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 |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
fc46d0 | nt_count_digit_sum_v1_1742523217_4877 | Let $s$ be the largest prime number less than or equal to $19$. Compute the number of positive integers $n$ such that $1 \leq n \leq 320356$ and the sum of the decimal digits of $n$ is equal to $s$. | 15,702 | graphs = [
Graph(
let={
"_n": Const(19),
"upper": Const(320356),
"target_sum": MaxOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(2)), Leq(Var("n"), Ref("_n")), IsPrime(Var("n"))))),
"result": CountOverSet(set=SolutionsSet(var=Var("n")... | NT | null | COUNT | sympy | MAX_PRIME_BELOW | [
"MAX_PRIME_BELOW"
] | dc3ad3 | nt_count_digit_sum_v1 | null | 5 | 0 | [
"MAX_PRIME_BELOW"
] | 1 | 14.715 | 2026-02-08T09:19:37.585199Z | {
"verified": true,
"answer": 15702,
"timestamp": "2026-02-08T09:19:52.300603Z"
} | 6f5a9c | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 103,
"completion_tokens": 4962
},
"timestamp": "2026-02-14T02:51:31.637Z",
"answer": 15702
},
... | 1 | [
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok"
},
{
"lemma": "MOD_FACTORIAL",
"st... | {
"lo": -5.49,
"mid": 0.22,
"hi": 6.51
} | ||
a1a51f | antilemma_sum_primes_v1_1742523217_440 | Let $n = 4$. Let $p$ be a positive integer. Define $S$ to be the set of all positive integers $p$ for which there exists a positive integer $q$ such that $p \cdot q = 216$, $\gcd(p, q) = 1$, and $p < q$. Let $m$ be the number of elements in $S$. Let $T$ be the set of all prime numbers $n$ such that $m \leq n \leq n$. L... | 28,895 | graphs = [
Graph(
let={
"_n": Const(4),
"x": SumOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), CountOverSet(set=SolutionsSet(var=Var("p"), condition=And(IsPositive(arg=Var(name='p')), Exists(var=Var(name='q'), condition=And(Eq(left=Mul(Var(name='p'), Var(name='q')... | NT | null | COMPUTE | sympy | COPRIME_PAIRS | [
"COPRIME_PAIRS/SUM_PRIMES",
"SUM_PRIMES"
] | 020700 | antilemma_sum_primes_v1 | null | 5 | 0 | [
"COPRIME_PAIRS",
"SUM_PRIMES"
] | 2 | 0.002 | 2026-02-08T03:02:13.538015Z | {
"verified": true,
"answer": 28895,
"timestamp": "2026-02-08T03:02:13.539991Z"
} | f94ed3 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 244,
"completion_tokens": 1318
},
"timestamp": "2026-02-09T18:02:01.550Z",
"answer": 28895
},
{
"... | 1 | [
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
... | {
"lo": -6.51,
"mid": -0.31,
"hi": 5.43
} | ||
9fbc4e | comb_bell_compute_v1_601307018_2330 | Let $B_n$ denote the $n$-th Bell number. Let $S = \{ t : \text{there exist integers } a, b \text{ with } 1 \leq a \leq 4, 1 \leq b \leq 3 \text{ such that } t = 2a + 3b,\ 5 \leq t \leq 17 \}$, and let $m = |S|$. Let $N = B_9$, and let $Q = B_{N \bmod m}$. Compute $Q$. | 52 | graphs = [
Graph(
let={
"n": Const(9),
"result": Bell(Ref("n")),
"Q": Bell(Mod(value=Abs(arg=Ref(name='result')), modulus=CountOverSet(set=SolutionsSet(var=Var("t"), condition=Exists(var=Var(name='a'), condition=Exists(var=Var(name='b'), condition=And(Geq(left=Var(name='a... | COMB | null | COMPUTE | sympy | STARS_BARS | [
"LIN_FORM"
] | 1ae498 | comb_bell_compute_v1 | bell_mod | 5 | 0 | [
"LIN_FORM",
"STARS_BARS"
] | 2 | 0.054 | 2026-03-10T02:59:02.789219Z | {
"verified": true,
"answer": 52,
"timestamp": "2026-03-10T02:59:02.843577Z"
} | 288ad0 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 236,
"completion_tokens": 804
},
"timestamp": "2026-03-29T05:02:04.607Z",
"answer": 52
},
{
"id":... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "V7",
"st... | {
"lo": -2.46,
"mid": 1.23,
"hi": 4.93
} | ||
72c8fd | diophantine_fbi2_count_v1_655260480_4572 | Let $k$ be the number of positive integers $j \le 1260$ such that $j^3 \le 2000376000$. Let $T$ be the set of all integers $t$ such that $t = 2a + 5b$ for some integers $a,b$ with $1 \le a \le 36$ and $1 \le b \le 17$, and $7 \le t \le 157$. Let $m$ be the number of divisors $d$ of $k$ such that $4 \le d \le |T|$, $2 \... | 673 | graphs = [
Graph(
let={
"_n": Const(2),
"k": CountOverSet(set=SolutionsSet(var=Var("j"), condition=And(Geq(Var("j"), Const(1)), Leq(Var("j"), Const(1260)), Leq(Pow(Var("j"), Const(3)), Const(2000376000))), domain='positive_integers')),
"result": CountOverSet(set=Solutions... | NT | null | COUNT | sympy | LIN_FORM | [
"LIN_FORM",
"C3"
] | ea43fe | diophantine_fbi2_count_v1 | null | 5 | 0 | [
"C3",
"LIN_FORM"
] | 2 | 0.013 | 2026-02-08T17:59:44.795493Z | {
"verified": true,
"answer": 673,
"timestamp": "2026-02-08T17:59:44.808329Z"
} | d678da | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 203,
"completion_tokens": 3995
},
"timestamp": "2026-02-18T11:44:10.181Z",
"answer": 673
},
{
... | 1 | [
{
"lemma": "C3",
"status": "ok"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
eafde1 | sequence_fibonacci_compute_v1_458359167_568 | Let $n$ be the largest prime number less than or equal to 24. Define $F_n$ to be the $n$th Fibonacci number, where $F_1 = 1$, $F_2 = 1$, and $F_k = F_{k-1} + F_{k-2}$ for $k \geq 3$. Let $S$ be the set of all integers $t$ such that $14 \leq t \leq 80$ and there exist integers $a$ and $b$ with $1 \leq a \leq 7$, $1 \leq... | 43,550 | graphs = [
Graph(
let={
"_n": Const(2),
"n": MaxOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(2)), Leq(Var("n"), Const(24)), IsPrime(Var("n"))))),
"result": Fibonacci(arg=Ref(name='n')),
"Q": Mod(value=Sum(Pow(Ref("result"), Ref("_n"... | NT | null | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM",
"MAX_PRIME_BELOW"
] | 2b068d | sequence_fibonacci_compute_v1 | quadratic_mod | 6 | 0 | [
"LIN_FORM",
"MAX_PRIME_BELOW"
] | 2 | 0.004 | 2026-02-08T03:25:36.401552Z | {
"verified": true,
"answer": 43550,
"timestamp": "2026-02-08T03:25:36.405087Z"
} | f67206 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 293,
"completion_tokens": 4610
},
"timestamp": "2026-02-10T13:29:02.895Z",
"answer": 43550
},
{
... | 1 | [
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"... | {
"lo": -3.42,
"mid": 1.86,
"hi": 7.55
} | ||
be5b7d | algebra_poly_eval_v1_2051736721_895 | Let $n = 9216$. Consider the set of all ordered pairs $(x_1, y)$ of positive integers such that $x_1 \cdot y = n$. Let $s$ be the minimum possible value of $x_1 + y$ over all such pairs. Compute the value of $$\frac{90 \cdot 19^3 - 42 \cdot 19^2 - 102 \cdot 19 - 18}{s}.$$ | 3,126 | graphs = [
Graph(
let={
"_n": Const(9216),
"x": Const(19),
"result": Div(Sum(Mul(Const(90), Pow(Ref("x"), Const(3))), Mul(Const(-42), Pow(Ref("x"), Const(2))), Mul(Const(-102), Ref("x")), Const(-18)), MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x1"... | NT | null | COMPUTE | sympy | B3 | [
"B3"
] | 0cd20d | algebra_poly_eval_v1 | null | 4 | 0 | [
"B3"
] | 1 | 0.003 | 2026-02-08T15:44:06.732653Z | {
"verified": true,
"answer": 3126,
"timestamp": "2026-02-08T15:44:06.735948Z"
} | 4520db | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 143,
"completion_tokens": 1342
},
"timestamp": "2026-02-16T12:32:56.146Z",
"answer": 3126
},
{... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
dc9a2e | nt_sum_gcd_range_mod_v1_458359167_1273 | Let $N$ be the number of ordered pairs $(i, j)$ of positive integers with $1 \leq i \leq 34$ and $1 \leq j \leq 199$ such that $\gcd(i, j) = 1$. Let $k = 90$ and $M = 10459$. Define $\displaystyle \text{sum} = \sum_{n=1}^{N} \gcd(n, k)$. Compute the remainder when $\text{sum}$ is divided by $M$. | 5,371 | graphs = [
Graph(
let={
"N": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("i"), Var("j")]), condition=Eq(GCD(a=Var("i"), b=Var("j")), Const(1)), domain=CartesianProduct(left=IntegerRange(start=Const(1), end=Const(34)), right=IntegerRange(start=Const(1), end=Const(199))))),
"... | NT | null | COMPUTE | sympy | COUNT_COPRIME_GRID | [
"COUNT_COPRIME_GRID"
] | 20ec03 | nt_sum_gcd_range_mod_v1 | null | 6 | 0 | [
"COUNT_COPRIME_GRID"
] | 1 | 0.851 | 2026-02-08T04:31:37.592553Z | {
"verified": true,
"answer": 5371,
"timestamp": "2026-02-08T04:31:38.443535Z"
} | 35a77b | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 223,
"completion_tokens": 6699
},
"timestamp": "2026-02-10T16:55:35.372Z",
"answer": 5371
},
{
"... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "ok"
},
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "MOD_MUL",
"sta... | {
"lo": -3.42,
"mid": 1.86,
"hi": 7.55
} | ||
b8fd46_n | comb_sum_binomial_row_v1_1218484723_3162 | A cryptographic function applies a four-stage transformation to integers $a$ from $0$ to $60$: at each stage, the value is updated as $x \mapsto 2x^3 \bmod 61$. After four iterations, the result must equal $a$, but $a$ must not be a fixed point at any earlier stage. Additionally, a checksum involving powers modulo $61$... | 65,536 | COMB | null | SUM | sympy | POLY_ORBIT_LEGENDRE | [
"MAX_PRIME_BELOW/POLY_ORBIT_LEGENDRE"
] | f66d45 | comb_sum_binomial_row_v1 | null | 7 | null | [
"MAX_PRIME_BELOW",
"POLY_ORBIT_LEGENDRE"
] | 2 | 0.144 | 2026-02-25T04:52:27.754681Z | null | 3338eb | b8fd46 | narrative | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 224,
"completion_tokens": 22844
},
"timestamp": "2026-03-30T19:45:00.009Z",
"answer": 65536
},
{
... | 1 | [
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok"
},
{
"lemma": "MOD_SUB"... | {
"lo": 3.8,
"mid": 6.33,
"hi": 9.49
} | |
e29daa | antilemma_k3_v1_1874849503_1083 | Let $x$ be the sum of $\phi(d)$ over all positive divisors $d$ of $48234$, where $\phi$ denotes Euler's totient function. Compute $x$. | 48,234 | graphs = [
Graph(
let={
"x": SumOverDivisors(n=Const(value=48234), var='d', expr=EulerPhi(n=Var(name='d'))),
},
goal=Ref("x"),
)
] | NT | COMB | COMPUTE | sympy | K3 | [
"K3"
] | 54c41e | antilemma_k3_v1 | null | 3 | 0 | [
"K3"
] | 1 | 0.001 | 2026-02-08T13:33:42.119490Z | {
"verified": true,
"answer": 48234,
"timestamp": "2026-02-08T13:33:42.120143Z"
} | 47ff98 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 150,
"completion_tokens": 1422
},
"timestamp": "2026-02-10T00:50:04.522Z",
"answer": 48234
},
{
"... | 1 | [
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "K3",
"status": "ok"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
}
] | {
"lo": -5.49,
"mid": 0.03,
"hi": 6.12
} | ||
c48288 | antilemma_count_primes_v1_1125832087_191 | Let $m = 3$ and define $k_{\text{max}}$ to be the largest positive integer $k$ such that $3^k \leq 23267604876$. Let $A$ be the set of all positive integers $n$ such that $1 \leq n \leq 20530$, $5$ divides $n$, and $\gcd(n, k_{\text{max}}) = 1$. Define $x$ to be the number of prime numbers $n$ such that $2 \leq n \leq ... | 600 | graphs = [
Graph(
let={
"_m": Const(3),
"_n": MaxOverSet(set=SolutionsSet(var=Var("k"), condition=Leq(Pow(Ref("_m"), Var("k")), Const(23267604876)))),
"x": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(2)), Leq(Var("n"), CountOverSet(set=So... | NT | null | COMPUTE | sympy | MIN_PRIME_FACTOR | [
"MAX_VAL/C5/COUNT_PRIMES",
"COUNT_PRIMES"
] | df6964 | antilemma_count_primes_v1 | null | 7 | 0 | [
"C5",
"COUNT_PRIMES",
"MAX_VAL",
"MIN_PRIME_FACTOR"
] | 4 | 0.027 | 2026-02-08T02:55:50.707464Z | {
"verified": true,
"answer": 600,
"timestamp": "2026-02-08T02:55:50.734264Z"
} | bb9cbb | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 252,
"completion_tokens": 457
},
"timestamp": "2026-02-17T15:50:01.981Z",
"answer": 13
}
] | 0 | [
{
"lemma": "C5",
"status": "ok_later"
},
{
"lemma": "COUNT_PRIMES",
"status": "ok"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K16",
"status": "same_pattern_wrong"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
... | {
"lo": -6.48,
"mid": 1.54,
"hi": 9.56
} | ||
824870 | comb_count_surjections_v1_1874849503_634 | Let $n$ be the number of ordered pairs $(x_1, x_2)$ of positive odd integers such that $x_1 + x_2 = 14$.
Let $k = 7$. Define $\text{result} = k! \cdot S(n, k)$, where $S(n, k)$ denotes the Stirling number of the second kind.
Let $Q$ be the smallest positive integer $m$ such that the $m$-th Fibonacci number is divisib... | 60 | graphs = [
Graph(
let={
"n": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x1"), Var("x2")]), condition=And(IsPositive(arg=Var(name='x1')), IsPositive(arg=Var(name='x2')), IsOdd(arg=Var(name='x1')), IsOdd(arg=Var(name='x2')), Eq(Sum(Var("x1"), Var("x2")), Const(14))))),
"k":... | COMB | NT | COUNT | sympy | COMB1 | [
"COMB1"
] | 567f58 | comb_count_surjections_v1 | null | 3 | 0 | [
"COMB1"
] | 1 | 0.003 | 2026-02-08T13:13:32.590154Z | {
"verified": true,
"answer": 60,
"timestamp": "2026-02-08T13:13:32.593478Z"
} | a5d53c | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 1,
"correct": {
"strict": false,
"boxed": false,
"relaxed": true
},
"usage": {
"prompt_tokens": 230,
"completion_tokens": 32768
},
"timestamp": "2026-02-24T17:32:57.442Z",
"answer": null
},
{
... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COMB1",
"status": "ok"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
}
] | {
"lo": 3.25,
"mid": 5.68,
"hi": 8.81
} | ||
e4b955 | nt_count_with_divisor_count_v1_1439011603_1199 | Let $N$ be the number of positive integers $n$ with $1 \leq n \leq 6084$ such that $n$ has exactly 10 positive divisors. Compute the value of $$ N + \left(2^{N \bmod 14}\right) \bmod 98376. $$ | 101 | graphs = [
Graph(
let={
"upper": Const(6084),
"div_count": Const(10),
"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"))))),
"Q": Sum(Ref("resu... | NT | null | COUNT | sympy | L3C | [
"COMB1"
] | fa9530 | nt_count_with_divisor_count_v1 | mod_exp | 5 | 0 | [
"COMB1",
"L3C"
] | 2 | 29.158 | 2026-02-08T15:58:06.234851Z | {
"verified": true,
"answer": 101,
"timestamp": "2026-02-08T15:58:35.392582Z"
} | 926556 | 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": 1941
},
"timestamp": "2026-02-16T18:33:27.803Z",
"answer": 101
},
{
... | 1 | [
{
"lemma": "COMB1",
"status": "ok"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
83335a | diophantine_fbi2_min_v1_655260480_2649 | Let $m=2$, and let $n$ be the largest prime number between $2$ and $11$, inclusive.
Let
$$k=\sum_{d\mid 14} \varphi(d),$$
where $\varphi$ denotes Euler's totient function.
Let $u=24$. Consider the set of all integers $d_1$ such that
$$m\le d_1\le u,\quad d_1\mid k,$$
and
$$\frac{k}{d_1}$$
is at least the number of po... | 2 | graphs = [
Graph(
let={
"_m": Const(2),
"_n": MaxOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(2)), Leq(Var("n"), Const(11)), IsPrime(Var("n"))))),
"k": SumOverDivisors(n=Const(value=14), var='d', expr=EulerPhi(n=Var(name='d'))),
"up... | NT | COMB | EXTREMUM | sympy | MAX_PRIME_BELOW | [
"MAX_PRIME_BELOW/K3",
"COPRIME_PAIRS"
] | 0073a8 | diophantine_fbi2_min_v1 | bell_mod | 7 | 0 | [
"COPRIME_PAIRS",
"K3",
"MAX_PRIME_BELOW"
] | 3 | 0.009 | 2026-02-08T16:53:03.592677Z | {
"verified": true,
"answer": 2,
"timestamp": "2026-02-08T16:53:03.601486Z"
} | f59e84 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 287,
"completion_tokens": 1816
},
"timestamp": "2026-02-17T15:06:34.149Z",
"answer": 2
},
{
... | 1 | [
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "K3",
"status": "ok_later"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok"
},
{
"lemma": "V1",
"status":... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
704f92 | alg_sum_powers_v1_1218484723_1992 | Find the remainder when $\sum_{k=1}^{\min\{ x + y : x > 0, y > 0, xy = 685584\}} k^3$ is divided by $\sum_{k_1=0}^{3} (3k_1 + 1513)$. | 626 | graphs = [
Graph(
let={
"_n": Const(3),
"result": Mod(value=Summation(var="k", 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')), Eq(Mul(Var("x"), Var("y"... | ALG | null | COMPUTE | sympy | SUM_AP | [
"SUM_AP",
"B3"
] | 639b1b | alg_sum_powers_v1 | null | 5 | 0 | [
"B3",
"SUM_AP"
] | 2 | 0.135 | 2026-02-25T03:42:40.794256Z | {
"verified": true,
"answer": 626,
"timestamp": "2026-02-25T03:42:40.929390Z"
} | f93f82 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 175,
"completion_tokens": 1430
},
"timestamp": "2026-03-29T02:23:33.410Z",
"answer": 626
},
{
"id... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "SUM_AP",
"status": "ok"
}
] | {
"lo": -2.47,
"mid": 1.2,
"hi": 4.81
} | ||
846500 | nt_count_coprime_v1_1978505735_7999 | Let $k$ be the number of positive integers $n$ such that $1 \leq n \leq 300$ and $11$ divides the $n$-th Fibonacci number. Let $N$ be the number of positive integers $n_1$ such that $1 \leq n_1 \leq 15625$ and $\gcd(n_1, k) = 1$. Compute $N$. | 4,167 | graphs = [
Graph(
let={
"_n": Const(300),
"upper": Const(15625),
"k": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Ref("_n")), Divides(divisor=Const(11), dividend=Fibonacci(arg=Var(name='n')))))),
"result": C... | NT | null | COUNT | sympy | COUNT_FIB_DIVISIBLE | [
"COUNT_FIB_DIVISIBLE"
] | 66de3c | nt_count_coprime_v1 | null | 6 | 0 | [
"COUNT_FIB_DIVISIBLE"
] | 1 | 1.12 | 2026-02-08T20:37:19.787107Z | {
"verified": true,
"answer": 4167,
"timestamp": "2026-02-08T20:37:20.906648Z"
} | 054271 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 132,
"completion_tokens": 2186
},
"timestamp": "2026-02-19T00:46:56.580Z",
"answer": 4167
},
{... | 1 | [
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "ok"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "V8",
"status": "n... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
5382bd | nt_sum_totient_over_divisors_v1_124444284_6825 | Let $n$ be the sum of all solutions $x$ to the equation $x^2 - 9237x + 786986 = 0$. Compute the sum of $\phi(d)$ over all positive divisors $d$ of $n$, where $\phi$ denotes Euler's totient function. | 9,237 | graphs = [
Graph(
let={
"_n": Const(2),
"n": SumOverSet(set=SolutionsSet(var=Var("x"), condition=Eq(Sum(Pow(Var("x"), Ref("_n")), Mul(Const(-9237), Var("x")), Const(786986)), Const(0)))),
"result": SumOverDivisors(n=Ref(name='n'), var='d', expr=EulerPhi(n=Var(name='d'))),... | NT | null | COMPUTE | sympy | VIETA_SUM | [
"VIETA_SUM"
] | b33a7a | nt_sum_totient_over_divisors_v1 | null | 5 | 0 | [
"VIETA_SUM"
] | 1 | 0.003 | 2026-02-08T08:39:21.478795Z | {
"verified": true,
"answer": 9237,
"timestamp": "2026-02-08T08:39:21.482026Z"
} | 8d963f | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 1,
"correct": {
"strict": false,
"boxed": false,
"relaxed": true
},
"usage": {
"prompt_tokens": 128,
"completion_tokens": 703
},
"timestamp": "2026-02-15T20:18:13.880Z",
"answer": 10791
},
{
"id": 11,... | 1 | [
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "VIETA_SUM",
"status": "... | {
"lo": -7.01,
"mid": -4.68,
"hi": -2.15
} | ||
a9337f | diophantine_sum_product_min_v1_1915831931_1574 | Let $S$ be the number of integers $t$ such that $7 \leq t \leq 54$ and there exist integers $a$ and $b$ with $1 \leq a \leq 2$, $1 \leq b \leq 22$, and $t = 5a + 2b$. Let $P = 448$. Consider the set of all positive integers $x$ such that $1 \leq x \leq N$, where $N$ is the number of integers $t_1$ such that $7 \leq t_1... | 30,609 | graphs = [
Graph(
let={
"S": CountOverSet(set=SolutionsSet(var=Var("t"), condition=Exists(var=Var(name='a'), condition=Exists(var=Var(name='b'), condition=And(Geq(left=Var(name='a'), right=Const(value=1)), Leq(left=Var(name='a'), right=Const(value=2)), Geq(left=Var(name='b'), right=Const(value=1... | NT | null | EXTREMUM | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | diophantine_sum_product_min_v1 | null | 6 | 0 | [
"LIN_FORM"
] | 1 | 0.013 | 2026-02-08T16:15:58.948781Z | {
"verified": true,
"answer": 30609,
"timestamp": "2026-02-08T16:15:58.961587Z"
} | f15172 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 254,
"completion_tokens": 1729
},
"timestamp": "2026-02-17T00:32:28.264Z",
"answer": 30609
},
... | 1 | [
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "V3",
"status": "no"
},
{
"lemma": "V7",
"status": ... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
99fe52 | geo_count_lattice_rect_v1_655260480_809 | Compute the number of lattice points in the rectangle $[0, 17] \times [0, 58]$, including the boundary. Then find the remainder when this number is multiplied by $44121$ and divided by $86203$. | 48,273 | graphs = [
Graph(
let={
"a": Const(17),
"b": Const(58),
"result": LatticePointsRect(a=Ref(name='a'), b=Ref(name='b')),
"Q": Mod(value=Mul(Const(44121), Ref("result")), modulus=Const(86203)),
},
goal=Ref("Q"),
)
] | GEOM | null | COUNT | sympy | [] | geo_count_lattice_rect_v1 | null | 3 | 0 | null | null | 0.002 | 2026-02-08T15:37:35.512111Z | {
"verified": true,
"answer": 48273,
"timestamp": "2026-02-08T15:37:35.513668Z"
} | a2d22c | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 160,
"completion_tokens": 677
},
"timestamp": "2026-02-24T18:14:29.143Z",
"answer": 48273
},
{
"... | 1 | [] | {
"lo": -2.4,
"mid": 1.57,
"hi": 5.75
} | ||||
a37f73 | sequence_count_fib_divisible_v1_48377204_252 | Let $U$ be the number of integers $t$ with $16 \leq t \leq 242$ for which there exist positive integers $a \leq 22$ and $b \leq 11$ such that $t = 6a + 10b$.
Compute the number of positive integers $n \leq U$ such that $11$ divides $F_n$, where $F_n$ denotes the $n$-th Fibonacci number. Let this count be $C$. Find $30... | 30,615 | graphs = [
Graph(
let={
"upper": CountOverSet(set=SolutionsSet(var=Var("t"), condition=Exists(var=Var(name='a'), condition=Exists(var=Var(name='b'), condition=And(Geq(left=Var(name='a'), right=Const(value=1)), Leq(left=Var(name='a'), right=Const(value=22)), Geq(left=Var(name='b'), right=Const(va... | NT | null | COUNT | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | sequence_count_fib_divisible_v1 | null | 6 | 0 | [
"LIN_FORM"
] | 1 | 0.029 | 2026-02-08T15:19:13.982177Z | {
"verified": true,
"answer": 30615,
"timestamp": "2026-02-08T15:19:14.010993Z"
} | 134332 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 154,
"completion_tokens": 4097
},
"timestamp": "2026-02-16T03:07:10.004Z",
"answer": 30615
},
... | 1 | [
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "V1",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
564899 | v7_endings_v1_1742523217_866 | For each integer $k$ with $0\le k\le 4093$, consider the binomial coefficient $\binom{4093}{k}$. Let $v_3\!\left(\binom{4093}{k}\right)$ denote the largest integer $e$ such that $3^e$ divides $\binom{4093}{k}$.
Let $N$ be the number of integers $k$ with $0\le k\le 4093$ such that $v_3\!\left(\binom{4093}{k}\right)=2$.... | 49,144 | graphs = [
Graph(
let={
"_inner_result": CountOverSet(set=SolutionsSet(var=Var("k"), condition=And(Geq(Var("k"), Const(0)), Leq(Var("k"), Const(4093)), Eq(MaxKDivides(target=Binom(n=Const(4093), k=Var("k")), base=Const(3)), Const(2))))),
"_scale_k": Const(16409),
"_scaled... | NT | null | COMPUTE | sympy | V7 | [
"V7"
] | 0672d4 | v7_endings_v1 | null | 8 | null | [
"V7"
] | 1 | 0.008 | 2026-02-08T03:19:00.795198Z | {
"verified": true,
"answer": 49144,
"timestamp": "2026-02-08T03:19:00.802869Z"
} | c7a9ce | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 266,
"completion_tokens": 6426
},
"timestamp": "2026-02-09T08:03:26.094Z",
"answer": 49144
},
{
... | 1 | [
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "V7",
"status": "ok"
},
{
"lemma": "V8_SUM",
"status": "no"
}
] | {
"lo": -6.49,
"mid": 0.51,
"hi": 7.52
} | ||
2b964c | geo_visible_lattice_v1_677425708_184 | Let $n = 89$. A lattice point $(x, y)$ is called *visible* if $1 \leq x, y \leq n$ and $\gcd(x, y) = 1$. Compute the number of visible lattice points $(x, y)$ in the $n \times n$ grid. | 4,911 | graphs = [
Graph(
let={
"n": Const(89),
"result": VisibleLatticePoints(n=Ref(name='n')),
},
goal=Ref("result"),
)
] | GEOM | null | COUNT | sympy | [] | geo_visible_lattice_v1 | null | 7 | 0 | null | null | 0.201 | 2026-02-08T03:06:59.246745Z | {
"verified": true,
"answer": 4911,
"timestamp": "2026-02-08T03:06:59.447909Z"
} | 11f0b2 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 182,
"completion_tokens": 4055
},
"timestamp": "2026-02-08T20:20:21.976Z",
"answer": 4911
},
{
"i... | 1 | [] | {
"lo": 3.03,
"mid": 4.42,
"hi": 5.71
} | ||||
65bd71 | nt_count_digit_sum_v1_784195855_1261 | Let $n$ be a positive integer. Define $S$ as the set of all positive integers $n \leq 74$ that are even and relatively prime to 15. Let $T$ be the set of all positive integers $n \leq 478864$ such that the sum of the decimal digits of $n$ is equal to the number of elements in $S$. Compute the number of elements in $T$. | 23,595 | graphs = [
Graph(
let={
"_n": Const(74),
"upper": Const(478864),
"target_sum": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Ref("_n")), Divides(divisor=Const(2), dividend=Var("n")), Eq(GCD(a=Var("n"), b=Const(15)), Const... | NT | null | COUNT | sympy | C5 | [
"C5"
] | 1d9668 | nt_count_digit_sum_v1 | null | 6 | 0 | [
"C5"
] | 1 | 28.485 | 2026-02-08T04:56:23.667258Z | {
"verified": true,
"answer": 23595,
"timestamp": "2026-02-08T04:56:52.152204Z"
} | 3b3fbd | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 200,
"completion_tokens": 4218
},
"timestamp": "2026-02-11T22:30:28.738Z",
"answer": 23595
},
{
... | 1 | [
{
"lemma": "C5",
"status": "ok"
},
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
},
{
"lemma": "VAL_SUM_EQ",
"status": "no"
}
] | {
"lo": -3.42,
"mid": 1.86,
"hi": 7.55
} | ||
a677d9 | nt_count_intersection_v1_809748730_862 | Let $N = 100000$, $a = 9$, and $b = 20$. Let $r$ be the number of positive integers $n$ such that $1 \leq n \leq 100000$, $9$ divides $n$, and $\gcd(n, 20) = 1$. Let
$$
s = \sum_{k=1}^{5} \phi(k) \left\lfloor \frac{5}{k} \right\rfloor,
$$
where $\phi(k)$ denotes Euler's totient function. Compute
$$
r + \left(2^{r \bmod... | 4,477 | graphs = [
Graph(
let={
"N": Const(100000),
"a": Const(9),
"b": Const(20),
"result": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Ref("N")), Divides(divisor=Ref("a"), dividend=Var("n")), Eq(GCD(a=Var("n"), b=... | NT | null | COUNT | sympy | K2 | [
"K2"
] | 63106b | nt_count_intersection_v1 | mod_exp | 4 | 0 | [
"K2"
] | 1 | 3.727 | 2026-02-08T11:47:22.061110Z | {
"verified": true,
"answer": 4477,
"timestamp": "2026-02-08T11:47:25.788054Z"
} | 19b8b2 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 184,
"completion_tokens": 1129
},
"timestamp": "2026-02-14T19:02:16.537Z",
"answer": 4477
},
{... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "K2",
"status": "ok"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
}
] | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
182790_l | nt_count_primes_v1_798873815_95 | Let $m = 7$ and $n = 2$. Let $\text{result}$ be the number of prime numbers $p$ such that $n \leq p \leq 76729$. Let $S$ be the set of all positive integers $d$ such that $d$ is prime, $d \leq 11$, and $d$ is at least the number of positive integers $k \leq 35$ that are divisible by $m$ and satisfy $\gcd(k, 6) = 1$. Le... | 1 | NT | COMB | COUNT | sympy | C5 | [
"C5/MAX_PRIME_BELOW"
] | d53851 | nt_count_primes_v1 | bell_mod | 6 | 0 | [
"C5",
"MAX_PRIME_BELOW"
] | 2 | 1.98 | 2026-02-08T02:26:08.806672Z | {
"verified": false,
"answer": 21147,
"timestamp": "2026-02-08T02:26:10.786619Z"
} | ddbf03 | 182790 | 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": 260,
"completion_tokens": 32768
},
"timestamp": "2026-02-23T15:27:12.464Z",
"answer": 21147
},
{
... | 1 | [
{
"lemma": "C5",
"status": "ok"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok_later"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status... | {
"lo": 4.89,
"mid": 6.37,
"hi": 8.31
} | |
8219a8 | comb_count_partitions_v1_124444284_4617 | Let $S$ be the set of all ordered pairs $(x,y)$ of positive integers such that $x + y = 6$. Define $m$ to be the maximum value of $xy$ over all such pairs in $S$. Let $n = \sum_{k=1}^{9} \phi(k) \left\lfloor \frac{m}{k} \right\rfloor$, where $\phi$ denotes Euler's totient function. Compute the number of integer partiti... | 89,134 | graphs = [
Graph(
let={
"_m": Const(9),
"_n": MaxOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(Sum(Var("x"), Var("y")), Const(6)))), expr=Mul(Var("x"), Var("y")))),
... | NT | COMB | COUNT | sympy | B1 | [
"B1/K2"
] | ebd04c | comb_count_partitions_v1 | null | 7 | 0 | [
"B1",
"K2"
] | 2 | 0.003 | 2026-02-08T06:06:29.877756Z | {
"verified": true,
"answer": 89134,
"timestamp": "2026-02-08T06:06:29.880492Z"
} | 960dd3 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 148,
"completion_tokens": 1188
},
"timestamp": "2026-02-12T20:34:14.899Z",
"answer": 89134
},
... | 1 | [
{
"lemma": "B1",
"status": "ok"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "K2",
"status": "ok_later"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": ... | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
fcff02 | comb_count_surjections_v1_1218484723_2433 | Let $n$ be the number of non-negative integers $a$ with $0 \le a \le 1848$ such that
$$
\left(\left(\left(\left(a^{2} - 637 \bmod 1849\right)^{2} - 637 \bmod 1849\right)^{2} - 637 \bmod 1849\right)^{2} - 637 \bmod 1849\right)^{2} - 637 \bmod 1849 = a,
$$
and
$$
a^{2} - 637 \bmod 1849 \ne a,\quad \left(a^{2} - 637 \bmo... | 120 | graphs = [
Graph(
let={
"_n": Const(1849),
"n": CountOverSet(set=SolutionsSet(var=Var("a"), condition=And(Geq(Var("a"), Const(0)), Leq(Var("a"), Const(1848)), Eq(Mod(value=Sum(Pow(Mod(value=Sum(Pow(Mod(value=Sum(Pow(Mod(value=Sum(Pow(Mod(value=Sum(Pow(Var("a"), Const(2)), Const(-637)... | COMB | null | COUNT | sympy | POLY_ORBIT_HENSEL | [
"POLY_ORBIT_HENSEL"
] | 53b6eb | comb_count_surjections_v1 | null | 6 | 0 | [
"POLY_ORBIT_HENSEL"
] | 1 | 0.002 | 2026-02-25T04:13:00.134177Z | {
"verified": true,
"answer": 120,
"timestamp": "2026-02-25T04:13:00.136278Z"
} | 2b2374 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 1,
"correct": {
"strict": false,
"boxed": false,
"relaxed": true
},
"usage": {
"prompt_tokens": 444,
"completion_tokens": 13548
},
"timestamp": "2026-03-29T04:46:20.655Z",
"answer": 0
},
{
"i... | 1 | [
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "POLY_ORBIT_HENSEL",
"status": "ok"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8",... | {
"lo": 1.55,
"mid": 4.7,
"hi": 7.23
} | ||
0ae8dd | lin_form_endings_v1_1918700295_289 | Let $a = 56$ and $b = 32$. Let $l$ be the least common multiple of $a$ and $b$. Let $k = 16162$. Define $s = k \cdot l$. Compute the remainder when $s$ is divided by $62320$. | 5,728 | graphs = [
Graph(
let={
"a_coeff": Const(56),
"b_coeff": Const(32),
"_inner_result": LCM(a=Ref("a_coeff"), b=Ref("b_coeff")),
"_scale_k": Const(16162),
"_scaled": Mul(Ref("_scale_k"), Ref("_inner_result")),
"_mod_M": Const(62320),
... | COMB | NT | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | lin_form_endings_v1 | null | 2 | null | [
"LIN_FORM"
] | 1 | 0.001 | 2026-02-08T03:08:45.994639Z | {
"verified": true,
"answer": 5728,
"timestamp": "2026-02-08T03:08:45.995185Z"
} | 41307d | 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": 1117
},
"timestamp": "2026-02-10T13:11:36.695Z",
"answer": 5728
},
{
"i... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "V8",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
... | {
"lo": -3.46,
"mid": 1.03,
"hi": 5.49
} | ||
3221ae | nt_count_with_divisor_count_v1_1439011603_2537 | Let $n$ be a positive integer. Define $S$ to be the set of all ordered pairs $(x,y)$ of positive integers such that $xy = 13675204$. Let $T$ be the set of all values $x + y$ where $(x, y) \in S$. Let $m$ be the minimum value in $T$.
Now, define $U$ to be the set of all integers $t$ such that $21 \leq t \leq 81$ and th... | 23 | graphs = [
Graph(
let={
"_n": Const(2),
"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(13675204)))), expr=Sum(Var("x"), Var("y"... | NT | null | COUNT | sympy | LIN_FORM | [
"LIN_FORM/MIN_PRIME_FACTOR",
"B3"
] | b13e15 | nt_count_with_divisor_count_v1 | null | 6 | 0 | [
"B3",
"LIN_FORM",
"MIN_PRIME_FACTOR"
] | 3 | 0.313 | 2026-02-08T16:51:14.668919Z | {
"verified": true,
"answer": 23,
"timestamp": "2026-02-08T16:51:14.981435Z"
} | c2a944 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 299,
"completion_tokens": 2752
},
"timestamp": "2026-02-17T13:38:48.833Z",
"answer": 23
},
{
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MIN_PRIME_FACTOR",
"status": "ok_later"
... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
a72733 | nt_count_digit_sum_v1_458359167_1732 | Let $S$ be the set of all positive integers $n \leq 99999$ such that the sum of the decimal digits of $n$ is equal to $1 + 2 + 3 + 4 + 5$. Compute the number of elements in $S$. | 3,246 | graphs = [
Graph(
let={
"_n": Const(5),
"upper": Const(99999),
"target_sum": Summation(var="k", start=Const(1), end=Ref("_n"), expr=Var("k")),
"result": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Ref("upper... | NT | null | COUNT | sympy | SUM_ARITHMETIC | [
"SUM_ARITHMETIC"
] | eb34f0 | nt_count_digit_sum_v1 | null | 4 | 0 | [
"SUM_ARITHMETIC"
] | 1 | 3.925 | 2026-02-08T04:49:26.663606Z | {
"verified": true,
"answer": 3246,
"timestamp": "2026-02-08T04:49:30.588157Z"
} | 243a76 | 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": 1263
},
"timestamp": "2026-02-11T22:11:04.455Z",
"answer": 3246
},
{
"... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "SUM_ARITHMETIC",
"status": "ok"
}
] | {
"lo": -3.42,
"mid": 1.86,
"hi": 7.55
} | ||
07c939 | comb_count_permutations_fixed_v1_655260480_1576 | Let $n = 5$ and $k = 3$. Define $r = \binom{n}{k} \cdot !(n - k)$, where $!m$ denotes the number of derangements of $m$ elements. Let $T$ be the set of all integers $t$ with $10 \le t \le 34$ for which there exist positive integers $a$ and $b$ such that $1 \le a \le 3$, $1 \le b \le 4$, and $t = 6a + 4b$. Let $d$ be th... | 38,067 | graphs = [
Graph(
let={
"_n": Const(77908),
"n": Const(5),
"k": Const(3),
"result": Mul(Binom(n=Ref("n"), k=Ref("k")), Subfactorial(arg=Sub(left=Ref(name='n'), right=Ref(name='k')))),
"Q": Mod(value=Bell(Mod(value=Abs(arg=Ref(name='result')), modul... | COMB | null | COUNT | sympy | MIN_PRIME_FACTOR | [
"LIN_FORM"
] | 1ae498 | comb_count_permutations_fixed_v1 | bell_mod | 4 | 0 | [
"LIN_FORM",
"MIN_PRIME_FACTOR"
] | 2 | 0.031 | 2026-02-08T16:13:32.972672Z | {
"verified": true,
"answer": 38067,
"timestamp": "2026-02-08T16:13:33.003176Z"
} | fdd699 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 289,
"completion_tokens": 1018
},
"timestamp": "2026-02-24T20:08:36.392Z",
"answer": 38067
},
{
... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "V7",
"st... | {
"lo": -5.65,
"mid": -3.17,
"hi": -0.81
} | ||
80599e | antilemma_sum_equals_v1_124444284_9917 | Let $x$ be the number of ordered pairs $(i, j)$ of integers such that $1 \leq i \leq 59$, $1 \leq j \leq 59$, and $i + j = 61$. Compute $$\sum_{n=\binom{4}{0}}^{x} \phi(n).$$ | 1,028 | graphs = [
Graph(
let={
"x": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("i"), Var("j")]), condition=Eq(Sum(Var("i"), Var("j")), Const(61)), domain=CartesianProduct(left=IntegerRange(start=Const(1), end=Const(59)), right=IntegerRange(start=Const(1), end=Const(59))))),
"Q": ... | COMB | GEOM | COMPUTE | sympy | COUNT_SUM_EQUALS | [
"COUNT_SUM_EQUALS",
"ONE_BINOM_0"
] | ec98de | antilemma_sum_equals_v1 | null | 4 | 0 | [
"COUNT_SUM_EQUALS",
"ONE_BINOM_0"
] | 2 | 0.021 | 2026-02-08T12:43:38.120178Z | {
"verified": true,
"answer": 1028,
"timestamp": "2026-02-08T12:43:38.141470Z"
} | 15668d | 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": 2676
},
"timestamp": "2026-02-24T16:16:25.635Z",
"answer": 1028
},
{
"i... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "ok"
},
{
"lemma": "ONE_BINOM_0",
"status": "ok"
},
{
"lemma": "V7",
"st... | {
"lo": 1.15,
"mid": 4.18,
"hi": 6.61
} | ||
b1dc1f | algebra_quadratic_discriminant_v1_1470522791_1690 | Let $a = -2$, $b = -24$, $c = -54$, and let $n = 4$. Define $D = b^k - 4ac$, where $k$ is the number of positive integers $p$ for which there exists an integer $q$ such that $pq = 72$, $\gcd(p, q) = 1$, and $p < q$. Let $\alpha = 1$ if $D > 0$, and $0$ otherwise. Let $\beta = 1$ if $D = 0$, and $0$ otherwise. Compute $... | 88,242 | graphs = [
Graph(
let={
"_n": Const(4),
"a": Const(-2),
"b": Const(-24),
"c": Const(-54),
"D": Sub(Pow(Ref("b"), CountOverSet(set=SolutionsSet(var=Var("p"), condition=And(IsPositive(arg=Var(name='p')), Exists(var=Var(name='q'), condition=And(Eq(lef... | NT | null | COMPUTE | sympy | COPRIME_PAIRS | [
"COPRIME_PAIRS"
] | 2bb3aa | algebra_quadratic_discriminant_v1 | null | 5 | 0 | [
"COPRIME_PAIRS"
] | 1 | 0.002 | 2026-02-08T13:51:15.937181Z | {
"verified": true,
"answer": 88242,
"timestamp": "2026-02-08T13:51:15.939542Z"
} | 6932af | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 184,
"completion_tokens": 866
},
"timestamp": "2026-02-15T21:14:00.967Z",
"answer": 88242
},
{... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "V3",
"status": "no"
},
{
"lemma": "VAL_SUM_EQ",
"status": "no"
... | {
"lo": -5.49,
"mid": 0.22,
"hi": 6.51
} | ||
8da09d | comb_catalan_compute_v1_2051736721_1243 | Let $S$ be the set of all ordered pairs $(a,b)$ of positive integers such that $1 \leq a \leq 4$, $1 \leq b \leq 6$, and let $T$ be the set of all integers $t$ such that $21 \leq t \leq 102$ and $t = 12a + 9b$ for some $(a,b) \in S$. Let $n$ be the number of ordered pairs $(x_1, x_2)$ of positive odd integers such that... | 53,836 | graphs = [
Graph(
let={
"_n": Const(76810),
"n": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x1"), Var("x2")]), condition=And(IsPositive(arg=Var(name='x1')), IsPositive(arg=Var(name='x2')), IsOdd(arg=Var(name='x1')), IsOdd(arg=Var(name='x2')), Eq(Sum(Var("x1"), Var("x2")),... | COMB | null | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM/COMB1"
] | 268a62 | comb_catalan_compute_v1 | null | 4 | 0 | [
"COMB1",
"LIN_FORM"
] | 2 | 0.003 | 2026-02-08T15:54:55.583982Z | {
"verified": true,
"answer": 53836,
"timestamp": "2026-02-08T15:54:55.586927Z"
} | a04baa | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 277,
"completion_tokens": 3895
},
"timestamp": "2026-02-24T18:59:00.353Z",
"answer": 53836
},
{
... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COMB1",
"status": "ok_later"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "V7",
"status": "n... | {
"lo": -2.4,
"mid": 1.57,
"hi": 5.75
} | ||
7bbeb8 | geo_count_lattice_rect_v1_809748730_1448 | Compute the number of lattice points $(x, y)$ such that $0 \leq x \leq 289$ and $0 \leq y \leq 204$. | 59,450 | graphs = [
Graph(
let={
"a": Const(289),
"b": Const(204),
"result": LatticePointsRect(a=Ref(name='a'), b=Ref(name='b')),
},
goal=Ref("result"),
)
] | GEOM | null | COUNT | sympy | [] | geo_count_lattice_rect_v1 | null | 3 | 0 | null | null | 0.002 | 2026-02-08T12:25:58.044772Z | {
"verified": true,
"answer": 59450,
"timestamp": "2026-02-08T12:25:58.046304Z"
} | d50b78 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 148,
"completion_tokens": 113
},
"timestamp": "2026-02-24T15:42:35.923Z",
"answer": 59450
},
{
"i... | 1 | [] | {
"lo": -7.18,
"mid": -5,
"hi": -3.01
} | ||||
ecd0ab_n | alg_sum_powers_v1_1218484723_7739 | A pyramid-shaped warehouse stacks boxes in layers: the first layer has $1^3$ boxes, the second $2^3$, up to the $1067$th layer with $1067^3$ boxes. Boxes are packed into trucks that hold $2215$ each. After filling as many trucks as possible, how many boxes remain? | 1,084 | ALG | null | COMPUTE | sympy | POLY_ORBIT_HENSEL | [
"POLY_ORBIT_HENSEL/QF_PSD_COUNT_LEQ",
"LIN_FORM"
] | 0f1844 | alg_sum_powers_v1 | null | 2 | null | [
"LIN_FORM",
"POLY_ORBIT_HENSEL",
"QF_PSD_COUNT_LEQ"
] | 3 | 0.23 | 2026-02-25T09:18:20.423044Z | null | 9a1f8a | ecd0ab | narrative | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 181,
"completion_tokens": 675
},
"timestamp": "2026-03-31T02:59:50.757Z",
"answer": 1084
},
{
"id... | 1 | [
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "POLY_ORBIT_HENSEL",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "QF_PSD_COUNT_LEQ",
"status": "ok_later"
}
] | {
"lo": -5.37,
"mid": 0.23,
"hi": 5.22
} | |
fce19e | diophantine_fbi2_count_v1_1125832087_184 | Let $n$ range over the integers from $1$ to $4620$, inclusive. Define $k$ to be the number of such integers $n$ for which
$$
n \equiv \left\lfloor \frac{n}{2} \right\rfloor \pmod{11}.
$$
Now consider the positive integers $d$ satisfying $2 \leq d \leq 129$ such that $d$ divides $k$, and $\frac{k}{d}$ is an integer sat... | 18 | graphs = [
Graph(
let={
"_n": Const(4620),
"k": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Ref("_n")), Congruent(a=Var(name='n'), b=Floor(arg=Div(left=Var(name='n'), right=Const(value=2))), modulus=Const(value=11))))),
... | NT | null | COUNT | sympy | K2 | [
"L3C"
] | 73f8b0 | diophantine_fbi2_count_v1 | null | 6 | 0 | [
"K2",
"L3C"
] | 2 | 0.214 | 2026-02-08T02:55:26.269217Z | {
"verified": true,
"answer": 18,
"timestamp": "2026-02-08T02:55:26.483561Z"
} | 2e518d | 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": 1466
},
"timestamp": "2026-02-10T12:49:20.016Z",
"answer": 18
},
{
"id"... | 1 | [
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "L3C",
"status": "ok"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
... | {
"lo": -0.03,
"mid": 1.72,
"hi": 3.3
} | ||
0ca029 | modular_sum_quadratic_residues_v1_601307018_4862 | Let $p$ be the largest prime number $n$ with $2 \le n \le 510$. Let $M = \frac{p(p - 1)}{4}$. Find the remainder when $20609 \cdot M$ is divided by $71116$. | 11,559 | graphs = [
Graph(
let={
"_n": Const(20609),
"p": MaxOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(2)), Leq(Var("n"), Const(510)), IsPrime(Var("n"))))),
"result": Div(Mul(Ref("p"), Sub(Ref("p"), Const(1))), Const(4)),
"Q": Mod(value=M... | NT | null | SUM | sympy | POLY_ORBIT_LEGENDRE | [
"MAX_PRIME_BELOW"
] | dc3ad3 | modular_sum_quadratic_residues_v1 | null | 2 | 0 | [
"MAX_PRIME_BELOW",
"POLY_ORBIT_LEGENDRE"
] | 2 | 0.009 | 2026-03-10T05:34:12.278875Z | {
"verified": true,
"answer": 11559,
"timestamp": "2026-03-10T05:34:12.287997Z"
} | cecdd6 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 169,
"completion_tokens": 3639
},
"timestamp": "2026-03-29T13:40:52.160Z",
"answer": 11559
},
{
"... | 1 | [
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok"
},
{
"lemma": "MAX_VAL",
"status": "no"
}
] | {
"lo": -3.34,
"mid": 0.9,
"hi": 4.9
} | ||
eadba4 | modular_sum_quadratic_residues_v1_1439011603_2896 | Let $m = 4$. Let $n$ be the sum of $\phi(d)$ over all positive divisors $d$ of $257$. Let $p$ be the largest positive divisor of $69647$ that is at most $n$. Define $\text{result} = \frac{p(p-1)}{m}$ and $Q = 22801 - \text{result}$. Compute $Q$. | 6,353 | graphs = [
Graph(
let={
"_m": Const(4),
"_n": SumOverDivisors(n=Const(value=257), var='d', expr=EulerPhi(n=Var(name='d'))),
"p": MaxOverSet(set=SolutionsSet(var=Var("d1"), condition=And(Geq(Var("d1"), Const(1)), Leq(Var("d1"), Ref("_n")), Divides(divisor=Var("d1"), divide... | NT | null | SUM | sympy | K3 | [
"K3/MAX_DIVISOR"
] | 43ff77 | modular_sum_quadratic_residues_v1 | null | 5 | 0 | [
"K3",
"MAX_DIVISOR"
] | 2 | 0.007 | 2026-02-08T17:03:36.011925Z | {
"verified": true,
"answer": 6353,
"timestamp": "2026-02-08T17:03:36.019360Z"
} | ec543b | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 131,
"completion_tokens": 863
},
"timestamp": "2026-02-17T19:09:00.375Z",
"answer": 6353
},
{
... | 1 | [
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "K3",
"status": "ok"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "MAX_DIVISOR",
"status": "ok_later"
},
{
"lemma": "POLY_PADIC_VAL_... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
fb20f1 | diophantine_fbi2_min_v1_124444284_7233 | Let $m = 143$ and let $n$ be the largest divisor of $21307$ that is at most $m$. Let $k = 10$ and define $\text{result}$ to be the smallest integer $d \geq 2$ such that $d \leq 20$, $d$ divides $k$, and $\frac{k}{d} \geq 4$. Let $p$ be the smallest prime divisor of $n$ that is at least $2$. Define $Q = B_r$, where $r =... | 2 | graphs = [
Graph(
let={
"_m": Const(143),
"_n": MaxOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Const(1)), Leq(Var("d"), Ref("_m")), Divides(divisor=Var("d"), dividend=Const(21307))))),
"k": Const(10),
"upper": Const(20),
"res... | NT | COMB | EXTREMUM | sympy | MAX_DIVISOR | [
"MAX_DIVISOR/MIN_PRIME_FACTOR"
] | 73c65a | diophantine_fbi2_min_v1 | bell_mod | 6 | 0 | [
"MAX_DIVISOR",
"MIN_PRIME_FACTOR"
] | 2 | 0.005 | 2026-02-08T08:57:43.797156Z | {
"verified": true,
"answer": 2,
"timestamp": "2026-02-08T08:57:43.802447Z"
} | ae5dd1 | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 1,
"correct": {
"strict": false,
"boxed": false,
"relaxed": true
},
"usage": {
"prompt_tokens": 209,
"completion_tokens": 310
},
"timestamp": "2026-02-15T20:26:22.153Z",
"answer": 52
},
{
"id": 11,
... | 1 | [
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "MAX_DIVISOR",
"status": "ok"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "MIN_PRIME_FACTOR",
"status": "ok_later"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
... | {
"lo": -9.14,
"mid": -6.05,
"hi": -3.73
} | ||
5a912c_n | comb_binomial_compute_v1_601307018_1137 | A game board has positions labeled from $0$ to $\pi(69911)$, where $\pi(69911)$ counts the primes up to $69911$. On each turn, a player picks integers $a$ and $b$ between $1$ and $14$, and computes the score $41a^2 - 82ab + 41b^2$. A score is valid if it lands on the board. Let $n$ be the number of distinct valid score... | 3,003 | COMB | null | COMPUTE | sympy | COUNT_PRIMES | [
"COUNT_PRIMES/QF_PSD_DISTINCT"
] | fff0c5 | comb_binomial_compute_v1 | null | 6 | null | [
"COUNT_PRIMES",
"QF_PSD_DISTINCT"
] | 2 | 0.009 | 2026-03-10T01:43:32.641468Z | null | 9e9b36 | 5a912c | narrative | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 246,
"completion_tokens": 26720
},
"timestamp": "2026-03-29T14:56:19.456Z",
"answer": 1287
},
{
... | 1 | [
{
"lemma": "COUNT_PRIMES",
"status": "ok"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "QF_PSD_DISTINCT",
"status": "ok_later"
},
{
"lemma": "V5",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
},
... | {
"lo": -5.36,
"mid": 0.27,
"hi": 5.45
} | |
6fa36a | nt_count_divisible_v1_798873815_316 | Let $a = \sum_{d \mid \gcd(5,7)} \mu(d)$, where $\mu$ denotes the Möbius function. Let $S$ be the set of all integers $n$ such that $n \geq a$, $n \leq 32768$, and $n$ is divisible by 4. Compute the number of elements in $S$. | 8,192 | graphs = [
Graph(
let={
"upper": Const(32768),
"divisor": Const(4),
"result": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), SumOverDivisors(n=GCD(a=Const(value=5), b=Const(value=7)), var='d', expr=MoebiusMu(n=Var(name='d')))), Leq(Var("n"), Ref("... | NT | null | COUNT | sympy | MOBIUS_COPRIME | [
"MOBIUS_COPRIME"
] | ac54ac | nt_count_divisible_v1 | null | 3 | 0 | [
"MOBIUS_COPRIME"
] | 1 | 1.007 | 2026-02-08T02:33:12.173622Z | {
"verified": true,
"answer": 8192,
"timestamp": "2026-02-08T02:33:13.180557Z"
} | 382415 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 198,
"completion_tokens": 582
},
"timestamp": "2026-02-08T19:20:45.112Z",
"answer": 8192
},
{
"id... | 2 | [
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MOBIUS_COPRIME",
"status": "ok"
},
{
"lemma": "MOD_ADD",
"s... | {
"lo": -10,
"mid": -6.87,
"hi": -3.74
} | ||
fc5a82 | comb_count_surjections_v1_971394319_1403 | Let $n = 5$ and $k = 3$. Compute the value of $k! \cdot S(n, k)$, where $S(n, k)$ denotes the Stirling number of the second kind. Let $Q$ be the remainder when $44121$ times this value is divided by $94936$. Find the value of $Q$. | 67,566 | graphs = [
Graph(
let={
"n": Const(5),
"k": Const(3),
"result": Mul(Factorial(Ref("k")), Stirling2(n=Ref(name='n'), k=Ref(name='k'))),
"Q": Mod(value=Mul(Const(44121), Ref("result")), modulus=Const(94936)),
},
goal=Ref("Q"),
)
] | COMB | null | COUNT | sympy | COMB1 | [
"COMB1/COUNT_SUM_EQUALS"
] | 4d9cac | comb_count_surjections_v1 | null | 3 | 0 | [
"COMB1",
"COUNT_SUM_EQUALS"
] | 2 | 0.024 | 2026-02-08T13:39:59.698222Z | {
"verified": true,
"answer": 67566,
"timestamp": "2026-02-08T13:39:59.722241Z"
} | 8efd9d | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 186,
"completion_tokens": 1179
},
"timestamp": "2026-02-24T18:53:47.324Z",
"answer": 67566
},
{
"... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COMB1",
"status": "ok"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "ok_later"
},
{
"lemma": "V7",
"sta... | {
"lo": -3.84,
"mid": -1.67,
"hi": 1.32
} | ||
7a8c4b | alg_poly_orbit_count_v1_1218484723_5075 | For a non-negative integer $a$, define
\[N \equiv a^{5} + 3a^{3} - 4a + 2 \pmod{59},\]
\[M \equiv N^{5} + 3N^{3} - 4N + 2 \pmod{59},\]
\[R \equiv M^{5} + 3M^{3} - 4M + 2 \pmod{59},\]
\[S \equiv R^{5} + 3R^{3} - 4R + 2 \pmod{59},\]
\[T \equiv S^{5} + 3S^{3} - 4S + 2 \pmod{59}.\]
Let $Q$ be the number of integers $a$ wit... | 9,475 | graphs = [
Graph(
let={
"p1": Mod(value=Sum(Pow(Var("a"), Const(5)), Mul(Const(3), Pow(Var("a"), Const(3))), Mul(Const(-4), Var("a")), Const(2)), modulus=Const(59)),
"p2": Mod(value=Sum(Pow(Ref("p1"), Const(5)), Mul(Const(3), Pow(Ref("p1"), Const(3))), Mul(Const(-4), Ref("p1")), Cons... | ALG | null | COUNT | sympy | POLY_ORBIT_COUNT | [
"POLY_ORBIT_COUNT"
] | 4ad965 | alg_poly_orbit_count_v1 | null | 7 | null | [
"POLY_ORBIT_COUNT"
] | 1 | 0.045 | 2026-02-25T06:42:50.980412Z | {
"verified": true,
"answer": 9475,
"timestamp": "2026-02-25T06:42:51.025600Z"
} | e85756 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 336,
"completion_tokens": 32768
},
"timestamp": "2026-03-29T19:24:49.629Z",
"answer": 9475
},
{
"... | 1 | [
{
"lemma": "POLY_ORBIT_COUNT",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
}
] | {
"lo": 3.81,
"mid": 6.33,
"hi": 9.49
} | ||
e72e31 | nt_max_prime_below_v1_1978505735_8413 | Let $P$ be the set of all positive integers $p$ for which there exists a positive integer $q$ such that $pq = 216$, $\gcd(p, q) = 1$, and $p < q$. Let $m$ be the number of elements in $P$. Let $S$ be the set of all prime numbers $n$ such that $m \leq n \leq 61009$. Determine the value of the largest element in $S$. | 61,007 | graphs = [
Graph(
let={
"upper": Const(61009),
"result": MaxOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), CountOverSet(set=SolutionsSet(var=Var("p"), condition=And(IsPositive(arg=Var(name='p')), Exists(var=Var(name='q'), condition=And(Eq(left=Mul(Var(name='p'), V... | NT | null | EXTREMUM | sympy | COPRIME_PAIRS | [
"COPRIME_PAIRS"
] | 2bb3aa | nt_max_prime_below_v1 | null | 5 | 0 | [
"COPRIME_PAIRS"
] | 1 | 1.335 | 2026-02-08T20:49:17.324458Z | {
"verified": true,
"answer": 61007,
"timestamp": "2026-02-08T20:49:18.659312Z"
} | f913c5 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 146,
"completion_tokens": 2715
},
"timestamp": "2026-02-19T01:12:19.684Z",
"answer": 61007
},
... | 1 | [
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "V1",
"status": "no"
... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
b82b5c | modular_mod_compute_v1_349078426_1516 | Let $a$ be the number of ordered pairs $(x_1, x_2)$ of positive odd integers such that $x_1 + x_2 = 8712$. Compute the remainder when $a$ is divided by $49284$. | 4,356 | graphs = [
Graph(
let={
"a": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x1"), Var("x2")]), condition=And(IsPositive(arg=Var(name='x1')), IsPositive(arg=Var(name='x2')), IsOdd(arg=Var(name='x1')), IsOdd(arg=Var(name='x2')), Eq(Sum(Var("x1"), Var("x2")), Const(8712))))),
"m... | NT | null | COMPUTE | sympy | COMB1 | [
"COMB1"
] | 567f58 | modular_mod_compute_v1 | null | 3 | 0 | [
"COMB1"
] | 1 | 0.002 | 2026-02-08T13:41:26.567034Z | {
"verified": true,
"answer": 4356,
"timestamp": "2026-02-08T13:41:26.569425Z"
} | 43e6b9 | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 113,
"completion_tokens": 417
},
"timestamp": "2026-02-16T04:56:06.365Z",
"answer": 4356
},
{
"id": 11,
... | 2 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COMB1",
"status": "ok"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no... | {
"lo": -10,
"mid": -7.27,
"hi": -4.54
} | ||
6471cc | alg_qf_psd_orbit_v1_1218484723_6427 | Let $Q$ be the number of ordered triples $(a, b, c)$ of positive integers with $1 \le a \le b$, $1 \le b \le c$, and $1 \le c \le 54$ such that
$$\left|\{ (a2, b2) : a2 \ge 1, a2 \le 25, b2 \ge 1, b2 \le 25,\, 10a2 b2 + 5 a2^{2} + \min\{ 29 b3^{2} + 4 a3^{2} - 20a3 b3 : (a3, b3),\, a3 \ge 1, a3 \le 29, b3 \ge 1, b3 \le... | 6 | graphs = [
Graph(
let={
"_d": Const(2),
"_c": Const(2),
"_m": Const(2),
"_n": Const(2),
"result": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("a"), Var("b"), Var("c")]), condition=And(Geq(Var("a"), Const(1)), Leq(Var("a"), Const(54)), Geq... | ALG | null | COUNT | sympy | POLY_ORBIT_HENSEL | [
"QF_PSD_MIN/QF_PSD_COUNT",
"LIN_FORM/QF_PSD_COUNT",
"POLY4_COUNT"
] | 70f38c | alg_qf_psd_orbit_v1 | null | 8 | 0 | [
"LIN_FORM",
"POLY4_COUNT",
"POLY_ORBIT_HENSEL",
"QF_PSD_COUNT",
"QF_PSD_MIN"
] | 5 | 1.674 | 2026-02-25T07:59:38.377861Z | {
"verified": true,
"answer": 6,
"timestamp": "2026-02-25T07:59:40.052188Z"
} | 2af7de | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 1,
"correct": {
"strict": false,
"boxed": false,
"relaxed": true
},
"usage": {
"prompt_tokens": 421,
"completion_tokens": 32768
},
"timestamp": "2026-03-30T01:44:49.209Z",
"answer": null
},
{
... | 1 | [
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "POLY4_COUNT",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "QF_PSD_COUNT",
"status": "ok_later"
},
{
"lemma": "QF_PSD_MIN",
"status": "ok"
}
] | {
"lo": 3.81,
"mid": 6.33,
"hi": 9.49
} | ||
e47430 | nt_count_with_divisor_count_v1_865884756_565 | Let $t$ be an integer. Determine how many values of $t$ between $7$ and $20$, inclusive, can be expressed as $2a + 5b$ for positive integers $a \leq 5$ and $b \leq 2$. Let this count be $c$. Compute the number of positive integers $n$ at most $26569$ such that the number of positive divisors of $n$ is exactly $c$. Find... | 37,114 | graphs = [
Graph(
let={
"upper": Const(26569),
"div_count": CountOverSet(set=SolutionsSet(var=Var("t"), condition=Exists(var=Var(name='a'), condition=Exists(var=Var(name='b'), condition=And(Geq(left=Var(name='a'), right=Const(value=1)), Leq(left=Var(name='a'), right=Const(value=5)), ... | NT | null | COUNT | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | nt_count_with_divisor_count_v1 | null | 5 | 0 | [
"LIN_FORM"
] | 1 | 1.117 | 2026-02-08T15:30:58.245234Z | {
"verified": true,
"answer": 37114,
"timestamp": "2026-02-08T15:30:59.362506Z"
} | 46c663 | 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": 2732
},
"timestamp": "2026-02-16T07:39:28.509Z",
"answer": 37114
},
... | 1 | [
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "V3",
"status": "no"... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
e3bd7e | nt_sum_divisors_mod_v1_1440796553_538 | Let $S$ be the set of all ordered pairs $(x, y)$ of positive integers such that $xy = 396900$. Let $n$ be the minimum value of $x + y$ as $(x, y)$ ranges over $S$.
Let $\sigma(n)$ denote the sum of the positive divisors of $n$, and let $M = 11317$.
Compute the remainder when $\sigma(n)$ is divided by $M$. | 4,368 | graphs = [
Graph(
let={
"n": MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(Mul(Var("x"), Var("y")), Const(396900)))), expr=Sum(Var("x"), Var("y")))),
"M": Const(11317... | NT | null | COMPUTE | sympy | B3 | [
"B3"
] | 0cd20d | nt_sum_divisors_mod_v1 | null | 5 | 0 | [
"B3"
] | 1 | 0.003 | 2026-02-08T11:51:00.741649Z | {
"verified": true,
"answer": 4368,
"timestamp": "2026-02-08T11:51:00.744466Z"
} | 9946d1 | 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": 2672
},
"timestamp": "2026-02-14T20:23:36.060Z",
"answer": 4368
},
{... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
}
] | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
f0a612 | geo_count_lattice_rect_v1_898971024_285 | Let $a = 169$ and $b = 78$. The number of lattice points $(x, y)$ such that $0 \leq x \leq a$ and $0 \leq y \leq b$ is denoted by $L$. Compute the remainder when $44121 \cdot L$ is divided by $88607$. | 30,021 | graphs = [
Graph(
let={
"a": Const(169),
"b": Const(78),
"result": LatticePointsRect(a=Ref(name='a'), b=Ref(name='b')),
"Q": Mod(value=Mul(Const(44121), Ref("result")), modulus=Const(88607)),
},
goal=Ref("Q"),
)
] | GEOM | null | COUNT | sympy | [] | geo_count_lattice_rect_v1 | null | 3 | 0 | null | null | 0.001 | 2026-02-08T15:20:02.103081Z | {
"verified": true,
"answer": 30021,
"timestamp": "2026-02-08T15:20:02.103683Z"
} | f31c45 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 185,
"completion_tokens": 9683
},
"timestamp": "2026-02-24T20:25:19.013Z",
"answer": 30021
},
{
"... | 1 | [] | {
"lo": -2.43,
"mid": 1.2,
"hi": 4.84
} | ||||
aa7b13 | modular_min_linear_v1_1116507919_420 | Let $\mu(n)$ denote the M\"obius function. Define $c = \sum_{d \mid \gcd(4,9)} \mu(d)$. Let $S$ be the set of all integers $x$ such that $x \geq c$, $x \leq 72898$, and $44255x \equiv 34404 \pmod{72898}$. Compute the minimum value of $x$ in $S$. | 27,068 | graphs = [
Graph(
let={
"a": Const(44255),
"b": Const(34404),
"m": Const(72898),
"result": MinOverSet(set=SolutionsSet(var=Var("x"), condition=And(Geq(Var("x"), SumOverDivisors(n=GCD(a=Const(value=4), b=Const(value=9)), var='d', expr=MoebiusMu(n=Var(name='d'))... | NT | null | EXTREMUM | sympy | MOBIUS_COPRIME | [
"MOBIUS_COPRIME"
] | ac54ac | modular_min_linear_v1 | null | 5 | 0 | [
"MOBIUS_COPRIME"
] | 1 | 2.644 | 2026-02-08T02:34:06.071802Z | {
"verified": true,
"answer": 27068,
"timestamp": "2026-02-08T02:34:08.715641Z"
} | b8103c | 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": 4290
},
"timestamp": "2026-02-08T19:32:39.039Z",
"answer": 27068
},
{
"... | 1 | [
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "MOBIUS_COPRIME",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
... | {
"lo": -4.6,
"mid": 0.19,
"hi": 4.77
} | ||
26be2f | diophantine_fbi2_count_v1_1520064083_5239 | Let $k$ be the number of positive integers $t$ such that $5 \leq t \leq 1266$ and there exist positive integers $a \leq 188$, $b \leq 351$ satisfying $t = 3a + 2b$. Compute the number of positive integers $d$ such that $3 \leq d \leq 66$, $d$ divides $k$, and $3 \leq \frac{k}{d} \leq 66$. | 10 | graphs = [
Graph(
let={
"_n": Const(66),
"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=188)), Geq(left=Var... | NT | null | COUNT | sympy | V5 | [
"LIN_FORM"
] | 7b2633 | diophantine_fbi2_count_v1 | null | 6 | 0 | [
"LIN_FORM",
"V5"
] | 2 | 0.032 | 2026-02-08T06:42:00.054288Z | {
"verified": true,
"answer": 10,
"timestamp": "2026-02-08T06:42:00.086453Z"
} | 35ed72 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 148,
"completion_tokens": 3980
},
"timestamp": "2026-02-13T03:26:04.123Z",
"answer": 0
},
{... | 1 | [
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
}
... | {
"lo": -3.51,
"mid": 1.33,
"hi": 6.56
} | ||
54e08d | algebra_quadratic_discriminant_v1_397696148_2442 | Let $n = 2401$. Consider the set of all ordered pairs $(x,y)$ of positive integers such that $xy = n$. For each such pair, compute $x + y$, and let $c$ be the minimum value of $x + y$ over all such pairs.
Let $b = 28$ and $a = 2$. Compute $b^2 - 4ac$. | 0 | graphs = [
Graph(
let={
"_n": Const(2401),
"a": Const(2),
"b": Const(28),
"c": MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(Mul(Var("x"), Var... | NT | null | COMPUTE | sympy | B3 | [
"B3"
] | 0cd20d | algebra_quadratic_discriminant_v1 | null | 3 | 0 | [
"B3"
] | 1 | 0.002 | 2026-02-08T13:20:05.976897Z | {
"verified": true,
"answer": 0,
"timestamp": "2026-02-08T13:20:05.979019Z"
} | 709612 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 131,
"completion_tokens": 573
},
"timestamp": "2026-02-15T14:31:01.649Z",
"answer": 0
},
{
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "V3",
"status": "no"
... | {
"lo": -8.26,
"mid": -5.01,
"hi": -1.76
} | ||
717d79 | nt_count_digit_sum_v1_1440796553_933 | Let $T$ be the set of all integers $t$ with $9 \leq t \leq 40$ for which there exist positive integers $a \leq 4$ and $b \leq 5$ such that $t = 5a + 4b$. Let $\text{target\_sum}$ be the number of elements in $T$. Let $\text{result}$ be the number of positive integers $n \leq 9999$ such that the sum of the decimal digit... | 52,325 | graphs = [
Graph(
let={
"upper": Const(9999),
"target_sum": CountOverSet(set=SolutionsSet(var=Var("t"), condition=Exists(var=Var(name='a'), condition=Exists(var=Var(name='b'), condition=And(Geq(left=Var(name='a'), right=Const(value=1)), Leq(left=Var(name='a'), right=Const(value=4)), ... | NT | null | COUNT | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | nt_count_digit_sum_v1 | null | 4 | 0 | [
"LIN_FORM"
] | 1 | 0.358 | 2026-02-08T12:03:51.707048Z | {
"verified": true,
"answer": 52325,
"timestamp": "2026-02-08T12:03:52.064618Z"
} | ebaddb | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 185,
"completion_tokens": 2523
},
"timestamp": "2026-02-14T21:57:21.288Z",
"answer": 52325
},
... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "MAX_PRIME_BELOW",
"s... | {
"lo": -5.49,
"mid": 0.22,
"hi": 6.51
} | ||
af125e | algebra_poly_eval_v1_1978505735_1144 | Let $n = 20$ and let $\ell = 4$. Consider the set of all ordered pairs $(x, y)$ of positive integers such that $xy = \ell$. For each such pair, compute the sum $x + y$, and let $S$ be the set of all such sums. Let $m$ be the minimum value in $S$. Compute $m \cdot n^2 - 10n - 3$. | 1,397 | graphs = [
Graph(
let={
"_n": Const(4),
"n": Const(20),
"result": Sum(Mul(MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(Mul(Var("x"), Var("y")), Ref("_n")... | NT | null | COMPUTE | sympy | B3 | [
"B3"
] | 0cd20d | algebra_poly_eval_v1 | null | 3 | 0 | [
"B3"
] | 1 | 0.004 | 2026-02-08T15:51:49.201495Z | {
"verified": true,
"answer": 1397,
"timestamp": "2026-02-08T15:51:49.205707Z"
} | 91fc8d | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 151,
"completion_tokens": 412
},
"timestamp": "2026-02-16T06:34:12.385Z",
"answer": 1397
},
{
"id": 11,
... | 2 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "V3",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
}
] | {
"lo": -10,
"mid": -7.27,
"hi": -4.54
} | ||
b18739 | nt_max_prime_below_v1_124444284_4840 | Let $A$ be the number of positive integers $p$ for which there exists a positive integer $q$ such that $pq = 108$, $\gcd(p, q) = 1$, and $p < q$. Let $B$ be the largest prime number $n$ such that $n \leq 62500$ and $n \geq A$. Find the value of $B$. | 62,497 | graphs = [
Graph(
let={
"upper": Const(62500),
"result": MaxOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), CountOverSet(set=SolutionsSet(var=Var("p"), condition=And(IsPositive(arg=Var(name='p')), Exists(var=Var(name='q'), condition=And(Eq(left=Mul(Var(name='p'), V... | NT | null | EXTREMUM | sympy | COPRIME_PAIRS | [
"COPRIME_PAIRS"
] | 2bb3aa | nt_max_prime_below_v1 | null | 4 | 0 | [
"COPRIME_PAIRS"
] | 1 | 4.697 | 2026-02-08T06:14:57.533330Z | {
"verified": true,
"answer": 62497,
"timestamp": "2026-02-08T06:15:02.230409Z"
} | 7e1797 | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 146,
"completion_tokens": 353
},
"timestamp": "2026-02-15T17:09:02.611Z",
"answer": 62489
},
{
"id": 11... | 1 | [
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "V5",
"... | {
"lo": -8.32,
"mid": -5.11,
"hi": -2.37
} | ||
0728bb | diophantine_product_count_v1_1520064083_710 | Let $k = 120$ and let $u = \sum_{d \mid 116} \phi(d)$. Find the number of positive integers $x$ such that $1 \le x \le u$, $x$ divides $k$, and $\frac{k}{x} \le u$. | 14 | graphs = [
Graph(
let={
"k": Const(120),
"upper": SumOverDivisors(n=Const(value=116), var='d', expr=EulerPhi(n=Var(name='d'))),
"result": CountOverSet(set=SolutionsSet(var=Var("x"), condition=And(Geq(Var("x"), Const(1)), Leq(Var("x"), Ref("upper")), Divides(divisor=Var("x... | NT | null | COUNT | sympy | SUM_DIVISIBLE | [
"K3"
] | 54c41e | diophantine_product_count_v1 | null | 4 | 0 | [
"K3",
"SUM_DIVISIBLE"
] | 2 | 17.902 | 2026-02-08T03:33:49.707311Z | {
"verified": true,
"answer": 14,
"timestamp": "2026-02-08T03:34:07.609622Z"
} | 47ab26 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 174,
"completion_tokens": 1535
},
"timestamp": "2026-02-10T14:58:22.326Z",
"answer": 14
},
{
"id"... | 1 | [
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "K3",
"status": "ok"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"st... | {
"lo": -5.55,
"mid": -3.02,
"hi": 0.31
} | ||
98f626 | comb_count_permutations_fixed_v1_1874849503_671 | Let $S$ be the set of all ordered pairs $(x,y)$ of positive integers such that $x + y = 6$. Let $n$ be the maximum value of $xy$ over all pairs in $S$. Compute the remainder when $88672 \cdot \binom{n}{5} \cdot !(n-5)$ is divided by $82551$, where $!m$ denotes the number of derangements of $m$ elements. | 6,930 | graphs = [
Graph(
let={
"_n": Const(82551),
"n": MaxOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(Sum(Var("x"), Var("y")), Const(6)))), expr=Mul(Var("x"), Var("y")))),
... | COMB | null | COUNT | sympy | B1 | [
"B1"
] | 5b950e | comb_count_permutations_fixed_v1 | null | 5 | 0 | [
"B1"
] | 1 | 0.002 | 2026-02-08T13:15:08.495689Z | {
"verified": true,
"answer": 6930,
"timestamp": "2026-02-08T13:15:08.497578Z"
} | a03f1a | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 207,
"completion_tokens": 1609
},
"timestamp": "2026-02-09T19:37:59.287Z",
"answer": 6930
},
{
"i... | 1 | [
{
"lemma": "B1",
"status": "ok"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8",
"status": ... | {
"lo": -2.35,
"mid": 1.22,
"hi": 4.84
} | ||
c2b73c | antilemma_sum_factor_cartesian_v1_1116507919_337 | Let $S$ be the set of all ordered pairs $(i, j)$ such that $1 \le i \le 10$ and $1 \le j \le 17$. Let $x$ be the sum of $i \cdot j$ over all pairs $(i, j)$ in $S$. Define $Q = x + \phi(|x| + 1) + \tau(|x| + 1)$, where $\phi$ is Euler's totient function and $\tau(n)$ is the number of positive divisors of $n$. Compute $Q... | 12,619 | graphs = [
Graph(
let={
"x": SumOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("i"), Var("j")]), condition=Const(1), domain=CartesianProduct(left=IntegerRange(start=Const(1), end=Const(10)), right=IntegerRange(start=Const(1), end=Const(17)))), expr=Mul(Var("i"), Var("j")))),
... | NT | null | COMPUTE | sympy | SUM_FACTOR_CARTESIAN | [
"SUM_FACTOR_CARTESIAN"
] | d9e436 | antilemma_sum_factor_cartesian_v1 | null | 4 | 0 | [
"SUM_FACTOR_CARTESIAN"
] | 1 | 0.001 | 2026-02-08T02:31:44.605020Z | {
"verified": true,
"answer": 12619,
"timestamp": "2026-02-08T02:31:44.605959Z"
} | adedae | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 236,
"completion_tokens": 831
},
"timestamp": "2026-02-08T19:23:24.250Z",
"answer": 12619
},
{
"i... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "SUM_FACTOR_CARTESIAN",
"status": "ok"
}
] | {
"lo": -4.6,
"mid": 0.15,
"hi": 4.61
} | ||
dfde21 | algebra_poly_eval_v1_124444284_1306 | Let $t = 16$. Let $s$ be the number of positive integers $p$ for which there exists an integer $q$ such that $pq = 108$, $\gcd(p,q) = 1$, and $p < q$. Define
$$
\text{result} = t^4 + 5t^3 + 3t^s - 9t + 8.
$$
Compute the remainder when $86077 \cdot \text{result}$ is divided by $63729$. | 3,839 | graphs = [
Graph(
let={
"_n": Const(63729),
"t": Const(16),
"result": Sum(Pow(Ref("t"), Const(4)), Mul(Const(5), Pow(Ref("t"), Const(3))), Mul(Const(3), Pow(Ref("t"), CountOverSet(set=SolutionsSet(var=Var("p"), condition=And(IsPositive(arg=Var(name='p')), Exists(var=Var(n... | NT | null | COMPUTE | sympy | COPRIME_PAIRS | [
"COPRIME_PAIRS"
] | 2bb3aa | algebra_poly_eval_v1 | null | 4 | 0 | [
"COPRIME_PAIRS"
] | 1 | 0.003 | 2026-02-08T03:49:05.814096Z | {
"verified": true,
"answer": 3839,
"timestamp": "2026-02-08T03:49:05.817219Z"
} | b6e99e | 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": 1987
},
"timestamp": "2026-02-10T05:55:08.631Z",
"answer": 3839
},
{
"i... | 1 | [
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
}
] | {
"lo": -3.53,
"mid": 1.02,
"hi": 5.49
} | ||
51960b | diophantine_product_count_v1_784195855_1926 | Let $n = 2$. Define $k$ to be the number of nonnegative integers $j$ such that $0 \le j \le 60$ and $\binom{60}{j} \equiv 1 \pmod{2}$. Let $\text{upper} = 274$. Let $r$ be the number of positive integers $x$ such that $1 \le x \le \text{upper}$, $x$ divides $k$, and $\frac{k}{x} \le \text{upper}$. Compute the smallest ... | 12 | graphs = [
Graph(
let={
"_n": Const(2),
"k": SumOverSet(set=SolutionsSet(var=Var("j"), condition=And(Geq(Var("j"), Const(0)), Leq(Var("j"), Const(60)), Eq(Mod(value=Binom(n=Const(60), k=Var("j")), modulus=Ref("_n")), Const(1))), domain='nonnegative_integers')),
"upper": C... | NT | null | COUNT | sympy | MIN_PRIME_FACTOR | [
"V8"
] | 86348e | diophantine_product_count_v1 | null | 7 | 0 | [
"MIN_PRIME_FACTOR",
"V8"
] | 2 | 29.738 | 2026-02-08T05:23:33.490830Z | {
"verified": true,
"answer": 12,
"timestamp": "2026-02-08T05:24:03.229141Z"
} | b6ea44 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 185,
"completion_tokens": 1408
},
"timestamp": "2026-02-12T08:08:29.851Z",
"answer": 8
},
{... | 1 | [
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8",
"status": "ok"
},
{
"lemma": "V8_SUM",
"status": "no"
}
] | {
"lo": -3.51,
"mid": 1.33,
"hi": 6.56
} | ||
2fb999 | geo_count_lattice_triangle_v1_1419126231_739 | Let $B_n$ denote the $n$-th Bell number. Let $N = |144 \cdot 100 + 12 \cdot (0 - 8)|$, $M = \gcd(144, 8) + \gcd(|12 - 144|, |100 - 8|) + \gcd(|0 - 12|, |0 - 100|)$, and $R = \frac{N + 2 - M}{2}$. Compute $B_{|R| \bmod 11}$. | 203 | graphs = [
Graph(
let={
"area_2x": Abs(arg=Sum(Mul(Const(value=144), Const(value=100)), Mul(Const(value=12), Sub(left=Const(value=0), right=Const(value=8))))),
"boundary": Sum(GCD(a=Abs(arg=Const(value=144)), b=Abs(arg=Const(value=8))), GCD(a=Abs(arg=Sub(left=Const(value=12), right=C... | GEOM | COMB | COUNT | sympy | STARS_BARS | [
"POLY_ORBIT_HENSEL",
"STARS_BARS"
] | a12b60 | geo_count_lattice_triangle_v1 | null | 4 | 0 | [
"POLY_ORBIT_HENSEL",
"STARS_BARS"
] | 2 | 0.266 | 2026-02-25T10:14:04.342828Z | {
"verified": true,
"answer": 203,
"timestamp": "2026-02-25T10:14:04.608954Z"
} | 5dc45a | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 229,
"completion_tokens": 619
},
"timestamp": "2026-03-30T09:50:46.495Z",
"answer": 203
},
{
"id"... | 2 | [
{
"lemma": "POLY_ORBIT_HENSEL",
"status": "ok"
},
{
"lemma": "STARS_BARS",
"status": "ok"
}
] | {
"lo": -10,
"mid": -5.89,
"hi": -1.79
} | ||
8efbda_n | alg_sum_powers_v1_1218484723_1448 | A delivery drone must travel along a rectangular grid path with area exactly $85849$ square units, moving only east and north. The shortest such path has length $S = x + y$, where $x \cdot y = 85849$ and $x, y > 0$. The drone computes the sum of squares from $1$ to $S$, then takes the result modulo $8782$, calling it $... | 91,483 | ALG | null | COMPUTE | sympy | B3 | [
"B3"
] | 0cd20d | alg_sum_powers_v1 | null | 3 | null | [
"B3"
] | 1 | 0.023 | 2026-02-25T03:10:01.469160Z | null | 74db8a | 8efbda | narrative | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 217,
"completion_tokens": 1485
},
"timestamp": "2026-03-30T16:52:38.581Z",
"answer": 91483
},
{
"... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
}
] | {
"lo": -5.37,
"mid": 0.23,
"hi": 5.22
} | |
70802b | comb_catalan_compute_v1_601307018_8402 | Let $C_n$ denote the $n$-th Catalan number. Define $e = \sum_{k=0}^{0} (-1)^k \binom{0}{k}$, $t = \sum_{k=0}^{0} (-1)^k \binom{0}{k}$, $u = 6e$, $S = u + \binom{15}{0}$, $w = \sum_{k=0}^{S} (-1)^k \binom{S}{k}$, and $n = \sum_{k=1}^{4} k \cdot t + w$. Compute $24025 - C_n$. | 7,229 | graphs = [
Graph(
let={
"n3": Const(0),
"t": Summation(var="k", start=Const(0), end=Ref("n3"), expr=Mul(Pow(Const(-1), Var("k")), Binom(n=Ref("n3"), k=Var("k")))),
"n2": Const(0),
"e": Summation(var="k1", start=Const(0), end=Ref("n2"), expr=Mul(Pow(Const(-1), ... | COMB | null | COMPUTE | sympy | SUM_ARITHMETIC | [
"SUM_ARITHMETIC/BINOMIAL_ALTERNATING",
"ONE_BINOM_0"
] | 83f2e4 | comb_catalan_compute_v1 | null | 3 | 3 | [
"BINOMIAL_ALTERNATING",
"ONE_BINOM_0",
"SUM_ARITHMETIC"
] | 3 | 0.008 | 2026-03-10T08:54:36.686996Z | {
"verified": true,
"answer": 7229,
"timestamp": "2026-03-10T08:54:36.695328Z"
} | f11e50 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 252,
"completion_tokens": 732
},
"timestamp": "2026-04-19T08:57:37.432Z",
"answer": 7229
},
{
"i... | 2 | [
{
"lemma": "BINOMIAL_ALTERNATING",
"status": "ok_later"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "ONE_BINOM_0",
"status": "ok"
},
{
"lemma": "SUM_ARITHMETIC",
"status": "ok"
},
{
"le... | {
"lo": -10,
"mid": -5.89,
"hi": -1.79
} | ||
07c078 | geo_count_lattice_triangle_v1_1978505735_5191 | Let $A$ be twice the area of the polygon with vertices at $(0,0)$, $(100,88)$, and $(11,169)$. Let $S$ be the set of all integers $t$ with $9 \leq t \leq 102$ for which there exist positive integers $a$ and $b$, $1 \leq a \leq 4$, $1 \leq b \leq 37$, such that $t = 7a + 2b$. Let $B = 88$ and let $C$ be the number of el... | 85,266 | graphs = [
Graph(
let={
"_m": Const(169),
"_n": Const(11),
"area_2x": Abs(arg=Sum(Mul(MaxOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var(name='x'), Var(name='y')]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(left=Sum(Var... | ALG | NT | COUNT | sympy | LIN_FORM | [
"LIN_FORM",
"B1"
] | 2f9b70 | geo_count_lattice_triangle_v1 | null | 6 | 0 | [
"B1",
"LIN_FORM"
] | 2 | 0.008 | 2026-02-08T18:49:05.489199Z | {
"verified": true,
"answer": 85266,
"timestamp": "2026-02-08T18:49:05.497266Z"
} | 822364 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 280,
"completion_tokens": 3527
},
"timestamp": "2026-02-18T19:52:36.674Z",
"answer": 85266
},
... | 1 | [
{
"lemma": "B1",
"status": "ok"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
8e6f06 | geo_count_lattice_rect_v1_601307018_319 | Let $a = \sum_{d \mid 196} \varphi(d)$. Compute $44444$ minus the number of lattice points $(x, y)$ with $0 \le x \le a$ and $0 \le y \le 58$. | 32,821 | graphs = [
Graph(
let={
"_n": Const(196),
"a": SumOverDivisors(n=Ref(name='_n'), var='d', expr=EulerPhi(n=Var(name='d'))),
"b": Const(58),
"result": LatticePointsRect(a=Ref(name='a'), b=Ref(name='b')),
"_c": Const(44444),
"Q": Sub(Ref("... | GEOM | NT | COUNT | sympy | K3 | [
"K3"
] | 54c41e | geo_count_lattice_rect_v1 | null | 3 | 0 | [
"K3"
] | 1 | 0.003 | 2026-03-10T00:51:07.972621Z | {
"verified": true,
"answer": 32821,
"timestamp": "2026-03-10T00:51:07.975465Z"
} | b1d580 | CC BY 4.0 | null | null | [
{
"lemma": "K3",
"status": "ok"
}
] | {
"lo": -10,
"mid": 0,
"hi": 10
} | ||
392f81 | alg_poly3_min_v1_1218484723_7590 | Find the remainder when $$\min\left\{ -33ab^2 -26a^3 -7b^3 -51a^2b \mid a, b \in \mathbb{Z}^+,\, 1 \le a \le 461,\, 1 \le b \le \min\{d \ge 2 : d \mid 213443\}\right\}$$ is divided by $94101€. | 74,037 | graphs = [
Graph(
let={
"_n": Const(3),
"result": Mod(value=MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("a"), Var("b")]), condition=And(Geq(Var("a"), Const(1)), Leq(Var("a"), Const(461)), Geq(Var("b"), Const(1)), Leq(Var("b"), MinOverSet(set=SolutionsSet(var=Va... | NT | null | COMPUTE | sympy | MIN_PRIME_FACTOR | [
"MIN_PRIME_FACTOR"
] | bc3776 | alg_poly3_min_v1 | null | 6 | 0 | [
"MIN_PRIME_FACTOR"
] | 1 | 0.589 | 2026-02-25T09:01:56.708578Z | {
"verified": true,
"answer": 74037,
"timestamp": "2026-02-25T09:01:57.297097Z"
} | 1a026a | 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": 4120
},
"timestamp": "2026-03-30T05:25:14.193Z",
"answer": 74037
},
{
"... | 1 | [
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MIN_PRIME_FACTOR",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONS... | {
"lo": -3.33,
"mid": 1.03,
"hi": 5.26
} | ||
5d9d22 | algebra_quadratic_discriminant_v1_1520064083_8733 | Let $a = -9$, $b = 9$, and $c = 1$. Define $D = b^2 - 4ac$. Let $\alpha = 1$ if $D > 0$, and $0$ otherwise. Let $\beta = 1$ if $D = 0$, and $0$ otherwise. Define $r = 2\alpha + \beta$.
Let $S$ be the set of all ordered pairs $(x, y)$ of positive integers such that $xy = 196$. Let $s$ be the minimum value of $x + y$ ov... | 421 | graphs = [
Graph(
let={
"a": Const(-9),
"b": Const(9),
"c": Const(1),
"D": Sub(Pow(Ref("b"), Const(2)), Mul(Const(4), Ref("a"), Ref("c"))),
"result": Sum(Mul(Const(2), Iverson(condition=Gt(Ref("D"), Const(0)))), Iverson(condition=Eq(Ref("D"), Const... | NT | null | COMPUTE | sympy | B3 | [
"B3"
] | d720b5 | algebra_quadratic_discriminant_v1 | quadratic_mod | 5 | 0 | [
"B3"
] | 1 | 0.014 | 2026-02-08T10:20:55.824724Z | {
"verified": true,
"answer": 421,
"timestamp": "2026-02-08T10:20:55.838349Z"
} | 5ed591 | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 209,
"completion_tokens": 322
},
"timestamp": "2026-02-15T20:58:56.871Z",
"answer": 411
},
{
"id": 11,
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "V3",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
}
] | {
"lo": -9.12,
"mid": -6.02,
"hi": -3.62
} | ||
33cf89 | algebra_quadratic_discriminant_v1_151522320_1756 | Let $a = -7$, $b = 10$, and $c = -5$. Let $S$ be the set of all ordered pairs $(x, y)$ of positive integers such that $xy = 4$. Define $m = \min\{x + y \mid (x, y) \in S\}$. Let $D = b^2 - 4amc$. Define $r = 2 \cdot [D > 0] + [D = 0]$, where $[P]$ denotes the Iverson bracket (1 if $P$ is true, 0 otherwise). Compute $24... | 0 | graphs = [
Graph(
let={
"_n": Const(2),
"a": Const(-7),
"b": Const(10),
"c": Const(-5),
"D": Sub(Pow(Ref("b"), Const(2)), Mul(MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name... | NT | null | COMPUTE | sympy | B3 | [
"B3"
] | 0cd20d | algebra_quadratic_discriminant_v1 | null | 3 | 0 | [
"B3"
] | 1 | 0.002 | 2026-02-08T04:20:55.732711Z | {
"verified": true,
"answer": 0,
"timestamp": "2026-02-08T04:20:55.735134Z"
} | 6dd2fb | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 250,
"completion_tokens": 669
},
"timestamp": "2026-02-10T16:18:46.449Z",
"answer": 0
},
{
"id":... | 2 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
}
] | {
"lo": -9.14,
"mid": -6.05,
"hi": -3.73
} | ||
dc0562 | comb_binomial_compute_v1_1353956133_257 | Let $S$ be the set of prime numbers between $2$ and $5$, inclusive. Let $m$ be the maximum element of $S$. Define $n = \sum_{k=1}^{5} \phi(k) \left\lfloor \frac{m}{k} \right\rfloor$, where $\phi(k)$ denotes Euler's totient function. Compute $\binom{n}{7}$. | 6,435 | graphs = [
Graph(
let={
"_m": Const(5),
"_n": Const(5),
"n": Summation(var="k", start=Const(1), end=Ref("_n"), expr=Mul(EulerPhi(n=Var("k")), Floor(Div(MaxOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(2)), Leq(Var("n"), Ref("_m")), IsPrime(Var("... | NT | null | COMPUTE | sympy | MAX_PRIME_BELOW | [
"MAX_PRIME_BELOW/K2"
] | 7eb1ee | comb_binomial_compute_v1 | null | 5 | 0 | [
"K2",
"MAX_PRIME_BELOW"
] | 2 | 0.004 | 2026-02-08T11:21:34.688292Z | {
"verified": true,
"answer": 6435,
"timestamp": "2026-02-08T11:21:34.692363Z"
} | 825569 | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 147,
"completion_tokens": 620
},
"timestamp": "2026-02-15T21:49:20.283Z",
"answer": 6435
},
{
"id": 11,
... | 2 | [
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "K2",
"status": "ok_later"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok"
},
{
"lemma": "MOD_MUL",
"status": "no"... | {
"lo": -10,
"mid": -7.71,
"hi": -5.43
} | ||
611c54 | sequence_fibonacci_compute_v1_1874849503_179 | Let $n$ be the largest integer such that $2^n$ divides $28!$. Compute the $n$-th Fibonacci number. | 75,025 | graphs = [
Graph(
let={
"_n": Const(28),
"n": MaxKDivides(target=Factorial(Ref("_n")), base=Const(2)),
"result": Fibonacci(arg=Ref(name='n')),
},
goal=Ref("result"),
)
] | NT | null | COMPUTE | sympy | V1 | [
"V1"
] | dae96f | sequence_fibonacci_compute_v1 | null | 4 | 0 | [
"V1"
] | 1 | 0.001 | 2026-02-08T12:52:16.286590Z | {
"verified": true,
"answer": 75025,
"timestamp": "2026-02-08T12:52:16.287198Z"
} | 26971d | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 144,
"completion_tokens": 673
},
"timestamp": "2026-02-09T14:25:04.331Z",
"answer": 75025
},
{
"i... | 2 | [
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K5",
"status": "same_pattern_wrong"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status... | {
"lo": -10,
"mid": -6.47,
"hi": -2.95
} | ||
a7ae59 | modular_count_residue_v1_1125832087_503 | Let $m$ be the number of positive integers $p$ for which there exists a positive integer $q$ such that $p \cdot q = 18900$, $\gcd(p, q) = 1$, and $p < q$. Let $r = 4$. Let $S$ be the set of all positive integers $n$ such that $1 \le n \le 78400$ and $n \equiv r \pmod{m}$. Compute the number of elements in $S$, and let ... | 46,425 | graphs = [
Graph(
let={
"upper": Const(78400),
"m": 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=18900)), Eq(left=GCD(a=Var(name='p'), b=Va... | NT | null | COUNT | sympy | COPRIME_PAIRS | [
"COPRIME_PAIRS"
] | 2bb3aa | modular_count_residue_v1 | null | 6 | 0 | [
"COPRIME_PAIRS"
] | 1 | 2.707 | 2026-02-08T03:07:33.119063Z | {
"verified": true,
"answer": 46425,
"timestamp": "2026-02-08T03:07:35.826456Z"
} | 9943fc | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 250,
"completion_tokens": 3058
},
"timestamp": "2026-02-10T13:02:46.925Z",
"answer": 45425
},
{
... | 1 | [
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "... | {
"lo": 1.1,
"mid": 4.17,
"hi": 6.61
} | ||
b67939 | algebra_vieta_sum_v1_784195855_4825 | Let $n = 2$. Consider the set of all integers $x$ such that
$$
2x^2 - 16x + \left|\left\{(i,j) \in \{1, 2, \dots, 30\}^2 \mid i + j = 31\right\}\right| = 0.
$$
Compute the sum of all elements in this set. | 8 | graphs = [
Graph(
let={
"_n": Const(2),
"result": SumOverSet(set=SolutionsSet(var=Var("x"), condition=Eq(Sum(Mul(Ref("_n"), Pow(Var("x"), Const(2))), Mul(Const(-16), Var("x")), CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("i"), Var("j")]), condition=Eq(Sum(Var("i"), Var("j")... | NT | null | COMPUTE | sympy | LIN_FORM | [
"COUNT_SUM_EQUALS"
] | 75ab0f | algebra_vieta_sum_v1 | null | 3 | 0 | [
"COUNT_SUM_EQUALS",
"LIN_FORM"
] | 2 | 0.109 | 2026-02-08T07:23:50.257581Z | {
"verified": true,
"answer": 8,
"timestamp": "2026-02-08T07:23:50.366401Z"
} | dc5f1e | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 145,
"completion_tokens": 674
},
"timestamp": "2026-02-15T18:57:11.340Z",
"answer": 8
},
{
"id": 11,
"... | 2 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "ok"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "V3",
"status": "no"
... | {
"lo": -10,
"mid": -7.73,
"hi": -5.46
} | ||
229221 | comb_sum_binomial_row_v1_1918700295_3057 | Let $n = 13$ and $r = 2^n$. Let $S$ be the set of all integers $t$ with $15 \leq t \leq 51$ for which there exist integers $a$ and $b$ such that $1 \leq a \leq 3$, $1 \leq b \leq 4$, and $t = 9a + 6b$. Compute the Bell number $B_m$, where $m = |r| \bmod |S|$. | 4,140 | graphs = [
Graph(
let={
"n": Const(13),
"result": Pow(Const(2), Ref("n")),
"Q": Bell(Mod(value=Abs(arg=Ref(name='result')), modulus=CountOverSet(set=SolutionsSet(var=Var("t"), condition=Exists(var=Var(name='a'), condition=Exists(var=Var(name='b'), condition=And(Geq(left=V... | COMB | null | SUM | sympy | LIN_FORM | [
"LIN_FORM"
] | 1ae498 | comb_sum_binomial_row_v1 | bell_mod | 4 | 0 | [
"LIN_FORM"
] | 1 | 0.001 | 2026-02-08T08:22:16.385626Z | {
"verified": true,
"answer": 4140,
"timestamp": "2026-02-08T08:22:16.386623Z"
} | af76f4 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 224,
"completion_tokens": 763
},
"timestamp": "2026-02-24T09:25:31.330Z",
"answer": 4140
},
{
"id... | 1 | [
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
... | {
"lo": -4.92,
"mid": -2.91,
"hi": -0.68
} | ||
676c66 | nt_lcm_compute_v1_1439011603_844 | Let $a = 1327$, $b = 2238$, and $n = 43$. Let $\text{result}$ be the least common multiple of $a$ and $b$. Let $p$ be the number of prime numbers $k$ such that $2 \leq k \leq n$. Compute the remainder when $\text{result} + 2^{\text{result} \bmod p}$ is divided by $86685$. | 22,600 | graphs = [
Graph(
let={
"_n": Const(43),
"a": Const(1327),
"b": Const(2238),
"result": LCM(a=Ref("a"), b=Ref("b")),
"Q": Mod(value=Sum(Ref("result"), Mod(value=Pow(Const(2), Mod(value=Ref("result"), modulus=CountOverSet(set=SolutionsSet(var=Var("n"... | NT | null | COMPUTE | sympy | COUNT_PRIMES | [
"COUNT_PRIMES"
] | 6ccaed | nt_lcm_compute_v1 | mod_exp | 4 | 0 | [
"COUNT_PRIMES"
] | 1 | 0.004 | 2026-02-08T15:46:36.746345Z | {
"verified": true,
"answer": 22600,
"timestamp": "2026-02-08T15:46:36.750074Z"
} | 47868f | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 141,
"completion_tokens": 1665
},
"timestamp": "2026-02-16T12:44:16.314Z",
"answer": 22600
},
... | 1 | [
{
"lemma": "COUNT_PRIMES",
"status": "ok"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "V1",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
95d3ef | comb_count_permutations_fixed_v1_1440796553_1042 | Let $n$ be the largest prime number satisfying $2 \leq n \leq 9$. Let $k = 3$. Compute the value of
$$
\binom{n}{k} \cdot !(n - k),
$$
where $!m$ denotes the number of derangements of $m$ elements. | 315 | graphs = [
Graph(
let={
"_n": Const(2),
"n": MaxOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Ref("_n")), Leq(Var("n"), Const(9)), IsPrime(Var("n"))))),
"k": Const(3),
"result": Mul(Binom(n=Ref("n"), k=Ref("k")), Subfactorial(arg=Sub(left=... | NT | COMB | COUNT | sympy | COPRIME_PAIRS | [
"MAX_PRIME_BELOW"
] | dc3ad3 | comb_count_permutations_fixed_v1 | null | 3 | 0 | [
"COPRIME_PAIRS",
"MAX_PRIME_BELOW"
] | 2 | 0.01 | 2026-02-08T12:07:47.025381Z | {
"verified": true,
"answer": 315,
"timestamp": "2026-02-08T12:07:47.035461Z"
} | 17f438 | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 125,
"completion_tokens": 285
},
"timestamp": "2026-02-16T03:31:53.524Z",
"answer": 315
},
{
"id": 11,
... | 2 | [
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status"... | {
"lo": -10,
"mid": -7.71,
"hi": -5.43
} | ||
482cca | antilemma_k2_v1_579913215_187 | Let $m = 290$. Define $n$ to be the sum of $\phi(d)$ over all positive divisors $d$ of $m$, where $\phi$ is Euler's totient function. Let
$$
x = \sum_{k=1}^{n} \phi(k) \left\lfloor \frac{290}{k} \right\rfloor.
$$
Let $Q$ be the remainder when the Bell number $B_{|x| \bmod 11}$ is divided by $64141$.
Compute $Q$. | 51,834 | graphs = [
Graph(
let={
"_m": Const(290),
"_n": SumOverDivisors(n=Ref(name='_m'), var='d', expr=EulerPhi(n=Var(name='d'))),
"x": Summation(var="k", start=Const(1), end=Ref("_n"), expr=Mul(EulerPhi(n=Var("k")), Floor(Div(Const(290), Var("k"))))),
"Q": Mod(value... | NT | COMB | COMPUTE | sympy | K3 | [
"K3/K2",
"K2"
] | c7f244 | antilemma_k2_v1 | null | 6 | 0 | [
"K2",
"K3"
] | 2 | 0.002 | 2026-02-08T12:58:09.715417Z | {
"verified": true,
"answer": 51834,
"timestamp": "2026-02-08T12:58:09.717458Z"
} | 47c21a | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 157,
"completion_tokens": 2656
},
"timestamp": "2026-02-15T07:59:57.129Z",
"answer": 51834
},
... | 1 | [
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "K2",
"status": "ok"
},
{
"lemma": "K3",
"status": "ok"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"... | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
c0230e | comb_catalan_compute_v1_1742523217_2861 | Let $n$ be the number of integers $t$ such that $15 \leq t \leq 27$ and there exist integers $a$ and $b$ with $1 \leq a \leq 4$, $1 \leq b \leq 3$, and $t = 2a + 3b + 10$. Compute the remainder when $35668$ times the $n$th Catalan number is divided by $94227$. | 39,844 | graphs = [
Graph(
let={
"_n": Const(94227),
"n": CountOverSet(set=SolutionsSet(var=Var("t"), condition=Exists(var=Var(name='a'), condition=Exists(var=Var(name='b'), condition=And(Geq(left=Var(name='a'), right=Const(value=1)), Leq(left=Var(name='a'), right=Const(value=4)), Geq(left=Va... | COMB | null | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | comb_catalan_compute_v1 | null | 5 | 0 | [
"LIN_FORM"
] | 1 | 0.002 | 2026-02-08T05:25:04.725961Z | {
"verified": true,
"answer": 39844,
"timestamp": "2026-02-08T05:25:04.727606Z"
} | 36e500 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 211,
"completion_tokens": 4570
},
"timestamp": "2026-02-24T03:33:12.506Z",
"answer": 39844
},
{
"... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
}
] | {
"lo": -0.06,
"mid": 2.89,
"hi": 5.27
} | ||
921e7a | comb_count_surjections_v1_1353956133_640 | Let $n = 8$. Let $k$ be the number of ordered pairs $(i, j)$ of integers such that $1 \leq i \leq 3$, $1 \leq j \leq 4$, and $i + j = 5$. Compute $k! \cdot S(n, k)$, where $S(n, k)$ denotes the Stirling number of the second kind. | 5,796 | graphs = [
Graph(
let={
"_n": Const(5),
"n": Const(8),
"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(3)), right=IntegerRang... | COMB | null | COUNT | sympy | COUNT_SUM_EQUALS | [
"COUNT_SUM_EQUALS"
] | 75ab0f | comb_count_surjections_v1 | null | 5 | 0 | [
"COUNT_SUM_EQUALS"
] | 1 | 0.012 | 2026-02-08T11:45:20.464505Z | {
"verified": true,
"answer": 5796,
"timestamp": "2026-02-08T11:45:20.476216Z"
} | 0e9bb4 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 199,
"completion_tokens": 1081
},
"timestamp": "2026-02-24T14:34:24.414Z",
"answer": 5796
},
{
"i... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "ok"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8_SUM",
"status"... | {
"lo": -2.35,
"mid": 1.22,
"hi": 4.84
} | ||
6ff73b | nt_count_gcd_equals_v1_1918700295_2024 | Let $A$ be the set of positive integers $n$ such that $1 \leq n \leq 1129$ and $\gcd(n, 12) = 1$. Let $d$ be the number of positive integers $k$ such that $1 \leq k \leq 2986217$ and $|A|$ divides $k$. Compute the number of positive integers $n$ such that $1 \leq n \leq d$ and $\gcd(n, 13) = 13$. | 609 | graphs = [
Graph(
let={
"upper": CountOverSet(set=SolutionsSet(var=Var("k"), condition=And(Geq(Var("k"), Const(1)), Leq(Var("k"), Const(2986217)), Divides(divisor=CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Const(1129)), Eq(GCD(a=Var("n"), b=C... | NT | null | COUNT | sympy | C4 | [
"C4/C2"
] | 705e18 | nt_count_gcd_equals_v1 | null | 5 | 0 | [
"C2",
"C4"
] | 2 | 0.608 | 2026-02-08T07:37:58.576435Z | {
"verified": true,
"answer": 609,
"timestamp": "2026-02-08T07:37:59.184718Z"
} | 592918 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 154,
"completion_tokens": 1602
},
"timestamp": "2026-02-13T11:31:20.571Z",
"answer": 609
},
{
... | 1 | [
{
"lemma": "C2",
"status": "ok_later"
},
{
"lemma": "C4",
"status": "ok"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "V1",
"status": "no"
},
{
... | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
88ede1 | comb_factorial_compute_v1_48377204_3095 | Let $n$ be the largest prime number such that $2 \leq n \leq 8$. Compute the remainder when $81515 \cdot n!$ is divided by $53902$. | 48,458 | graphs = [
Graph(
let={
"_n": Const(8),
"n": MaxOverSet(set=SolutionsSet(var=Var("n1"), condition=And(Geq(Var("n1"), Const(2)), Leq(Var("n1"), Ref("_n")), IsPrime(Var("n1"))))),
"result": Factorial(Ref("n")),
"Q": Mod(value=Mul(Const(81515), Ref("result")), mo... | NT | null | COMPUTE | sympy | MAX_PRIME_BELOW | [
"MAX_PRIME_BELOW"
] | dc3ad3 | comb_factorial_compute_v1 | null | 3 | 0 | [
"MAX_PRIME_BELOW"
] | 1 | 0.001 | 2026-02-08T17:11:20.021208Z | {
"verified": true,
"answer": 48458,
"timestamp": "2026-02-08T17:11:20.022429Z"
} | 08827c | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 87,
"completion_tokens": 1526
},
"timestamp": "2026-02-17T20:38:23.065Z",
"answer": 48458
},
{... | 1 | [
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok"
},
{
"lemma": "MAX_VAL",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
fc4015 | comb_bell_compute_v1_655260480_3310 | Let $n$ be the number of ordered pairs $(a, b)$ such that $a \in \{1, 2\}$ and $b \in \{1, 2, 3, 4\}$. Let $B$ be the $n$-th Bell number, which counts the number of partitions of a set of size $n$. Compute the remainder when $12470 \cdot B$ is divided by $83611$. | 37,813 | graphs = [
Graph(
let={
"n": CountOverSet(set=CartesianProduct(left=IntegerRange(start=Const(1), end=Const(2)), right=IntegerRange(start=Const(1), end=Const(4)))),
"result": Bell(Ref("n")),
"_c": Const(12470),
"Q": Mod(value=Mul(Ref("_c"), Ref("result")), modu... | COMB | null | COMPUTE | sympy | COUNT_CARTESIAN | [
"COUNT_CARTESIAN"
] | 409d7d | comb_bell_compute_v1 | null | 3 | 0 | [
"COUNT_CARTESIAN"
] | 1 | 0.002 | 2026-02-08T17:18:54.874422Z | {
"verified": true,
"answer": 37813,
"timestamp": "2026-02-08T17:18:54.875986Z"
} | 61ef8d | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 138,
"completion_tokens": 847
},
"timestamp": "2026-02-17T23:40:05.529Z",
"answer": 37813
},
{... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "ok"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
}
] | {
"lo": -2.38,
"mid": 1.74,
"hi": 6.59
} | ||
3baf4a | nt_sum_gcd_range_mod_v1_1742523217_3995 | Let $N = 2017$ and $k = 84$. Define
$$
S = \sum_{n=1}^{N} \gcd(n, k).
$$
Let $r$ be the remainder when $S$ is divided by $10771$. Let $c$ be the sum of all real solutions $x$ to the equation
$$
x^2 - 8836x - 453237 = 0.
$$
Compute the remainder when $r^2 + 49r + c$ is divided by $56895$. | 1,291 | graphs = [
Graph(
let={
"_n": Const(2),
"N": Const(2017),
"k": Const(84),
"M": Const(10771),
"sum": Summation(var="n", start=Const(1), end=Ref("N"), expr=GCD(a=Var("n"), b=Ref("k"))),
"result": Mod(value=Ref("sum"), modulus=Ref("M")),
... | NT | null | COMPUTE | sympy | VIETA_SUM | [
"VIETA_SUM"
] | 833c91 | nt_sum_gcd_range_mod_v1 | quadratic_mod | 5 | 0 | [
"VIETA_SUM"
] | 1 | 0.095 | 2026-02-08T06:10:19.963938Z | {
"verified": true,
"answer": 1291,
"timestamp": "2026-02-08T06:10:20.058757Z"
} | 3641cb | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 159,
"completion_tokens": 2410
},
"timestamp": "2026-02-13T06:27:11.313Z",
"answer": 1291
},
{... | 1 | [
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "V3",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "VAL_SUM_EQ",
"status": "no"
},
{
"lemma": "VIETA_SUM",
"status": "ok"
}
] | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
01641b | diophantine_product_count_v1_1978505735_6696 | Let $k$ be the minimum value of $x + y$ over all pairs of positive integers $(x, y)$ such that $xy = 57600$. Determine the number of positive integers $x_1$ such that $1 \leq x_1 \leq 228$, $x_1$ divides $k$, and $\frac{k}{x_1} \leq 228$. | 20 | graphs = [
Graph(
let={
"k": MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(Mul(Var("x"), Var("y")), Const(57600)))), expr=Sum(Var("x"), Var("y")))),
"upper": Const(22... | NT | null | COUNT | sympy | B3 | [
"B3"
] | 0cd20d | diophantine_product_count_v1 | null | 4 | 0 | [
"B3"
] | 1 | 0.009 | 2026-02-08T19:45:07.615373Z | {
"verified": true,
"answer": 20,
"timestamp": "2026-02-08T19:45:07.624824Z"
} | a765ec | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 129,
"completion_tokens": 2483
},
"timestamp": "2026-02-18T23:25:59.909Z",
"answer": 20
},
{
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "V8_SUM",
"sta... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
623b7b | nt_min_crt_v1_458359167_4863 | Let $m = 7$. Let $k$ be the number of positive integers $p$ for which there exists a positive integer $q$ such that $p \cdot q = 4410$, $\gcd(p, q) = 1$, and $p < q$. Let $a = 5$ and $b = 6$. Find the minimum positive integer $n$ such that $1 \leq n \leq 56$, $n \equiv a \pmod{m}$, and $n \equiv b \pmod{k}$. Compute th... | 54 | graphs = [
Graph(
let={
"m": Const(7),
"k": 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=4410)), Eq(left=GCD(a=Var(name='p'), b=Var(name='q... | NT | null | EXTREMUM | sympy | COPRIME_PAIRS | [
"COPRIME_PAIRS"
] | 2bb3aa | nt_min_crt_v1 | null | 6 | 0 | [
"COPRIME_PAIRS"
] | 1 | 0.009 | 2026-02-08T12:06:33.193323Z | {
"verified": true,
"answer": 54,
"timestamp": "2026-02-08T12:06:33.202469Z"
} | d1d756 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 167,
"completion_tokens": 1593
},
"timestamp": "2026-02-14T22:17:08.526Z",
"answer": 54
},
{
... | 1 | [
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "V1",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
}
] | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
4d47ee | alg_poly_orbit_count_v1_1218484723_6821 | Let $f(x) = x^2 + x - 36 \bmod 73$. For a non-negative integer $a$ with $0 \le a \le 51464$, define the sequence $N = f(a)$, $M = f(N)$, $R = f(M)$, $S = f(R)$, $T = f(S)$. Find the number of values of $a$ such that $T = a$, but $N \ne a$, $M \ne a$, $R \ne a$, and $S \ne a$. | 3,525 | graphs = [
Graph(
let={
"p1": Mod(value=Sum(Pow(Var("a"), Const(2)), Var("a"), Const(-36)), modulus=Const(73)),
"p2": Mod(value=Sum(Pow(Ref("p1"), Const(2)), Ref("p1"), Const(-36)), modulus=Const(73)),
"p3": Mod(value=Sum(Pow(Ref("p2"), Const(2)), Ref("p2"), Const(-36)), ... | ALG | null | COUNT | sympy | POLY_ORBIT_COUNT | [
"POLY_ORBIT_COUNT"
] | 4ad965 | alg_poly_orbit_count_v1 | null | 6 | null | [
"POLY_ORBIT_COUNT"
] | 1 | 0.03 | 2026-02-25T08:18:02.691177Z | {
"verified": true,
"answer": 3525,
"timestamp": "2026-02-25T08:18:02.720712Z"
} | 8f7555 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 230,
"completion_tokens": 10661
},
"timestamp": "2026-03-30T02:44:48.516Z",
"answer": 5
},
{
"... | 1 | [
{
"lemma": "POLY_ORBIT_COUNT",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
}
] | {
"lo": 1.53,
"mid": 4.7,
"hi": 7.23
} | ||
a5ac74 | diophantine_fbi2_count_v1_898971024_2849 | Let $T$ be the set of all integers $t$ such that $14 \leq t \leq 1704$ and there exist positive integers $a$ and $b$ with $1 \leq a \leq 64$, $1 \leq b \leq 165$, and $t = 6a + 8b$. Let $k$ be the number of elements in $T$. Define $D$ as the set of all integers $d$ such that $3 \leq d \leq 83$, $d$ divides $k$, and $4 ... | 15 | 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=64)), Geq(left=Var(name='b'), right=Const(value=... | NT | null | COUNT | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | diophantine_fbi2_count_v1 | null | 5 | 0 | [
"LIN_FORM"
] | 1 | 0.014 | 2026-02-08T17:01:35.128862Z | {
"verified": true,
"answer": 15,
"timestamp": "2026-02-08T17:01:35.142839Z"
} | 3a44ca | 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": 5056
},
"timestamp": "2026-02-17T17:37:53.672Z",
"answer": 15
},
{
... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
231797 | comb_binomial_compute_v1_1520064083_7470 | Compute $\binom{14}{6}$. | 3,003 | graphs = [
Graph(
let={
"n": Const(14),
"k": Const(6),
"result": Binom(n=Ref("n"), k=Ref("k")),
},
goal=Ref("result"),
)
] | ALG | COMB | COMPUTE | sympy | LTE_DIFF | [
"LTE_DIFF/B1"
] | 3fb469 | comb_binomial_compute_v1 | null | 2 | 0 | [
"B1",
"LTE_DIFF"
] | 2 | 0.012 | 2026-02-08T09:03:41.774880Z | {
"verified": true,
"answer": 3003,
"timestamp": "2026-02-08T09:03:41.786609Z"
} | 030787 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 120,
"completion_tokens": 305
},
"timestamp": "2026-02-24T10:20:35.451Z",
"answer": 3003
},
{
"id... | 2 | [
{
"lemma": "B1",
"status": "ok_later"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "ok"
},
{
"lemma": "V1",
"status": "no"
},
{
... | {
"lo": -10,
"mid": -7.79,
"hi": -5.57
} | ||
867139 | modular_mod_compute_v1_601307018_911 | Let $m$ be the minimum value of $x + y$ over all ordered pairs $(x, y)$ of positive integers with $1 \le x \le y$ and $xy = 8340544$. Find the remainder when $-29584$ is divided by $m$. | 5,072 | graphs = [
Graph(
let={
"a": Const(-29584),
"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(8340544)), Leq(Var("x"), Var("y")))), ex... | NT | null | COMPUTE | sympy | B3 | [
"B3"
] | 0cd20d | modular_mod_compute_v1 | null | 3 | 0 | [
"B3"
] | 1 | 0.004 | 2026-03-10T01:31:51.325870Z | {
"verified": true,
"answer": 5072,
"timestamp": "2026-03-10T01:31:51.329897Z"
} | a61203 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 170,
"completion_tokens": 2072
},
"timestamp": "2026-03-29T00:32:49.343Z",
"answer": 5072
},
{
"i... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "V3",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
}
] | {
"lo": -0.92,
"mid": 2.07,
"hi": 4.68
} | ||
1ef3db | algebra_quadratic_discriminant_v1_1915831931_2658 | Let $a = -2$, $b = 8$, and $c = -8$. Define the discriminant $D = b^n - 4ac$, where $n$ is the number of prime integers between 2 and 3, inclusive. Let $r = 2$ if $D > 0$, $r = 1$ if $D = 0$, and $r = 0$ otherwise. Compute $|r|$. | 1 | graphs = [
Graph(
let={
"a": Const(-2),
"b": Const(8),
"c": Const(-8),
"D": Sub(Pow(Ref("b"), CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(2)), Leq(Var("n"), Const(3)), IsPrime(Var("n")))))), Mul(Const(4), Ref("a"), Ref("c"))),... | NT | null | COMPUTE | sympy | COUNT_PRIMES | [
"COUNT_PRIMES"
] | 07c874 | algebra_quadratic_discriminant_v1 | null | 3 | 0 | [
"COUNT_PRIMES"
] | 1 | 0.003 | 2026-02-08T17:02:40.945272Z | {
"verified": true,
"answer": 1,
"timestamp": "2026-02-08T17:02:40.948385Z"
} | e6561c | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 141,
"completion_tokens": 338
},
"timestamp": "2026-02-17T18:19:08.093Z",
"answer": 1
},
{
... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_PRIMES",
"status": "ok"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
53fe92 | antilemma_cartesian_v1_655260480_2256 | Let $x$ be the number of ordered pairs $(i, j)$ such that $1 \leq i \leq 28$ and $1 \leq j \leq 29$. Compute the Bell number corresponding to $x \bmod 11$. | 21,147 | graphs = [
Graph(
let={
"x": CountOverSet(set=CartesianProduct(left=IntegerRange(start=Const(1), end=Const(28)), right=IntegerRange(start=Const(1), end=Const(29)))),
"Q": Bell(Mod(value=Abs(arg=Ref(name='x')), modulus=Const(11))),
},
goal=Ref("Q"),
)
] | COMB | GEOM | COMPUTE | sympy | COUNT_CARTESIAN | [
"COUNT_CARTESIAN"
] | 409d7d | antilemma_cartesian_v1 | null | 3 | 0 | [
"COUNT_CARTESIAN"
] | 1 | 0.001 | 2026-02-08T16:38:58.860793Z | {
"verified": true,
"answer": 21147,
"timestamp": "2026-02-08T16:38:58.861393Z"
} | ba852c | 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": 549
},
"timestamp": "2026-02-17T08:25:31.567Z",
"answer": 21147
},
{
... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "ok"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
}
] | {
"lo": -2.38,
"mid": 1.74,
"hi": 6.59
} | ||
79829f | nt_count_gcd_equals_v1_1440796553_1543 | Let $k$ be the number of integers $t$ such that $11 \leq t \leq 495$ and there exist integers $a$ and $b$ with $1 \leq a \leq 9$, $1 \leq b \leq 108$, and $t = 7a + 4b$. Let $d = 467$ and let $N = 10946$. Compute the number of positive integers $n \leq N$ such that $\gcd(n, k) = d$. | 23 | graphs = [
Graph(
let={
"upper": Const(10946),
"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=9)), Geq(left... | NT | null | COUNT | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | nt_count_gcd_equals_v1 | null | 6 | 0 | [
"LIN_FORM"
] | 1 | 2.336 | 2026-02-08T14:02:49.686398Z | {
"verified": true,
"answer": 23,
"timestamp": "2026-02-08T14:02:52.022536Z"
} | d19368 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 1,
"correct": {
"strict": false,
"boxed": false,
"relaxed": true
},
"usage": {
"prompt_tokens": 154,
"completion_tokens": 5951
},
"timestamp": "2026-02-15T23:23:22.579Z",
"answer": 16
},
{... | 1 | [
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"... | {
"lo": -5.49,
"mid": 0.22,
"hi": 6.51
} | ||
1c8350 | sequence_lucas_compute_v1_809748730_1493 | Let $d$ be the smallest integer greater than or equal to $2$ that divides $3051493651$. Compute the $d$-th Lucas number. | 9,349 | graphs = [
Graph(
let={
"_n": Const(2),
"n": MinOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Ref("_n")), Divides(divisor=Var("d"), dividend=Const(3051493651))))),
"result": Lucas(arg=Ref(name='n')),
},
goal=Ref("result"),
)
] | NT | null | COMPUTE | sympy | MIN_PRIME_FACTOR | [
"MIN_PRIME_FACTOR"
] | bc3776 | sequence_lucas_compute_v1 | null | 3 | 0 | [
"MIN_PRIME_FACTOR"
] | 1 | 0.001 | 2026-02-08T12:29:45.979005Z | {
"verified": true,
"answer": 9349,
"timestamp": "2026-02-08T12:29:45.980357Z"
} | 02fd88 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 80,
"completion_tokens": 1970
},
"timestamp": "2026-02-15T02:09:42.552Z",
"answer": 9349
},
{
... | 1 | [
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "MIN_PRIME_FACTOR",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"statu... | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
4cde3f | comb_catalan_compute_v1_124444284_1497 | Let $n = 22$. Define $S$ to be the set of all ordered pairs $(x_1, x_2)$ of positive odd integers such that $x_1 + x_2 = 22$. Let $n_S$ be the number of elements in $S$. Let $C_{n_S}$ denote the $n_S$-th Catalan number. Find the remainder when $95440 \cdot C_{n_S}$ is divided by $54109$. | 27,739 | graphs = [
Graph(
let={
"_n": Const(22),
"n": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x1"), Var("x2")]), condition=And(IsPositive(arg=Var(name='x1')), IsPositive(arg=Var(name='x2')), IsOdd(arg=Var(name='x1')), IsOdd(arg=Var(name='x2')), Eq(Sum(Var("x1"), Var("x2")), Re... | COMB | null | COMPUTE | sympy | COMB1 | [
"COMB1"
] | 567f58 | comb_catalan_compute_v1 | null | 5 | 0 | [
"COMB1"
] | 1 | 0.002 | 2026-02-08T03:56:18.841863Z | {
"verified": true,
"answer": 27739,
"timestamp": "2026-02-08T03:56:18.843624Z"
} | d62457 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 211,
"completion_tokens": 4346
},
"timestamp": "2026-02-10T16:17:27.654Z",
"answer": 27739
},
{
"... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COMB1",
"status": "ok"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
}
... | {
"lo": -0.05,
"mid": 2.89,
"hi": 5.27
} | ||
82d6d4 | nt_sum_divisors_mod_v1_1915831931_260 | Let $N$ be the smallest positive integer that can be expressed as the sum of two positive integers $x$ and $y$ such that $xy = 8100$. Compute the remainder when the sum of all positive divisors of $N$ is divided by $11597$. | 546 | graphs = [
Graph(
let={
"_n": Const(8100),
"n": MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(Mul(Var("x"), Var("y")), Ref("_n")))), expr=Sum(Var("x"), Var("y")))),
... | NT | null | COMPUTE | sympy | B3 | [
"B3"
] | 0cd20d | nt_sum_divisors_mod_v1 | null | 4 | 0 | [
"B3"
] | 1 | 0.005 | 2026-02-08T15:17:56.061226Z | {
"verified": true,
"answer": 546,
"timestamp": "2026-02-08T15:17:56.066587Z"
} | 36377a | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 119,
"completion_tokens": 255
},
"timestamp": "2026-02-16T05:36:45.803Z",
"answer": 336
},
{
"id": 11,
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "V5",
"status": "no"... | {
"lo": -8.26,
"mid": -5.01,
"hi": -1.76
} | ||
4e6745 | nt_euler_phi_compute_v1_717093673_3147 | Let $n = 83521$. Define $\varphi(n)$ to be the number of positive integers less than or equal to $n$ that are relatively prime to $n$. Let $P$ be the set of all prime numbers $p$ such that $2 \leq p \leq 12$. Let $m$ be the largest element of $P$. Compute the Bell number $B_k$, where $k = \varphi(n) \bmod m$. | 2 | graphs = [
Graph(
let={
"_n": Const(2),
"n": Const(83521),
"result": EulerPhi(n=Ref("n")),
"Q": Bell(Mod(value=Abs(arg=Ref(name='result')), modulus=MaxOverSet(set=SolutionsSet(var=Var("n1"), condition=And(Geq(Var("n1"), Ref("_n")), Leq(Var("n1"), Const(12)), I... | NT | COMB | COMPUTE | sympy | MAX_PRIME_BELOW | [
"MAX_PRIME_BELOW"
] | 88ea9c | nt_euler_phi_compute_v1 | bell_mod | 4 | 0 | [
"MAX_PRIME_BELOW"
] | 1 | 0.001 | 2026-02-08T17:24:34.637964Z | {
"verified": true,
"answer": 2,
"timestamp": "2026-02-08T17:24:34.639122Z"
} | 7ec7d1 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 142,
"completion_tokens": 730
},
"timestamp": "2026-02-18T01:21:36.566Z",
"answer": 2
},
{
... | 1 | [
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "V8_SUM",
... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
de5254 | antilemma_k2_v1_124444284_9068 | Let $n = 428$ and define
$$
x = \sum_{k=1}^{428} \phi(k) \left\lfloor \frac{428}{k} \right\rfloor,
$$
where $\phi(k)$ denotes Euler's totient function. Compute the value of
$$
(x \bmod 317) + 1009 \cdot (x \bmod 313).
$$ | 98,066 | graphs = [
Graph(
let={
"_n": Const(428),
"x": Summation(var="k", start=Const(1), end=Const(428), expr=Mul(EulerPhi(n=Var("k")), Floor(Div(Ref("_n"), Var("k"))))),
"_c": Const(1009),
"Q": Sum(Mod(value=Ref("x"), modulus=Const(317)), Mul(Ref("_c"), Mod(value=Re... | NT | COMB | COMPUTE | sympy | K2 | [
"K2"
] | 6897ab | antilemma_k2_v1 | null | 6 | 0 | [
"K2"
] | 1 | 0.001 | 2026-02-08T12:11:02.896165Z | {
"verified": true,
"answer": 98066,
"timestamp": "2026-02-08T12:11:02.896689Z"
} | e615f4 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 129,
"completion_tokens": 796
},
"timestamp": "2026-02-14T22:41:09.645Z",
"answer": 98066
},
{... | 1 | [
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "K2",
"status": "ok"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
},
{
"lemma": "VAL_SUM_EQ",
"status": "no"
}
] | {
"lo": -5.49,
"mid": 0.22,
"hi": 6.51
} | ||
5cccc0 | nt_sum_divisors_compute_v1_655260480_1954 | Let $n = 31684$ and $m = 3600$. Define $\text{result}$ to be the sum of all positive divisors of $n$. Let $c$ be the largest positive divisor $d$ of 12985200 such that $1 \leq d \leq m$. Compute $(c - \text{result}) \bmod 75310$. | 22,833 | graphs = [
Graph(
let={
"_n": Const(3600),
"n": Const(31684),
"result": SumDivisors(n=Ref("n")),
"_c": MaxOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Const(1)), Leq(Var("d"), Ref("_n")), Divides(divisor=Var("d"), dividend=Const(12985200)... | NT | null | COMPUTE | sympy | SUM_ARITHMETIC | [
"MAX_DIVISOR"
] | ad1a9b | nt_sum_divisors_compute_v1 | negation_mod | 3 | 0 | [
"MAX_DIVISOR",
"SUM_ARITHMETIC"
] | 2 | 0.011 | 2026-02-08T16:29:19.055673Z | {
"verified": true,
"answer": 22833,
"timestamp": "2026-02-08T16:29:19.066327Z"
} | 65daa0 | 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": 1236
},
"timestamp": "2026-02-17T04:28:07.346Z",
"answer": 22833
},
... | 1 | [
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "MAX_DIVISOR",
"status": "ok"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
094079 | antilemma_v1_legendre_1742523217_905 | Let $S$ be the set of all ordered pairs $(x, y)$ of positive integers such that $xy = 16695396$. For each such pair, compute $x + y$. Let $T$ be the set of all such sums. Let $m$ be the minimum element of $T$. Determine the largest integer $k$ such that $2^k$ divides $m!$. | 8,162 | graphs = [
Graph(
let={
"_n": Const(2),
"x": MaxKDivides(target=Factorial(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(16695396)))), e... | NT | null | COMPUTE | sympy | B3 | [
"B3/V1",
"V1"
] | 25e8f3 | antilemma_v1_legendre | null | 7 | 0 | [
"B3",
"V1"
] | 2 | 0.001 | 2026-02-08T03:21:13.771467Z | {
"verified": true,
"answer": 8162,
"timestamp": "2026-02-08T03:21:13.772202Z"
} | 9f68cb | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 193,
"completion_tokens": 4202
},
"timestamp": "2026-02-10T00:22:41.710Z",
"answer": 8162
},
{
"i... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "K5",
"status": "same_pattern_wrong"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "V1",
"status": "ok"
},
{
"lemm... | {
"lo": -6.51,
"mid": -0.31,
"hi": 5.43
} | ||
da313b | nt_num_divisors_compute_v1_655260480_3871 | Let $S$ be the set of all ordered pairs $(x, y)$ of positive integers such that $x + y = 50$. Let $n$ be the maximum value of $xy$ over all such pairs. Let $d(n)$ denote the number of positive divisors of $n$. Compute the remainder when $52511 \cdot d(n)$ is divided by 66126. | 64,177 | graphs = [
Graph(
let={
"_n": Const(66126),
"n": MaxOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(Sum(Var("x"), Var("y")), Const(50)))), expr=Mul(Var("x"), Var("y")))),
... | NT | null | COMPUTE | sympy | B1 | [
"B1"
] | 5b950e | nt_num_divisors_compute_v1 | null | 4 | 0 | [
"B1"
] | 1 | 0.004 | 2026-02-08T17:35:22.270968Z | {
"verified": true,
"answer": 64177,
"timestamp": "2026-02-08T17:35:22.274590Z"
} | 5d03d4 | 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": 619
},
"timestamp": "2026-02-18T04:16:35.249Z",
"answer": 64177
},
{... | 1 | [
{
"lemma": "B1",
"status": "ok"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
}... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
e4788f | lte_diff_endings_v1_784195855_5159 | Let $a = 23$, $b = 2$, $p = 3$, and $T = 11$. Let $v$ be the largest integer $k$ such that $p^k$ divides $a - b$. Compute $p^{T - v}$. | 59,049 | graphs = [
Graph(
let={
"a_val": Const(23),
"b_val": Const(2),
"p_val": Const(3),
"T_val": Const(11),
"diff": Sub(Ref("a_val"), Ref("b_val")),
"vp_diff": MaxKDivides(target=Ref("diff"), base=Ref("p_val")),
"exp": Sub(Ref("T_... | NT | null | COMPUTE | sympy | LTE_DIFF | [
"LTE_DIFF"
] | cf8260 | lte_diff_endings_v1 | null | 3 | null | [
"LTE_DIFF"
] | 1 | 0 | 2026-02-08T07:42:28.805733Z | {
"verified": true,
"answer": 59049,
"timestamp": "2026-02-08T07:42:28.806081Z"
} | 2daf72 | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 153,
"completion_tokens": 461
},
"timestamp": "2026-02-20T04:50:56.054Z",
"answer": 59049
}
] | 2 | [
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "ok"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "V7",
"status... | {
"lo": -10,
"mid": -6.47,
"hi": -2.95
} |
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