": 8.57
} | ||
f9fc03_l | comb_binomial_compute_v1_458359167_618 | Let $u = 9$, $n_2 = u + 1$, and
$$
s = \sum_{k=0}^{n_2} (-1)^k \binom{n_2}{k}.
$$
Let $a = 3 + s$ and $b = 2$, so $n_1 = a + b$. Define
$$
f = \sum_{k=0}^{n_1} (-1)^k \binom{n_1}{k}.
$$
Let $n = 16$ and $k = 7$, and let $r = \binom{n}{k}$. Compute the value of
$$
r + \phi(|r| + 1) + \tau(|r| + 1 + f),
$$
where $\phi$ d... | 22,882 | COMB | NT | COMPUTE | sympy | BINOMIAL_ALTERNATING | [
"BINOMIAL_ALTERNATING",
"ZERO_BINOM_0"
] | 38a409 | comb_binomial_compute_v1 | null | 4 | 2 | [
"BINOMIAL_ALTERNATING",
"ZERO_BINOM_0"
] | 2 | 0.002 | 2026-02-08T03:26:24.262619Z | {
"verified": false,
"answer": 22196,
"timestamp": "2026-02-08T03:26:24.264777Z"
} | 2b11bd | f9fc03 | 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": 305,
"completion_tokens": 1112
},
"timestamp": "2026-02-10T14:22:53.749Z",
"answer": 22196
},
{
"... | 1 | [
{
"lemma": "BINOMIAL_ALTERNATING",
"status": "ok"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "... | {
"lo": 1.71,
"mid": 5.04,
"hi": 8.38
} | |
6452bb | nt_count_coprime_and_v1_1978505735_6869 | Let $k_1$ be the maximum value of $xy$ over all ordered pairs $(x,y)$ of positive integers such that $x + y = 6$, and let $k_2 = 16$. Compute the number of positive integers $n \le 67425$ such that $\gcd(n, k_1) = 1$ and $\gcd(n, k_2) = 1$. | 22,475 | graphs = [
Graph(
let={
"_n": Const(6),
"upper": Const(67425),
"k1": MaxOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(Sum(Var("x"), Var("y")), Ref("_n")))), ... | NT | null | COUNT | sympy | B1 | [
"B1"
] | 5b950e | nt_count_coprime_and_v1 | null | 4 | 0 | [
"B1"
] | 1 | 6.486 | 2026-02-08T19:51:06.072386Z | {
"verified": true,
"answer": 22475,
"timestamp": "2026-02-08T19:51:12.558484Z"
} | 898369 | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 1,
"correct": {
"strict": false,
"boxed": false,
"relaxed": true
},
"usage": {
"prompt_tokens": 152,
"completion_tokens": 458
},
"timestamp": "2026-02-16T18:46:36.205Z",
"answer": 33722
},
{
"id": 11,... | 1 | [
{
"lemma": "B1",
"status": "ok"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
}
] | {
"lo": -8.26,
"mid": -5.01,
"hi": -1.76
} | ||
64450e | comb_factorial_compute_v1_717093673_933 | Let $T$ be the set of all integers $t$ such that $51 \leq t \leq 3294$ and there exist positive integers $a$ and $b$ with $1 \leq a \leq 94$, $1 \leq b \leq 87$, and $t = 21a + 15b + 15$. Let $n$ be the number of elements in $T$. Let $m = 1058$. Consider the set of all nonnegative integers $j$ such that $0 \leq j \leq ... | 42,273 | graphs = [
Graph(
let={
"_m": Const(1058),
"_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=94)), Geq(left=V... | ALG | COMB | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM/V8"
] | 654a7e | comb_factorial_compute_v1 | null | 7 | 0 | [
"LIN_FORM",
"V8"
] | 2 | 0.005 | 2026-02-08T15:45:41.451419Z | {
"verified": true,
"answer": 42273,
"timestamp": "2026-02-08T15:45:41.455933Z"
} | 0410d5 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 283,
"completion_tokens": 8693
},
"timestamp": "2026-02-24T18:27:05.512Z",
"answer": 42273
},
{
... | 1 | [
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "V8",
"status": "ok_later"
}
] | {
"lo": -2.4,
"mid": 1.57,
"hi": 5.75
} | ||
7e8e64 | nt_count_divisible_v1_784195855_3035 | Let $d$ be the smallest divisor of $71383$ that is at least $2$. Let $S$ be the set of all positive integers $n$ such that $n \leq 41616$ and $n$ is divisible by $d$. Compute the number of elements in $S$. | 3,201 | graphs = [
Graph(
let={
"upper": Const(41616),
"divisor": MinOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Const(2)), Divides(divisor=Var("d"), dividend=Const(71383))))),
"result": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n")... | NT | null | COUNT | sympy | MIN_PRIME_FACTOR | [
"MIN_PRIME_FACTOR"
] | bc3776 | nt_count_divisible_v1 | null | 3 | 0 | [
"MIN_PRIME_FACTOR"
] | 1 | 1.362 | 2026-02-08T06:11:46.116589Z | {
"verified": true,
"answer": 3201,
"timestamp": "2026-02-08T06:11:47.478117Z"
} | 732635 | 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": 715
},
"timestamp": "2026-02-12T20:59:09.234Z",
"answer": 3201
},
{
... | 1 | [
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "MIN_PRIME_FACTOR",
"status": "ok"
},
{
"lemma": "V1",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
}
] | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
95fc63_n | geo_count_lattice_triangle_v1_1218484723_2603 | A digital artist creates pixel art using a $25 \times 25$ grid. Each pixel at position $(a,b)$ has brightness level $10a^2 - 18ab + 25b^2$. The system only displays pixels with brightness at most the smallest prime factor of $6380651$. Let $C$ be the number of such visible pixels. The artist applies a transformation wi... | 4,680 | GEOM | null | COUNT | sympy | MIN_PRIME_FACTOR | [
"MIN_PRIME_FACTOR/QF_PSD_COUNT_LEQ",
"TELESCOPE"
] | 3dcccd | geo_count_lattice_triangle_v1 | null | 5 | null | [
"MIN_PRIME_FACTOR",
"QF_PSD_COUNT_LEQ",
"TELESCOPE"
] | 3 | 0.019 | 2026-02-25T04:21:38.248085Z | null | 810624 | 95fc63 | narrative | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 289,
"completion_tokens": 32768
},
"timestamp": "2026-03-30T18:46:04.637Z",
"answer": null
},
{
... | 1 | [
{
"lemma": "MIN_PRIME_FACTOR",
"status": "ok"
},
{
"lemma": "QF_PSD_COUNT_LEQ",
"status": "ok_later"
},
{
"lemma": "TELESCOPE",
"status": "ok"
}
] | {
"lo": 3.8,
"mid": 6.33,
"hi": 9.49
} | |
be6972 | diophantine_fbi2_min_v1_1470522791_1571 | Let $m=12$. Let $r$ be the number of integers $n$ with $1\le n\le 31$ and $\gcd(n,m)=1$.
Let $k=10$. Consider all ordered pairs $(x,y)$ of positive integers such that $xy=100$. Let $U$ be the minimum value of $x+y$ over all such pairs.
Consider all integers $d$ such that
\begin{itemize}
\item $d\ge p$, where $p$ is... | 52 | graphs = [
Graph(
let={
"_c": Const(2),
"_m": Const(12),
"_n": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Const(31)), Eq(GCD(a=Var("n"), b=Ref("_m")), Const(1))))),
"k": Const(10),
"upper": MinO... | NT | COMB | EXTREMUM | sympy | LIN_FORM | [
"C4/MAX_PRIME_BELOW",
"COPRIME_PAIRS",
"B3"
] | 0fd59e | diophantine_fbi2_min_v1 | bell_mod | 7 | 0 | [
"B3",
"C4",
"COPRIME_PAIRS",
"LIN_FORM",
"MAX_PRIME_BELOW"
] | 5 | 0.07 | 2026-02-08T13:45:00.305833Z | {
"verified": true,
"answer": 52,
"timestamp": "2026-02-08T13:45:00.375714Z"
} | 5ae6fc | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 317,
"completion_tokens": 1303
},
"timestamp": "2026-02-15T20:14:15.006Z",
"answer": 52
},
{
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "C4",
"status": "ok"
},
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemm... | {
"lo": -8.26,
"mid": -5.01,
"hi": -1.76
} | ||
6a69df | algebra_quadratic_discriminant_v1_784195855_5609 | Let $m$ be the maximum value of $xy$ over all pairs of positive integers $(x, y)$ such that $x + y = 30$. Let $c$ be the minimum value of $x + y$ over all pairs of positive integers $(x, y)$ such that $xy = m$.
Let $p$ be a positive integer such that there exists a positive integer $q$ with $pq = 54$, $\gcd(p, q) = 1... | 121 | graphs = [
Graph(
let={
"_m": MaxOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(Sum(Var("x"), Var("y")), Const(30)))), expr=Mul(Var("x"), Var("y")))),
"_n": Const(4),
... | NT | null | COMPUTE | sympy | COPRIME_PAIRS | [
"COPRIME_PAIRS",
"B1/B3"
] | 0209f3 | algebra_quadratic_discriminant_v1 | null | 6 | 0 | [
"B1",
"B3",
"COPRIME_PAIRS"
] | 3 | 0.013 | 2026-02-08T07:59:34.774034Z | {
"verified": true,
"answer": 121,
"timestamp": "2026-02-08T07:59:34.786903Z"
} | 37f7b7 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 188,
"completion_tokens": 1554
},
"timestamp": "2026-02-13T14:03:31.989Z",
"answer": 121
},
{
... | 1 | [
{
"lemma": "B1",
"status": "ok"
},
{
"lemma": "B3",
"status": "ok_later"
},
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
... | {
"lo": -7.01,
"mid": -4.68,
"hi": -2.15
} | ||
3044da | modular_sum_quadratic_residues_v1_601307018_8455 | Let $M$ be the minimum value of $25b^2 - 62ab + 41a^2$ over all ordered pairs $(a, b)$ of positive integers with $1 \le a, b \le 8$. Let $p$ be the minimum value of $|x - y|$ over all ordered pairs $(x, y)$ of positive integers such that $xy = 237348$. Compute $\frac{p(p - 1)}{M}$. | 28,308 | graphs = [
Graph(
let={
"_m": Const(2),
"_n": MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("a"), Var("b")]), condition=And(Geq(Var("a"), Const(1)), Leq(Var("a"), Const(8)), Geq(Var("b"), Const(1)), Leq(Var("b"), Const(8)))), expr=Sum(Mul(Const(25), Pow(Var("b"),... | NT | null | SUM | sympy | QF_PSD_MIN | [
"QF_PSD_MIN/B3_DIFF"
] | 166f76 | modular_sum_quadratic_residues_v1 | null | 5 | 0 | [
"B3_DIFF",
"QF_PSD_MIN"
] | 2 | 0.004 | 2026-03-10T08:56:30.890171Z | {
"verified": true,
"answer": 28308,
"timestamp": "2026-03-10T08:56:30.893836Z"
} | 43d8c7 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 211,
"completion_tokens": 3703
},
"timestamp": "2026-04-19T09:05:39.158Z",
"answer": 28308
},
{
... | 1 | [
{
"lemma": "B3_DIFF",
"status": "ok_later"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "QF_PSD_MIN",
"status": "ok"
},
{
"lemma": "V5",
"status": "no"
},
{
... | {
"lo": -5.34,
"mid": 1.1,
"hi": 7.53
} | ||
a57f67 | diophantine_fbi2_count_v1_1520064083_8360 | Let $k = 180$. Let $d$ be a positive integer satisfying the following conditions:
\begin{itemize}
\item $3 \leq d \leq 123$,
\item $d$ divides $k$,
\item $\frac{k}{d} \geq 6$,
\item $\frac{k}{d} \leq t_{\text{max}}$, where $t_{\text{max}}$ is the number of integers $t$ in the range $14 \leq t \leq 276$ for which there ... | 1 | graphs = [
Graph(
let={
"k": Const(180),
"result": CountOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Const(3)), Leq(Var("d"), Const(123)), Divides(divisor=Var("d"), dividend=Ref("k")), Geq(Div(Ref("k"), Var("d")), Const(6)), Leq(Div(Ref("k"), Var("d")), CountOve... | NT | COMB | COUNT | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | diophantine_fbi2_count_v1 | null | 6 | 0 | [
"LIN_FORM"
] | 1 | 0.008 | 2026-02-08T10:09:35.287871Z | {
"verified": true,
"answer": 1,
"timestamp": "2026-02-08T10:09:35.296205Z"
} | efc68e | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 1,
"correct": {
"strict": false,
"boxed": false,
"relaxed": true
},
"usage": {
"prompt_tokens": 223,
"completion_tokens": 3930
},
"timestamp": "2026-02-14T06:36:07.055Z",
"answer": 7
},
{
... | 0 | [
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
}
] | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
280286 | antilemma_k2_v1_1125832087_1134 | Let
$$
x = \sum_{k=1}^{304} \phi(k) \left\lfloor \frac{304}{k} \right\rfloor,
$$
where $\phi$ denotes Euler's totient function. Compute the remainder when $x^2 + 25x + 2028$ is divided by $55315$. | 40,003 | graphs = [
Graph(
let={
"x": Summation(var="k", start=Const(1), end=Const(304), expr=Mul(EulerPhi(n=Var("k")), Floor(Div(Const(304), Var("k"))))),
"Q": Mod(value=Sum(Pow(Ref("x"), Const(2)), Mul(Const(25), Ref("x")), Const(2028)), modulus=Const(55315)),
},
goal=Ref("Q... | NT | COMB | COMPUTE | sympy | K13 | [
"K2"
] | 6897ab | antilemma_k2_v1 | null | 5 | 0 | [
"K13",
"K2"
] | 2 | 0.001 | 2026-02-08T03:33:05.553867Z | {
"verified": true,
"answer": 40003,
"timestamp": "2026-02-08T03:33:05.555337Z"
} | 8961ab | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 184,
"completion_tokens": 6913
},
"timestamp": "2026-02-10T14:54:03.844Z",
"answer": 11398
},
{
... | 1 | [
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "K2",
"status": "ok"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
}
] | {
"lo": 1.71,
"mid": 5.04,
"hi": 8.38
} | ||
a53ec3 | nt_count_divisible_v1_124444284_6098 | Let $n = 10$. Let $D$ be the number of ordered pairs $(i,j)$ of positive integers such that $i + j = 19$, $1 \leq i \leq 18$, and $1 \leq j \leq 18$. Let $S$ be the set of all integers $n$ such that $1 \leq n \leq 58081$ and $n \equiv \sum_{k=0}^{10} (-1)^k \binom{10}{k} \pmod{D}$. Let $r$ be the number of elements in ... | 7,383 | graphs = [
Graph(
let={
"_n": Const(10),
"upper": Const(58081),
"divisor": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("i"), Var("j")]), condition=Eq(Sum(Var("i"), Var("j")), Const(19)), domain=CartesianProduct(left=IntegerRange(start=Const(1), end=Const(18)), r... | COMB | null | COUNT | sympy | BINOMIAL_ALTERNATING | [
"BINOMIAL_ALTERNATING",
"COUNT_SUM_EQUALS"
] | b9499e | nt_count_divisible_v1 | null | 6 | 0 | [
"BINOMIAL_ALTERNATING",
"COUNT_SUM_EQUALS"
] | 2 | 4.088 | 2026-02-08T08:07:49.300130Z | {
"verified": true,
"answer": 7383,
"timestamp": "2026-02-08T08:07:53.387756Z"
} | 99e883 | 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": 952
},
"timestamp": "2026-02-24T08:51:05.279Z",
"answer": 7383
},
{
"id... | 2 | [
{
"lemma": "BINOMIAL_ALTERNATING",
"status": "ok"
},
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "ok"
},
{
"lemma": "V7",... | {
"lo": -9.23,
"mid": -6.18,
"hi": -4.06
} | ||
4730ee | nt_min_coprime_above_v1_655260480_132 | Let $n = 17161$. Consider the set of all ordered pairs $(x,y)$ of positive integers such that $xy = n$. Let $s$ be the sum $x + y$ for each such pair. Define $m$ to be the minimum value of $s$ over all such pairs.
Now, let $S$ be the set of all integers $n$ satisfying $12321 < n \leq 12593$ such that $\gcd(n, m) = 1$.... | 25,811 | graphs = [
Graph(
let={
"_n": Const(17161),
"start": Const(12321),
"upper": Const(12593),
"modulus": MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y'))... | NT | null | EXTREMUM | sympy | B3 | [
"B3"
] | 0cd20d | nt_min_coprime_above_v1 | null | 5 | 0 | [
"B3"
] | 1 | 0.03 | 2026-02-08T15:14:02.244540Z | {
"verified": true,
"answer": 25811,
"timestamp": "2026-02-08T15:14:02.274501Z"
} | 5e672f | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 180,
"completion_tokens": 1905
},
"timestamp": "2026-02-16T02:48:57.817Z",
"answer": 25811
},
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
890c90 | alg_qf_psd_min_v1_1218484723_7420 | Let $Q$ be the minimum value of
$$\left|\{n : 1 \le n \le 49280,\ n \equiv \left\lfloor \tfrac{n}{2} \right\rfloor \pmod{11}\}\right| \cdot a \cdot b
+ \min\{x + y : x, y > 0,\ xy = 5017600\} \cdot b^{2}
+ 3640 \cdot a^{2}$$
over all ordered pairs $(a, b)$ of positive integers with $1 \le a \le 113$ and $1 \le b \le ... | 12,600 | graphs = [
Graph(
let={
"_m": Const(113),
"_n": Const(113),
"result": MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("a"), Var("b")]), condition=And(Geq(Var("a"), Const(1)), Leq(Var("a"), Ref("_n")), Geq(Var("b"), Const(1)), Leq(Var("b"), Ref("_m")))),... | NT | null | COMPUTE | sympy | L3C | [
"L3C",
"B3"
] | 8ca9f5 | alg_qf_psd_min_v1 | null | 7 | 0 | [
"B3",
"L3C"
] | 2 | 0.03 | 2026-02-25T08:52:17.716806Z | {
"verified": true,
"answer": 12600,
"timestamp": "2026-02-25T08:52:17.746699Z"
} | b9cf99 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 261,
"completion_tokens": 2293
},
"timestamp": "2026-03-30T04:27:17.377Z",
"answer": 12600
},
{
"... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "L3C",
"status": "ok"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma... | {
"lo": -3.33,
"mid": 1.03,
"hi": 5.26
} | ||
baf93f | alg_qf_psd_count_leq_v1_601307018_6438 | Let $Q$ be the number of ordered triples $(a, b, c)$ of positive integers with $1 \le a, b, c \le 11$ such that $$
136c^2 + \left|\left\{ (a_1, b_1) \in \mathbb{Z}^2 : 1 \le a_1, b_1 \le 30,\ 13a_1^2 - 2a_1b_1 + 2b_1^2 \le 1192 \right\}\right| \cdot bc + 152a^2 + 208ab + 360b^2 + 240ac \le 81968.
$$
Find $Q$. | 1,107 | graphs = [
Graph(
let={
"_n": Const(240),
"result": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("a"), Var("b"), Var("c")]), condition=And(Geq(Var("a"), Const(1)), Leq(Var("a"), Const(11)), Geq(Var("b"), Const(1)), Leq(Var("b"), Const(11)), Geq(Var("c"), Const(1)), Leq(Var("... | ALG | null | COUNT | sympy | QF_PSD_COUNT_LEQ | [
"QF_PSD_COUNT_LEQ"
] | 009d0f | alg_qf_psd_count_leq_v1 | null | 6 | 0 | [
"QF_PSD_COUNT_LEQ"
] | 1 | 0.398 | 2026-03-10T07:06:20.491826Z | {
"verified": true,
"answer": 1107,
"timestamp": "2026-03-10T07:06:20.889702Z"
} | a294be | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 267,
"completion_tokens": 25210
},
"timestamp": "2026-04-19T04:26:39.548Z",
"answer": 1107
},
{
... | 1 | [
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "QF_PSD_COUNT_LEQ",
"status": "ok"
}
] | {
"lo": -5.34,
"mid": 1.1,
"hi": 7.53
} | ||
42569e | modular_count_residue_v1_124444284_3992 | Let $m = 21$ and $r = 0$. Let $\text{result}$ be the number of positive integers $n$ such that $1 \le n \le 31817$ and $n \equiv r \pmod{m}$. Let $p$ be the largest prime number satisfying $2 \le p \le 11$. Define $Q$ to be the Bell number $B_k$, where $k$ is the remainder when $|\text{result}|$ is divided by $p$. Comp... | 4,140 | graphs = [
Graph(
let={
"upper": Const(31817),
"m": Const(21),
"r": Const(0),
"result": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Ref("upper")), Eq(Mod(value=Var("n"), modulus=Ref("m")), Ref("r"))))),
... | NT | COMB | COUNT | sympy | MAX_PRIME_BELOW | [
"MAX_PRIME_BELOW"
] | 88ea9c | modular_count_residue_v1 | bell_mod | 5 | 0 | [
"MAX_PRIME_BELOW"
] | 1 | 3.557 | 2026-02-08T05:42:20.011362Z | {
"verified": true,
"answer": 4140,
"timestamp": "2026-02-08T05:42:23.568063Z"
} | 8007a0 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 158,
"completion_tokens": 691
},
"timestamp": "2026-02-12T12:59:22.564Z",
"answer": 4140
},
{
... | 1 | [
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "n... | {
"lo": -5.55,
"mid": -3.01,
"hi": 0.32
} | ||
7acf58 | comb_count_surjections_v1_1742523217_3694 | Let $n$ be the number of ordered pairs $(i, j)$ of integers with $1 \leq i \leq 5$ and $1 \leq j \leq 5$ such that $i + j = 6$. Let $k = 4$. Compute $k! \cdot S(n, k)$, where $S(n, k)$ denotes the Stirling number of the second kind. | 240 | graphs = [
Graph(
let={
"_n": Const(6),
"n": 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(5)), right=IntegerRange(start=Const(1), end=Const... | COMB | null | COUNT | sympy | COMB1 | [
"COUNT_SUM_EQUALS"
] | 75ab0f | comb_count_surjections_v1 | null | 5 | 0 | [
"COMB1",
"COUNT_SUM_EQUALS"
] | 2 | 0.055 | 2026-02-08T06:03:01.930783Z | {
"verified": true,
"answer": 240,
"timestamp": "2026-02-08T06:03:01.985696Z"
} | 7ebe8e | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 200,
"completion_tokens": 726
},
"timestamp": "2026-02-24T05:11:57.193Z",
"answer": 240
},
{
"id"... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "ok"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8",
"status":... | {
"lo": -5.98,
"mid": -3.97,
"hi": -1.94
} | ||
fb2c3d | comb_count_surjections_v1_1978505735_3448 | Let $n = 6$. Let $P$ be the set of all ordered pairs $(i, j)$ of integers such that $1 \le i \le 5$, $1 \le j \le 5$, and $i + j = n$. Let $k$ be the number of elements in $P$. Define $\text{result} = k! \cdot S(n, k)$, where $S(n, k)$ is the Stirling number of the second kind. Compute $\text{result}$. | 1,800 | graphs = [
Graph(
let={
"_n": Const(6),
"n": Const(6),
"k": 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(5)), right=IntegerRang... | COMB | null | COUNT | sympy | COUNT_SUM_EQUALS | [
"COUNT_SUM_EQUALS"
] | 75ab0f | comb_count_surjections_v1 | null | 5 | 0 | [
"COUNT_SUM_EQUALS"
] | 1 | 0.016 | 2026-02-08T17:38:54.323606Z | {
"verified": true,
"answer": 1800,
"timestamp": "2026-02-08T17:38:54.339970Z"
} | 653b69 | 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": 604
},
"timestamp": "2026-02-18T06:08:55.314Z",
"answer": 1800
},
{
... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "ok"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8_SUM",
"status":... | {
"lo": -4.1,
"mid": -1.76,
"hi": 1.32
} | ||
103cf2 | nt_count_divisible_and_v1_655260480_1704 | Let $a = \sum_{k=0}^{4} (-1)^k \binom{4}{k}$ and $b = \sum_{k=0}^{3} (-1)^k \binom{3}{k}$. Determine the number of positive integers $n \le 31464$ such that $n \equiv a \pmod{9}$ and $n \equiv b \pmod{12}$. | 874 | graphs = [
Graph(
let={
"upper": Const(31464),
"d1": Const(9),
"d2": Const(12),
"result": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Ref("upper")), Eq(Mod(value=Var("n"), modulus=Ref("d1")), Summation(var="... | COMB | null | COUNT | sympy | BINOMIAL_ALTERNATING | [
"BINOMIAL_ALTERNATING"
] | c21569 | nt_count_divisible_and_v1 | null | 5 | 0 | [
"BINOMIAL_ALTERNATING"
] | 1 | 9.934 | 2026-02-08T16:18:05.833740Z | {
"verified": true,
"answer": 874,
"timestamp": "2026-02-08T16:18:15.767342Z"
} | 0a624f | 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": 543
},
"timestamp": "2026-02-24T20:37:13.933Z",
"answer": 874
},
{
"id... | 1 | [
{
"lemma": "BINOMIAL_ALTERNATING",
"status": "ok"
},
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
}
] | {
"lo": -5.65,
"mid": -3.17,
"hi": -0.81
} | ||
5883d9 | comb_count_partitions_v1_784195855_372 | Let $m = 92$. Define $n$ to be the largest prime number less than or equal to $m$. Let $k$ be the number of positive integers less than or equal to $n$ whose digit sum is even. Compute the number of integer partitions of $k$. | 75,175 | graphs = [
Graph(
let={
"_m": Const(92),
"_n": MaxOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(2)), Leq(Var("n"), Ref("_m")), IsPrime(Var("n"))))),
"n": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var(... | NT | COMB | COUNT | sympy | MAX_PRIME_BELOW | [
"MAX_PRIME_BELOW/L3B"
] | 5f10c3 | comb_count_partitions_v1 | null | 5 | 0 | [
"L3B",
"MAX_PRIME_BELOW"
] | 2 | 0.003 | 2026-02-08T03:07:24.365611Z | {
"verified": true,
"answer": 75175,
"timestamp": "2026-02-08T03:07:24.368478Z"
} | 4e8be1 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 169,
"completion_tokens": 1577
},
"timestamp": "2026-02-10T16:13:59.324Z",
"answer": 75175
},
{
... | 1 | [
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "L3B",
"status": "ok_later"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "V3",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
},
{
"l... | {
"lo": -3.42,
"mid": 1.86,
"hi": 7.55
} | ||
0dc083 | nt_count_divisors_in_range_v1_458359167_1861 | Let $n = 45360$. Define $b$ to be the number of integers $t$ with $12 \leq t \leq 1552$ such that there exist positive integers $a$ and $b'$ satisfying $1 \leq a \leq 81$, $1 \leq b' \leq 197$, and $t = 7a + 5b'$. Let $a = 2$. Determine the value of the number of positive divisors $d$ of $n$ such that $a \leq d \leq b$... | 79 | graphs = [
Graph(
let={
"n": Const(45360),
"a": Const(2),
"b": 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=Co... | NT | null | COUNT | sympy | B3 | [
"LIN_FORM"
] | 7b2633 | nt_count_divisors_in_range_v1 | null | 6 | 0 | [
"B3",
"LIN_FORM"
] | 2 | 0.115 | 2026-02-08T04:54:40.638502Z | {
"verified": true,
"answer": 79,
"timestamp": "2026-02-08T04:54:40.753557Z"
} | cbcabf | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 234,
"completion_tokens": 5707
},
"timestamp": "2026-02-11T22:26:44.750Z",
"answer": 79
},
{
"id... | 1 | [
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "V1",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
}
] | {
"lo": -3.42,
"mid": 1.86,
"hi": 7.55
} | ||
5bc3bc | algebra_poly_eval_v1_865884756_3899 | Let $n = 6$ and $k = 6$. Let $S$ be the set of all prime numbers $p$ such that $2 \leq p \leq \sum_{k_1=1}^{2} \phi(k_1) \left\lfloor \frac{2}{k_1} \right\rfloor$, where $\phi$ denotes Euler's totient function. Let $m$ be the largest element of $S$. Compute the value of $44121 \cdot (6 \cdot 6^m - 7 \cdot 6^2 - 2 \cdot... | 41,164 | graphs = [
Graph(
let={
"_n": Const(6),
"k": Const(6),
"result": Sum(Mul(Ref("_n"), Pow(Ref("k"), MaxOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(2)), Leq(Var("n"), Summation(var="k1", start=Const(1), end=Const(2), expr=Mul(EulerPhi(n=Var("k1")... | NT | null | COMPUTE | sympy | K2 | [
"K2/MAX_PRIME_BELOW"
] | f058da | algebra_poly_eval_v1 | null | 4 | 0 | [
"K2",
"MAX_PRIME_BELOW"
] | 2 | 0.006 | 2026-02-08T17:39:34.203331Z | {
"verified": true,
"answer": 41164,
"timestamp": "2026-02-08T17:39:34.208884Z"
} | 7e9bc8 | 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": 1024
},
"timestamp": "2026-02-18T05:30:13.058Z",
"answer": 41164
},
... | 1 | [
{
"lemma": "K2",
"status": "ok"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok_later"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "V1",
"status"... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
30d833 | modular_count_residue_v1_1918700295_1440 | Let $n$ be a positive integer such that $1 \leq n \leq 40804$ and $n \equiv 16 \pmod{20}$. Let $R$ denote the number of such integers $n$. Define $$ Q = \left( \sum_{k=1}^{8} \phi(k) \left\lfloor \frac{8}{k} \right\rfloor \right) - R. $$ Find the remainder when $Q$ is divided by $79189$. | 77,185 | graphs = [
Graph(
let={
"_n": Const(8),
"upper": Const(40804),
"m": Const(20),
"r": Const(16),
"result": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Ref("upper")), Eq(Mod(value=Var("n"), modulus=... | NT | null | COUNT | sympy | K2 | [
"K2"
] | 9468ae | modular_count_residue_v1 | negation_mod | 5 | 0 | [
"K2"
] | 1 | 1.605 | 2026-02-08T05:50:22.723178Z | {
"verified": true,
"answer": 77185,
"timestamp": "2026-02-08T05:50:24.327943Z"
} | f76e09 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 150,
"completion_tokens": 1178
},
"timestamp": "2026-02-12T15:17:04.619Z",
"answer": 77185
},
... | 1 | [
{
"lemma": "K2",
"status": "ok"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "V3",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
}
] | {
"lo": -5.55,
"mid": -3.01,
"hi": 0.32
} | ||
5f9ae6 | nt_sum_divisors_mod_v1_1978505735_7678 | Let $S$ be the set of all integers $t$ such that there exist integers $a$ and $b$ satisfying:
- $1 \leq a \leq 24$,
- $1 \leq b \leq 1245$,
- $7 \leq t \leq 5052$, and
- $t = 3a + 4b$.
Let $n = |S|$, the number of elements in $S$. Let $\sigma$ be the sum of all positive divisors of $n$. Let $M = 11701$, and let $r$ be... | 7,643 | 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=24)), Geq(left=Var(name='b'), right=Const(value=... | NT | null | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | nt_sum_divisors_mod_v1 | null | 4 | 0 | [
"LIN_FORM"
] | 1 | 0.005 | 2026-02-08T20:23:07.225306Z | {
"verified": true,
"answer": 7643,
"timestamp": "2026-02-08T20:23:07.230031Z"
} | b5fb53 | 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": 7332
},
"timestamp": "2026-02-19T00:29:28.218Z",
"answer": 7643
},
{... | 1 | [
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "V1",
"status": "no"
},
{
"lemma": "VAL_SUM_EQ",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
8eb5b4 | comb_sum_binomial_row_v1_717093673_3700 | Let $s_k = \min\{d \in \mathbb{Z} \mid d \geq 2 \text{ and } d \text{ divides } 6125\}$ for each $k$. Define $n = \sum_{k=1}^{5} \phi(k) \cdot \left\lfloor \frac{s_k}{k} \right\rfloor$, where $\phi$ denotes Euler's totient function. Let $r = 2^n$. Compute the remainder when $40291 \cdot r$ is divided by $51115$. Find t... | 6,153 | graphs = [
Graph(
let={
"_n": Const(2),
"n": Summation(var="k", start=Const(1), end=Const(5), expr=Mul(EulerPhi(n=Var("k")), Floor(Div(MinOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Const(2)), Divides(divisor=Var("d"), dividend=Const(6125))))), Var("k"))))),
... | NT | null | SUM | sympy | MIN_PRIME_FACTOR | [
"MIN_PRIME_FACTOR/K2"
] | 352a97 | comb_sum_binomial_row_v1 | null | 6 | 0 | [
"K2",
"MIN_PRIME_FACTOR"
] | 2 | 0.005 | 2026-02-08T17:46:20.896436Z | {
"verified": true,
"answer": 6153,
"timestamp": "2026-02-08T17:46:20.901648Z"
} | 65b557 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 168,
"completion_tokens": 2542
},
"timestamp": "2026-02-18T07:18:38.000Z",
"answer": 6153
},
{... | 1 | [
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "K2",
"status": "ok_later"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "MIN_PRIME_FACTOR",
"status": "ok"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
78a940 | comb_bell_compute_v1_1248542787_124 | Let $ n $ be the number of ordered pairs $ (i, j) $ where $ i $ is a positive integer with $ 1 \leq i \leq 2 $ and $ j $ is a positive integer with $ 1 \leq j \leq 4 $. Let $ B_n $ denote the $ n $-th Bell number, which counts the number of partitions of a set of $ n $ elements. Compute the remainder when $ 68442 \cdot... | 27,227 | graphs = [
Graph(
let={
"_n": Const(76553),
"n": CountOverSet(set=CartesianProduct(left=IntegerRange(start=Const(1), end=Const(2)), right=IntegerRange(start=Const(1), end=Const(4)))),
"result": Bell(Ref("n")),
"Q": Mod(value=Mul(Const(68442), Ref("result")), m... | COMB | null | COMPUTE | sympy | COUNT_CARTESIAN | [
"COUNT_CARTESIAN"
] | 409d7d | comb_bell_compute_v1 | null | 3 | 0 | [
"COUNT_CARTESIAN"
] | 1 | 0.001 | 2026-02-08T02:57:55.528490Z | {
"verified": true,
"answer": 27227,
"timestamp": "2026-02-08T02:57:55.529231Z"
} | 654777 | 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": 1386
},
"timestamp": "2026-02-09T00:28:11.311Z",
"answer": 27227
},
{
"... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "ok"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
}
] | {
"lo": -0.94,
"mid": 0.82,
"hi": 2.34
} | ||
116460 | nt_count_digit_sum_v1_349078426_1803 | Let $n = 154$. Define $s$ to be the number of positive integers $m$ such that $1 \leq m \leq \sum_{d \mid n} \phi(d)$ and $13$ divides the $m$-th Fibonacci number.
Let $N$ be the number of positive integers $n$ such that $1 \leq n \leq 99999$ and the sum of the decimal digits of $n$ is equal to $s$.
Compute the value... | 6,000 | graphs = [
Graph(
let={
"_n": Const(154),
"upper": Const(99999),
"target_sum": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), SumOverDivisors(n=Ref(name='_n'), var='d', expr=EulerPhi(n=Var(name='d')))), Divides(divisor=Con... | NT | null | COUNT | sympy | K3 | [
"K3/COUNT_FIB_DIVISIBLE"
] | b1cab1 | nt_count_digit_sum_v1 | null | 6 | 0 | [
"COUNT_FIB_DIVISIBLE",
"K3"
] | 2 | 6.412 | 2026-02-08T13:56:26.485297Z | {
"verified": true,
"answer": 6000,
"timestamp": "2026-02-08T13:56:32.897272Z"
} | 31f17a | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 152,
"completion_tokens": 2241
},
"timestamp": "2026-02-15T22:06:32.358Z",
"answer": 6000
},
{... | 1 | [
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "ok_later"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K3",
"status": "ok"
},
{
"lemma": "MOD_FACTORIAL"... | {
"lo": -5.49,
"mid": 0.22,
"hi": 6.51
} | ||
3d40c8 | lin_form_endings_v1_1918700295_994 | Let $a = 63$ and $b = 18$. Let $\ell = \operatorname{lcm}(a,b)$. Define $s = 1 \cdot \ell + a + b$. Compute the remainder when $13320 \cdot s$ is divided by 75025. | 56,340 | graphs = [
Graph(
let={
"a_coeff": Const(63),
"b_coeff": Const(18),
"k_val": Const(1),
"lcm_node": LCM(a=Ref("a_coeff"), b=Ref("b_coeff")),
"_inner_result": Sum(Mul(Ref("k_val"), Ref("lcm_node")), Ref("a_coeff"), Ref("b_coeff")),
"_scal... | COMB | NT | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | lin_form_endings_v1 | null | 2 | null | [
"LIN_FORM"
] | 1 | 0.001 | 2026-02-08T05:26:15.683054Z | {
"verified": true,
"answer": 56340,
"timestamp": "2026-02-08T05:26:15.683637Z"
} | 472f1b | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 106,
"completion_tokens": 1794
},
"timestamp": "2026-02-12T09:58:32.701Z",
"answer": 56340
},
... | 1 | [
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "V8",
"status": "no"
},
{
"lemma": "V8_SUM",
"st... | {
"lo": -3.51,
"mid": 1.33,
"hi": 6.56
} | ||
8b35ee | nt_count_with_divisor_count_v1_655260480_6125 | Compute the number of positive integers $n$ not exceeding $26896$ that have exactly $6$ positive divisors. | 1,793 | graphs = [
Graph(
let={
"upper": Const(26896),
"div_count": Const(6),
"result": CountOverSet(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("r... | NT | null | COUNT | sympy | MIN_PRIME_FACTOR | [
"MIN_PRIME_FACTOR",
"ONE_PHI_1"
] | fb15c3 | nt_count_with_divisor_count_v1 | null | 4 | 0 | [
"MIN_PRIME_FACTOR",
"ONE_PHI_1"
] | 2 | 7.947 | 2026-02-08T18:50:10.229896Z | {
"verified": true,
"answer": 1793,
"timestamp": "2026-02-08T18:50:18.176900Z"
} | 1ace9c | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 71,
"completion_tokens": 4936
},
"timestamp": "2026-02-18T20:02:36.559Z",
"answer": 1793
},
{
... | 1 | [
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "MIN_PRIME_FACTOR",
"status": "ok"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "ONE_PHI_1",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
555196 | nt_sum_over_divisible_v1_677425708_3380 | Let $N = 94450$ and $U = 64261$. Define $D$ to be the number of ordered pairs $(a, b)$ such that $1 \leq a \leq 7$ and $1 \leq b \leq 9$. Let $S$ be the set of all positive integers $n$ such that $1 \leq n \leq U$ and $n$ is divisible by $D$. Compute the sum of all elements in $S$. Let $\text{result}$ denote this sum. ... | 1,930 | graphs = [
Graph(
let={
"_n": Const(94450),
"upper": Const(64261),
"divisor": CountOverSet(set=CartesianProduct(left=IntegerRange(start=Const(1), end=Const(7)), right=IntegerRange(start=Const(1), end=Const(9)))),
"result": SumOverSet(set=SolutionsSet(var=Var("... | NT | null | SUM | sympy | COUNT_CARTESIAN | [
"COUNT_CARTESIAN"
] | 409d7d | nt_sum_over_divisible_v1 | null | 3 | 0 | [
"COUNT_CARTESIAN"
] | 1 | 2.031 | 2026-02-08T05:40:54.351500Z | {
"verified": true,
"answer": 1930,
"timestamp": "2026-02-08T05:40:56.382872Z"
} | 3ef62c | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 177,
"completion_tokens": 2264
},
"timestamp": "2026-02-12T12:23:01.837Z",
"answer": 1930
},
{... | 1 | [
{
"lemma": "COUNT_CARTESIAN",
"status": "ok"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",... | {
"lo": -3.51,
"mid": 1.33,
"hi": 6.56
} | ||
c57408 | nt_count_digit_sum_v1_1520064083_8960 | Let $S$ be the set of all ordered pairs $(x,y)$ of positive integers such that $xy = 144$. Define $T$ to be the set consisting of the sum $x + y$ for each pair $(x,y) \in S$. Let $s$ be the minimum value in $T$. Compute the number of positive integers $n$, with $1 \le n \le 99999$, such that the sum of the digits of $n... | 37,677 | graphs = [
Graph(
let={
"_n": Const(44121),
"upper": Const(99999),
"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")), Co... | NT | null | COUNT | sympy | B3 | [
"B3"
] | 0cd20d | nt_count_digit_sum_v1 | null | 4 | 0 | [
"B3"
] | 1 | 3.999 | 2026-02-08T10:26:56.583917Z | {
"verified": true,
"answer": 37677,
"timestamp": "2026-02-08T10:27:00.583125Z"
} | acbcfa | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 176,
"completion_tokens": 1992
},
"timestamp": "2026-02-14T07:27:35.102Z",
"answer": 37677
},
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
}
] | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
7d9dc2 | diophantine_fbi2_min_v1_349078426_503 | Let $n = 44121$ and $k = 22$. Define $\text{upper}$ to be the sum of all real solutions $x$ to the equation $x^2 - 32x + 207 = 0$. Let $S$ be the set of all integers $d$ such that $2 \leq d \leq \text{upper}$, $d$ divides $k$, and $\frac{k}{d} \geq 2$. Compute the minimum value of $S$, and let $Q = n$ multiplied by thi... | 88,242 | graphs = [
Graph(
let={
"_n": Const(44121),
"k": Const(22),
"upper": SumOverSet(set=SolutionsSet(var=Var("x"), condition=Eq(Sum(Pow(Var("x"), Const(2)), Mul(Const(-32), Var("x")), Const(207)), Const(0)))),
"result": MinOverSet(set=SolutionsSet(var=Var("d"), co... | NT | null | EXTREMUM | sympy | VIETA_SUM | [
"VIETA_SUM"
] | b33a7a | diophantine_fbi2_min_v1 | null | 3 | 0 | [
"VIETA_SUM"
] | 1 | 0.008 | 2026-02-08T13:06:11.626794Z | {
"verified": true,
"answer": 88242,
"timestamp": "2026-02-08T13:06:11.635080Z"
} | e6adfc | 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": 604
},
"timestamp": "2026-02-15T09:27:01.057Z",
"answer": 88242
},
{... | 1 | [
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "V1",
"status": "no"
},
{
"lemma": "VIETA_SUM",
"status": "ok"
... | {
"lo": -9.12,
"mid": -6.02,
"hi": -3.62
} | ||
1b99c2_l | antilemma_sum_equals_v1_124444284_1420 | Let $S$ be the set of all ordered pairs of positive integers $(i, j)$ such that $i + j = 47$, $1 \leq i \leq 45$, and $1 \leq j \leq 45$. Determine the number of elements in $S$. | 45 | COMB | GEOM | COMPUTE | sympy | COUNT_SUM_EQUALS | [
"COUNT_SUM_EQUALS"
] | 75ab0f | antilemma_sum_equals_v1 | null | 2 | 0 | [
"COUNT_SUM_EQUALS"
] | 1 | 0.041 | 2026-02-08T03:52:39.292575Z | {
"verified": false,
"answer": 44,
"timestamp": "2026-02-08T03:52:39.333215Z"
} | 2c8e0b | 1b99c2 | 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": 173,
"completion_tokens": 432
},
"timestamp": "2026-02-10T16:14:24.157Z",
"answer": 44
},
{
"id":... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "ok"
},
{
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"status": "no"
},
{
"lemma": "V8",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
}
] | {
"lo": -4.92,
"mid": -2.9,
"hi": -0.7
} | |
8f4775 | diophantine_sum_product_min_v1_153355830_285 | Let $n = 1624$ and $S = 86$. Let $P$ be the largest positive divisor $d$ of $2658488$ such that $1 \leq d \leq n$. Determine the value of $Q$, where $Q$ is the remainder when $34323 \cdot x$ is divided by $64538$, and $x$ is the smallest positive integer such that $1 \leq x \leq 85$ and $x(S - x) = P$. | 57,512 | graphs = [
Graph(
let={
"_n": Const(1624),
"S": Const(86),
"P": MaxOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Const(1)), Leq(Var("d"), Ref("_n")), Divides(divisor=Var("d"), dividend=Const(2658488))))),
"result": MinOverSet(set=Solutions... | NT | null | EXTREMUM | sympy | MAX_DIVISOR | [
"MAX_DIVISOR"
] | 51757e | diophantine_sum_product_min_v1 | null | 6 | 0 | [
"MAX_DIVISOR"
] | 1 | 0.011 | 2026-02-08T03:00:20.782920Z | {
"verified": true,
"answer": 57512,
"timestamp": "2026-02-08T03:00:20.793655Z"
} | be4271 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 219,
"completion_tokens": 1821
},
"timestamp": "2026-02-10T12:31:09.513Z",
"answer": 57512
},
{
... | 1 | [
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "MAX_DIVISOR",
"status": "ok"
},
{
"lemma": "MAX_VAL",
"status": "no"
}
] | {
"lo": -3.45,
"mid": 1.18,
"hi": 5.72
} | ||
86d05d | comb_binomial_compute_v1_2051736721_4795 | Let $n$ be the number of ordered pairs $(i, j)$ such that $1 \leq i \leq 3$ and $1 \leq j \leq 4$. Let $k$ be the minimum value of $x + y$ over all ordered pairs $(x, y)$ of positive integers such that $xy = 9$. Compute $\binom{n}{k}$. | 924 | graphs = [
Graph(
let={
"_n": Const(9),
"n": CountOverSet(set=CartesianProduct(left=IntegerRange(start=Const(1), end=Const(3)), right=IntegerRange(start=Const(1), end=Const(4)))),
"k": MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), co... | ALG | COMB | COMPUTE | sympy | COUNT_CARTESIAN | [
"COUNT_CARTESIAN",
"B3"
] | 0ad34f | comb_binomial_compute_v1 | null | 3 | 0 | [
"B3",
"COUNT_CARTESIAN"
] | 2 | 0.191 | 2026-02-08T18:09:48.137709Z | {
"verified": true,
"answer": 924,
"timestamp": "2026-02-08T18:09:48.328790Z"
} | fd58d4 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 126,
"completion_tokens": 852
},
"timestamp": "2026-02-24T23:29:17.918Z",
"answer": 924
},
{
... | 2 | [
{
"lemma": "B3",
"status": "ok"
},
{
"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": -10,
"mid": -7.4,
"hi": -4.8
} | ||
11c16e_l | comb_factorial_compute_v1_1520064083_4417 | Let $m = 256$. Define $c$ to be the number of positive integers $k$ such that $1 \leq k \leq 256256$ and $m$ divides $k$. Let $n$ be the smallest integer greater than or equal to 2 that divides $c$. Compute $n!$. | 2 | NT | null | COMPUTE | sympy | C2 | [
"C2/MIN_PRIME_FACTOR"
] | 59c94d | comb_factorial_compute_v1 | null | 4 | 0 | [
"C2",
"MIN_PRIME_FACTOR"
] | 2 | 0.002 | 2026-02-08T06:15:48.358925Z | {
"verified": false,
"answer": 5040,
"timestamp": "2026-02-08T06:15:48.360794Z"
} | dc8f01 | 11c16e | legacy_text | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 168,
"completion_tokens": 373
},
"timestamp": "2026-02-19T03:14:16.095Z",
"answer": 2
},
{
"id": 11,
... | 1 | [
{
"lemma": "C2",
"status": "ok"
},
{
"lemma": "COUNT_COPRIME_GRID",
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},
{
"lemma": "K18",
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},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "MIN_PRIME_FACTOR",
"status": "ok_later"
},
{
"lemma": "V5",
"status": ... | {
"lo": -5.55,
"mid": -3.01,
"hi": 0.34
} | |
90b0a7 | antilemma_k2_v1_784195855_6355 | Let $m = 552$. Consider the quadratic equation $x^2 - 47x + m = 0$. Let $n$ be the sum of all (not necessarily distinct) integer solutions to this equation.
Now compute the sum
$$
\sum_{k=1}^{n} \phi(k) \left\lfloor \frac{47}{k} \right\rfloor,
$$
where $\phi$ denotes Euler's totient function.
Let $s$ be the value of ... | 285 | graphs = [
Graph(
let={
"_m": Const(552),
"_n": SumOverSet(set=SolutionsSet(var=Var("x"), condition=Eq(Sum(Pow(Var("x"), Const(2)), Mul(Const(-47), Var("x")), Ref("_m")), Const(0)))),
"x": Summation(var="k", start=Const(1), end=Ref("_n"), expr=Mul(EulerPhi(n=Var("k")), Fl... | NT | COMB | COMPUTE | sympy | K13 | [
"VIETA_SUM/K2",
"K2"
] | 6be084 | antilemma_k2_v1 | null | 6 | 0 | [
"K13",
"K2",
"VIETA_SUM"
] | 3 | 0.007 | 2026-02-08T08:35:46.559660Z | {
"verified": true,
"answer": 285,
"timestamp": "2026-02-08T08:35:46.566540Z"
} | 359cd6 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 177,
"completion_tokens": 2252
},
"timestamp": "2026-02-13T20:03:02.991Z",
"answer": 285
},
{
... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K2",
"status": "ok"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "VIETA... | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
7e65a6 | nt_sum_over_divisible_v1_1248542787_367 | Let $n = 98332$ and $d = 148$. Define $S$ to be the set of all positive integers $n'$ such that $1 \leq n' \leq 88209$ and $n'$ is divisible by $d$. Let $s$ be the sum of all elements in $S$.\\
Let $T$ be the set of all ordered pairs $(i, j)$ of positive integers with $1 \leq i \leq 102$ and $1 \leq j \leq 118$ such t... | 3,144 | graphs = [
Graph(
let={
"_n": Const(98332),
"upper": Const(88209),
"divisor": Const(148),
"result": SumOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Ref("upper")), Eq(Mod(value=Var("n"), modulus=Ref("divisor")), Co... | NT | null | SUM | sympy | COUNT_COPRIME_GRID | [
"COUNT_COPRIME_GRID"
] | 53d469 | nt_sum_over_divisible_v1 | affine_mod | 5 | 0 | [
"COUNT_COPRIME_GRID"
] | 1 | 2.814 | 2026-02-08T03:05:01.980473Z | {
"verified": true,
"answer": 3144,
"timestamp": "2026-02-08T03:05:04.794671Z"
} | 37d109 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 273,
"completion_tokens": 24926
},
"timestamp": "2026-02-23T16:21:23.911Z",
"answer": 3144
},
{
... | 1 | [
{
"lemma": "COUNT_COPRIME_GRID",
"status": "ok"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "V1",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
},
{
"lemma": "VAL_SUM_EQ",
"status": "no"
}
] | {
"lo": 1.3,
"mid": 3.64,
"hi": 5.81
} | ||
a03a91 | antilemma_cartesian_v1_153355830_2312 | Let $A$ be the set of all ordered pairs $(i,j)$ such that $1 \le i \le 11$, $1 \le j \le 12$, and $i + j = 13$. Let $m$ be the number of elements in $A$. Let $x$ be the number of ordered pairs $(a,b)$ such that $1 \le a \le 33$ and $1 \le b \le 40$. Compute the Bell number $B_r$, where $r$ is the remainder when $|x|$ i... | 1 | graphs = [
Graph(
let={
"_n": Const(13),
"x": CountOverSet(set=CartesianProduct(left=IntegerRange(start=Const(1), end=Const(33)), right=IntegerRange(start=Const(1), end=Const(40)))),
"Q": Bell(Mod(value=Abs(arg=Ref(name='x')), modulus=CountOverSet(set=SolutionsSet(var=Tup... | COMB | GEOM | COMPUTE | sympy | COUNT_SUM_EQUALS | [
"COUNT_SUM_EQUALS",
"COUNT_CARTESIAN"
] | fe8f6f | antilemma_cartesian_v1 | bell_mod | 5 | 0 | [
"COUNT_CARTESIAN",
"COUNT_SUM_EQUALS"
] | 2 | 0.01 | 2026-02-08T07:03:02.090945Z | {
"verified": true,
"answer": 1,
"timestamp": "2026-02-08T07:03:02.101075Z"
} | ee0950 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 233,
"completion_tokens": 592
},
"timestamp": "2026-02-24T07:31:32.582Z",
"answer": 1
},
{
"id": ... | 2 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "ok"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "ok"
},
{
"lemma": "V8",
... | {
"lo": -10,
"mid": -7.79,
"hi": -5.57
} | ||
ac80bf | alg_qf_psd_min_v1_1218484723_1771 | Let $Q$ be the minimum value of
$$41615a^{2} + 7175b^{2} -63140ac + 58835c^{2} + 31570bc -17220ab$$
over all ordered triples $(a, b, c)$ of positive integers with $1 \le b, c \le 29$ and $1 \le a \le N$, where $N$ is the number of ordered pairs $(a_1, b_1)$ with $1 \le a_1, b_1 \le 30$ satisfying
$$12a_1^{2}b_1^{2} + ... | 58,835 | graphs = [
Graph(
let={
"_n": Const(4),
"result": MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("a"), Var("b"), Var("c")]), condition=And(Geq(Var("a"), Const(1)), Leq(Var("a"), CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("a1"), Var("b1")]), condition=An... | ALG | null | COMPUTE | sympy | POLY4_COUNT | [
"POLY4_COUNT"
] | 861d91 | alg_qf_psd_min_v1 | null | 6 | 0 | [
"POLY4_COUNT"
] | 1 | 0.068 | 2026-02-25T03:26:14.210815Z | {
"verified": true,
"answer": 58835,
"timestamp": "2026-02-25T03:26:14.278968Z"
} | 4eb4ba | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 300,
"completion_tokens": 8479
},
"timestamp": "2026-03-29T01:17:19.907Z",
"answer": 58835
},
{
"... | 1 | [
{
"lemma": "POLY4_COUNT",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
}
] | {
"lo": 3.14,
"mid": 5.37,
"hi": 7.61
} | ||
d38579 | nt_min_phi_inverse_v1_48377204_68 | Let $k$ be the number of positive integers $j$ such that $1 \le j \le 22$ and $j^3 \le 10648$. Compute the smallest positive integer $n$ such that $1 \le n \le 50$ and $\phi(n) = k$. | 23 | graphs = [
Graph(
let={
"upper": Const(50),
"k": CountOverSet(set=SolutionsSet(var=Var("j"), condition=And(Geq(Var("j"), Const(1)), Leq(Var("j"), Const(22)), Leq(Pow(Var("j"), Const(3)), Const(10648))), domain='positive_integers')),
"result": MinOverSet(set=SolutionsSet(v... | NT | null | EXTREMUM | sympy | B3 | [
"C3"
] | 8a214c | nt_min_phi_inverse_v1 | null | 6 | 0 | [
"B3",
"C3"
] | 2 | 0.037 | 2026-02-08T15:12:15.545784Z | {
"verified": true,
"answer": 23,
"timestamp": "2026-02-08T15:12:15.582977Z"
} | 149f27 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 111,
"completion_tokens": 2385
},
"timestamp": "2026-02-16T01:50:01.279Z",
"answer": 23
},
{
... | 1 | [
{
"lemma": "C3",
"status": "ok"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "V1",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
b9e44a | alg_poly4_sum_v1_1218484723_2759 | Let $S_1$ be the number of pairs $(a1, b1)$ with $1 \le a1, b1 \le 25$ such that $2b1^2 - 2a1b1 + 13a1^2 \le 900$. Let $S_2$ be the number of pairs $(a2, b2)$ with $1 \le a2, b2 \le 40$ such that $16b2^2 - 8a2b2 + 17a2^2 \le 23201$. Compute the remainder when $$\sum_{\substack{1 \le a \le 146 \\ 1 \le b \le S_1}} \left... | 4,641 | graphs = [
Graph(
let={
"_m": Const(23201),
"_n": Const(17),
"result": Mod(value=SumOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("a"), Var("b")]), condition=And(Geq(Var("a"), Const(1)), Leq(Var("a"), Const(146)), Geq(Var("b"), Const(1)), Leq(Var("b"), C... | ALG | null | COMPUTE | sympy | POLY_ORBIT_HENSEL | [
"QF_PSD_COUNT_LEQ"
] | 009d0f | alg_poly4_sum_v1 | null | 6 | 0 | [
"POLY_ORBIT_HENSEL",
"QF_PSD_COUNT_LEQ"
] | 2 | 0.53 | 2026-02-25T04:27:46.287343Z | {
"verified": true,
"answer": 4641,
"timestamp": "2026-02-25T04:27:46.816952Z"
} | 7420e9 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 315,
"completion_tokens": 10475
},
"timestamp": "2026-03-29T06:28:00.311Z",
"answer": 59884
},
{
... | 1 | [
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "QF_PSD_COUNT_LEQ",
"status": "ok"
}
] | {
"lo": 3.81,
"mid": 6.33,
"hi": 9.49
} | ||
c6df0b | comb_factorial_compute_v1_1820931509_427 | Let $m = 7$. Define $n$ to be the sum of $\phi(d)$ over all positive divisors $d$ of $m$, where $\phi$ denotes Euler's totient function. Then define $n'$ to be the sum of $\phi(d)$ over all positive divisors $d$ of $n$. Compute $n'!$ (the factorial of $n'$). | 5,040 | graphs = [
Graph(
let={
"_m": Const(7),
"_n": SumOverDivisors(n=Ref(name='_m'), var='d', expr=EulerPhi(n=Var(name='d'))),
"n": SumOverDivisors(n=Ref(name='_n'), var='d', expr=EulerPhi(n=Var(name='d'))),
"result": Factorial(Ref("n")),
},
goal=Re... | NT | null | COMPUTE | sympy | K3 | [
"K3/K3"
] | 4ddc06 | comb_factorial_compute_v1 | null | 3 | 0 | [
"K3"
] | 1 | 0.001 | 2026-02-08T11:35:31.497993Z | {
"verified": true,
"answer": 5040,
"timestamp": "2026-02-08T11:35:31.499195Z"
} | ab3380 | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 143,
"completion_tokens": 381
},
"timestamp": "2026-02-16T03:01:44.804Z",
"answer": 5040
},
{
"id": 11,
... | 2 | [
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "K3",
"status": "ok"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
}
] | {
"lo": -10,
"mid": -7.71,
"hi": -5.43
} | ||
4388a2 | alg_poly4_count_v1_601307018_1905 | Let $T$ be the number of ordered pairs $(a_1, b_1)$ of positive integers with $1 \le a_1, b_1 \le 30$ such that $10a_1^2 - 18a_1b_1 + 25b_1^2 \le d_{\min}$, where $d_{\min}$ is the smallest divisor of $67302907753$ that is at least $2$. Find the number of ordered pairs $(a, b)$ of positive integers with $1 \le a \le 32... | 326 | graphs = [
Graph(
let={
"_m": Const(41200),
"_n": Const(41200),
"result": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("a"), Var("b")]), condition=And(Geq(Var("a"), Const(1)), Leq(Var("a"), Const(326)), Geq(Var("b"), Const(1)), Leq(Var("b"), CountOverSet(set=Solu... | NT | null | COUNT | sympy | MIN_PRIME_FACTOR | [
"MIN_PRIME_FACTOR/QF_PSD_COUNT_LEQ"
] | bbcc84 | alg_poly4_count_v1 | null | 6 | 0 | [
"MIN_PRIME_FACTOR",
"QF_PSD_COUNT_LEQ"
] | 2 | 2.578 | 2026-03-10T02:40:07.052415Z | {
"verified": true,
"answer": 326,
"timestamp": "2026-03-10T02:40:09.630420Z"
} | 19a006 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 1,
"correct": {
"strict": false,
"boxed": false,
"relaxed": true
},
"usage": {
"prompt_tokens": 251,
"completion_tokens": 32768
},
"timestamp": "2026-03-29T03:48:47.350Z",
"answer": null
},
{
... | 1 | [
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "MIN_PRIME_FACTOR",
"status": "ok"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "QF_PSD_COUNT_LEQ",... | {
"lo": 3.99,
"mid": 6.11,
"hi": 9.15
} | ||
7e8f22 | algebra_poly_eval_v1_1218484723_6437 | Let $x = 19$. Compute $\max\{ x_1 \cdot y : x_1 > 0, y > 0, x_1 + y = 4 \} \cdot x^2 - 4x - 6$. | 1,362 | graphs = [
Graph(
let={
"x": Const(19),
"result": Sum(Mul(MaxOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x1"), Var("y")]), condition=And(IsPositive(arg=Var(name='x1')), IsPositive(arg=Var(name='y')), Eq(Sum(Var("x1"), Var("y")), Const(4)))), expr=Mul(Var("x1"), V... | ALG | null | COMPUTE | sympy | ONE_PHI_1 | [
"B1"
] | 5b950e | algebra_poly_eval_v1 | null | 2 | 0 | [
"B1",
"ONE_PHI_1"
] | 2 | 0.012 | 2026-02-25T07:59:42.797619Z | {
"verified": true,
"answer": 1362,
"timestamp": "2026-02-25T07:59:42.809999Z"
} | fbbb1e | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 166,
"completion_tokens": 584
},
"timestamp": "2026-03-30T01:43:10.060Z",
"answer": 1362
},
{
"id... | 2 | [
{
"lemma": "B1",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
}
] | {
"lo": -10,
"mid": -6.24,
"hi": -2.48
} | ||
7e78bf | nt_sum_totient_over_divisors_v1_1742523217_1752 | Let $n = 82898$. Define $R = \sum_{d \mid n} \phi(d)$, where $\phi$ is Euler's totient function. Let $M$ be the maximum value of $xy$ over all pairs of positive integers $(x, y)$ such that $x + y = 116$. Compute the remainder when $R^2 + 33R + M$ is divided by $75613$. | 7,829 | graphs = [
Graph(
let={
"_n": Const(33),
"n": Const(82898),
"result": SumOverDivisors(n=Ref(name='n'), var='d', expr=EulerPhi(n=Var(name='d'))),
"_c": MaxOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive... | NT | null | COMPUTE | sympy | B1 | [
"B1"
] | bf138c | nt_sum_totient_over_divisors_v1 | quadratic_mod | 5 | 0 | [
"B1"
] | 1 | 0.002 | 2026-02-08T04:12:53.714900Z | {
"verified": true,
"answer": 7829,
"timestamp": "2026-02-08T04:12:53.716873Z"
} | 7acd4f | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 201,
"completion_tokens": 1072
},
"timestamp": "2026-02-10T15:51:04.570Z",
"answer": 7829
},
{
"... | 1 | [
{
"lemma": "B1",
"status": "ok"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "V1",
"status": "no"
},
{
"lemma": "V3",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
}
] | {
"lo": -3.42,
"mid": 1.86,
"hi": 7.55
} | ||
325355 | alg_poly_preperiod_count_v1_1218484723_2139 | For a non-negative integer $a$, define the sequence
\[
N = (2a^3 + 2a) \bmod 17,\quad M = (2N^3 + 2N) \bmod 17,\quad R = (2M^3 + 2M) \bmod 17,
\]
\[
S = (2R^3 + 2R) \bmod 17,\quad T = (2S^3 + 2S) \bmod 17,\quad K = (2T^3 + 2T) \bmod 17.
\]
Find the number of integers $a$ with $0 \le a \le 9417$ such that $K = M$, but $... | 5,540 | graphs = [
Graph(
let={
"p1": Mod(value=Sum(Mul(Const(2), Pow(Var("a"), Const(3))), Mul(Const(2), Var("a"))), modulus=Const(17)),
"p2": Mod(value=Sum(Mul(Const(2), Pow(Ref("p1"), Const(3))), Mul(Const(2), Ref("p1"))), modulus=Const(17)),
"p3": Mod(value=Sum(Mul(Const(2), ... | ALG | null | COUNT | sympy | POLY_ORBIT_COUNT | [
"POLY_ORBIT_COUNT"
] | 4ad965 | alg_poly_preperiod_count_v1 | null | 6 | null | [
"POLY_ORBIT_COUNT"
] | 1 | 0.034 | 2026-02-25T03:52:04.419678Z | {
"verified": true,
"answer": 5540,
"timestamp": "2026-02-25T03:52:04.453577Z"
} | 64ced6 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 289,
"completion_tokens": 10449
},
"timestamp": "2026-03-29T03:14:14.011Z",
"answer": 5540
},
{
"... | 1 | [
{
"lemma": "POLY_ORBIT_COUNT",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
}
] | {
"lo": -2.47,
"mid": 1.2,
"hi": 4.81
} | ||
427073 | comb_count_derangements_v1_1125832087_884 | Let $S$ be the set of all positive integers $n$ such that $1 \leq n \leq 104472$ and $9$ divides $F_n$, where $F_n$ denotes the $n$th Fibonacci number. Let $m = |S|$. Define $T$ to be the set of all nonnegative integers $j$ such that $0 \leq j \leq m$ and $\binom{8706}{j}$ is odd. Let $t = |T|$. Compute the subfactoria... | 14,833 | graphs = [
Graph(
let={
"_n": Const(8706),
"n": CountOverSet(set=SolutionsSet(var=Var("j"), condition=And(Geq(Var("j"), Const(0)), Leq(Var("j"), CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Const(104472)), Divides(divisor=Const(9), ... | COMB | NT | COUNT | sympy | COUNT_FIB_DIVISIBLE | [
"COUNT_FIB_DIVISIBLE/V8"
] | 82a267 | comb_count_derangements_v1 | null | 6 | 0 | [
"COUNT_FIB_DIVISIBLE",
"V8"
] | 2 | 0.002 | 2026-02-08T03:21:12.622445Z | {
"verified": true,
"answer": 14833,
"timestamp": "2026-02-08T03:21:12.624157Z"
} | 9bdd56 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 235,
"completion_tokens": 3354
},
"timestamp": "2026-02-10T14:02:15.848Z",
"answer": 14833
},
{
"... | 1 | [
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "ok"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
... | {
"lo": -3.46,
"mid": 1.03,
"hi": 5.49
} | ||
47eb7d | comb_binomial_compute_v1_124444284_6553 | Let $n_2 = 3$. Define $t = \sum_{k=-1}^{n_2} (-1)^k \binom{n_2}{k}$. Let $n_1 = 0$ and $m = \sum_{k=0}^{n_1} (-1)^k \binom{n_1}{k}$. Define $n = (16 + t) \cdot m$. Let $k = 8$ and $\text{result} = \binom{n}{k}$. Let $c = 63133$ and $Q$ be the remainder when $c \cdot \text{result}$ is divided by $99829$. Compute $Q$. | 13,479 | graphs = [
Graph(
let={
"n2": Const(3),
"t": Summation(var="k", start=Sub(Binom(n=Const(5), k=Const(0)), Const(1)), end=Ref("n2"), expr=Mul(Pow(Const(-1), Var("k")), Binom(n=Ref("n2"), k=Var("k")))),
"n1": Const(0),
"m": Summation(var="k", start=Const(0), end=... | COMB | null | COMPUTE | sympy | BINOMIAL_ALTERNATING | [
"BINOMIAL_ALTERNATING",
"ZERO_BINOM_0"
] | 38a409 | comb_binomial_compute_v1 | null | 3 | 2 | [
"BINOMIAL_ALTERNATING",
"ZERO_BINOM_0"
] | 2 | 0.002 | 2026-02-08T08:31:52.883191Z | {
"verified": true,
"answer": 13479,
"timestamp": "2026-02-08T08:31:52.885528Z"
} | 7c1fc5 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 262,
"completion_tokens": 1686
},
"timestamp": "2026-02-24T09:38:08.143Z",
"answer": 13479
},
{
"... | 1 | [
{
"lemma": "BINOMIAL_ALTERNATING",
"status": "ok"
},
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8",
"status... | {
"lo": 1.15,
"mid": 4.18,
"hi": 6.61
} | ||
8c3f7d | antilemma_cartesian_v1_458359167_4067 | Let $x$ be the number of ordered pairs $(a,b)$ where $a$ is an integer from 1 to 33 and $b$ is an integer from 1 to 45. Compute
$$
x + \phi(|x| + 1) + \tau(|x| + \binom{4}{4}),
$$
where $\phi(n)$ denotes Euler's totient function and $\tau(n)$ denotes the number of positive divisors of $n$. | 2,231 | graphs = [
Graph(
let={
"x": CountOverSet(set=CartesianProduct(left=IntegerRange(start=Const(1), end=Const(33)), right=IntegerRange(start=Const(1), end=Const(45)))),
"Q": Sum(Ref("x"), EulerPhi(n=Sum(Abs(arg=Ref(name='x')), Const(1))), NumDivisors(n=Sum(Abs(arg=Ref(name='x')), Binom(... | COMB | GEOM | COMPUTE | sympy | COUNT_CARTESIAN | [
"COUNT_CARTESIAN",
"ONE_BINOM_N"
] | f14704 | antilemma_cartesian_v1 | null | 3 | 0 | [
"COUNT_CARTESIAN",
"ONE_BINOM_N"
] | 2 | 0.002 | 2026-02-08T11:30:02.741920Z | {
"verified": true,
"answer": 2231,
"timestamp": "2026-02-08T11:30:02.744231Z"
} | 53b2a5 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 210,
"completion_tokens": 907
},
"timestamp": "2026-02-24T14:10:24.654Z",
"answer": 2231
},
{
"id... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "ok"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "ONE_BINOM_N",
"status": "ok"
},
{
"lemma": "V7",
"st... | {
"lo": -4.92,
"mid": -2.91,
"hi": -0.68
} | ||
092646 | sequence_count_fib_divisible_v1_124444284_1880 | Let $T$ be the set of all integers $t$ such that $19 \leq t \leq 3043$ and there exist positive integers $a$, $b$ with $1 \leq a \leq 313$, $1 \leq b \leq 145$, satisfying $t = 6a + 8b + 5$. Let $u$ be the number of positive integers $n$ such that $1 \leq n \leq |T|$ and $\gcd(n, 20) = 1$. Let $r$ be the number of posi... | 202 | graphs = [
Graph(
let={
"upper": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), CountOverSet(set=SolutionsSet(var=Var("t"), condition=Exists(var=Var(name='a'), condition=Exists(var=Var(name='b'), condition=And(Geq(left=Var(name='a'), right=Const(... | NT | null | COUNT | sympy | LIN_FORM | [
"LIN_FORM/C4"
] | 067e5d | sequence_count_fib_divisible_v1 | null | 6 | 0 | [
"C4",
"LIN_FORM"
] | 2 | 0.055 | 2026-02-08T04:11:51.975734Z | {
"verified": true,
"answer": 202,
"timestamp": "2026-02-08T04:11:52.030837Z"
} | 770353 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 314,
"completion_tokens": 7219
},
"timestamp": "2026-02-10T15:42:55.998Z",
"answer": 202
},
{
"i... | 1 | [
{
"lemma": "C4",
"status": "ok_later"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
},... | {
"lo": -3.42,
"mid": 1.86,
"hi": 7.55
} | ||
3738d0 | nt_sum_divisors_mod_v1_349078426_303 | Let $n$ be the minimum value of $x + y$ over all pairs of positive integers $(x, y)$ such that $xy = 14288400$. Let $\sigma(n)$ denote the sum of the positive divisors of $n$. Define $r$ to be the remainder when $\sigma(n)$ is divided by $10691$. Compute the remainder when $44121 \cdot r$ is divided by $78535$. | 34,233 | graphs = [
Graph(
let={
"n": MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(Mul(Var("x"), Var("y")), Const(14288400)))), expr=Sum(Var("x"), Var("y")))),
"M": Const(106... | NT | null | COMPUTE | sympy | B3 | [
"B3"
] | 0cd20d | nt_sum_divisors_mod_v1 | null | 5 | 0 | [
"B3"
] | 1 | 0.002 | 2026-02-08T12:55:15.808966Z | {
"verified": true,
"answer": 34233,
"timestamp": "2026-02-08T12:55:15.810736Z"
} | 5df44e | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 136,
"completion_tokens": 2339
},
"timestamp": "2026-02-15T07:21:12.966Z",
"answer": 34233
},
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
},
{
"lemma": "VAL_SUM_EQ",
"status": "no"
}
] | {
"lo": -5.49,
"mid": 0.22,
"hi": 6.51
} | ||
5d35a9 | nt_sum_divisors_mod_v1_655260480_5464 | Let $n = \sum_{k=1}^{15} \phi(k) \left\lfloor \frac{15}{k} \right\rfloor$, where $\phi(k)$ denotes Euler's totient function. Let $\sigma$ be the sum of the positive divisors of $n$. Compute the remainder when $\sigma$ is divided by $10889$. | 360 | graphs = [
Graph(
let={
"_n": Const(15),
"n": Summation(var="k", start=Const(1), end=Ref("_n"), expr=Mul(EulerPhi(n=Var("k")), Floor(Div(Const(15), Var("k"))))),
"M": Const(10889),
"sigma": SumDivisors(n=Ref("n")),
"result": Mod(value=Ref("sigma"),... | NT | null | COMPUTE | sympy | K2 | [
"K2"
] | 6897ab | nt_sum_divisors_mod_v1 | null | 5 | 0 | [
"K2"
] | 1 | 0.002 | 2026-02-08T18:28:44.878950Z | {
"verified": true,
"answer": 360,
"timestamp": "2026-02-08T18:28:44.880696Z"
} | 614c76 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 120,
"completion_tokens": 1737
},
"timestamp": "2026-02-18T17:24:47.486Z",
"answer": 360
},
{
... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "K2",
"status": "ok"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
8b4e0e | nt_lcm_compute_v1_48377204_404 | Let $ a = 2135 $ and $ b = 1703 $. Define $ \ell = \text{lcm}(a, b) $. Let $ m $ be the maximum value of $ xy $ over all pairs of positive integers $ (x, y) $ such that $ x + y = 80 $. Compute the value of
$$
(\ell^2 + 33\ell + m) \bmod 98874.
$$ | 23,132 | graphs = [
Graph(
let={
"a": Const(2135),
"b": Const(1703),
"result": LCM(a=Ref("a"), b=Ref("b")),
"_c": MaxOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='... | NT | null | COMPUTE | sympy | B1 | [
"B1"
] | bf138c | nt_lcm_compute_v1 | quadratic_mod | 3 | 0 | [
"B1"
] | 1 | 0.003 | 2026-02-08T15:25:37.825063Z | {
"verified": true,
"answer": 23132,
"timestamp": "2026-02-08T15:25:37.827753Z"
} | ddde53 | 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": 2099
},
"timestamp": "2026-02-16T05:55:58.377Z",
"answer": 23132
},
... | 1 | [
{
"lemma": "B1",
"status": "ok"
},
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
77ad2a | geo_count_lattice_rect_v1_124444284_8872 | Let $a = 37$ and $b = 52$. Define a lattice point as a point in the plane with integer coordinates. Compute the number of lattice points in the rectangle defined by $0 \leq x \leq a$ and $0 \leq y \leq b$, including all boundary points. Find the value of this number. | 2,014 | graphs = [
Graph(
let={
"a": Const(37),
"b": Const(52),
"result": LatticePointsRect(a=Ref(name='a'), b=Ref(name='b')),
},
goal=Ref("result"),
)
] | GEOM | null | COUNT | sympy | [] | geo_count_lattice_rect_v1 | null | 3 | 0 | null | null | 0.001 | 2026-02-08T11:56:28.414617Z | {
"verified": true,
"answer": 2014,
"timestamp": "2026-02-08T11:56:28.415316Z"
} | 8e85b8 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 184,
"completion_tokens": 270
},
"timestamp": "2026-02-24T15:00:07.832Z",
"answer": 2014
},
{
"id... | 1 | [] | {
"lo": -7.18,
"mid": -5,
"hi": -3.01
} | ||||
2f7226 | alg_telescope_v1_601307018_4518 | Let $M$ be the number of ordered pairs $(a, b)$ of positive integers with $1 \le a, b \le 40$ such that $13a^2 - 2ab + 2b^2 \le 5237$. Find the remainder when $\sum_{k=0}^{M} (3k^2 + 3k + 1)$ is divided by $\min\{ x + y : x > 0, y > 0, xy = 5731236 \}$. | 3,032 | graphs = [
Graph(
let={
"_m": Const(13),
"_n": 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(40)), Leq(Sum(Mul(Const(-2), Var("a"), Var("b")), Mul(R... | ALG | null | COMPUTE | sympy | QF_PSD_COUNT_LEQ | [
"QF_PSD_COUNT_LEQ/B3"
] | 837d99 | alg_telescope_v1 | null | 6 | 0 | [
"B3",
"QF_PSD_COUNT_LEQ"
] | 2 | 0.105 | 2026-03-10T05:08:54.191755Z | {
"verified": true,
"answer": 3032,
"timestamp": "2026-03-10T05:08:54.297109Z"
} | 729d47 | 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": 19417
},
"timestamp": "2026-03-29T12:37:35.157Z",
"answer": 3032
},
{
"... | 1 | [
{
"lemma": "B3",
"status": "ok_later"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "QF_PSD_COUNT_LEQ",
"status": "ok"
}
] | {
"lo": -3.34,
"mid": 0.9,
"hi": 4.9
} | ||
b9e433 | nt_min_coprime_above_v1_809748730_992 | Let $A$ be the set of all ordered pairs $(x,y)$ of positive integers such that $xy = 366025$. Let $S$ be the set of all values $x+y$ where $(x,y) \in A$. Define $m$ to be the minimum value in $S$. Let $n$ be the smallest integer greater than $1111$ and at most $m$ such that $\gcd(n, 89) = 1$. Compute $n + \phi(|n| + 1)... | 1,744 | graphs = [
Graph(
let={
"start": Const(1111),
"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(366025)))), expr=Sum(Var("x"), Var... | NT | null | EXTREMUM | sympy | B3 | [
"B3"
] | 0cd20d | nt_min_coprime_above_v1 | null | 6 | 0 | [
"B3"
] | 1 | 0.044 | 2026-02-08T11:52:19.163250Z | {
"verified": true,
"answer": 1744,
"timestamp": "2026-02-08T11:52:19.207209Z"
} | 75e8c3 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 190,
"completion_tokens": 1632
},
"timestamp": "2026-02-14T21:30:15.959Z",
"answer": 1744
},
{... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
}
] | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
108edb | modular_sum_quadratic_residues_v1_168721529_988 | Let $p$ be the largest prime number such that $2 \leq p \leq 614$. Define $Q = 44121 \cdot \frac{p(p-1)}{4}$. Compute the remainder when $Q$ is divided by $94702$. | 60,579 | graphs = [
Graph(
let={
"_n": Const(2),
"p": MaxOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Ref("_n")), Leq(Var("n"), Const(614)), IsPrime(Var("n"))))),
"result": Div(Mul(Ref("p"), Sub(Ref("p"), Const(1))), Const(4)),
"Q": Mod(value=Mul(... | NT | null | SUM | sympy | MAX_PRIME_BELOW | [
"MAX_PRIME_BELOW"
] | dc3ad3 | modular_sum_quadratic_residues_v1 | null | 3 | 0 | [
"MAX_PRIME_BELOW"
] | 1 | 0.003 | 2026-02-08T13:23:24.492022Z | {
"verified": true,
"answer": 60579,
"timestamp": "2026-02-08T13:23:24.495209Z"
} | 4faab4 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 173,
"completion_tokens": 1382
},
"timestamp": "2026-02-09T11:36:43.907Z",
"answer": 4771
},
{
... | 1 | [
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no... | {
"lo": 1.84,
"mid": 5.05,
"hi": 8.38
} | ||
322aa2 | modular_min_linear_v1_784195855_133 | Compute the smallest positive integer $x$ such that $x \leq 60450$ and $$ 49489x \equiv 58105 \pmod{60450}. $$ | 25,645 | graphs = [
Graph(
let={
"a": Const(49489),
"b": Const(58105),
"m": Const(60450),
"result": MinOverSet(set=SolutionsSet(var=Var("x"), condition=And(Geq(Var("x"), EulerPhi(n=Const(1))), Leq(Var("x"), Ref("m")), Eq(Mod(value=Mul(Ref("a"), Var("x")), modulus=Ref("... | NT | null | EXTREMUM | sympy | ONE_PHI_1 | [
"ONE_PHI_1"
] | f6b5a5 | modular_min_linear_v1 | null | 5 | 0 | [
"ONE_PHI_1"
] | 1 | 4.92 | 2026-02-08T02:59:00.729205Z | {
"verified": true,
"answer": 25645,
"timestamp": "2026-02-08T02:59:05.648780Z"
} | 5fce93 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 153,
"completion_tokens": 2929
},
"timestamp": "2026-02-08T23:04:06.524Z",
"answer": 25645
},
{
... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "ONE_PHI_1",
"status": "ok"
},
{
"lemma": "V8_SUM",
"status": "no"
}
] | {
"lo": -6.49,
"mid": 0.51,
"hi": 7.52
} | ||
fe1bcf | alg_qf_psd_orbit_v1_601307018_1791 | Find the number of ordered pairs $(a, b)$ of positive integers with $1 \leq a \leq b \leq 316$ such that $8b^2 - 16ab + 8a^2 = 75272$. | 219 | graphs = [
Graph(
let={
"_n": Const(3),
"result": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("a"), Var("b")]), condition=And(Geq(Var("a"), Const(1)), Leq(Var("a"), CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Const(2211))... | NT | null | COUNT | sympy | C5 | [
"C5"
] | 1d9668 | alg_qf_psd_orbit_v1 | null | 6 | 0 | [
"C5"
] | 1 | 0.475 | 2026-03-10T02:32:22.194820Z | {
"verified": true,
"answer": 219,
"timestamp": "2026-03-10T02:32:22.670080Z"
} | c09186 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 163,
"completion_tokens": 727
},
"timestamp": "2026-03-29T03:24:24.792Z",
"answer": 219
},
{
"id"... | 2 | [
{
"lemma": "C5",
"status": "ok"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
}
] | {
"lo": -10,
"mid": -6.41,
"hi": -2.82
} | ||
099aa8 | geo_visible_lattice_v1_48377204_2080 | Let $ n = 120 $. Define $ L $ to be the number of ordered pairs $ (x, y) $ of positive integers such that $ 1 \leq x, y \leq n $ and $ \gcd(x, y) = 1 $. Compute the remainder when $ 8 - L $ is divided by $ 82199 $. | 73,436 | graphs = [
Graph(
let={
"n": Const(120),
"result": VisibleLatticePoints(n=Ref(name='n')),
"_c": Const(8),
"Q": Mod(value=Sub(Ref("_c"), Ref("result")), modulus=Const(82199)),
},
goal=Ref("Q"),
)
] | GEOM | null | COUNT | sympy | [] | geo_visible_lattice_v1 | null | 3 | 0 | null | null | 1.103 | 2026-02-08T16:35:46.667776Z | {
"verified": true,
"answer": 73436,
"timestamp": "2026-02-08T16:35:47.770398Z"
} | 9ef7c3 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 119,
"completion_tokens": 3147
},
"timestamp": "2026-02-17T07:24:36.250Z",
"answer": 73436
},
... | 1 | [] | {
"lo": -2.38,
"mid": 1.74,
"hi": 6.59
} | ||||
346d6c | nt_gcd_compute_v1_677425708_2999 | Let $a = 196566$ and $b = 458654$. Define $\text{result} = \gcd(a, b)$. Let $S$ be the set of all ordered pairs $(x, y)$ of positive integers such that $xy = 62500$. Define $c$ to be the minimum value of $x + y$ as $(x, y)$ ranges over $S$. Compute the remainder when $c - \text{result}$ is divided by $87424$. | 22,402 | graphs = [
Graph(
let={
"_n": Const(87424),
"a": Const(196566),
"b": Const(458654),
"result": GCD(a=Ref("a"), b=Ref("b")),
"_c": MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(n... | NT | null | COMPUTE | sympy | B3 | [
"B3"
] | fc629c | nt_gcd_compute_v1 | negation_mod | 4 | 0 | [
"B3"
] | 1 | 0.003 | 2026-02-08T05:25:40.187680Z | {
"verified": true,
"answer": 22402,
"timestamp": "2026-02-08T05:25:40.190180Z"
} | 56ca1d | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 174,
"completion_tokens": 1086
},
"timestamp": "2026-02-11T22:48:50.205Z",
"answer": 498
},
{
"id": 11,... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "VAL_SUM_EQ",
"status": "no"
}
] | {
"lo": -5.55,
"mid": -3.01,
"hi": 0.34
} | ||
86f9ce | nt_count_gcd_equals_v1_809748730_786 | Let $k$ be the maximum value of $xy$ over all ordered pairs $(x,y)$ of positive integers such that $x + y = 36$. Let $d = 12$ and $N = 33333$. Determine the number of positive integers $n$ such that $1 \leq n \leq N$ and $\gcd(n, k) = d$. Let $Q$ be the remainder when $4$ minus this number is divided by $83929$. Comput... | 82,081 | graphs = [
Graph(
let={
"_n": Const(83929),
"upper": Const(33333),
"k": 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(36)))... | NT | null | COUNT | sympy | B1 | [
"B1"
] | 5b950e | nt_count_gcd_equals_v1 | null | 4 | 0 | [
"B1"
] | 1 | 3.01 | 2026-02-08T11:45:23.614909Z | {
"verified": true,
"answer": 82081,
"timestamp": "2026-02-08T11:45:26.624740Z"
} | 413e02 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 150,
"completion_tokens": 1032
},
"timestamp": "2026-02-14T18:27:01.233Z",
"answer": 82081
},
... | 1 | [
{
"lemma": "B1",
"status": "ok"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
}
] | {
"lo": -5.49,
"mid": 0.22,
"hi": 6.51
} | ||
f89a98 | nt_count_digit_sum_v1_153355830_2045 | Let $A$ be the number of positive integers $n \le 104329$ such that the sum of the decimal digits of $n$ is 31. Let $B$ be the number of ordered pairs $(x_1, x_2)$ of positive odd integers such that $x_1 + x_2 = 4438$. Compute the remainder when $A \cdot B$ is divided by 78678. | 36,181 | graphs = [
Graph(
let={
"_n": Const(78678),
"upper": Const(104329),
"target_sum": Const(31),
"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 | COMB1 | [
"COMB1"
] | 54ff32 | nt_count_digit_sum_v1 | affine_mod | 5 | 0 | [
"COMB1"
] | 1 | 4.664 | 2026-02-08T06:52:55.940591Z | {
"verified": true,
"answer": 36181,
"timestamp": "2026-02-08T06:53:00.604240Z"
} | aec4dd | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 136,
"completion_tokens": 3694
},
"timestamp": "2026-02-13T05:32:40.590Z",
"answer": 36181
},
... | 1 | [
{
"lemma": "COMB1",
"status": "ok"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "V1",
"status": "no"
}
] | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
b7e009 | alg_poly_preperiod_count_v1_1218484723_7651 | Define the sequence $N = (2a^3 + 2) \bmod 37$, $M = (2N^3 + 2) \bmod 37$, $R = (2M^3 + 2) \bmod 37$, $S = (2R^3 + 2) \bmod 37$, $T = (2S^3 + 2) \bmod 37$. Find the number of non-negative integers $a$ with $0 \le a \le 24863$ such that $T = N$, $M \neq N$, $R \neq N$, and $S \neq N$. | 6,720 | graphs = [
Graph(
let={
"p1": Mod(value=Sum(Mul(Const(2), Pow(Var("a"), Const(3))), Const(2)), modulus=Const(37)),
"p2": Mod(value=Sum(Mul(Const(2), Pow(Ref("p1"), Const(3))), Const(2)), modulus=Const(37)),
"p3": Mod(value=Sum(Mul(Const(2), Pow(Ref("p2"), Const(3))), Cons... | ALG | null | COUNT | sympy | POLY_ORBIT_COUNT | [
"POLY_ORBIT_COUNT"
] | 4ad965 | alg_poly_preperiod_count_v1 | null | 6 | null | [
"POLY_ORBIT_COUNT"
] | 1 | 0.019 | 2026-02-25T09:06:34.887160Z | {
"verified": true,
"answer": 6720,
"timestamp": "2026-02-25T09:06:34.906299Z"
} | dff2f0 | 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": 19165
},
"timestamp": "2026-03-30T05:44:45.074Z",
"answer": 6720
},
{
"... | 1 | [
{
"lemma": "POLY_ORBIT_COUNT",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
}
] | {
"lo": -3.33,
"mid": 1.03,
"hi": 5.26
} | ||
f1ea68 | lin_form_endings_v1_349078426_1768 | Let $ a = 12 $, $ b = 42 $, $ A = 31 $, and $ B = 4 $. Let $ g $ be the greatest common divisor of $ a $ and $ b $. Define $ a' = \left\lfloor \frac{a}{g} \right\rfloor $ and $ b' = \left\lfloor \frac{b}{g} \right\rfloor $. Let $ r = a' \cdot A + b' \cdot B - a' \cdot b' $. Let $ s = 6149 \cdot r $, and let $ M = 78910... | 72,774 | graphs = [
Graph(
let={
"a_coeff": Const(12),
"b_coeff": Const(42),
"A_val": Const(31),
"B_val": Const(4),
"g_step": GCD(a=Ref("a_coeff"), b=Ref("b_coeff")),
"ap_node": Floor(Div(Ref("a_coeff"), Ref("g_step"))),
"bp_node": F... | COMB | NT | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | lin_form_endings_v1 | null | 2 | null | [
"LIN_FORM"
] | 1 | 0.002 | 2026-02-08T13:55:15.478934Z | {
"verified": true,
"answer": 72774,
"timestamp": "2026-02-08T13:55:15.480644Z"
} | 9fd9d8 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 197,
"completion_tokens": 612
},
"timestamp": "2026-02-15T22:02:19.727Z",
"answer": 72774
},
{... | 1 | [
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
... | {
"lo": -5.49,
"mid": 0.22,
"hi": 6.51
} | ||
ab60fc | comb_count_derangements_v1_655260480_4061 | Let $p$ and $q$ be positive integers such that $pq = 108$, $\gcd(p, q) = 1$, and $p < q$. Let $m$ be the number of such pairs $(p, q)$. Let $n$ be the largest prime number satisfying $m \leq n \leq 9$. Compute the subfactorial of $n$. | 1,854 | graphs = [
Graph(
let={
"_m": Const(9),
"_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=108)), Eq(left=GCD(a=Var(name='p'), b=Var(name='... | NT | COMB | COUNT | sympy | COPRIME_PAIRS | [
"COPRIME_PAIRS/MAX_PRIME_BELOW"
] | 2248fc | comb_count_derangements_v1 | null | 4 | 0 | [
"COPRIME_PAIRS",
"MAX_PRIME_BELOW"
] | 2 | 0.004 | 2026-02-08T17:41:50.133428Z | {
"verified": true,
"answer": 1854,
"timestamp": "2026-02-08T17:41:50.137517Z"
} | 34dc92 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 126,
"completion_tokens": 1403
},
"timestamp": "2026-02-18T06:45:44.521Z",
"answer": 1854
},
{... | 1 | [
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok_later"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma"... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
05774e | diophantine_fbi2_min_v1_2051736721_923 | Let $k = 180$. Let $\text{result}$ be the smallest integer $d$ such that $6 \le d \le 190$, $d$ divides $k$, and $\frac{k}{d} \ge 5$. Let $T$ be the set of integers $t$ such that $7 \le t \le 113$ and there exist positive integers $a \le 17$, $b \le 15$ for which $t = 4a + 3b$. Let $N = |T|$. Compute the remainder when... | 36,072 | graphs = [
Graph(
let={
"_n": Const(103),
"k": Const(180),
"upper": Const(190),
"result": MinOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Const(6)), Leq(Var("d"), Ref("upper")), Divides(divisor=Var("d"), dividend=Ref("k")), Geq(Div(Ref("k... | NT | null | EXTREMUM | sympy | LIN_FORM | [
"LIN_FORM"
] | 13c63b | diophantine_fbi2_min_v1 | crt_mix_3 | 5 | 0 | [
"LIN_FORM"
] | 1 | 0.011 | 2026-02-08T15:45:39.107800Z | {
"verified": true,
"answer": 36072,
"timestamp": "2026-02-08T15:45:39.118911Z"
} | 71506c | 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": 3633
},
"timestamp": "2026-02-16T12:36:23.423Z",
"answer": 36072
},
... | 1 | [
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
4396b2 | alg_sym_quad_system_v1_601307018_248 | Let $R = \left(\sum_{\substack{a, b, c \geq 1 \\ a^2 + b^2 + c^2 = ab + bc + ca \\ 7a + 2b + 3c = \max\{ d \mid 12634464 : d^2 \leq 12634464 \}}} \left(a^5 + b^5 + c^{\sum_{\substack{n=2 \\ n \text{ prime}}}^{4} n}\right)\right) \bmod \max\{ d_1 \mid 36029986 : d_1^2 \leq 36029986 \}$. Let $Q$ be the multiplicative ord... | 648 | graphs = [
Graph(
let={
"_m": Const(2),
"_n": Const(5),
"result": Mod(value=SumOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("a"), Var("b"), Var("c")]), condition=And(Eq(Sum(Pow(Var("a"), Ref("_m")), Pow(Var("b"), Const(2)), Pow(Var("c"), Const(2))), Sum... | NT | NT | COMPUTE | sympy | MIN_PRIME_FACTOR | [
"SUM_PRIMES",
"B3_CLOSEST"
] | d1bcf4 | alg_sym_quad_system_v1 | null | 8 | 0 | [
"B3_CLOSEST",
"MIN_PRIME_FACTOR",
"SUM_PRIMES"
] | 3 | 0.282 | 2026-03-10T00:48:43.109874Z | {
"verified": true,
"answer": 648,
"timestamp": "2026-03-10T00:48:43.391789Z"
} | c5875b | CC BY 4.0 | null | null | [
{
"lemma": "B3_CLOSEST",
"status": "ok"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "SUM_PRIMES",
"statu... | {
"lo": -10,
"mid": 0,
"hi": 10
} | ||
04ea92 | comb_count_surjections_v1_655260480_3635 | Let $k$ be the number of ordered pairs $(i, j)$ of integers such that $1 \leq i \leq 4$, $1 \leq j \leq 4$, and $i + j = 6$. Compute the value of $k! \cdot S(6, k)$, where $S(6, k)$ denotes the Stirling number of the second kind. | 540 | graphs = [
Graph(
let={
"n": Const(6),
"k": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("i"), Var("j")]), condition=Eq(Sum(Var("i"), Var("j")), Const(6)), domain=CartesianProduct(left=IntegerRange(start=Const(1), end=Const(4)), right=IntegerRange(start=Const(1), end=Const(4... | COMB | null | COUNT | sympy | COMB1 | [
"COUNT_SUM_EQUALS"
] | 75ab0f | comb_count_surjections_v1 | null | 3 | 0 | [
"COMB1",
"COUNT_SUM_EQUALS"
] | 2 | 0.04 | 2026-02-08T17:28:43.336228Z | {
"verified": true,
"answer": 540,
"timestamp": "2026-02-08T17:28:43.376436Z"
} | f49fcb | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 127,
"completion_tokens": 1107
},
"timestamp": "2026-02-18T02:35:13.236Z",
"answer": 540
},
{
... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "ok"
},
{
"lemma": "V7",
... | {
"lo": -5.64,
"mid": -3.17,
"hi": -0.81
} | ||
36976e | modular_count_residue_v1_168721529_1276 | Let $S$ be the set of all ordered pairs $(x, y)$ of positive integers such that $xy = 16$. Define $m$ to be the minimum value of $x + y$ over all such pairs. Let $u = 64009$ and $r = 4$. Compute the number of positive integers $n$ such that $1 \leq n \leq u$ and $n \equiv r \pmod{m}$. | 8,001 | graphs = [
Graph(
let={
"upper": Const(64009),
"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(16)))), expr=Sum(Var("x"), Var("y")))... | NT | null | COUNT | sympy | B3 | [
"B3"
] | 0cd20d | modular_count_residue_v1 | null | 3 | 0 | [
"B3"
] | 1 | 2.258 | 2026-02-08T13:33:42.868680Z | {
"verified": true,
"answer": 8001,
"timestamp": "2026-02-08T13:33:45.126635Z"
} | 80bb1a | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 212,
"completion_tokens": 763
},
"timestamp": "2026-02-09T15:11:50.089Z",
"answer": 8001
},
{
"id... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
}
] | {
"lo": -5.65,
"mid": -2.15,
"hi": 1.88
} | ||
c7d06e | antilemma_v1_legendre_1874849503_993 | Let $A$ be the set of all positive integers $p$ such that there exists a positive integer $q$ with $p < q$, $pq = 108$, and $\gcd(p, q) = 1$. Let $d$ be the number of elements in $A$. Define $S$ as the set of all integers $n$ with $1 \leq n \leq 10628$ such that the sum of the decimal digits of $n$ leaves a remainder o... | 40,290 | graphs = [
Graph(
let={
"_m": Const(41616),
"_n": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Const(10628)), Eq(Mod(value=DigitSum(Var("n")), modulus=CountOverSet(set=SolutionsSet(var=Var("p"), condition=And(IsPositive(arg=Var(name... | NT | null | COMPUTE | sympy | COPRIME_PAIRS | [
"COPRIME_PAIRS/L3B/V1",
"V1"
] | aae8bc | antilemma_v1_legendre | null | 7 | 0 | [
"COPRIME_PAIRS",
"L3B",
"V1"
] | 3 | 0.005 | 2026-02-08T13:30:07.317728Z | {
"verified": true,
"answer": 40290,
"timestamp": "2026-02-08T13:30:07.323053Z"
} | edb0d3 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 272,
"completion_tokens": 5558
},
"timestamp": "2026-02-09T23:39:05.523Z",
"answer": 40290
},
{
"... | 1 | [
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "K5",
"status": "same_pattern_wrong"
},
{
"lemma": "L3B",
"status": "ok_later"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status... | {
"lo": -6.5,
"mid": -0.2,
"hi": 6.11
} | ||
30ce4e | comb_sum_binomial_row_v1_655260480_1793 | Let $d$ be an integer satisfying $d \geq 2$ and $d \mid 537251$. Let $n$ be the smallest such $d$. Define $\alpha = 2^n$. Let $Q$ be the remainder when $61363 \cdot \alpha$ is divided by $51642$. Compute $Q$. | 26,438 | graphs = [
Graph(
let={
"n": MinOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Const(2)), Divides(divisor=Var("d"), dividend=Const(537251))))),
"result": Pow(Const(2), Ref("n")),
"_c": Const(61363),
"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 | 0.002 | 2026-02-08T16:22:42.713681Z | {
"verified": true,
"answer": 26438,
"timestamp": "2026-02-08T16:22:42.715502Z"
} | e92e1d | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 117,
"completion_tokens": 1336
},
"timestamp": "2026-02-17T01:19:13.229Z",
"answer": 26438
},
... | 1 | [
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "MIN_PRIME_FACTOR",
"status": "ok"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "V1",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} |
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