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 |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
10695c | diophantine_sum_product_min_v1_784195855_3538 | Let $p_1 = 67$ and $n_1 = p_1^2$. Define $\lambda(n)$ to be the Liouville function. Let $e = \lambda(n_1)$. Let $p = 13$ and $n = p^{3e}$. Define $s = \lambda(n) + 1$. Let $P'$ be the number of positive integers $t$ such that $7 \leq t \leq 622$ and there exist positive integers $a$, $b$ with $1 \leq a \leq 139$, $1 \l... | 10 | graphs = [
Graph(
let={
"p1": Const(67),
"n1": Pow(Ref("p1"), Const(2)),
"e": LiouvilleLambda(n=Ref(name='n1')),
"p": Const(13),
"n": Pow(Ref("p"), Mul(Const(3), Ref("e"))),
"s": Sum(LiouvilleLambda(n=Ref(name='n')), Const(1)),
... | NT | null | EXTREMUM | sympy | C2 | [
"LIN_FORM/LIOUVILLE_MINUS_ONE",
"LIOUVILLE_ONE"
] | fe86f6 | diophantine_sum_product_min_v1 | null | 7 | 2 | [
"C2",
"LIN_FORM",
"LIOUVILLE_MINUS_ONE",
"LIOUVILLE_ONE"
] | 4 | 0.417 | 2026-02-08T06:29:24.629369Z | {
"verified": true,
"answer": 10,
"timestamp": "2026-02-08T06:29:25.046213Z"
} | 2a5580 | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 294,
"completion_tokens": 867
},
"timestamp": "2026-02-19T09:12:04.463Z",
"answer": 10
}
] | 2 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "LIOUVILLE_MINUS_ONE",
"status": "ok_later"
},
{
"lemma": "LIOUVILLE_ONE",
"status": "ok"
... | {
"lo": -10,
"mid": -6.47,
"hi": -2.95
} | ||
f7e592 | alg_poly4_sum_v1_1218484723_4544 | Let $M$ be the number of integers $j$ with $0 \le j \le 70674$ such that
$$\binom{70674}{j} \bmod 2 = 1.$$
Define
$$A = \bigl|\{v : v \ge \max\{d : 1 \le d \le 130,\ d \mid 18070\},\ v \le 37570,\ \text{there exist integers } a,b \text{ with } 1 \le a,b \le 17 \\ \text{such that } 64ab + 41a^{2} + 25b^{2} = v\}\bigr|,$... | 37,391 | graphs = [
Graph(
let={
"_c": Const(37570),
"_m": CountOverSet(set=SolutionsSet(var=Var("j"), condition=And(Geq(Var("j"), Const(0)), Leq(Var("j"), Const(70674)), Eq(Mod(value=Binom(n=Const(70674), k=Var("j")), modulus=Const(2)), Const(1))), domain='nonnegative_integers')),
... | NT | null | COMPUTE | sympy | MAX_DIVISOR | [
"MAX_DIVISOR/QF_PSD_DISTINCT",
"V8/QF_PSD_DISTINCT"
] | fe9c52 | alg_poly4_sum_v1 | null | 7 | 0 | [
"MAX_DIVISOR",
"QF_PSD_DISTINCT",
"V8"
] | 3 | 0.155 | 2026-02-25T06:13:03.709409Z | {
"verified": true,
"answer": 37391,
"timestamp": "2026-02-25T06:13:03.864152Z"
} | 0704af | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 395,
"completion_tokens": 31715
},
"timestamp": "2026-03-29T16:13:07.018Z",
"answer": 37391
},
{
... | 1 | [
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "MAX_DIVISOR",
"status": "ok"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "QF_PSD_DISTINCT",
"status": "... | {
"lo": 1.53,
"mid": 4.7,
"hi": 7.23
} | ||
5c74be | antilemma_sum_equals_v1_579913215_177 | Let $m = 80711$ and $c = 55318$. Let $S$ be the set of all ordered pairs $(i, j)$ of integers such that $1 \leq i \leq 81$, $1 \leq j \leq 81$, and $i + j = 83$. Let $n$ be the number of elements in $S$.
Let $T$ be the set of all ordered pairs $(i, j)$ of integers such that $1 \leq i \leq 80$, $1 \leq j \leq 80$, and ... | 11,728 | graphs = [
Graph(
let={
"_m": Const(80711),
"_n": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("i"), Var("j")]), condition=Eq(Sum(Var("i"), Var("j")), Const(83)), domain=CartesianProduct(left=IntegerRange(start=Const(1), end=Const(81)), right=IntegerRange(start=Const(1), end... | COMB | GEOM | COMPUTE | sympy | COUNT_SUM_EQUALS | [
"COUNT_SUM_EQUALS/COUNT_SUM_EQUALS",
"COUNT_SUM_EQUALS"
] | ae9919 | antilemma_sum_equals_v1 | null | 3 | 0 | [
"COUNT_SUM_EQUALS"
] | 1 | 0.009 | 2026-02-08T12:55:58.135863Z | {
"verified": true,
"answer": 11728,
"timestamp": "2026-02-08T12:55:58.144479Z"
} | dd7fa7 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 276,
"completion_tokens": 1373
},
"timestamp": "2026-02-24T16:49:47.536Z",
"answer": 11728
},
{
"... | 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
} | ||
27d96f | nt_sum_gcd_range_mod_v1_717093673_1604 | Consider the set of all ordered pairs $(x,y)$ of positive integers such that $x + y = 146$. Let $N$ be the maximum value of $xy$ over all such pairs. Let $k = 480$ and $M = 10177$. Compute the remainder when $\sum_{n=1}^{N} \gcd(n, k)$ is divided by $M$. | 4,928 | graphs = [
Graph(
let={
"N": MaxOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(Sum(Var("x"), Var("y")), Const(146)))), expr=Mul(Var("x"), Var("y")))),
"k": Const(480),
... | NT | null | COMPUTE | sympy | B1 | [
"B1"
] | 5b950e | nt_sum_gcd_range_mod_v1 | null | 4 | 0 | [
"B1"
] | 1 | 0.461 | 2026-02-08T16:12:24.966116Z | {
"verified": true,
"answer": 4928,
"timestamp": "2026-02-08T16:12:25.427158Z"
} | 474fc5 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 128,
"completion_tokens": 4347
},
"timestamp": "2026-02-16T23:13:58.732Z",
"answer": 4928
},
{... | 1 | [
{
"lemma": "B1",
"status": "ok"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
3ff0c8 | sequence_count_fib_divisible_v1_784195855_5434 | Let $m = 44121$ and $n = 61504$. Define $S$ as the set of all ordered pairs $(x, y)$ of positive integers such that $xy = n$. Let $T$ be the set of all values $x + y$ where $(x, y) \in S$. Let $u$ be the minimum value in $T$.
Let $P$ be the set of all prime integers $k$ such that $2 \leq k \leq 5$. Let $d$ be the larg... | 67,329 | graphs = [
Graph(
let={
"_m": Const(44121),
"_n": Const(61504),
"upper": MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(Mul(Var("x"), Var("y")), Ref("_n"))... | NT | null | COUNT | sympy | MAX_PRIME_BELOW | [
"MAX_PRIME_BELOW/MAX_VAL",
"B3"
] | 87c1ea | sequence_count_fib_divisible_v1 | null | 7 | 0 | [
"B3",
"MAX_PRIME_BELOW",
"MAX_VAL"
] | 3 | 0.037 | 2026-02-08T07:54:04.514772Z | {
"verified": true,
"answer": 67329,
"timestamp": "2026-02-08T07:54:04.551682Z"
} | bd376e | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 249,
"completion_tokens": 1339
},
"timestamp": "2026-02-13T13:19:11.946Z",
"answer": 67329
},
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok"
},
{
"lemma": "MAX_VAL",
"status": "ok_later"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},... | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
925fcd | nt_min_phi_inverse_v1_1742523217_280 | Let $k = 24$. Determine the value of the smallest positive integer $n$ such that $1 \leq n \leq 100$ and $\phi(n) = k$. | 35 | graphs = [
Graph(
let={
"upper": Const(100),
"k": Const(24),
"result": MinOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Ref("upper")), Eq(EulerPhi(n=Var("n")), Ref("k"))))),
},
goal=Ref("result"),
)
] | NT | null | EXTREMUM | sympy | MIN_PRIME_FACTOR | [
"MOBIUS_COPRIME"
] | ac54ac | nt_min_phi_inverse_v1 | null | 6 | 0 | [
"MIN_PRIME_FACTOR",
"MOBIUS_COPRIME"
] | 2 | 0.047 | 2026-02-08T02:57:35.963893Z | {
"verified": true,
"answer": 35,
"timestamp": "2026-02-08T02:57:36.010534Z"
} | 1e0cf9 | 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": 1202
},
"timestamp": "2026-02-09T15:54:41.222Z",
"answer": 35
},
{
"id"... | 1 | [
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "MOBIUS_COPRIME",
"status": "ok"
},
{
"lemma": "MOD_MUL",
"status": "... | {
"lo": -8.31,
"mid": -5.11,
"hi": -2.4
} | ||
3eac17 | nt_sum_divisors_mod_v1_153355830_1997 | Let $S$ be the set of all ordered pairs $(x,y)$ of positive integers such that $xy = 6350400$. Define $n$ to be the minimum value of $x + y$ over all such pairs. Let $\sigma(n)$ denote the sum of the positive divisors of $n$. Find the remainder when $\sigma(n)$ is divided by $11527$. | 7,817 | 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(6350400)))), expr=Sum(Var("x"), Var("y")))),
"M": Const(1152... | NT | null | COMPUTE | sympy | B3 | [
"B3"
] | 0cd20d | nt_sum_divisors_mod_v1 | null | 4 | 0 | [
"B3"
] | 1 | 0.002 | 2026-02-08T06:50:46.761623Z | {
"verified": true,
"answer": 7817,
"timestamp": "2026-02-08T06:50:46.763467Z"
} | ffc323 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 126,
"completion_tokens": 1406
},
"timestamp": "2026-02-13T05:16:26.716Z",
"answer": 7817
},
{... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
}
] | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
7ba46c | antilemma_sum_equals_v1_238844314_408 | Let $n$ be the number of ordered pairs $(i, j)$ such that $1 \leq i \leq 6$ and $1 \leq j \leq 13$. Let $x$ be the number of ordered pairs $(i, j)$ of positive integers with $1 \leq i \leq 76$, $1 \leq j \leq 77$, and $i + j = n$. Compute the value of $$x + \phi\left(|x| + \binom{15}{15}\right) + \tau\left(|x| + \binom... | 140 | graphs = [
Graph(
let={
"_n": CountOverSet(set=CartesianProduct(left=IntegerRange(start=Const(1), end=Const(6)), right=IntegerRange(start=Const(1), end=Const(13)))),
"x": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("i"), Var("j")]), condition=Eq(Sum(Var("i"), Var("j")), Ref... | COMB | GEOM | COMPUTE | sympy | LIN_FORM | [
"COUNT_CARTESIAN/COUNT_SUM_EQUALS",
"COUNT_SUM_EQUALS",
"ONE_BINOM_N"
] | 3dfc63 | antilemma_sum_equals_v1 | null | 4 | 0 | [
"COUNT_CARTESIAN",
"COUNT_SUM_EQUALS",
"LIN_FORM",
"ONE_BINOM_N"
] | 4 | 0.253 | 2026-02-08T13:20:00.490145Z | {
"verified": true,
"answer": 140,
"timestamp": "2026-02-08T13:20:00.743186Z"
} | 3934d8 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 288,
"completion_tokens": 965
},
"timestamp": "2026-02-24T17:49:13.469Z",
"answer": 140
},
{
"id"... | 1 | [
{
"lemma": "COUNT_CARTESIAN",
"status": "ok"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "ok"
},
{
"lemma": "ONE_BINOM_N",
"status": "ok"
},
{
"lemma... | {
"lo": -5.97,
"mid": -3.97,
"hi": -1.93
} | ||
17f9ce | sequence_count_fib_divisible_v1_48377204_2892 | Let $P$ be the set of all ordered pairs $(x, y)$ of positive integers such that $xy = 106929$. Let $s$ be the sum $x + y$ for each such pair. Let $u$ be the minimum value of $s$ over all pairs in $P$. Let $S$ be the set of all positive integers $n \leq u$ such that the $n$-th Fibonacci number is divisible by $5$. Compu... | 130 | graphs = [
Graph(
let={
"upper": MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(Mul(Var("x"), Var("y")), Const(106929)))), expr=Sum(Var("x"), Var("y")))),
"d": Const(5... | NT | null | COUNT | sympy | B3 | [
"B3"
] | 0cd20d | sequence_count_fib_divisible_v1 | null | 5 | 0 | [
"B3"
] | 1 | 0.04 | 2026-02-08T17:03:30.160957Z | {
"verified": true,
"answer": 130,
"timestamp": "2026-02-08T17:03:30.201205Z"
} | e6b258 | 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": 845
},
"timestamp": "2026-02-17T17:59:20.954Z",
"answer": 130
},
{
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "VAL_SUM_EQ",
"stat... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
337940 | nt_count_coprime_and_v1_168721529_380 | Let $n$ be the number of integers $t$ for which there exist integers $a$ and $b$ satisfying $1\le a\le2$, $1\le b\le7$, $15\le t\le60$, and
\[
t=9a+6b.
\]
Let $k_1=7$ and $k_2=9$. Let $U=40516$, and let $R$ be the number of integers $x$ with $1\le x\le U$, $\gcd(x,k_1)=1$, and $\gcd(x,k_2)=1$.
Let $P$ be the largest ... | 35,109 | graphs = [
Graph(
let={
"_m": Const(2),
"_n": CountOverSet(set=SolutionsSet(var=Var("t"), condition=Exists(var=Var(name='a'), condition=Exists(var=Var(name='b'), condition=And(Geq(left=Var(name='a'), right=Const(value=1)), Leq(left=Var(name='a'), right=Const(value=2)), Geq(left=Var(n... | NT | null | COUNT | sympy | LIN_FORM | [
"LIN_FORM/MAX_PRIME_BELOW/MOBIUS_SUM"
] | 4761d9 | nt_count_coprime_and_v1 | digits_weighted_mod | 7 | 0 | [
"LIN_FORM",
"MAX_PRIME_BELOW",
"MOBIUS_SUM"
] | 3 | 4.84 | 2026-02-08T13:00:53.743215Z | {
"verified": true,
"answer": 35109,
"timestamp": "2026-02-08T13:00:58.583040Z"
} | 929ea9 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 412,
"completion_tokens": 1702
},
"timestamp": "2026-02-09T04:18:16.439Z",
"answer": 35109
},
{
"... | 1 | [
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok... | {
"lo": -2.06,
"mid": 1.85,
"hi": 5.2
} | ||
eb7601 | comb_binomial_compute_v1_784195855_3319 | Let $n = 14$ and $k = 6$. Define $\binom{n}{k}$ as the binomial coefficient $C(n, k)$. Let $c = 31597$ and define $Q$ as the remainder when $c \cdot \binom{14}{6}$ is divided by 54746. Find the value of $Q$. | 10,973 | graphs = [
Graph(
let={
"n": Const(14),
"k": Const(6),
"result": Binom(n=Ref("n"), k=Ref("k")),
"_c": Const(31597),
"Q": Mod(value=Mul(Ref("_c"), Ref("result")), modulus=Const(54746)),
},
goal=Ref("Q"),
)
] | ALG | COMB | COMPUTE | sympy | K2 | [
"K2"
] | 6897ab | comb_binomial_compute_v1 | null | 2 | 0 | [
"K2"
] | 1 | 0.01 | 2026-02-08T06:20:10.964338Z | {
"verified": true,
"answer": 10973,
"timestamp": "2026-02-08T06:20:10.974524Z"
} | 2a367c | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 189,
"completion_tokens": 1606
},
"timestamp": "2026-02-24T06:05:12.314Z",
"answer": 10973
},
{
"... | 1 | [
{
"lemma": "K2",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
}
] | {
"lo": -2.46,
"mid": 0.47,
"hi": 3.59
} | ||
56702b | alg_poly3_min_v1_601307018_2614 | Find the remainder when $$\min\left\{ -99a^3 + 63a^2b - 27ab^2 + b^3 + 315a^2c - 90abc + 30b^2c - 405ac^2 + 30bc^2 + c^3 \cdot \left|\left\{ (a_1, b_1) : \substack{1 \leq a_1 \leq 25, \\ 1 \leq b_1 \leq N, \\ 2b_1^2 - 2a_1b_1 + 13a_1^2 \leq 1168} \right\}\right| : a,b,c \in [1,24] \cap \mathbb{Z} \right\}$$ is divided ... | 49,373 | graphs = [
Graph(
let={
"_m": Const(3),
"_n": Const(3),
"result": Mod(value=MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("a"), Var("b"), Var("c")]), condition=And(Geq(Var("a"), Const(1)), Leq(Var("a"), Const(24)), Geq(Var("b"), Const(1)), Leq(Var("b"... | ALG | null | COMPUTE | sympy | POLY_ORBIT_COUNT | [
"POLY4_COUNT/QF_PSD_COUNT_LEQ"
] | 94cd2a | alg_poly3_min_v1 | null | 7 | 0 | [
"POLY4_COUNT",
"POLY_ORBIT_COUNT",
"QF_PSD_COUNT_LEQ"
] | 3 | 0.251 | 2026-03-10T03:17:24.173293Z | {
"verified": true,
"answer": 49373,
"timestamp": "2026-03-10T03:17:24.424266Z"
} | 19ae98 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 401,
"completion_tokens": 6217
},
"timestamp": "2026-03-29T05:54:00.988Z",
"answer": 49373
},
{
"... | 1 | [
{
"lemma": "POLY4_COUNT",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "QF_PSD_COUNT_LEQ",
"status": "ok_later"
}
] | {
"lo": 1.23,
"mid": 4.27,
"hi": 6.7
} | ||
daf1da | nt_count_divisors_in_range_v1_1520064083_5045 | Let $n = 166320$. Define $a = 44$ and let $b$ be the minimum value of $x + y$ over all ordered pairs $(x, y)$ of positive integers such that $x \cdot y = 12040900$. Let $d$ be a positive divisor of $n$. Define $r$ to be the number of such divisors $d$ satisfying $a \leq d \leq b$. Compute the value of $$\sum_{k=1}^{r} ... | 554 | graphs = [
Graph(
let={
"n": Const(166320),
"a": Const(44),
"b": 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(12040900))))... | NT | null | COUNT | sympy | B3 | [
"B3"
] | 0cd20d | nt_count_divisors_in_range_v1 | null | 5 | 0 | [
"B3"
] | 1 | 0.062 | 2026-02-08T06:34:54.122174Z | {
"verified": true,
"answer": 554,
"timestamp": "2026-02-08T06:34:54.184621Z"
} | 963851 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 171,
"completion_tokens": 3835
},
"timestamp": "2026-02-13T02:08:12.963Z",
"answer": 554
},
{
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "... | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
b12ba8 | sequence_lucas_compute_v1_1915831931_3120 | Let $m = 2$. Let $S$ be the set of all integers $n_1$ such that $n_1 \geq m$, $n_1 \leq 20$, and $n_1$ is prime. Let $n$ be the largest prime number less than or equal to the maximum element of $S$. Compute the $n$th Lucas number. | 9,349 | graphs = [
Graph(
let={
"_m": Const(2),
"_n": MaxOverSet(set=SolutionsSet(var=Var("n1"), condition=And(Geq(Var("n1"), Ref("_m")), Leq(Var("n1"), Const(20)), IsPrime(Var("n1"))))),
"n": MaxOverSet(set=SolutionsSet(var=Var("n2"), condition=And(Geq(Var("n2"), Const(2)), Leq(... | NT | null | COMPUTE | sympy | MAX_PRIME_BELOW | [
"MAX_PRIME_BELOW/MAX_PRIME_BELOW"
] | 15be89 | sequence_lucas_compute_v1 | null | 3 | 0 | [
"MAX_PRIME_BELOW"
] | 1 | 0.002 | 2026-02-08T17:22:19.034715Z | {
"verified": true,
"answer": 9349,
"timestamp": "2026-02-08T17:22:19.037192Z"
} | 7047b2 | 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": 744
},
"timestamp": "2026-02-18T01:10:37.201Z",
"answer": 9349
},
{
... | 1 | [
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "VAL_SUM_EQ",
"status": "n... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
ff04ae | algebra_poly_eval_v1_784195855_31 | Let $a$ be the largest integer $k$ such that $7^k \leq 32262$. Let $b$ be the number of unordered pairs of coprime positive integers $(p, q)$ with $p < q$ and $pq = 108$. Let $c$ be the sum of all real solutions $x$ to the equation $x^2 - 3x - 990 = 0$. Compute
$$
18496 - \left( a \cdot 12^3 + 4 \cdot 12^b + c \cdot 12... | 9,243 | graphs = [
Graph(
let={
"_d": Const(7),
"_m": Const(2),
"_n": Const(4),
"k": Const(12),
"result": Sum(Mul(MaxOverSet(set=SolutionsSet(var=Var("k"), condition=Leq(Pow(Ref("_d"), Var("k")), Const(32262)))), Pow(Ref("k"), Const(3))), Mul(Ref("_n"), Po... | NT | null | COMPUTE | sympy | COPRIME_PAIRS | [
"COPRIME_PAIRS",
"VIETA_SUM",
"MAX_VAL"
] | d336db | algebra_poly_eval_v1 | null | 7 | 0 | [
"COPRIME_PAIRS",
"MAX_VAL",
"VIETA_SUM"
] | 3 | 0.008 | 2026-02-08T02:54:53.769396Z | {
"verified": true,
"answer": 9243,
"timestamp": "2026-02-08T02:54:53.777179Z"
} | 99ab8e | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 242,
"completion_tokens": 1050
},
"timestamp": "2026-02-10T11:53:37.689Z",
"answer": 9253
},
{
... | 1 | [
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K16",
"status": "same_pattern_wrong"
},
{
"lemma": "MAX_VAL",
"status": "ok"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "MOD_MUL",
"statu... | {
"lo": -0.71,
"mid": 1.42,
"hi": 3.32
} | ||
9c9dea | algebra_quadratic_discriminant_v1_1116507919_172 | Let $a=-2$, $b=-2$, and $c=24$. Let
$$D=b^2-4ac$$
be the discriminant of the quadratic polynomial $ax^2+bx+c$.
Let $N$ be the number of integers $t$ such that $26\le t\le 6186$ and there exist integers $u$ and $v$ with $1\le u\le 36$, $1\le v\le 856$, and
$$t=5u+7v+14.$$
Let $d$ range over all integers with $d\ge 2$ ... | 1,070 | graphs = [
Graph(
let={
"_n": Const(2),
"a": Const(-2),
"b": Const(-2),
"c": Const(24),
"result": Sub(Pow(Ref("b"), Const(2)), Mul(Const(4), Ref("a"), Ref("c"))),
"Q": Summation(var="n", start=SumOverDivisors(n=GCD(a=Const(value=13), b=... | NT | null | COMPUTE | sympy | ONE_PHI_2 | [
"LIN_FORM/MIN_PRIME_FACTOR/MOBIUS_COPRIME"
] | a67c0f | algebra_quadratic_discriminant_v1 | sum_divisor_count | 8 | 0 | [
"LIN_FORM",
"MIN_PRIME_FACTOR",
"MOBIUS_COPRIME",
"ONE_PHI_2"
] | 4 | 0.021 | 2026-02-08T02:27:14.436310Z | {
"verified": true,
"answer": 1070,
"timestamp": "2026-02-08T02:27:14.456842Z"
} | efeeed | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 347,
"completion_tokens": 4036
},
"timestamp": "2026-02-09T14:06:09.565Z",
"answer": 1070
},
{
"... | 1 | [
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "MIN_PRIME_FACTOR",
"status": "ok_later"
},
{
"lemma": "MOBIUS_COPRIME",
"status": "ok_later"
},
{
"lemma": "MOD_FACTORIAL"... | {
"lo": -4.58,
"mid": 0.57,
"hi": 5.69
} | ||
a1f76e | geo_count_lattice_rect_v1_655260480_5199 | Compute the number of lattice points in the rectangle $[0,89] \times [0,95]$. | 8,640 | graphs = [
Graph(
let={
"a": Const(89),
"b": Const(95),
"result": LatticePointsRect(a=Ref(name='a'), b=Ref(name='b')),
},
goal=Ref("result"),
)
] | GEOM | null | COUNT | sympy | [] | geo_count_lattice_rect_v1 | null | 3 | 0 | null | null | 0.001 | 2026-02-08T18:20:56.464769Z | {
"verified": true,
"answer": 8640,
"timestamp": "2026-02-08T18:20:56.465862Z"
} | 52d73d | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 70,
"completion_tokens": 474
},
"timestamp": "2026-02-24T23:48:34.775Z",
"answer": 8640
},
{
... | 1 | [] | {
"lo": -8.48,
"mid": -5.37,
"hi": -3.03
} | ||||
cf90bc | antilemma_k2_v1_1439011603_1405 | Let $n=1605$. For each integer $k$ with $1\le k\le 326$, consider the set of all integers $x$ such that
\[
x^2-326x+n=0.
\]
Let $S_k$ be the sum of all integers $x$ in this set (if there are no such integers, take $S_k=0$). Let $\varphi(k)$ denote Euler's totient function.
Define
\[
x=\sum_{k=1}^{326} \varphi(k)\left... | 54,157 | graphs = [
Graph(
let={
"_n": Const(1605),
"x": Summation(var="k", start=Const(1), end=Const(326), expr=Mul(EulerPhi(n=Var("k")), Floor(Div(SumOverSet(set=SolutionsSet(var=Var("x1"), condition=Eq(Sum(Pow(Var("x1"), Const(2)), Mul(Const(-326), Var("x1")), Ref("_n")), Const(0)))), Var(... | NT | COMB | COMPUTE | sympy | K13 | [
"VIETA_SUM/K2",
"K2"
] | 6be084 | antilemma_k2_v1 | null | 8 | 0 | [
"K13",
"K2",
"VIETA_SUM"
] | 3 | 0.003 | 2026-02-08T16:03:41.581412Z | {
"verified": true,
"answer": 54157,
"timestamp": "2026-02-08T16:03:41.584416Z"
} | dc4d3c | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 214,
"completion_tokens": 2207
},
"timestamp": "2026-02-16T21:24:25.770Z",
"answer": 54157
},
... | 1 | [
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K2",
"status": "ok"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
},
{
"lemma": "V... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
eca7fa | nt_gcd_compute_v1_548369836_150 | Let $a = 198450$ and $b = 368550$. Define $d$ as the greatest common divisor of $a$ and $b$. Let $S$ be the set of all ordered pairs $(x, y)$ of positive integers such that $xy = 5041$. Let $s_{\min}$ be the minimum value of $x + y$ over all pairs in $S$. Now, let $T$ be the set of all ordered pairs $(x, y)$ of positiv... | 5,266 | graphs = [
Graph(
let={
"_n": Const(2),
"a": Const(198450),
"b": Const(368550),
"result": GCD(a=Ref("a"), b=Ref("b")),
"_c": MaxOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name=... | NT | null | COMPUTE | sympy | B3 | [
"B3/B1"
] | b6e303 | nt_gcd_compute_v1 | digits_weighted_mod | 6 | 0 | [
"B1",
"B3"
] | 2 | 0.004 | 2026-02-08T02:47:14.725467Z | {
"verified": true,
"answer": 5266,
"timestamp": "2026-02-08T02:47:14.729173Z"
} | 4454ec | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 325,
"completion_tokens": 1200
},
"timestamp": "2026-02-08T19:54:43.762Z",
"answer": 5266
},
{
"i... | 1 | [
{
"lemma": "B1",
"status": "ok_later"
},
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MOD_... | {
"lo": -2.86,
"mid": -0.85,
"hi": 1.07
} | ||
e1def4 | alg_sum_powers_v1_1218484723_428 | Find the remainder when $\sum_{k=1}^{1120} k^2$ is divided by $\min\{ x + y : x, y \in \mathbb{Z}^+,\ xy = 4016016 \}$. | 720 | graphs = [
Graph(
let={
"_n": Const(1120),
"result": Mod(value=Summation(var="k", start=Const(1), end=Ref("_n"), expr=Pow(Var("k"), Const(2))), modulus=MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), Is... | ALG | null | COMPUTE | sympy | B3 | [
"B3"
] | 0cd20d | alg_sum_powers_v1 | null | 4 | 0 | [
"B3"
] | 1 | 0.05 | 2026-02-25T02:08:10.449079Z | {
"verified": true,
"answer": 720,
"timestamp": "2026-02-25T02:08:10.499008Z"
} | 1b7092 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 162,
"completion_tokens": 4239
},
"timestamp": "2026-03-10T01:10:02.903Z",
"answer": 720
},
{
"id... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
}
] | {
"lo": 1.22,
"mid": 3.76,
"hi": 5.73
} | ||
dd617b | comb_count_surjections_v1_784195855_3472 | Let $n$ be the number of ordered pairs $(x_1, x_2)$ of positive odd integers such that $x_1 + x_2 = 14$. Let $k$ be the number of ordered pairs $(i, j)$ of integers with $1 \le i \le 6$ and $1 \le j \le 6$ such that $i + j = 6$. Compute the remainder when $44121 \cdot k! \cdot S(n, k)$ is divided by 69904, where $S(n, ... | 40,688 | graphs = [
Graph(
let={
"_n": Const(6),
"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")), Con... | COMB | null | COUNT | sympy | COUNT_SUM_EQUALS | [
"COUNT_SUM_EQUALS",
"COMB1"
] | 938829 | comb_count_surjections_v1 | null | 6 | 0 | [
"COMB1",
"COUNT_SUM_EQUALS"
] | 2 | 0.012 | 2026-02-08T06:27:33.194567Z | {
"verified": true,
"answer": 40688,
"timestamp": "2026-02-08T06:27:33.206126Z"
} | db3ff3 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 252,
"completion_tokens": 8261
},
"timestamp": "2026-02-24T06:12:51.310Z",
"answer": 40688
},
{
"... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COMB1",
"status": "ok"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "ok"
},
{
"lemma": "V8",
"status":... | {
"lo": -0.06,
"mid": 2.89,
"hi": 5.27
} | ||
d8237e_l | antilemma_cartesian_v1_153355830_2522 | Let $x$ be the number of ordered pairs $(a,b)$ such that $1 \leq a \leq 14$ and $1 \leq b \leq 21$. Let $Q$ be the value of
$$
\sum_{i=0}^{\lfloor \log_{10} |x| \rfloor} \left( \text{the } i\text{-th digit of } |x| \right) \cdot (i+1)^2 + 2.
$$
Compute $Q$. | 76 | COMB | GEOM | COMPUTE | sympy | COUNT_CARTESIAN | [
"COUNT_CARTESIAN",
"ONE_FACTORIAL_0"
] | cb6f65 | antilemma_cartesian_v1 | null | 2 | 0 | [
"COUNT_CARTESIAN",
"ONE_FACTORIAL_0"
] | 2 | 0.012 | 2026-02-08T07:12:24.106121Z | {
"verified": false,
"answer": 60,
"timestamp": "2026-02-08T07:12:24.117981Z"
} | 571900 | d8237e | legacy_text | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 1,
"correct": {
"strict": false,
"boxed": false,
"relaxed": true
},
"usage": {
"prompt_tokens": 225,
"completion_tokens": 2032
},
"timestamp": "2026-02-24T07:39:45.952Z",
"answer": 64
},
{
"i... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "ok"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "ONE_F... | {
"lo": -2.35,
"mid": 1.22,
"hi": 4.84
} | |
7d26b0 | alg_poly_orbit_count_v1_601307018_2125 | For a non-negative integer $a$, define $N = (a^3 + 3a) \bmod 41$, $M = (N^3 + 3N) \bmod 41$, $R = (M^3 + 3M) \bmod 41$, and $S = (R^3 + 3R) \bmod 41$. Find the number of integers $a$ with $0 \le a \le 56907$ such that $S = a$, $N \ne a$, $M \ne a$, and $R \ne a$. | 16,656 | graphs = [
Graph(
let={
"p1": Mod(value=Sum(Pow(Var("a"), Const(3)), Mul(Const(3), Var("a"))), modulus=Const(41)),
"p2": Mod(value=Sum(Pow(Ref("p1"), Const(3)), Mul(Const(3), Ref("p1"))), modulus=Const(41)),
"p3": Mod(value=Sum(Pow(Ref("p2"), Const(3)), Mul(Const(3), Ref(... | ALG | null | COUNT | sympy | POLY_ORBIT_COUNT | [
"POLY_ORBIT_COUNT"
] | 4ad965 | alg_poly_orbit_count_v1 | null | 6 | null | [
"POLY_ORBIT_COUNT"
] | 1 | 0.022 | 2026-03-10T02:49:39.684169Z | {
"verified": true,
"answer": 16656,
"timestamp": "2026-03-10T02:49:39.706305Z"
} | ad2e6b | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 238,
"completion_tokens": 10579
},
"timestamp": "2026-03-29T04:24:35.530Z",
"answer": 16656
},
{
... | 1 | [
{
"lemma": "POLY_ORBIT_COUNT",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
}
] | {
"lo": 1.23,
"mid": 4.27,
"hi": 6.7
} | ||
04a3cf | comb_count_surjections_v1_1218484723_4634 | Let $k = \sum_{k_1=1}^{2} \varphi(k_1) \cdot \left\lfloor \frac{2}{k_1} \right\rfloor$. Compute $k! \cdot S(7, k)$, where $S(7, k)$ denotes the Stirling number of the second kind. | 1,806 | graphs = [
Graph(
let={
"n": Const(7),
"k": Summation(var="k1", start=Const(1), end=Const(2), expr=Mul(EulerPhi(n=Var("k1")), Floor(Div(Const(2), Var("k1"))))),
"result": Mul(Factorial(Ref("k")), Stirling2(n=Ref(name='n'), k=Ref(name='k'))),
},
goal=Ref("r... | COMB | NT | COUNT | sympy | K2 | [
"K2"
] | 6897ab | comb_count_surjections_v1 | null | 3 | 0 | [
"K2"
] | 1 | 0.002 | 2026-02-25T06:19:08.347796Z | {
"verified": true,
"answer": 1806,
"timestamp": "2026-02-25T06:19:08.349938Z"
} | f9b519 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 187,
"completion_tokens": 1021
},
"timestamp": "2026-03-29T16:36:12.352Z",
"answer": 1806
},
{
"i... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "K2",
"status": "ok"
},
{
"lemma": "V8",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
}
] | {
"lo": -6.2,
"mid": -2.87,
"hi": 0.44
} | ||
1de353 | comb_bell_compute_v1_1125832087_1654 | Let $n$ be the number of positive integers $p$ for which there exists a positive integer $q > p$ such that $pq = 7560$ and $\gcd(p, q) = 1$. Let $B_n$ denote the $n$-th Bell number. Let $c$ be the minimum value of $x + y$ over all pairs of positive integers $(x, y)$ such that $xy = 5880625$. Compute the remainder when ... | 26,030 | graphs = [
Graph(
let={
"_n": Const(64687),
"n": CountOverSet(set=SolutionsSet(var=Var("p"), condition=And(IsPositive(arg=Var(name='p')), Exists(var=Var(name='q'), condition=And(Eq(left=Mul(Var(name='p'), Var(name='q')), right=Const(value=7560)), Eq(left=GCD(a=Var(name='p'), b=Var(na... | NT | COMB | COMPUTE | sympy | B3 | [
"B3",
"COPRIME_PAIRS"
] | fec8c0 | comb_bell_compute_v1 | affine_mod | 6 | 0 | [
"B3",
"COPRIME_PAIRS"
] | 2 | 0.002 | 2026-02-08T03:51:33.761799Z | {
"verified": true,
"answer": 26030,
"timestamp": "2026-02-08T03:51:33.763395Z"
} | 1454d1 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 225,
"completion_tokens": 1985
},
"timestamp": "2026-02-10T14:36:33.873Z",
"answer": 26030
},
{
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"... | {
"lo": -3.42,
"mid": 1.86,
"hi": 7.55
} | ||
1fdb68 | antilemma_k2_v1_717093673_3305 | Compute the value of
$$
\sum_{k=1}^{295} \varphi(k) \left\lfloor \frac{1}{k} \sum_{d \mid 295} \varphi(d) \right\rfloor,
$$
where $\varphi$ denotes Euler's totient function. | 43,660 | graphs = [
Graph(
let={
"_n": Const(295),
"x": Summation(var="k", start=Const(1), end=Ref("_n"), expr=Mul(EulerPhi(n=Var("k")), Floor(Div(SumOverDivisors(n=Const(value=295), var='d', expr=EulerPhi(n=Var(name='d'))), Var("k"))))),
},
goal=Ref("x"),
)
] | NT | COMB | COMPUTE | sympy | K13 | [
"K3/K2",
"K2"
] | c7f244 | antilemma_k2_v1 | null | 5 | 0 | [
"K13",
"K2",
"K3"
] | 3 | 0.003 | 2026-02-08T17:29:32.260167Z | {
"verified": true,
"answer": 43660,
"timestamp": "2026-02-08T17:29:32.263074Z"
} | 0fc0a3 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 105,
"completion_tokens": 818
},
"timestamp": "2026-02-18T03:48:54.414Z",
"answer": 43660
},
{... | 1 | [
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "K2",
"status": "ok"
},
{
"lemma": "K3",
"status": "ok"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
},
{
"lemma": "VAL_SUM_EQ"... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
7a9367 | comb_count_permutations_fixed_v1_1978505735_8211 | Let $n_2 = 0$. Define $f = \sum_{k1=0}^{n_2} (-1)^{k1} \binom{n_2}{k1}$. Let $u = 2$ and $n_1 = u + 1$. Define $t = \sum_{k2=0}^{n_1} (-1)^{k2} \binom{n_1}{k2}$. Let $n = 11 + t$. Let $k$ be $f$ multiplied by the number of ordered pairs $(x_1, x_2)$ of positive odd integers such that $x_1 + x_2 = 16$. Compute $\binom{n... | 330 | graphs = [
Graph(
let={
"_n": Const(11),
"n2": Const(0),
"f": Summation(var="k1", start=Const(0), end=Ref("n2"), expr=Mul(Pow(Const(-1), Var("k1")), Binom(n=Ref("n2"), k=Var("k1")))),
"u": Const(2),
"n1": Sum(Ref("u"), Const(1)),
"t": S... | COMB | null | COUNT | sympy | COMB1 | [
"COMB1/BINOMIAL_ALTERNATING"
] | e72f96 | comb_count_permutations_fixed_v1 | null | 6 | 2 | [
"BINOMIAL_ALTERNATING",
"COMB1"
] | 2 | 0.003 | 2026-02-08T20:43:55.206435Z | {
"verified": true,
"answer": 330,
"timestamp": "2026-02-08T20:43:55.209054Z"
} | 6acc6c | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 219,
"completion_tokens": 1063
},
"timestamp": "2026-02-19T01:01:19.844Z",
"answer": 330
},
{
... | 1 | [
{
"lemma": "BINOMIAL_ALTERNATING",
"status": "ok_later"
},
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COMB1",
"status": "ok"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT... | {
"lo": -7.92,
"mid": -4.6,
"hi": -1.84
} | ||
8d65db | algebra_poly_eval_v1_601307018_3330 | Let $k = 7$. Define
$$
M = 7k^4 + \left( \min_{\substack{1 \leq a \leq 14 \\ 1 \leq b \leq 14}} \left( -28ab + a^2 \cdot \min\{ d \geq 2 : d \mid 82861 \} + 5b^2 \right) \right) \cdot k^3 + 6k^2 - 7k - 10.
$$
Find the remainder when $69743M$ is divided by $64912$. | 25,040 | graphs = [
Graph(
let={
"_n": Const(14),
"k": Const(7),
"result": Sum(Mul(Const(7), Pow(Ref("k"), Const(4))), Mul(MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("a"), Var("b")]), condition=And(Geq(Var("a"), Const(1)), Leq(Var("a"), Const(14)), Geq(Var(... | NT | null | COMPUTE | sympy | MIN_PRIME_FACTOR | [
"MIN_PRIME_FACTOR/QF_PSD_MIN"
] | 0e8074 | algebra_poly_eval_v1 | null | 5 | 0 | [
"MIN_PRIME_FACTOR",
"QF_PSD_MIN"
] | 2 | 0.008 | 2026-03-10T03:53:12.307959Z | {
"verified": true,
"answer": 25040,
"timestamp": "2026-03-10T03:53:12.315856Z"
} | 9d9504 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 243,
"completion_tokens": 2528
},
"timestamp": "2026-03-29T08:17:40.154Z",
"answer": 28594
},
{
... | 1 | [
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MIN_PRIME_FACTOR",
"status": "ok"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "QF_PSD_MIN",
"status": "ok_la... | {
"lo": 1.23,
"mid": 4.27,
"hi": 6.7
} | ||
556b68 | diophantine_product_count_v1_677425708_2720 | Let $k$ be the number of integers $t$ with $11 \leq t \leq 208$ that can be expressed as $t = 7a + 4b$ for some integers $a$ and $b$ satisfying $1 \leq a \leq 4$ and $1 \leq b \leq 45$. Let $r$ be the number of positive integers $x$ such that $1 \leq x \leq 180$, $x$ divides $k$, and $\frac{k}{x} \leq 180$. Compute the... | 877 | graphs = [
Graph(
let={
"_n": Const(11),
"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=4)), Geq(left=Var(n... | NT | COMB | COUNT | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | diophantine_product_count_v1 | null | 6 | 0 | [
"LIN_FORM"
] | 1 | 0.02 | 2026-02-08T05:13:08.732867Z | {
"verified": true,
"answer": 877,
"timestamp": "2026-02-08T05:13:08.753211Z"
} | 660585 | 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": 6386
},
"timestamp": "2026-02-11T23:05:16.059Z",
"answer": 877
},
{
"i... | 1 | [
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "V1",
"status": "no"
}
] | {
"lo": -3.42,
"mid": 1.86,
"hi": 7.55
} | ||
6e6a09 | algebra_quadratic_discriminant_v1_1520064083_9912 | Let $m = 4$. Let $n$ be the number of positive integers $p$ for which there exists a positive integer $q$ such that $pq = 6$, $\gcd(p, q) = 1$, and $p < q$. Let $a$ be the number of positive integers $p$ for which there exists a positive integer $q$ such that $pq = 36$, $\gcd(p, q) = 1$, and $p < q$. Let $b = -8$ and $... | 144 | graphs = [
Graph(
let={
"_m": Const(4),
"_n": CountOverSet(set=SolutionsSet(var=Var("p"), condition=And(IsPositive(arg=Var(name='p')), Exists(var=Var(name='q'), condition=And(Eq(left=Mul(Var(name='p'), Var(name='q')), right=Const(value=6)), Eq(left=GCD(a=Var(name='p'), b=Var(name='q'... | NT | null | COMPUTE | sympy | COPRIME_PAIRS | [
"COPRIME_PAIRS/COPRIME_PAIRS"
] | 3bbd71 | algebra_quadratic_discriminant_v1 | null | 4 | 0 | [
"COPRIME_PAIRS"
] | 1 | 0.003 | 2026-02-08T11:02:40.138306Z | {
"verified": true,
"answer": 144,
"timestamp": "2026-02-08T11:02:40.141271Z"
} | 70043a | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 178,
"completion_tokens": 1318
},
"timestamp": "2026-02-14T10:09:08.949Z",
"answer": 144
},
{
... | 1 | [
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "VAL_SUM_EQ",
"status": "no"
}
] | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
b5117e_l | comb_sum_binomial_row_v1_784195855_2533 | Let $n = 16$ and $M = 82168$. Compute the remainder when $2^n$ multiplied by the number of ordered pairs $(i,j)$ of positive integers with $1 \leq i \leq 17$, $1 \leq j \leq 31$, and $\gcd(i,j) = 1$ is divided by $M$. | 0 | NT | null | SUM | sympy | COUNT_COPRIME_GRID | [
"COUNT_COPRIME_GRID"
] | 53d469 | comb_sum_binomial_row_v1 | affine_mod | 5 | 0 | [
"COUNT_COPRIME_GRID"
] | 1 | 0.002 | 2026-02-08T05:50:47.245720Z | {
"verified": false,
"answer": 46984,
"timestamp": "2026-02-08T05:50:47.247369Z"
} | 972717 | b5117e | legacy_text | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 121,
"completion_tokens": 2837
},
"timestamp": "2026-02-12T14:49:47.333Z",
"answer": 46984
},
... | 1 | [
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "ok"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "VAL_SUM_EQ",
"status": "no... | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | |
053f17 | antilemma_k3_v1_1742523217_2131 | Compute the sum of $\phi(d)$ over all positive divisors $d$ of $70818$. | 70,818 | graphs = [
Graph(
let={
"_n": Const(70818),
"x": SumOverDivisors(n=Ref(name='_n'), var='d', expr=EulerPhi(n=Var(name='d'))),
},
goal=Ref("x"),
)
] | NT | COMB | COMPUTE | sympy | K3 | [
"K3"
] | 54c41e | antilemma_k3_v1 | null | 2 | 0 | [
"K3"
] | 1 | 0 | 2026-02-08T04:30:03.927095Z | {
"verified": true,
"answer": 70818,
"timestamp": "2026-02-08T04:30:03.927470Z"
} | 61b936 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 131,
"completion_tokens": 313
},
"timestamp": "2026-02-10T17:11:44.401Z",
"answer": 70818
},
{
"... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K3",
"status": "ok"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
}
] | {
"lo": -5.55,
"mid": -3.01,
"hi": 0.33
} | ||
a5dea0 | nt_count_coprime_and_v1_1978505735_1653 | Let $k_1$ be the largest prime number between 2 and 9, inclusive. Let $k_2 = 11$ and let $U = 33248$. Define $S$ as the set of positive integers $n_1$ such that $1 \leq n_1 \leq U$, $\gcd(n_1, k_1) = 1$, and $\gcd(n_1, k_2) = 1$. Let $C$ be the number of ordered pairs $(a, b)$ where $1 \leq a \leq 55$ and $1 \leq b \le... | 66,438 | graphs = [
Graph(
let={
"upper": Const(33248),
"k1": MaxOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(2)), Leq(Var("n"), Const(9)), IsPrime(Var("n"))))),
"k2": Const(11),
"result": CountOverSet(set=SolutionsSet(var=Var("n1"), conditi... | NT | null | COUNT | sympy | COUNT_CARTESIAN | [
"COUNT_CARTESIAN",
"MAX_PRIME_BELOW"
] | 1b8c69 | nt_count_coprime_and_v1 | negation_mod | 4 | 0 | [
"COUNT_CARTESIAN",
"MAX_PRIME_BELOW"
] | 2 | 16.61 | 2026-02-08T16:19:00.632884Z | {
"verified": true,
"answer": 66438,
"timestamp": "2026-02-08T16:19:17.242719Z"
} | 4c175b | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 197,
"completion_tokens": 1242
},
"timestamp": "2026-02-17T01:00:12.945Z",
"answer": 66438
},
... | 1 | [
{
"lemma": "COUNT_CARTESIAN",
"status": "ok"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW"... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
865332 | nt_gcd_compute_v1_1742523217_810 | Let $a = 627887$ and $b = 1014279$. Define $d = \gcd(a, b)$. Let $m = 2$ and $n = 4$. Consider the set of all positive integers $j$ such that $j$ is at most the largest integer $k$ for which $37^k$ divides
$$
31654680139659126296833481434130569 \times 4017237793549122206855981242772726656235986954146868097743675702736... | 57,911 | graphs = [
Graph(
let={
"_m": Const(2),
"_n": Const(4),
"a": Const(627887),
"b": Const(1014279),
"result": GCD(a=Ref("a"), b=Ref("b")),
"Q": Mod(value=Sum(Pow(Ref("result"), Ref("_m")), Mul(Const(34), Ref("result")), CountOverSet(set=So... | NT | null | COMPUTE | sympy | K13 | [
"K13/C3"
] | 9d2010 | nt_gcd_compute_v1 | quadratic_mod | 2 | 0 | [
"C3",
"K13"
] | 2 | 0.003 | 2026-02-08T03:15:00.788645Z | {
"verified": true,
"answer": 57911,
"timestamp": "2026-02-08T03:15:00.791535Z"
} | 6b4f38 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 603,
"completion_tokens": 5401
},
"timestamp": "2026-02-09T07:20:44.694Z",
"answer": 57911
},
{
... | 1 | [
{
"lemma": "C3",
"status": "ok_later"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K13",
"status": "ok"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
... | {
"lo": -6.49,
"mid": 0.51,
"hi": 7.52
} | ||
466878 | antilemma_product_of_sums_v1_677425708_717 | Let $S_1$ be the sum of the first components $k$ over all ordered pairs $(k, j)$ where $1 \leq k \leq 13$ and $1 \leq j \leq 4$. Let $S_2 = \sum_{k=1}^{12} k$. Define $x = S_1 \cdot S_2$. Compute the value of
$$
\sum_{i=0}^{\lfloor \log_{10} |x| \rfloor} \left( \text{the } i\text{-th digit of } |x| \right) \cdot (i + ... | 40,243 | graphs = [
Graph(
let={
"_n": Const(12),
"S1": SumOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("k"), Var("_j")]), condition=Const(1), domain=CartesianProduct(left=IntegerRange(start=Const(1), end=Const(13)), right=IntegerRange(start=Const(1), end=Const(4)))), expr=... | NT | null | COMPUTE | sympy | PRODUCT_OF_SUMS | [
"PRODUCT_OF_SUMS",
"ONE_PHI_1"
] | 10ba65 | antilemma_product_of_sums_v1 | null | 3 | 0 | [
"ONE_PHI_1",
"PRODUCT_OF_SUMS"
] | 2 | 0.003 | 2026-02-08T03:42:08.595770Z | {
"verified": true,
"answer": 40243,
"timestamp": "2026-02-08T03:42:08.598940Z"
} | 6018e3 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 267,
"completion_tokens": 2902
},
"timestamp": "2026-02-08T20:58:12.833Z",
"answer": 40243
},
{
"... | 1 | [
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "ONE_PHI_1",
"status": "ok"
},
{
... | {
"lo": -6.5,
"mid": -0.2,
"hi": 6.11
} | ||
4da29c | antilemma_k2_v1_601307018_364 | Let $M$ be the minimum value of $|x - y|$ over all ordered pairs $(x, y)$ of positive integers such that $xy = 21115$. Let $S$ be the number of integers $t$ in the range $14 \le t \le 121$ that can be expressed as $t = 4a + 3b + 7$ for some integers $a, b$ with $1 \le a \le 24$, $1 \le b \le 6$. Compute $$\sum_{k=1}^{M... | 5,253 | graphs = [
Graph(
let={
"_m": Const(21115),
"_n": MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x1"), Var("y")]), condition=And(IsPositive(arg=Var(name='x1')), IsPositive(arg=Var(name='y')), Eq(Mul(Var("x1"), Var("y")), Ref("_m")))), expr=Abs(arg=Sub(left=Var(na... | NT | null | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM/K2",
"B3_DIFF/K2",
"ONE_PHI_2",
"K2"
] | e5377d | antilemma_k2_v1 | null | 7 | 0 | [
"B3_DIFF",
"K2",
"LIN_FORM",
"ONE_PHI_2"
] | 4 | 0.012 | 2026-03-10T00:54:21.118474Z | {
"verified": true,
"answer": 5253,
"timestamp": "2026-03-10T00:54:21.130107Z"
} | 3b007a | CC BY 4.0 | null | null | [
{
"lemma": "B3_DIFF",
"status": "ok"
},
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "K2",
"status": "ok"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
... | {
"lo": -10,
"mid": 0,
"hi": 10
} | ||
7271b7 | algebra_quadratic_discriminant_v1_1520064083_2711 | Let $a = -8$ and $b = 8$. Let $c = \phi(47) - 46$, where $\phi$ denotes Euler's totient function. Define
$$
D = b^2 - 4 \cdot \max\{xy \mid x, y \text{ are positive integers such that } x + y = 4\} \cdot c.
$$
Compute the value of
$$
2 \cdot \begin{cases} 1 & \text{if } D > \sum_{d \mid \gcd(51,136)} \mu(d), \\ 0 & \te... | 2 | graphs = [
Graph(
let={
"a": Const(-8),
"b": Const(8),
"c": Sub(EulerPhi(n=Const(47)), Const(46)),
"D": Sub(Pow(Ref("b"), Const(2)), Mul(MaxOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name=... | NT | null | COMPUTE | sympy | MOBIUS_COPRIME | [
"MOBIUS_COPRIME",
"ZERO_PHI_PRIME",
"B1"
] | 944869 | algebra_quadratic_discriminant_v1 | null | 4 | 0 | [
"B1",
"MOBIUS_COPRIME",
"ZERO_PHI_PRIME"
] | 3 | 0.008 | 2026-02-08T04:57:13.253004Z | {
"verified": true,
"answer": 2,
"timestamp": "2026-02-08T04:57:13.260829Z"
} | 187880 | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 278,
"completion_tokens": 501
},
"timestamp": "2026-02-18T14:54:34.523Z",
"answer": 2
}
] | 2 | [
{
"lemma": "B1",
"status": "ok"
},
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "MOBIUS_COPRIME",
"status": "ok"
},
... | {
"lo": -10,
"mid": -6.47,
"hi": -2.95
} | ||
5f9ec8 | antilemma_k3_v1_349078426_1136 | Let $n = 79681$. Compute the sum of $\phi(d)$ over all positive divisors $d$ of $n$, where $\phi$ denotes Euler's totient function. | 79,681 | graphs = [
Graph(
let={
"_n": Const(79681),
"x": SumOverDivisors(n=Ref(name='_n'), var='d', expr=EulerPhi(n=Var(name='d'))),
},
goal=Ref("x"),
)
] | NT | COMB | COMPUTE | sympy | K3 | [
"K3"
] | 54c41e | antilemma_k3_v1 | null | 3 | 0 | [
"K3"
] | 1 | 0.001 | 2026-02-08T13:25:51.215206Z | {
"verified": true,
"answer": 79681,
"timestamp": "2026-02-08T13:25:51.215936Z"
} | cbe8c6 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 84,
"completion_tokens": 368
},
"timestamp": "2026-02-15T16:01:18.080Z",
"answer": 79681
},
{
... | 1 | [
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K3",
"status": "ok"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
... | {
"lo": -5.49,
"mid": 0.22,
"hi": 6.51
} | ||
d0822f | comb_factorial_compute_v1_151522320_1989 | Let $S$ be the set of all positive integers $p$ for which there exists a positive integer $q$ such that $pq = 6$, $\gcd(p, q) = 1$, and $p < q$. Let $n$ be the largest prime number $p$ satisfying $|S| \leq p \leq 9$. Compute the remainder when $44121 \cdot n!$ is divided by $50075$. | 36,840 | graphs = [
Graph(
let={
"_n": Const(50075),
"n": MaxOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), CountOverSet(set=SolutionsSet(var=Var("p"), condition=And(IsPositive(arg=Var(name='p')), Exists(var=Var(name='q'), condition=And(Eq(left=Mul(Var(name='p'), Var(name=... | NT | null | COMPUTE | sympy | COPRIME_PAIRS | [
"COPRIME_PAIRS/MAX_PRIME_BELOW"
] | 2248fc | comb_factorial_compute_v1 | null | 5 | 0 | [
"COPRIME_PAIRS",
"MAX_PRIME_BELOW"
] | 2 | 0.003 | 2026-02-08T04:30:19.539291Z | {
"verified": true,
"answer": 36840,
"timestamp": "2026-02-08T04:30:19.542176Z"
} | 0ef8c0 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 206,
"completion_tokens": 1306
},
"timestamp": "2026-02-10T16:49:50.563Z",
"answer": 36840
},
{
... | 1 | [
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok_later"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "V1",
... | {
"lo": -3.42,
"mid": 1.86,
"hi": 7.55
} | ||
dde933 | modular_sum_quadratic_residues_v1_2051736721_2198 | Let $n = 349$, and let $p$ be the largest prime number less than or equal to $n$. Compute the value of $\frac{p(p-1)}{4}$. | 30,363 | graphs = [
Graph(
let={
"_n": Const(349),
"p": MaxOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(2)), Leq(Var("n"), Ref("_n")), IsPrime(Var("n"))))),
"result": Div(Mul(Ref("p"), Sub(Ref("p"), Const(1))), Const(4)),
},
goal=Ref("re... | NT | null | SUM | sympy | MAX_PRIME_BELOW | [
"MAX_PRIME_BELOW"
] | dc3ad3 | modular_sum_quadratic_residues_v1 | null | 3 | 0 | [
"MAX_PRIME_BELOW"
] | 1 | 0.002 | 2026-02-08T16:31:54.998912Z | {
"verified": true,
"answer": 30363,
"timestamp": "2026-02-08T16:31:55.000769Z"
} | c2bf2c | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 85,
"completion_tokens": 670
},
"timestamp": "2026-02-17T05:23:29.990Z",
"answer": 30363
},
{
... | 1 | [
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K16",
"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
} | ||
93b4d1 | geo_count_lattice_rect_v1_1915831931_2039 | Compute the number of lattice points in the rectangle defined by $0 \leq x \leq 333$ and $0 \leq y \leq 175$, including the boundary. | 58,784 | graphs = [
Graph(
let={
"a": Const(333),
"b": Const(175),
"result": LatticePointsRect(a=Ref(name='a'), b=Ref(name='b')),
},
goal=Ref("result"),
)
] | GEOM | null | COUNT | sympy | [] | geo_count_lattice_rect_v1 | null | 3 | 0 | null | null | 0.003 | 2026-02-08T16:35:49.513619Z | {
"verified": true,
"answer": 58784,
"timestamp": "2026-02-08T16:35:49.516977Z"
} | 3ab74f | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 83,
"completion_tokens": 711
},
"timestamp": "2026-02-24T21:44:58.290Z",
"answer": 58784
},
{
... | 1 | [] | {
"lo": -5.09,
"mid": -2.96,
"hi": -0.71
} | ||||
a834b5 | modular_modexp_compute_v1_1470522791_903 | Let $a = 7$, $e = \sum_{k=1}^{49} k$, and $m = 79524$. Compute the remainder when $a^e$ is divided by $m$. | 36,151 | graphs = [
Graph(
let={
"a": Const(7),
"e": Summation(var="k", start=Const(1), end=Const(49), expr=Var("k")),
"m": Const(79524),
"result": ModExp(base=Ref("a"), exp=Ref("e"), mod=Ref("m")),
},
goal=Ref("result"),
)
] | NT | null | COMPUTE | sympy | SUM_ARITHMETIC | [
"SUM_ARITHMETIC"
] | eb34f0 | modular_modexp_compute_v1 | null | 4 | 0 | [
"SUM_ARITHMETIC"
] | 1 | 0.001 | 2026-02-08T13:18:27.736052Z | {
"verified": true,
"answer": 36151,
"timestamp": "2026-02-08T13:18:27.736779Z"
} | 5ab2da | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 91,
"completion_tokens": 5313
},
"timestamp": "2026-02-15T13:12:33.189Z",
"answer": 36151
},
{... | 1 | [
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "SUM_ARITHMETIC",
"status": "ok"
}
] | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
6ccabe_n | alg_qf_psd_min_v1_1218484723_6569 | An architect designs triangular frames using rods of three types: horizontal ($a$), vertical ($b$), and diagonal ($c$), each type limited to 8 units in length. The number of diagonal rods available is determined by a structural test: it equals the number of distinct values $v = (3a - 3b)^2$ (for $1 \leq a,b \leq 8$) th... | 98,882 | ALG | null | COMPUTE | sympy | B1 | [
"B1/QF_PSD_DISTINCT"
] | 7bf560 | alg_qf_psd_min_v1 | null | 4 | null | [
"B1",
"QF_PSD_DISTINCT"
] | 2 | 0.02 | 2026-02-25T08:06:55.069376Z | null | b5ef65 | 6ccabe | narrative | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 1,
"correct": {
"strict": false,
"boxed": false,
"relaxed": true
},
"usage": {
"prompt_tokens": 266,
"completion_tokens": 32768
},
"timestamp": "2026-03-31T01:38:39.082Z",
"answer": null
},
{
... | 1 | [
{
"lemma": "B1",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "QF_PSD_DISTINCT",
"status": "ok_later"
}
] | {
"lo": 1.5,
"mid": 4.69,
"hi": 7.23
} | |
ab4c09 | comb_count_surjections_v1_1520064083_3635 | Let $n$ be the number of ordered pairs $(i,j)$ of integers such that $1 \le i \le 6$, $1 \le j \le 7$, and $i + j = 7$. Let $k$ be the number of ordered pairs $(x_1, x_2)$ of positive odd integers such that $x_1 + x_2 = 4$. Compute $k! \cdot S(n, k)$, where $S(n, k)$ denotes the Stirling number of the second kind.
Fin... | 62 | graphs = [
Graph(
let={
"_n": Const(4),
"n": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("i"), Var("j")]), condition=Eq(Sum(Var("i"), Var("j")), Const(7)), domain=CartesianProduct(left=IntegerRange(start=Const(1), end=Const(6)), right=IntegerRange(start=Const(1), end=Const(... | COMB | null | COUNT | sympy | COUNT_SUM_EQUALS | [
"COUNT_SUM_EQUALS",
"COMB1"
] | 938829 | comb_count_surjections_v1 | null | 4 | 0 | [
"COMB1",
"COUNT_SUM_EQUALS"
] | 2 | 0.013 | 2026-02-08T05:47:04.153659Z | {
"verified": true,
"answer": 62,
"timestamp": "2026-02-08T05:47:04.166441Z"
} | 04c079 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 231,
"completion_tokens": 849
},
"timestamp": "2026-02-24T04:34:42.979Z",
"answer": 62
},
{
"id":... | 1 | [
{
"lemma": "COMB1",
"status": "ok"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "ok"
},
{
"lemma": "V8... | {
"lo": -5.98,
"mid": -3.97,
"hi": -1.94
} | ||
ecd94c | lin_form_endings_v1_809748730_874 | Let $a = 18$, $b = 24$, and $k = 146$. Let $d = \gcd(a, b)$ and $g = \gcd(k, d)$. Define $m = \left\lfloor \frac{k}{g} \right\rfloor$. Compute the remainder when $16184 \times m$ is divided by $57419$. | 33,052 | graphs = [
Graph(
let={
"a_coeff": Const(18),
"b_coeff": Const(24),
"k_val": Const(146),
"step": GCD(a=Ref("a_coeff"), b=Ref("b_coeff")),
"_inner_result": Floor(Div(Ref("k_val"), GCD(a=Ref("k_val"), b=Ref("step")))),
"_scale_k": Const(1... | COMB | NT | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | lin_form_endings_v1 | null | 3 | null | [
"LIN_FORM"
] | 1 | 0.164 | 2026-02-08T11:47:34.932146Z | {
"verified": true,
"answer": 33052,
"timestamp": "2026-02-08T11:47:35.096074Z"
} | 266321 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 124,
"completion_tokens": 611
},
"timestamp": "2026-02-14T19:05:25.192Z",
"answer": 33052
},
{... | 1 | [
{
"lemma": "COUNT_CARTESIAN",
"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": ... | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
5f771d | sequence_count_fib_divisible_v1_1439011603_2746 | Let $A$ be the set of positive integers $n$ such that $1 \leq n \leq 4815$ and $$n \equiv \left\lfloor \frac{n}{2} \right\rfloor \pmod{7}.$$ Let $N = |A|$. Let $B$ be the set of positive integers $n_1$ such that $1 \leq n_1 \leq N$ and $14$ divides $F_{n_1}$, where $F_{n_1}$ denotes the $n_1$-th Fibonacci number. Let $... | 58,319 | graphs = [
Graph(
let={
"_n": Const(58339),
"upper": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Const(4815)), Congruent(a=Var(name='n'), b=Floor(arg=Div(left=Var(name='n'), right=Const(value=2))), modulus=Const(value=7))))),
... | NT | null | COUNT | sympy | LIN_FORM | [
"LIN_FORM",
"L3C"
] | 1709fd | sequence_count_fib_divisible_v1 | negation_mod | 6 | 0 | [
"L3C",
"LIN_FORM"
] | 2 | 0.034 | 2026-02-08T16:55:47.936751Z | {
"verified": true,
"answer": 58319,
"timestamp": "2026-02-08T16:55:47.970432Z"
} | e97564 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 266,
"completion_tokens": 2087
},
"timestamp": "2026-02-17T16:25:42.603Z",
"answer": 58319
},
... | 1 | [
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "L3C",
"status": "ok"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "V1",
"status": "no"
},
{
"lemma": "V... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
b078d5 | sequence_count_fib_divisible_v1_1520064083_7179 | Let $A$ be the set of all integers $t$ such that $11 \le t \le 894$ and there exist positive integers $a$ and $b$ with $1 \le a \le 98$, $1 \le b \le 52$, and $t = 7a + 4b$. Let $B$ be the set of all integers $t$ such that $8 \le t \le 33$ and there exist positive integers $a$ and $b$ with $1 \le a \le 6$, $1 \le b \le... | 72 | 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=98)), 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 | 0.038 | 2026-02-08T08:49:42.017949Z | {
"verified": true,
"answer": 72,
"timestamp": "2026-02-08T08:49:42.056244Z"
} | 43cc55 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 240,
"completion_tokens": 6235
},
"timestamp": "2026-02-13T22:01:46.799Z",
"answer": 72
},
{
... | 1 | [
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "VAL_SUM_EQ",
"status": "no"
}
] | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
cee4b4 | nt_count_divisors_in_range_v1_865884756_5596 | Let $ n = 720 $ and $ a = 15 $. Let $ b $ be the number of integers $ t $ such that $ 16 \leq t \leq 1474 $ and there exist positive integers $ a_1 $, $ b_1 $ with $ 1 \leq a_1 \leq 29 $, $ 1 \leq b_1 \leq 130 $, and $ t = 6a_1 + 10b_1 $. Compute the number of positive divisors $ d $ of $ n $ such that $ a \leq d \leq ... | 20 | graphs = [
Graph(
let={
"n": Const(720),
"a": Const(15),
"b": CountOverSet(set=SolutionsSet(var=Var("t"), condition=Exists(var=Var(name='a'), condition=Exists(var=Var(name='b'), condition=And(Geq(left=Var(name='a'), right=Const(value=1)), Leq(left=Var(name='a'), right=Con... | NT | null | COUNT | sympy | COUNT_PRIMES | [
"LIN_FORM"
] | 7b2633 | nt_count_divisors_in_range_v1 | null | 6 | 0 | [
"COUNT_PRIMES",
"LIN_FORM"
] | 2 | 0.071 | 2026-02-08T18:42:33.334108Z | {
"verified": true,
"answer": 20,
"timestamp": "2026-02-08T18:42:33.405233Z"
} | 12c5b7 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 172,
"completion_tokens": 6450
},
"timestamp": "2026-02-18T18:54:34.017Z",
"answer": 20
},
{
... | 1 | [
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "V3",
"status": "no"
... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
86030e | comb_sum_binomial_row_v1_1419126231_50 | Let $M = \left|\left\{ (a, b) \in \mathbb{Z}^+ \times \mathbb{Z}^+ : 1 \leq a, b \leq 15,\ -8b^3 -96a^2b + 91a^3 + 48ab^2 = 120744 \right\}\right|^{13}$. Find the remainder when $46106M$ is divided by $77677$. | 34,778 | graphs = [
Graph(
let={
"_n": Const(15),
"n": Const(13),
"result": Pow(CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("a"), Var("b")]), condition=And(Geq(Var("a"), Const(1)), Leq(Var("a"), Ref("_n")), Geq(Var("b"), Const(1)), Leq(Var("b"), Const(15)), Eq(Sum(Mul(Co... | COMB | null | SUM | sympy | POLY3_COUNT | [
"POLY3_COUNT"
] | 355dbe | comb_sum_binomial_row_v1 | null | 5 | 0 | [
"POLY3_COUNT"
] | 1 | 0.003 | 2026-02-25T09:36:41.615378Z | {
"verified": true,
"answer": 34778,
"timestamp": "2026-02-25T09:36:41.618293Z"
} | d8867f | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 213,
"completion_tokens": 32768
},
"timestamp": "2026-03-30T06:44:23.022Z",
"answer": null
},
{
... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "POLY3_COUNT",
"status": "ok"
},
{
"lemma": "V8_SUM",
... | {
"lo": 1.53,
"mid": 4.7,
"hi": 7.23
} | ||
dd5bea | comb_factorial_compute_v1_1125832087_830 | Let $T$ be the set of all integers $t$ such that $20 \leq t \leq 38$ and $t = 4a + 6b + 10$ for some integers $a$ and $b$ satisfying $1 \leq a \leq 4$ and $1 \leq b \leq 2$. Let $n$ be the number of elements in $T$. Define $f = n!$. Compute the remainder when $24531 - f$ is divided by $98610$. Determine the value of th... | 82,821 | graphs = [
Graph(
let={
"_n": Const(98610),
"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... | ALG | COMB | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | comb_factorial_compute_v1 | null | 4 | 0 | [
"LIN_FORM"
] | 1 | 0.002 | 2026-02-08T03:19:46.296035Z | {
"verified": true,
"answer": 82821,
"timestamp": "2026-02-08T03:19:46.297545Z"
} | dc892a | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 232,
"completion_tokens": 957
},
"timestamp": "2026-02-10T13:48:39.558Z",
"answer": 82821
},
{
"i... | 1 | [
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
}
] | {
"lo": -4.92,
"mid": -2.9,
"hi": -0.7
} | ||
25b172 | sequence_count_fib_divisible_v1_1353956133_280 | Let $T$ be the set of all integers $t$ such that $26 \leq t \leq 1029$ and there exist positive integers $a$ and $b$ with $1 \leq a \leq 265$, $1 \leq b \leq 96$, and $t = 2a + 5b + 19$. Let $u$ be the number of elements in $T$.
Let $S$ be the set of all positive integers $n$ such that $1 \leq n \leq u$ and $4$ divide... | 166 | 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=265)), Geq(left=Var(name='b'), right=Const(v... | NT | null | COUNT | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | sequence_count_fib_divisible_v1 | null | 5 | 0 | [
"LIN_FORM"
] | 1 | 0.068 | 2026-02-08T11:22:50.222320Z | {
"verified": true,
"answer": 166,
"timestamp": "2026-02-08T11:22:50.289955Z"
} | 18aa72 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 181,
"completion_tokens": 5475
},
"timestamp": "2026-02-14T13:20:12.908Z",
"answer": 166
},
{
... | 1 | [
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
}
] | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
727ed6 | antilemma_k2_v1_2051736721_6110 | Let $x = \sum_{k=1}^{404} \phi(k) \left\lfloor \frac{404}{k} \right\rfloor$, where $\phi(k)$ is Euler's totient function. Let $S$ be the set of all integers $x_1$ such that $x_1^2 - 14x_1 - 10560 = 0$. Let $m$ be the sum of all elements of $S$. Compute $x + 2^{x \bmod m} \bmod 90903$. | 82,066 | graphs = [
Graph(
let={
"_n": Const(2),
"x": Summation(var="k", start=Const(1), end=Const(404), expr=Mul(EulerPhi(n=Var("k")), Floor(Div(Const(404), Var("k"))))),
"Q": Sum(Ref("x"), Mod(value=Pow(Ref("_n"), Mod(value=Ref("x"), modulus=SumOverSet(set=SolutionsSet(var=Var("... | NT | COMB | COMPUTE | sympy | VIETA_SUM | [
"VIETA_SUM",
"K2"
] | 40539e | antilemma_k2_v1 | mod_exp | 6 | 0 | [
"K2",
"VIETA_SUM"
] | 2 | 0.002 | 2026-02-08T18:57:10.022795Z | {
"verified": true,
"answer": 82066,
"timestamp": "2026-02-08T18:57:10.024852Z"
} | 246feb | 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": 1597
},
"timestamp": "2026-02-18T20:46:38.901Z",
"answer": 82066
},
... | 1 | [
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K2",
"status": "ok"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "VAL_SUM_EQ",
"status": "no"
}... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
a8862d | comb_catalan_compute_v1_1520064083_2563 | Let $n$ be the number of integers $t$ with $10 \leq t \leq 32$ such that there exist positive integers $a$ and $b$ with $1 \leq a \leq 5$, $1 \leq b \leq 2$, and $t = 4a + 6b$. Compute the $n$-th Catalan number. | 16,796 | graphs = [
Graph(
let={
"n": CountOverSet(set=SolutionsSet(var=Var("t"), condition=Exists(var=Var(name='a'), condition=Exists(var=Var(name='b'), condition=And(Geq(left=Var(name='a'), right=Const(value=1)), Leq(left=Var(name='a'), right=Const(value=5)), Geq(left=Var(name='b'), right=Const(value=1... | COMB | null | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | comb_catalan_compute_v1 | null | 4 | 0 | [
"LIN_FORM"
] | 1 | 0.002 | 2026-02-08T04:51:59.234175Z | {
"verified": true,
"answer": 16796,
"timestamp": "2026-02-08T04:51:59.236615Z"
} | 851284 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 196,
"completion_tokens": 832
},
"timestamp": "2026-02-24T02:13:44.800Z",
"answer": 16796
},
{
"i... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
}
] | {
"lo": -3.83,
"mid": -1.68,
"hi": 1.09
} | ||
288ae6 | modular_mod_compute_v1_717093673_154 | Let $a$ be the minimum value of $x + y$ over all ordered pairs $(x, y)$ of positive integers such that $xy = 777924$. Let $m$ be the minimum value of $x_1 + y_1$ over all ordered pairs $(x_1, y_1)$ of positive integers such that $x_1 y_1 = 1000000$. Compute the remainder when $a$ is divided by $m$. | 1,764 | graphs = [
Graph(
let={
"a": MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(Mul(Var("x"), Var("y")), Const(777924)))), expr=Sum(Var("x"), Var("y")))),
"m": MinOverSet(... | NT | null | COMPUTE | sympy | B3 | [
"B3"
] | 0cd20d | modular_mod_compute_v1 | null | 4 | 0 | [
"B3"
] | 1 | 0.005 | 2026-02-08T15:12:46.803706Z | {
"verified": true,
"answer": 1764,
"timestamp": "2026-02-08T15:12:46.809050Z"
} | 4967d2 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 144,
"completion_tokens": 2918
},
"timestamp": "2026-02-16T01:36:34.564Z",
"answer": 1764
},
{... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "V3",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
e53ab5 | geo_count_lattice_triangle_v1_677425708_3804 | Let $A$ be the value of $|128 \cdot 144 + 2 \cdot (0 - 120)|$. Let $B$ be the sum
$$
\gcd(|128|, |120|) + \gcd(|2 - 128|, |144 - 120|) + \gcd\left(\left|\sum_{k=0}^{7} (-1)^k \binom{7}{k} - 2\right|, |0 - 144|\right).
$$
Let $C = 44775$ and define
$$
Q = \left(\frac{A + 2 - B}{2}\right) \cdot C \mod 77756.
$$
Compute $... | 62,827 | graphs = [
Graph(
let={
"area_2x": Abs(arg=Sum(Mul(Const(value=128), Const(value=144)), Mul(Const(value=2), Sub(left=Const(value=0), right=Const(value=120))))),
"boundary": Sum(GCD(a=Abs(arg=Const(value=128)), b=Abs(arg=Const(value=120))), GCD(a=Abs(arg=Sub(left=Const(value=2), right... | COMB | NT | COUNT | sympy | BINOMIAL_ALTERNATING | [
"BINOMIAL_ALTERNATING"
] | c21569 | geo_count_lattice_triangle_v1 | null | 6 | 0 | [
"BINOMIAL_ALTERNATING"
] | 1 | 0.008 | 2026-02-08T05:56:37.944599Z | {
"verified": true,
"answer": 62827,
"timestamp": "2026-02-08T05:56:37.952373Z"
} | abd898 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 194,
"completion_tokens": 1394
},
"timestamp": "2026-02-12T16:55:01.502Z",
"answer": 62827
},
... | 1 | [
{
"lemma": "BINOMIAL_ALTERNATING",
"status": "ok"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
},
{
"lemma": "V8_S... | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
2ce597 | comb_count_surjections_v1_1218484723_1716 | Let $n = \sum_{k=1}^{3} k$. Let $R = 6! \cdot S(n, 6)$, where $S(n, k)$ denotes the Stirling number of the second kind. Find the remainder when $22741R$ is divided by $89697$. | 48,666 | graphs = [
Graph(
let={
"_n": Const(89697),
"n": Summation(var="k1", start=Const(1), end=Const(3), expr=Var("k1")),
"k": Const(6),
"result": Mul(Factorial(Ref("k")), Stirling2(n=Ref(name='n'), k=Ref(name='k'))),
"_c": Const(22741),
"Q":... | COMB | null | COUNT | sympy | SUM_ARITHMETIC | [
"SUM_ARITHMETIC"
] | eb34f0 | comb_count_surjections_v1 | null | 3 | 0 | [
"SUM_ARITHMETIC"
] | 1 | 0.002 | 2026-02-25T03:24:29.091180Z | {
"verified": true,
"answer": 48666,
"timestamp": "2026-02-25T03:24:29.092687Z"
} | 266fb2 | 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": 1566
},
"timestamp": "2026-03-29T00:57:58.842Z",
"answer": 48666
},
{
"... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "SUM_ARITHMETIC",
"status": "ok"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8",
"status": "... | {
"lo": -2.47,
"mid": 1.2,
"hi": 4.81
} | ||
605731 | nt_min_phi_inverse_v1_898971024_1589 | Let $S$ be the set of all ordered pairs $(x, y)$ of positive integers such that $xy = 900$. For each such pair, compute $x + y$. Let $\text{upper}$ be the minimum value of $x + y$ over all such pairs. Let $k = 18$. Determine the smallest positive integer $n$ such that $1 \le n \le \text{upper}$ and $\phi(n) = k$, where... | 19 | graphs = [
Graph(
let={
"upper": MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(Mul(Var("x"), Var("y")), Const(900)))), expr=Sum(Var("x"), Var("y")))),
"k": Const(18),... | NT | null | EXTREMUM | sympy | B3 | [
"B3"
] | 0cd20d | nt_min_phi_inverse_v1 | null | 6 | 0 | [
"B3"
] | 1 | 0.015 | 2026-02-08T16:12:16.816436Z | {
"verified": true,
"answer": 19,
"timestamp": "2026-02-08T16:12:16.831271Z"
} | 8e6de1 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 153,
"completion_tokens": 3109
},
"timestamp": "2026-02-16T22:33:55.491Z",
"answer": 19
},
{
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "V1",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
b5a248 | comb_count_permutations_fixed_v1_971394319_1211 | Let $n = 9$. Define $$k = \sum_{k=1}^{3} \phi(k) \left\lfloor \frac{3}{k} \right\rfloor,$$ where $\phi$ denotes Euler's totient function. Let $$\text{result} = \binom{9}{k} \cdot !(9 - k),$$ where $!m$ denotes the number of derangements of $m$ elements. Compute the value of $$Q = (44121 \cdot \text{result}) \bmod 96827... | 53,476 | graphs = [
Graph(
let={
"_n": Const(3),
"n": Const(9),
"k": Summation(var="k", start=Const(1), end=Const(3), expr=Mul(EulerPhi(n=Var("k")), Floor(Div(Ref("_n"), Var("k"))))),
"result": Mul(Binom(n=Ref("n"), k=Ref("k")), Subfactorial(arg=Sub(left=Ref(name='n'),... | NT | COMB | COUNT | sympy | K2 | [
"K2"
] | 6897ab | comb_count_permutations_fixed_v1 | null | 5 | 0 | [
"K2"
] | 1 | 0.002 | 2026-02-08T13:31:49.749437Z | {
"verified": true,
"answer": 53476,
"timestamp": "2026-02-08T13:31:49.751614Z"
} | aa20ce | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 163,
"completion_tokens": 1051
},
"timestamp": "2026-02-15T17:40:36.461Z",
"answer": 53476
},
... | 1 | [
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K2",
"status": "ok"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
}
] | {
"lo": -5.49,
"mid": 0.22,
"hi": 6.51
} | ||
bdbacb | nt_sum_divisors_mod_v1_397696148_2113 | Let $n$ be the minimum value of $x + y$ over all ordered pairs of positive integers $(x, y)$ such that $xy = 14400$. Let $\sigma$ be the sum of the positive divisors of $n$. Define $M = 10463$ and let $r$ be the remainder when $\sigma$ is divided by $M$. Compute the remainder when $44121 \cdot r$ is divided by $76598$. | 42,080 | 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(14400)))), expr=Sum(Var("x"), Var("y")))),
"M": Const(10463)... | NT | null | COMPUTE | sympy | B3 | [
"B3"
] | 0cd20d | nt_sum_divisors_mod_v1 | null | 5 | 0 | [
"B3"
] | 1 | 0.006 | 2026-02-08T12:57:46.867386Z | {
"verified": true,
"answer": 42080,
"timestamp": "2026-02-08T12:57:46.873468Z"
} | c783f0 | 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": 927
},
"timestamp": "2026-02-15T07:43:01.348Z",
"answer": 42080
},
{... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "V1",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
}
] | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
0c87cc | nt_count_divisible_and_v1_153355830_476 | Let $n = 44121$ and $U = 52866$. Define
$$
d_1 = \sum_{k=1}^{3} \phi(k) \left\lfloor \frac{3}{k} \right\rfloor
\quad\text{and}\quad
d_2 = 9.
$$
Let $N$ be the number of positive integers $m$ such that $1 \leq m \leq U$, $m$ is divisible by $d_1$, and $m$ is divisible by $d_2$.
Let $Q$ be the remainder when $n \cdot N$... | 52,667 | graphs = [
Graph(
let={
"_n": Const(44121),
"upper": Const(52866),
"d1": Summation(var="k", start=Const(1), end=Const(3), expr=Mul(EulerPhi(n=Var("k")), Floor(Div(Const(3), Var("k"))))),
"d2": Const(9),
"result": CountOverSet(set=SolutionsSet(var=V... | NT | null | COUNT | sympy | K2 | [
"K2"
] | 6897ab | nt_count_divisible_and_v1 | null | 4 | 0 | [
"K2"
] | 1 | 2.312 | 2026-02-08T03:07:35.517406Z | {
"verified": true,
"answer": 52667,
"timestamp": "2026-02-08T03:07:37.829362Z"
} | 88c0fe | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 263,
"completion_tokens": 1490
},
"timestamp": "2026-02-10T12:54:54.279Z",
"answer": 52667
},
{
"... | 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": -3.47,
"mid": 0.81,
"hi": 4.81
} | ||
5296a0 | diophantine_fbi2_count_v1_1978505735_3219 | Let $k = 420$. Consider the set of all integers $d$ such that $3 \leq d \leq 101$, $d$ divides $k$, and $2 \leq \frac{k}{d} \leq 100$. Compute the number of elements in this set. | 16 | graphs = [
Graph(
let={
"k": Const(420),
"a": Const(2),
"b": Const(1),
"upper": Const(99),
"result": CountOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Const(3)), Leq(Var("d"), Const(101)), Divides(divisor=Var("d"), dividend=Re... | NT | null | COUNT | sympy | LIN_FORM | [
"LIN_FORM/MAX_PRIME_BELOW",
"B3"
] | 2a7052 | diophantine_fbi2_count_v1 | null | 4 | 0 | [
"B3",
"LIN_FORM",
"MAX_PRIME_BELOW"
] | 3 | 0.346 | 2026-02-08T17:29:04.797112Z | {
"verified": true,
"answer": 16,
"timestamp": "2026-02-08T17:29:05.142641Z"
} | 0e39b3 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 107,
"completion_tokens": 1521
},
"timestamp": "2026-02-18T03:43:37.204Z",
"answer": 16
},
{
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "MA... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
f5e6ed | antilemma_sum_equals_v1_397696148_2798 | Let $x$ be the number of ordered pairs $(i,j)$ of positive integers such that $i + j = 36$, where $1 \leq i \leq 35$ and $1 \leq j \leq 36$. Compute $x$. | 35 | graphs = [
Graph(
let={
"x": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("i"), Var("j")]), condition=Eq(Sum(Var("i"), Var("j")), Const(36)), domain=CartesianProduct(left=IntegerRange(start=Const(1), end=Const(35)), right=IntegerRange(start=Const(1), end=Const(36))))),
},
... | COMB | GEOM | COMPUTE | sympy | LIN_FORM | [
"COUNT_SUM_EQUALS"
] | 75ab0f | antilemma_sum_equals_v1 | null | 2 | 0 | [
"COUNT_SUM_EQUALS",
"LIN_FORM"
] | 2 | 0.109 | 2026-02-08T13:33:46.986604Z | {
"verified": true,
"answer": 35,
"timestamp": "2026-02-08T13:33:47.095466Z"
} | c3401e | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 167,
"completion_tokens": 504
},
"timestamp": "2026-02-24T19:50:32.850Z",
"answer": 35
},
{
"id":... | 2 | [
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "ok"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
},
{
"lemma": "V8_SUM",
"status":... | {
"lo": -10,
"mid": -7.42,
"hi": -4.85
} | ||
b62346 | nt_count_gcd_equals_v1_1978505735_4464 | Let $d$ be the largest prime number $n$ such that $2 \leq n \leq 358$. Let $\text{result}$ be the number of positive integers $n_1$ from 1 to $7744$ inclusive such that $\gcd(n_1, 353) = d$. Define $Q$ as the remainder when $84973 \cdot \text{result}$ is divided by $83802$. Compute $Q$. | 24,591 | graphs = [
Graph(
let={
"_n": Const(84973),
"upper": Const(7744),
"k": Const(353),
"d": MaxOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(2)), Leq(Var("n"), Const(358)), IsPrime(Var("n"))))),
"result": CountOverSet(set=Sol... | NT | null | COUNT | sympy | MAX_PRIME_BELOW | [
"MAX_PRIME_BELOW"
] | dc3ad3 | nt_count_gcd_equals_v1 | null | 4 | 0 | [
"MAX_PRIME_BELOW"
] | 1 | 1.436 | 2026-02-08T18:15:52.328171Z | {
"verified": true,
"answer": 24591,
"timestamp": "2026-02-08T18:15:53.764578Z"
} | 2af3df | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 140,
"completion_tokens": 1293
},
"timestamp": "2026-02-18T15:35:42.834Z",
"answer": 24591
},
... | 1 | [
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
56e8e2 | comb_sum_binomial_row_v1_2051736721_5604 | Let $n$ be the smallest divisor of $17303$ that is at least $2$. Compute $2^n$. | 2,048 | 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(17303))))),
"result": Pow(Const(2), Ref("n")),
},
goal=Ref("result"),
)
] | NT | null | SUM | sympy | MIN_PRIME_FACTOR | [
"MIN_PRIME_FACTOR"
] | bc3776 | comb_sum_binomial_row_v1 | null | 2 | 0 | [
"MIN_PRIME_FACTOR"
] | 1 | 0.001 | 2026-02-08T18:41:23.183506Z | {
"verified": true,
"answer": 2048,
"timestamp": "2026-02-08T18:41:23.184558Z"
} | d342fd | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 72,
"completion_tokens": 1002
},
"timestamp": "2026-02-18T18:36:11.193Z",
"answer": 2048
},
{
... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "MIN_PRIME_FACTOR",
... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
f1e6e1 | nt_min_with_divisor_count_v1_865884756_24 | Let $n$ be a positive integer such that $1 \leq n \leq 40$, $8$ divides $n$, and $\gcd(n, 21) = 1$. Let $d$ be the number of such integers $n$. Determine the smallest positive integer $n_1$ such that $1 \leq n_1 \leq 57600$ and the number of positive divisors of $n_1$ is exactly $d$. Compute this smallest $n_1$. | 6 | graphs = [
Graph(
let={
"_n": Const(40),
"upper": Const(57600),
"div_count": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Ref("_n")), Divides(divisor=Const(8), dividend=Var("n")), Eq(GCD(a=Var("n"), b=Const(21)), Const(1... | NT | null | EXTREMUM | sympy | LIOUVILLE_MINUS_ONE | [
"C5"
] | 1d9668 | nt_min_with_divisor_count_v1 | null | 6 | 0 | [
"C5",
"LIOUVILLE_MINUS_ONE"
] | 2 | 15.849 | 2026-02-08T15:07:06.161304Z | {
"verified": true,
"answer": 6,
"timestamp": "2026-02-08T15:07:22.010508Z"
} | 40ed35 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 218,
"completion_tokens": 1143
},
"timestamp": "2026-02-10T02:45:57.083Z",
"answer": 6
},
{
"id":... | 1 | [
{
"lemma": "C5",
"status": "ok"
},
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "VAL_SUM_EQ",
"status... | {
"lo": -7.09,
"mid": -0.49,
"hi": 6.1
} | ||
cf0d38 | diophantine_product_count_v1_168721529_1406 | Let $k$ be the number of positive integers $n$ with $1 \leq n \leq 895$ such that $5$ divides $n$ and $\gcd(n, 6) = 1$. Let $t$ be a positive integer expressible as $4a + 5b$ for integers $a, b$ in the range $1 \leq a \leq 5$, $1 \leq b \leq 5$, and $9 \leq t \leq 45$. Let $u$ be the number of such values $t$. Determin... | 8 | graphs = [
Graph(
let={
"_m": Const(895),
"_n": Const(6),
"k": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Ref("_m")), Divides(divisor=Const(5), dividend=Var("n")), Eq(GCD(a=Var("n"), b=Ref("_n")), Const(1))))),
... | NT | null | COUNT | sympy | LIN_FORM | [
"LIN_FORM",
"C5"
] | d0968e | diophantine_product_count_v1 | null | 6 | 0 | [
"C5",
"LIN_FORM"
] | 2 | 0.007 | 2026-02-08T13:41:08.295484Z | {
"verified": true,
"answer": 8,
"timestamp": "2026-02-08T13:41:08.302473Z"
} | 8dd0dd | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 283,
"completion_tokens": 2876
},
"timestamp": "2026-02-09T16:35:53.245Z",
"answer": 8
},
{
"id":... | 1 | [
{
"lemma": "C5",
"status": "ok"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma"... | {
"lo": -1.95,
"mid": 2.14,
"hi": 6.33
} | ||
baa0bd | comb_catalan_compute_v1_1742523217_3167 | Let $S$ be the set of all ordered pairs $(i,j)$ of integers with $1 \leq i \leq 12$ and $1 \leq j \leq 12$ such that $i + j = 13$. Let $m$ be the number of elements in $S$. Let $T$ be the set of all ordered pairs $(i,j)$ of integers with $1 \leq i \leq 11$ and $1 \leq j \leq 11$ such that $i + j = m$. Let $n$ be the nu... | 18,452 | graphs = [
Graph(
let={
"_m": Const(98742),
"_n": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("i"), Var("j")]), condition=Eq(Sum(Var("i"), Var("j")), Const(13)), domain=CartesianProduct(left=IntegerRange(start=Const(1), end=Const(12)), right=IntegerRange(start=Const(1), end... | COMB | null | COMPUTE | sympy | COUNT_SUM_EQUALS | [
"COUNT_SUM_EQUALS/COUNT_SUM_EQUALS"
] | 756129 | comb_catalan_compute_v1 | null | 4 | 0 | [
"COUNT_SUM_EQUALS"
] | 1 | 0.029 | 2026-02-08T05:41:21.964377Z | {
"verified": true,
"answer": 18452,
"timestamp": "2026-02-08T05:41:21.993162Z"
} | 7ae9bc | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 304,
"completion_tokens": 14323
},
"timestamp": "2026-02-24T04:18:00.033Z",
"answer": 18452
},
{
... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "ok"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8_SUM",
"stat... | {
"lo": -2.46,
"mid": 0.47,
"hi": 3.59
} | ||
e4374c | geo_count_lattice_rect_v1_151522320_1300 | Let $a = 169$ and $b = 106$. Define $R$ to be the number of lattice points $(x,y)$ such that $0 \leq x \leq a$ and $0 \leq y \leq b$. Compute the Bell number $B_r$, where $r$ is the remainder when $|R|$ is divided by $11$. | 877 | graphs = [
Graph(
let={
"a": Const(169),
"b": Const(106),
"result": LatticePointsRect(a=Ref(name='a'), b=Ref(name='b')),
"Q": Bell(Mod(value=Abs(arg=Ref(name='result')), modulus=Const(11))),
},
goal=Ref("Q"),
)
] | GEOM | COMB | COUNT | sympy | [] | geo_count_lattice_rect_v1 | null | 4 | 0 | null | null | 0.009 | 2026-02-08T03:52:29.294761Z | {
"verified": true,
"answer": 877,
"timestamp": "2026-02-08T03:52:29.303996Z"
} | fe710e | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 192,
"completion_tokens": 589
},
"timestamp": "2026-02-10T16:18:57.321Z",
"answer": 877
},
{
"id"... | 1 | [] | {
"lo": -3.83,
"mid": -1.68,
"hi": 1.09
} | ||||
0ad560 | comb_count_permutations_fixed_v1_865884756_2859 | Let $n_2 = 8$. Define
$$
s = \sum_{k_1=0}^{n_2} (-1)^{k_1} \binom{n_2}{k_1}.
$$
Let $n_1 = \binom{18}{0} - 1 + s$. Define
$$
c = \sum_{k_2=0}^{n_1} (-1)^{k_2} \binom{n_1}{k_2}.
$$
Let $n = 7$ and $k = 3c$. Compute $\binom{n}{k} \cdot !\!\left(n - k\right)$, where $!m$ denotes the number of derangements of $m$ elements. | 315 | graphs = [
Graph(
let={
"n2": Const(8),
"s": Summation(var="k1", start=Const(0), end=Ref("n2"), expr=Mul(Pow(Const(-1), Var("k1")), Binom(n=Ref("n2"), k=Var("k1")))),
"n1": Sum(Sub(Binom(n=Const(18), k=Const(0)), Const(1)), Ref("s")),
"c": Summation(var="k2", ... | COMB | null | COUNT | sympy | BINOMIAL_ALTERNATING | [
"BINOMIAL_ALTERNATING",
"ZERO_BINOM_0"
] | 38a409 | comb_count_permutations_fixed_v1 | null | 4 | 2 | [
"BINOMIAL_ALTERNATING",
"ZERO_BINOM_0"
] | 2 | 0.004 | 2026-02-08T16:59:01.415142Z | {
"verified": true,
"answer": 315,
"timestamp": "2026-02-08T16:59:01.419597Z"
} | 525889 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 196,
"completion_tokens": 1313
},
"timestamp": "2026-02-24T22:09:38.225Z",
"answer": 315
},
{
... | 2 | [
{
"lemma": "BINOMIAL_ALTERNATING",
"status": "ok"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
},
{
"lemma": "V8_SUM",
"sta... | {
"lo": -10,
"mid": -7.42,
"hi": -4.85
} | ||
f0d5eb | nt_count_divisors_in_range_v1_1520064083_4812 | Let $n = 55440$. Define $a = \sum_{k=1}^{6} \phi(k) \left\lfloor \frac{6}{k} \right\rfloor$, where $\phi$ denotes Euler's totient function. Let $b = 4621$. Let $r$ be the number of positive divisors $d$ of $n$ such that $a \leq d \leq b$. Compute the remainder when $44121 \cdot r$ is divided by $68122$. | 39,934 | graphs = [
Graph(
let={
"n": Const(55440),
"a": Summation(var="k", start=Const(1), end=Const(6), expr=Mul(EulerPhi(n=Var("k")), Floor(Div(Const(6), Var("k"))))),
"b": Const(4621),
"result": CountOverSet(set=SolutionsSet(var=Var("d"), condition=And(Divides(divi... | NT | null | COUNT | sympy | K2 | [
"K2"
] | 6897ab | nt_count_divisors_in_range_v1 | null | 4 | 0 | [
"K2"
] | 1 | 0.044 | 2026-02-08T06:26:34.516342Z | {
"verified": true,
"answer": 39934,
"timestamp": "2026-02-08T06:26:34.559850Z"
} | 4b1d7b | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 152,
"completion_tokens": 2477
},
"timestamp": "2026-02-13T00:20:19.037Z",
"answer": 39934
},
... | 1 | [
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "K2",
"status": "ok"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "VAL_SUM_EQ",
"status": "no"
}
] | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
47cb11 | nt_sum_gcd_range_mod_v1_1742523217_1982 | Let $N$ be the largest prime number less than or equal to $2286$. Compute the sum $\sum_{n=1}^{N} \gcd(n, 72)$, and let $R$ be the remainder when this sum is divided by $10093$. Determine the value of $R$. | 3,182 | graphs = [
Graph(
let={
"N": MaxOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(2)), Leq(Var("n"), Const(2286)), IsPrime(Var("n"))))),
"k": Const(72),
"M": Const(10093),
"sum": Summation(var="n", start=Const(1), end=Ref("N"), expr=GCD(... | NT | null | COMPUTE | sympy | MAX_PRIME_BELOW | [
"MAX_PRIME_BELOW"
] | dc3ad3 | nt_sum_gcd_range_mod_v1 | null | 5 | 0 | [
"MAX_PRIME_BELOW"
] | 1 | 0.103 | 2026-02-08T04:23:00.593823Z | {
"verified": true,
"answer": 3182,
"timestamp": "2026-02-08T04:23:00.696629Z"
} | d2c921 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 174,
"completion_tokens": 5751
},
"timestamp": "2026-02-10T16:25:25.466Z",
"answer": 3182
},
{
"... | 1 | [
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok"
},
{
"lemma": "V8",
"status": "no"
},
{
"lemma": "V8_SUM",
"sta... | {
"lo": -3.42,
"mid": 1.86,
"hi": 7.55
} | ||
81f878 | comb_binomial_compute_v1_1520064083_8802 | Let $n$ be the number of positive integers $p$ for which there exists a positive integer $q$ such that $p < q$, $\gcd(p, q) = 1$, and $pq = 3201660$. Let $k$ be the largest prime number less than or equal to 7 that is at least 2. Compute $\binom{n}{k}$. | 11,440 | graphs = [
Graph(
let={
"_n": Const(2),
"n": CountOverSet(set=SolutionsSet(var=Var("p"), condition=And(IsPositive(arg=Var(name='p')), Exists(var=Var(name='q'), condition=And(Eq(left=Mul(Var(name='p'), Var(name='q')), right=Const(value=3201660)), Eq(left=GCD(a=Var(name='p'), b=Var(nam... | NT | null | COMPUTE | sympy | MAX_PRIME_BELOW | [
"MAX_PRIME_BELOW",
"COPRIME_PAIRS"
] | 05d703 | comb_binomial_compute_v1 | null | 6 | 0 | [
"COPRIME_PAIRS",
"MAX_PRIME_BELOW"
] | 2 | 0.004 | 2026-02-08T10:24:10.096934Z | {
"verified": true,
"answer": 11440,
"timestamp": "2026-02-08T10:24:10.100610Z"
} | 6f4b16 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 126,
"completion_tokens": 2448
},
"timestamp": "2026-02-14T07:16:33.666Z",
"answer": 11440
},
... | 1 | [
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},... | {
"lo": -5.49,
"mid": 0.22,
"hi": 6.51
} | ||
aafd4b | geo_count_lattice_rect_v1_238844314_814 | Let $a = 128$ and $b = 136$. Define $\mathcal{P}$ to be the set of all lattice points $(x, y)$ such that $0 \leq x \leq a$ and $0 \leq y \leq b$. Let $N$ be the number of elements in $\mathcal{P}$. Find the remainder when the smallest positive integer $k$ such that the $k$-th Fibonacci number is divisible by $N + 2$ is... | 200 | graphs = [
Graph(
let={
"a": Const(128),
"b": Const(136),
"result": LatticePointsRect(a=Ref(name='a'), b=Ref(name='b')),
"Q": FibonacciEntryPoint(modulus=Sum(Abs(arg=Ref(name='result')), Const(value=2))),
},
goal=Ref("Q"),
)
] | GEOM | NT | COUNT | sympy | [] | geo_count_lattice_rect_v1 | null | 3 | 0 | null | null | 0.003 | 2026-02-08T13:37:49.228783Z | {
"verified": true,
"answer": 200,
"timestamp": "2026-02-08T13:37:49.231444Z"
} | 6fdb1a | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 223,
"completion_tokens": 4298
},
"timestamp": "2026-02-24T18:45:05.871Z",
"answer": 200
},
{
"id... | 1 | [] | {
"lo": -2.35,
"mid": 1.22,
"hi": 4.84
} | ||||
fc9edd | antilemma_k3_v1_1520064083_1724 | Let $n = 59133$. Compute the sum of $\phi(d)$ over all positive divisors $d$ of $n$, where $\phi$ denotes Euler's totient function. | 59,133 | graphs = [
Graph(
let={
"x": SumOverDivisors(n=Const(value=59133), var='d', expr=EulerPhi(n=Var(name='d'))),
},
goal=Ref("x"),
)
] | NT | COMB | COMPUTE | sympy | K3 | [
"K3"
] | 54c41e | antilemma_k3_v1 | null | 4 | 0 | [
"K3"
] | 1 | 0 | 2026-02-08T04:15:04.844081Z | {
"verified": true,
"answer": 59133,
"timestamp": "2026-02-08T04:15:04.844372Z"
} | 469628 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 149,
"completion_tokens": 270
},
"timestamp": "2026-02-10T16:02:19.261Z",
"answer": 59133
},
{
"... | 1 | [
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "K3",
"status": "ok"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "V1",
"status": "no"
}
] | {
"lo": -3.49,
"mid": 1.84,
"hi": 7.55
} | ||
7b5379 | alg_poly_preperiod_count_v1_1218484723_3250 | Let $N = (a^3 + 2a) \bmod 73$, $M = (N^3 + 2N) \bmod 73$, and $R = (M^3 + 2M) \bmod 73$. Find the number of non-negative integers $a$ with $0 \leq a \leq 38908$ such that $R = N$ and $M \neq N$. | 3,198 | graphs = [
Graph(
let={
"p1": Mod(value=Sum(Pow(Var("a"), Const(3)), Mul(Const(2), Var("a"))), modulus=Const(73)),
"p2": Mod(value=Sum(Pow(Ref("p1"), Const(3)), Mul(Const(2), Ref("p1"))), modulus=Const(73)),
"p3": Mod(value=Sum(Pow(Ref("p2"), Const(3)), Mul(Const(2), Ref(... | ALG | null | COUNT | sympy | POLY_ORBIT_COUNT | [
"POLY_ORBIT_COUNT"
] | 4ad965 | alg_poly_preperiod_count_v1 | null | 6 | null | [
"POLY_ORBIT_COUNT"
] | 1 | 0.014 | 2026-02-25T04:57:22.975390Z | {
"verified": true,
"answer": 3198,
"timestamp": "2026-02-25T04:57:22.989073Z"
} | c71639 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 204,
"completion_tokens": 15080
},
"timestamp": "2026-03-29T09:14:37.583Z",
"answer": 3198
},
{
"... | 1 | [
{
"lemma": "POLY_ORBIT_COUNT",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
}
] | {
"lo": -2.45,
"mid": 1.37,
"hi": 5.29
} | ||
b69e9e | comb_sum_binomial_row_v1_655260480_1760 | Let $n$ be the number of ordered pairs $(a,b)$ of integers such that $1 \leq a \leq 3$ and $1 \leq b \leq 4$. Let $k$ be the number of positive integers $n_1$ with $1 \leq n_1 \leq 8$ such that the Fibonacci number $F_{n_1}$ is divisible by 3. Define $\text{result} = k^n$. Let $Q$ be the remainder when $25763 \times \t... | 61,568 | graphs = [
Graph(
let={
"n": CountOverSet(set=CartesianProduct(left=IntegerRange(start=Const(1), end=Const(3)), right=IntegerRange(start=Const(1), end=Const(4)))),
"result": Pow(CountOverSet(set=SolutionsSet(var=Var("n1"), condition=And(Geq(Var("n1"), Const(1)), Leq(Var("n1"), Const(... | ALG | NT | SUM | sympy | COUNT_FIB_DIVISIBLE | [
"COUNT_FIB_DIVISIBLE",
"COUNT_CARTESIAN"
] | 966ef1 | comb_sum_binomial_row_v1 | null | 4 | 0 | [
"COUNT_CARTESIAN",
"COUNT_FIB_DIVISIBLE"
] | 2 | 0.002 | 2026-02-08T16:21:31.409715Z | {
"verified": true,
"answer": 61568,
"timestamp": "2026-02-08T16:21:31.411571Z"
} | 68d630 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 171,
"completion_tokens": 1095
},
"timestamp": "2026-02-17T01:18:03.824Z",
"answer": 61568
},
... | 1 | [
{
"lemma": "COUNT_CARTESIAN",
"status": "ok"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "ok"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
},... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
cc4cd2 | nt_sum_divisors_compute_v1_1248542787_579 | Let $ v = \lambda(11) + \phi(2) $, where $ \lambda $ is the Liouville function and $ \phi $ is Euler's totient function. Let $ t $ be the number of integers $ t $ with $ 7 \leq t \leq 42 $ such that there exist integers $ a, b $ with $ 1 \leq a \leq 6 $, $ 1 \leq b \leq 6 $, and $ t = 4a + 3b $. Define $ n_1 = t^{2 + v... | 86,831 | graphs = [
Graph(
let={
"_n": Const(60025),
"n2": Const(11),
"v": Sum(LiouvilleLambda(n=Ref(name='n2')), EulerPhi(n=Const(2))),
"t": CountOverSet(set=SolutionsSet(var=Var("t"), condition=Exists(var=Var(name='a'), condition=Exists(var=Var(name='b'), condition=A... | NT | null | COMPUTE | sympy | COPRIME_PAIRS | [
"COPRIME_PAIRS/DIVISOR_PARITY",
"LIN_FORM/DIVISOR_PARITY",
"LIOUVILLE_MINUS_ONE",
"ONE_PHI_2"
] | 29226b | nt_sum_divisors_compute_v1 | null | 6 | 2 | [
"COPRIME_PAIRS",
"DIVISOR_PARITY",
"LIN_FORM",
"LIOUVILLE_MINUS_ONE",
"ONE_PHI_2"
] | 5 | 0.005 | 2026-02-08T03:14:33.249244Z | {
"verified": true,
"answer": 86831,
"timestamp": "2026-02-08T03:14:33.254049Z"
} | 735696 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 335,
"completion_tokens": 1947
},
"timestamp": "2026-02-09T05:46:15.420Z",
"answer": 86831
},
{
"... | 1 | [
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "DIVISOR_PARITY",
"status": "ok_later"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "LIN_FORM",
"sta... | {
"lo": -6.51,
"mid": -0.31,
"hi": 5.43
} | ||
d17495 | comb_sum_binomial_row_v1_1116507919_449 | Let $d(n)$ denote the sum of the values of $\mu(d)$ over all positive divisors $d$ of $n$, where $\mu$ is the M\"obius function. Let $S$ be the set of all integers $n$ such that $n \ge d(\gcd(8,15))$, $n \le 35$, and $\gcd(n,6) = \phi(1)$, where $\phi$ is Euler's totient function. Let $N = |S|$. Compute $2^N$. | 4,096 | graphs = [
Graph(
let={
"_n": Const(2),
"n": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), SumOverDivisors(n=GCD(a=Const(value=8), b=Const(value=15)), var='d', expr=MoebiusMu(n=Var(name='d')))), Leq(Var("n"), Const(35)), Eq(GCD(a=Var("n"), b=Const(6)), Euler... | NT | null | SUM | sympy | MOBIUS_COPRIME | [
"MOBIUS_COPRIME",
"ONE_PHI_1",
"C4"
] | 09053b | comb_sum_binomial_row_v1 | null | 5 | 0 | [
"C4",
"MOBIUS_COPRIME",
"ONE_PHI_1"
] | 3 | 0.002 | 2026-02-08T02:34:22.653894Z | {
"verified": true,
"answer": 4096,
"timestamp": "2026-02-08T02:34:22.655830Z"
} | b54502 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 230,
"completion_tokens": 1449
},
"timestamp": "2026-02-08T19:34:04.467Z",
"answer": 4096
},
{
"i... | 1 | [
{
"lemma": "C4",
"status": "ok"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "MOBIUS_COPRIME",
"status": "ok"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "ONE_PHI_1",
"status": "ok"
},
{
"l... | {
"lo": -4.6,
"mid": 0.15,
"hi": 4.61
} | ||
eff0d0_l | nt_count_phi_equals_v1_1125832087_1268 | Let $m$ be the maximum value of $xy$ over all ordered pairs $(x, y)$ of positive integers such that $x + y = 102$. Let $k = 1872$. Determine the number of positive integers $n$ such that $1 \leq n \leq m$ and $\phi(n) = k$, where $\phi$ denotes Euler's totient function. | 1 | NT | null | COUNT | sympy | B1 | [
"B1"
] | 5b950e | nt_count_phi_equals_v1 | null | 7 | 0 | [
"B1"
] | 1 | 0.176 | 2026-02-08T03:39:32.075696Z | {
"verified": false,
"answer": 4,
"timestamp": "2026-02-08T03:39:32.251323Z"
} | 4e7488 | eff0d0 | legacy_text | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 193,
"completion_tokens": 14793
},
"timestamp": "2026-02-23T21:12:52.715Z",
"answer": 4
},
{
"id... | 1 | [
{
"lemma": "B1",
"status": "ok"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
}
] | {
"lo": 1.96,
"mid": 5.23,
"hi": 8.52
} | |
eb2535 | comb_count_permutations_fixed_v1_349078426_1501 | Let $n = 11$ and $k = 7$. Compute the value of $\binom{n}{k} \cdot !(n - k)$, where $!m$ denotes the number of derangements of $m$ elements. | 2,970 | graphs = [
Graph(
let={
"n": Const(11),
"k": Const(7),
"result": Mul(Binom(n=Ref("n"), k=Ref("k")), Subfactorial(arg=Sub(left=Ref(name='n'), right=Ref(name='k')))),
},
goal=Ref("result"),
)
] | COMB | null | COUNT | sympy | SUM_ARITHMETIC | [
"SUM_ARITHMETIC"
] | eb34f0 | comb_count_permutations_fixed_v1 | null | 3 | 0 | [
"SUM_ARITHMETIC"
] | 1 | 0.006 | 2026-02-08T13:40:52.848653Z | {
"verified": true,
"answer": 2970,
"timestamp": "2026-02-08T13:40:52.855009Z"
} | 4b28f9 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 162,
"completion_tokens": 324
},
"timestamp": "2026-02-24T18:48:39.155Z",
"answer": 2970
},
{
"id... | 2 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "SUM_ARITHMETIC",
"status": "ok"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8",
"status": "no... | {
"lo": -10,
"mid": -7.79,
"hi": -5.57
} | ||
b8a195 | comb_count_derangements_v1_1520064083_6127 | Let $n$ be the number of nonnegative integers $j \leq 20482$ for which $\binom{20482}{j}$ is odd. Compute the number of derangements of $n$ elements, denoted $!n$. | 14,833 | graphs = [
Graph(
let={
"_n": Const(20482),
"n": CountOverSet(set=SolutionsSet(var=Var("j"), condition=And(Geq(Var("j"), Const(0)), Leq(Var("j"), Const(20482)), Eq(Mod(value=Binom(n=Ref("_n"), k=Var("j")), modulus=Const(2)), Const(1))), domain='nonnegative_integers')),
"r... | COMB | null | COUNT | sympy | V8 | [
"V8"
] | 86348e | comb_count_derangements_v1 | null | 7 | 0 | [
"V8"
] | 1 | 0.001 | 2026-02-08T07:52:42.983886Z | {
"verified": true,
"answer": 14833,
"timestamp": "2026-02-08T07:52:42.985147Z"
} | 51b45a | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 162,
"completion_tokens": 1052
},
"timestamp": "2026-02-24T08:35:34.168Z",
"answer": 14833
},
{
"... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
},
{
"lemma": "V8",
"status": "ok"
}
] | {
"lo": -2.35,
"mid": 1.22,
"hi": 4.84
} | ||
f56825 | alg_qf_psd_sum_v1_601307018_1816 | Let $T = \left|\{ t : \text{there exist integers } a, b \text{ with } 1 \leq a \leq 78,\ 1 \leq b \leq 3394 \text{ such that } t = 7a + 2b,\ 9 \leq t \leq 7334 \}\right|$. Let $L = \min\{ |x - y| : x > 0,\ y > 0,\ xy = T \}$. Compute the remainder when $$\sum_{\substack{a=1}}^{L} \sum_{b=1}^{59} \sum_{c=1}^{59} \left( ... | 6,572 | graphs = [
Graph(
let={
"_m": Const(6),
"_n": Const(2),
"result": Mod(value=SumOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("a"), Var("b"), Var("c")]), condition=And(Geq(Var("a"), Const(1)), Leq(Var("a"), MinOverSet(set=MapOverSet(set=SolutionsSet(var=T... | ALG | null | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM/B3_DIFF"
] | 35f330 | alg_qf_psd_sum_v1 | null | 7 | 0 | [
"B3_DIFF",
"LIN_FORM"
] | 2 | 1.302 | 2026-03-10T02:33:43.790454Z | {
"verified": true,
"answer": 6572,
"timestamp": "2026-03-10T02:33:45.092715Z"
} | cc485f | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 1,
"correct": {
"strict": false,
"boxed": false,
"relaxed": true
},
"usage": {
"prompt_tokens": 301,
"completion_tokens": 32768
},
"timestamp": "2026-03-29T03:30:47.617Z",
"answer": null
},
{
... | 1 | [
{
"lemma": "B3_DIFF",
"status": "ok_later"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
}
] | {
"lo": 3.99,
"mid": 6.11,
"hi": 9.15
} | ||
3bf5b3 | antilemma_sum_equals_v1_124444284_1261 | Let $m$ be the number of ordered pairs $(x_1,x_2)$ of positive odd integers such that
$$x_1+x_2=202.$$
Let $x$ be the number of ordered pairs $(i,j)$ of integers with $1\le i\le 100$ and $1\le j\le 101$ such that
$$i+j=m.$$
Let $A$ be the number of integers $t$ for which there exist integers $a$ and $b$ satisfying $1\l... | 38,664 | graphs = [
Graph(
let={
"_c": Const(202),
"_m": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x1"), Var("x2")]), condition=And(IsPositive(arg=Var(name='x1')), IsPositive(arg=Var(name='x2')), IsOdd(arg=Var(name='x1')), IsOdd(arg=Var(name='x2')), Eq(Sum(Var("x1"), Var("x2")), ... | COMB | GEOM | COMPUTE | sympy | COMB1 | [
"COMB1/LIN_FORM/COUNT_SUM_EQUALS",
"LIN_FORM",
"COUNT_SUM_EQUALS"
] | 107a3e | antilemma_sum_equals_v1 | two_moduli | 7 | 0 | [
"COMB1",
"COUNT_SUM_EQUALS",
"LIN_FORM"
] | 3 | 0.011 | 2026-02-08T03:48:02.816648Z | {
"verified": true,
"answer": 38664,
"timestamp": "2026-02-08T03:48:02.827779Z"
} | 9f2e1e | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 446,
"completion_tokens": 5734
},
"timestamp": "2026-02-10T05:16:52.168Z",
"answer": 39564
},
{
... | 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"
},
{
"lemma": "LIN_FORM",
"sta... | {
"lo": 3.43,
"mid": 5.73,
"hi": 8.84
} | ||
32596e | nt_count_coprime_and_v1_655260480_616 | Let $k_1 = 7$ and let $k_2$ be the number of positive integers $n$ such that $1 \leq n \leq 21$ and $\gcd(n, 10) = 1$. Determine the number of positive integers $n_1$ such that $1 \leq n_1 \leq 17689$, $\gcd(n_1, k_1) = 1$, and $\gcd(n_1, k_2) = 1$. | 10,108 | graphs = [
Graph(
let={
"upper": Const(17689),
"k1": Const(7),
"k2": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Const(21)), Eq(GCD(a=Var("n"), b=Const(10)), Const(1))))),
"result": CountOverSet(set=Solution... | NT | null | COUNT | sympy | C4 | [
"C4"
] | 08d162 | nt_count_coprime_and_v1 | null | 4 | 0 | [
"C4"
] | 1 | 2.362 | 2026-02-08T15:29:22.959745Z | {
"verified": true,
"answer": 10108,
"timestamp": "2026-02-08T15:29:25.322043Z"
} | eed0f7 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 151,
"completion_tokens": 1116
},
"timestamp": "2026-02-16T07:08:17.941Z",
"answer": 10108
},
... | 1 | [
{
"lemma": "C4",
"status": "ok"
},
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "V3",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
a9ce5e | comb_count_surjections_v1_397696148_322 | Let $n$ be the number of ordered pairs of positive odd integers $(x_1, x_2)$ such that $x_1 + x_2 = 14$. Let $k$ be the number of ordered pairs $(i, j)$ with $1 \leq i \leq 5$ and $1 \leq j \leq 5$ such that $i + j = 5$. Define $r = k! \cdot S(n, k)$, where $S(n, k)$ denotes the number of ways to partition a set of $n$... | 29,625 | graphs = [
Graph(
let={
"_n": Const(5),
"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")), Con... | COMB | null | COUNT | sympy | COUNT_SUM_EQUALS | [
"COUNT_SUM_EQUALS",
"COMB1"
] | 938829 | comb_count_surjections_v1 | null | 6 | 0 | [
"COMB1",
"COUNT_SUM_EQUALS"
] | 2 | 0.012 | 2026-02-08T11:25:51.087737Z | {
"verified": true,
"answer": 29625,
"timestamp": "2026-02-08T11:25:51.099760Z"
} | 08a59f | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 251,
"completion_tokens": 2485
},
"timestamp": "2026-02-24T13:49:14.497Z",
"answer": 29625
},
{
"... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COMB1",
"status": "ok"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "ok"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
},
{... | {
"lo": -3.84,
"mid": -1.67,
"hi": 1.32
} | ||
51c5b6 | modular_modexp_compute_v1_601307018_5762 | Let $a$ be the largest prime with $2 \le a \le 46$. Let $e$ be the minimum value of $x + y$ over all positive integer pairs $(x, y)$ such that $xy = \max\{x_1 y_1 : x_1, y_1 > 0,\, x_1 + y_1 = 190\}$. Compute $a^e \bmod 60000$. | 58,249 | graphs = [
Graph(
let={
"_n": Const(46),
"a": MaxOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(2)), Leq(Var("n"), Ref("_n")), IsPrime(Var("n"))))),
"e": MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), conditi... | NT | null | COMPUTE | sympy | MAX_PRIME_BELOW | [
"MAX_PRIME_BELOW",
"B1/B3"
] | dfa9db | modular_modexp_compute_v1 | null | 5 | 0 | [
"B1",
"B3",
"MAX_PRIME_BELOW"
] | 3 | 0.007 | 2026-03-10T06:19:05.869828Z | {
"verified": true,
"answer": 58249,
"timestamp": "2026-03-10T06:19:05.876635Z"
} | 6188ab | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 206,
"completion_tokens": 3956
},
"timestamp": "2026-04-19T02:52:48.534Z",
"answer": 58249
},
{
... | 1 | [
{
"lemma": "B1",
"status": "ok"
},
{
"lemma": "B3",
"status": "ok_later"
},
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": ... | {
"lo": 2.1,
"mid": 5.36,
"hi": 8.63
} | ||
fd5c30_l | comb_sum_binomial_row_v1_677425708_1099 | Let $n$ be the largest prime number between $2$ and $14$, inclusive. Let $S$ be the set of all positive integers $p$ for which there exists a positive integer $q$ such that $p \cdot q = 108$, $\gcd(p, q) = 1$, and $p < q$. Compute the remainder when $44121 \cdot |S|^n$ is divided by $65657$. | 1 | NT | null | SUM | sympy | MAX_PRIME_BELOW | [
"MAX_PRIME_BELOW",
"COPRIME_PAIRS"
] | 05d703 | comb_sum_binomial_row_v1 | null | 6 | 0 | [
"COPRIME_PAIRS",
"MAX_PRIME_BELOW"
] | 2 | 0.002 | 2026-02-08T04:00:12.373257Z | {
"verified": false,
"answer": 63104,
"timestamp": "2026-02-08T04:00:12.375053Z"
} | bef490 | fd5c30 | 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": 205,
"completion_tokens": 6823
},
"timestamp": "2026-02-09T15:44:47.116Z",
"answer": 63104
},
{
"... | 1 | [
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
... | {
"lo": -3.46,
"mid": 1.03,
"hi": 5.49
} | |
96fc8d | antilemma_sum_factor_cartesian_v1_1520064083_4659 | For each integer $i$ from 1 to 6 and each integer $j$ from 1 to 22, compute the product $i \cdot j$. Find the sum of all such products. | 5,313 | 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(6)), right=IntegerRange(start=Const(1), end=Const(22)))), expr=Mul(Var("i"), Var("j")))),
... | NT | null | COMPUTE | sympy | SUM_FACTOR_CARTESIAN | [
"SUM_FACTOR_CARTESIAN"
] | d9e436 | antilemma_sum_factor_cartesian_v1 | null | 3 | 0 | [
"SUM_FACTOR_CARTESIAN"
] | 1 | 0.001 | 2026-02-08T06:22:14.805008Z | {
"verified": true,
"answer": 5313,
"timestamp": "2026-02-08T06:22:14.806074Z"
} | 5d2618 | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 134,
"completion_tokens": 578
},
"timestamp": "2026-02-19T04:40:13.874Z",
"answer": 5313
}
] | 2 | [
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "SUM_FACTOR_CARTESIAN",
"status": "ok"
},
{
"lemma": "V8",
"status": "no"... | {
"lo": -10,
"mid": -6.47,
"hi": -2.95
} | ||
4f4eef | antilemma_cartesian_v1_1116507919_214 | Let $x$ be the number of ordered pairs $(a,b)$ of integers such that $1 \leq a \leq 25$ and $1 \leq b \leq 28$. Compute $$\sum_{n=1}^{|x|} \tau(n),$$ where $\tau(n)$ denotes the number of positive divisors of $n$. Compute the value of this sum. | 4,700 | graphs = [
Graph(
let={
"x": CountOverSet(set=CartesianProduct(left=IntegerRange(start=Const(1), end=Const(25)), right=IntegerRange(start=Const(1), end=Const(28)))),
"Q": Summation(var="n", start=Const(1), end=Abs(arg=Ref(name='x')), expr=NumDivisors(n=Var("n"))),
},
... | COMB | GEOM | COMPUTE | sympy | COUNT_CARTESIAN | [
"COUNT_CARTESIAN"
] | 409d7d | antilemma_cartesian_v1 | null | 5 | 0 | [
"COUNT_CARTESIAN"
] | 1 | 0 | 2026-02-08T02:28:55.763156Z | {
"verified": true,
"answer": 4700,
"timestamp": "2026-02-08T02:28:55.763505Z"
} | 9b67a0 | 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": 2770
},
"timestamp": "2026-02-08T19:15:15.840Z",
"answer": 4700
},
{
"i... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "ok"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "V8_SU... | {
"lo": -1.36,
"mid": 0.77,
"hi": 2.48
} | ||
a922b5 | antilemma_count_primes_v1_124444284_1290 | Let $p$ be the largest prime number less than or equal to 137. Let $q$ be the largest prime number less than or equal to $p$. Define $x$ to be the number of prime numbers $n$ such that $2 \leq n \leq q$. Compute the remainder when $44121 \cdot x$ is divided by 80848. Find the value of this remainder. | 729 | graphs = [
Graph(
let={
"_m": Const(2),
"_n": MaxOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(2)), Leq(Var("n"), Const(137)), IsPrime(Var("n"))))),
"x": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Ref("_m")), Leq(Var... | NT | null | COMPUTE | sympy | MAX_PRIME_BELOW | [
"MAX_PRIME_BELOW/MAX_PRIME_BELOW/COUNT_PRIMES",
"COUNT_PRIMES"
] | 809ee8 | antilemma_count_primes_v1 | null | 4 | 0 | [
"COUNT_PRIMES",
"MAX_PRIME_BELOW"
] | 2 | 0.002 | 2026-02-08T03:48:45.878875Z | {
"verified": true,
"answer": 729,
"timestamp": "2026-02-08T03:48:45.880974Z"
} | 468cd2 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 197,
"completion_tokens": 917
},
"timestamp": "2026-02-10T05:40:06.116Z",
"answer": 729
},
{
"id"... | 1 | [
{
"lemma": "COUNT_PRIMES",
"status": "ok"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok"
}... | {
"lo": -6.51,
"mid": -0.31,
"hi": 5.43
} | ||
8f8e53 | antilemma_k2_v1_784195855_6407 | Let $N = 253$. Compute
$$
x = \sum_{k=1}^{253} \varphi(k) \left\lfloor \frac{N}{k} \right\rfloor,
$$
where $\varphi(k)$ is the number of positive integers at most $k$ that are relatively prime to $k$.
Now compute the remainder when $44121 \cdot x$ is divided by $63088$.
Find the value of this remainder. | 1,403 | graphs = [
Graph(
let={
"_n": Const(253),
"x": Summation(var="k", start=Const(1), end=Summation(var="k", start=Const(1), end=Const(22), expr=Var("k")), expr=Mul(EulerPhi(n=Var("k")), Floor(Div(Ref("_n"), Var("k"))))),
"Q": Mod(value=Mul(Const(44121), Ref("x")), modulus=Co... | NT | COMB | COMPUTE | sympy | K13 | [
"SUM_ARITHMETIC/K2",
"K2"
] | ec0b42 | antilemma_k2_v1 | null | 4 | 0 | [
"K13",
"K2",
"SUM_ARITHMETIC"
] | 3 | 0.003 | 2026-02-08T08:39:02.203180Z | {
"verified": true,
"answer": 1403,
"timestamp": "2026-02-08T08:39:02.205846Z"
} | 541a3a | 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": 5068
},
"timestamp": "2026-02-13T20:07:13.105Z",
"answer": 1403
},
{... | 1 | [
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "K2",
"status": "ok"
},
{
"lemma": "SUM_ARITHMETIC",
"status": "ok"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
},
{... | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
b8c938 | comb_catalan_compute_v1_397696148_1710 | Let $n$ be the number of integers $t$ with $5 \leq t \leq 17$ for which there exist integers $a$ and $b$ such that $1 \leq a \leq 4$, $1 \leq b \leq 3$, and $t = 2a + 3b$. Let $C_n$ denote the $n$-th Catalan number. Compute the remainder when $44121 \cdot C_n$ is divided by $83810$. | 29,036 | graphs = [
Graph(
let={
"_n": Const(44121),
"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 | 4 | 0 | [
"LIN_FORM"
] | 1 | 0.067 | 2026-02-08T12:43:28.469452Z | {
"verified": true,
"answer": 29036,
"timestamp": "2026-02-08T12:43:28.536223Z"
} | c9d543 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 221,
"completion_tokens": 4748
},
"timestamp": "2026-02-24T16:17:00.259Z",
"answer": 29036
},
{
"... | 1 | [
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8",
"status... | {
"lo": -2.35,
"mid": 1.22,
"hi": 4.84
} | ||
d68672 | nt_lcm_compute_v1_124444284_334 | Let $a = 679$. Let $b$ be the minimum value of $x + y$ over all pairs of positive integers $(x, y)$ such that $x \cdot y = 1104601$. Compute the least common multiple of $a$ and $b$, and find the remainder when this value is divided by $85106$. | 65,562 | graphs = [
Graph(
let={
"_n": Const(85106),
"a": Const(679),
"b": 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(1104601))))... | NT | null | COMPUTE | sympy | B3 | [
"B3"
] | 0cd20d | nt_lcm_compute_v1 | null | 6 | 0 | [
"B3"
] | 1 | 0.001 | 2026-02-08T03:13:12.173996Z | {
"verified": true,
"answer": 65562,
"timestamp": "2026-02-08T03:13:12.175110Z"
} | de8898 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 183,
"completion_tokens": 1081
},
"timestamp": "2026-02-09T16:17:54.679Z",
"answer": 65562
},
{
"... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "VAL_SUM_EQ",
"status": "no"
}
] | {
"lo": -3.46,
"mid": 1.03,
"hi": 5.49
} | ||
6a8f71 | diophantine_fbi2_min_v1_1918700295_353 | Let $k = 22$. Define $\text{upper}$ as the number of positive integers $p$ for which there exists an integer $q$ such that $pq = 128957528700$, $\gcd(p,q) = 1$, and $p < q$. Let $\text{result}$ be the smallest integer $d \geq 2$ such that $d \leq \text{upper}$, $d$ divides $k$, and $k/d \geq 7$. Let $c = 82785$ and $n ... | 18,112 | graphs = [
Graph(
let={
"_n": Const(73729),
"k": Const(22),
"upper": 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=128957528700)... | NT | null | EXTREMUM | sympy | COPRIME_PAIRS | [
"COPRIME_PAIRS"
] | 2bb3aa | diophantine_fbi2_min_v1 | null | 6 | 0 | [
"COPRIME_PAIRS"
] | 1 | 0.005 | 2026-02-08T03:10:24.957390Z | {
"verified": true,
"answer": 18112,
"timestamp": "2026-02-08T03:10:24.961944Z"
} | c60cbe | 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": 2569
},
"timestamp": "2026-02-10T12:59:39.231Z",
"answer": 18112
},
{
... | 1 | [
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
}
] | {
"lo": -5.92,
"mid": -3.14,
"hi": 0.27
} | ||
1746a8 | comb_binomial_compute_v1_48377204_1424 | Let $n$ be the minimum value of $x + y$ over all ordered pairs of positive integers $(x, y)$ such that $xy = m$, where $m$ is the number of integers $t$ in the interval $[27, 147]$ that can be expressed as $8a + 10b + 9$ for positive integers $a$ and $b$ with $1 \le a \le 11$ and $1 \le b \le 5$. Compute $\binom{n}{6}$... | 3,003 | graphs = [
Graph(
let={
"_n": CountOverSet(set=SolutionsSet(var=Var("t"), condition=Exists(var=Var(name='a'), condition=Exists(var=Var(name='b'), condition=And(Geq(left=Var(name='a'), right=Const(value=1)), Leq(left=Var(name='a'), right=Const(value=11)), Geq(left=Var(name='b'), right=Const(value... | ALG | COMB | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM/B3"
] | 05313e | comb_binomial_compute_v1 | null | 5 | 0 | [
"B3",
"LIN_FORM"
] | 2 | 0.004 | 2026-02-08T16:05:35.982670Z | {
"verified": true,
"answer": 3003,
"timestamp": "2026-02-08T16:05:35.986373Z"
} | ea3d2c | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 224,
"completion_tokens": 4764
},
"timestamp": "2026-02-24T19:52:42.289Z",
"answer": 3003
},
{
"... | 1 | [
{
"lemma": "B3",
"status": "ok_later"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
}
] | {
"lo": -2.4,
"mid": 1.57,
"hi": 5.75
} | ||
003646 | algebra_quadratic_discriminant_v1_1742523217_3679 | Let $a$ be the number of positive integers $j$ such that $1 \leq j \leq 4$ and $j^3 \leq 64$. Let $b = 3$ and $c = -10$. Define $\text{result} = b^2 - 4ac$. Let $Q$ be the remainder when \[\sum_{k=1}^{6} \phi(k) \left\lfloor \frac{6}{k} \right\rfloor - \text{result}\] is divided by $57088$. Find the value of $Q$. | 56,940 | graphs = [
Graph(
let={
"_m": Const(2),
"_n": Const(64),
"a": CountOverSet(set=SolutionsSet(var=Var("j"), condition=And(Geq(Var("j"), Const(1)), Leq(Var("j"), Const(4)), Leq(Pow(Var("j"), Const(3)), Ref("_n"))), domain='positive_integers')),
"b": Const(3),
... | NT | null | COMPUTE | sympy | SUM_DIVISIBLE | [
"K2",
"C3"
] | 9cc03b | algebra_quadratic_discriminant_v1 | negation_mod | 5 | 0 | [
"C3",
"K2",
"SUM_DIVISIBLE"
] | 3 | 0.043 | 2026-02-08T06:02:24.381094Z | {
"verified": true,
"answer": 56940,
"timestamp": "2026-02-08T06:02:24.424031Z"
} | 8f6a38 | 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": 843
},
"timestamp": "2026-02-12T18:36:23.491Z",
"answer": 56940
},
{... | 1 | [
{
"lemma": "C3",
"status": "ok"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "K2",
"status": "ok"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "V... | {
"lo": -5.55,
"mid": -3.01,
"hi": 0.32
} | ||
44355e | lin_form_endings_v1_153355830_1219 | Let $a = 35$, $b = 25$, $A = 10$, and $B = 14$. Let $g = \gcd(a, b)$, and define $a' = \left\lfloor \frac{a}{g} \right\rfloor$ and $b' = \left\lfloor \frac{b}{g} \right\rfloor$. Define $T$ to be a set with size $|T| = a' \cdot A + b' \cdot B - a' \cdot b'$. The total number of elements under consideration is $a \cdot A... | 15,368 | graphs = [
Graph(
let={
"a_coeff": Const(35),
"b_coeff": Const(25),
"A_val": Const(10),
"B_val": Const(14),
"g_step": GCD(a=Ref("a_coeff"), b=Ref("b_coeff")),
"ap_node": Floor(Div(Ref("a_coeff"), Ref("g_step"))),
"bp_node": ... | COMB | NT | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | lin_form_endings_v1 | null | 6 | null | [
"LIN_FORM"
] | 1 | 0.149 | 2026-02-08T06:11:41.035082Z | {
"verified": true,
"answer": 15368,
"timestamp": "2026-02-08T06:11:41.183978Z"
} | 36c798 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 218,
"completion_tokens": 797
},
"timestamp": "2026-02-12T21:44:17.033Z",
"answer": 15368
},
{... | 1 | [
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
... | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
451962 | diophantine_fbi2_min_v1_1520064083_2180 | Let $k = 35$ and let $u = \sum_{i=1}^{9} i$. Compute the smallest positive integer $d$ such that $4 \leq d \leq u$, $d$ divides $k$, and $\frac{k}{d} \geq 3$. | 5 | graphs = [
Graph(
let={
"k": Const(35),
"upper": Summation(var="k", start=Const(1), end=Const(9), expr=Var("k")),
"result": MinOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Const(4)), Leq(Var("d"), Ref("upper")), Divides(divisor=Var("d"), dividend=Ref... | NT | null | EXTREMUM | sympy | LIN_FORM | [
"SUM_ARITHMETIC"
] | eb34f0 | diophantine_fbi2_min_v1 | null | 3 | 0 | [
"LIN_FORM",
"SUM_ARITHMETIC"
] | 2 | 0.062 | 2026-02-08T04:33:07.555850Z | {
"verified": true,
"answer": 5,
"timestamp": "2026-02-08T04:33:07.618124Z"
} | ad2df6 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 174,
"completion_tokens": 390
},
"timestamp": "2026-02-10T17:07:48.597Z",
"answer": 5
},
{
"id":... | 2 | [
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "SUM_ARITHMETIC",
"status": "ok"
},
{
"lemma": "V8",
"status": "no"
}
] | {
"lo": -9.14,
"mid": -6.05,
"hi": -3.73
} | ||
d7cb78 | antilemma_k3_v1_784195855_9580 | Let $x$ be the sum of $\phi(d)$ over all positive divisors $d$ of $88863$, where $\phi$ denotes Euler's totient function. Compute the remainder when $50827x$ is divided by $54700$. | 6,001 | graphs = [
Graph(
let={
"x": SumOverDivisors(n=Const(value=88863), var='d', expr=EulerPhi(n=Var(name='d'))),
"Q": Mod(value=Mul(Const(50827), Ref("x")), modulus=Const(54700)),
},
goal=Ref("Q"),
)
] | NT | COMB | COMPUTE | sympy | K3 | [
"K3"
] | 54c41e | antilemma_k3_v1 | null | 3 | 0 | [
"K3"
] | 1 | 0.001 | 2026-02-08T16:53:56.552619Z | {
"verified": true,
"answer": 6001,
"timestamp": "2026-02-08T16:53:56.553304Z"
} | db4afb | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 97,
"completion_tokens": 1927
},
"timestamp": "2026-02-17T15:32:26.902Z",
"answer": 6001
},
{
... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "K3",
"status": "ok"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
d6f861 | antilemma_k2_v1_1520064083_7145 | Let $d=2$ and $n=281$. Define
$$x = \sum_{k=1}^{281} \varphi(k) \left\lfloor \frac{281}{k} \right\rfloor,$$
where $\varphi$ denotes Euler's totient function.
Consider the set of all integers $u$ satisfying
$$u^{d} - 6277u - 119624 = 0.$$
Let $S$ be the sum of all such integers $u$. Let
$$c = \sum_{t \mid S} \varphi(t)... | 38,685 | graphs = [
Graph(
let={
"_d": Const(2),
"_m": Const(281),
"_n": Const(281),
"x": Summation(var="k", start=Const(1), end=Ref("_m"), expr=Mul(EulerPhi(n=Var("k")), Floor(Div(Ref("_n"), Var("k"))))),
"_c": SumOverDivisors(n=SumOverSet(set=SolutionsSet... | NT | COMB | COMPUTE | sympy | VIETA_SUM | [
"VIETA_SUM/K3",
"K2"
] | 070306 | antilemma_k2_v1 | affine_mod | 7 | 0 | [
"K2",
"K3",
"VIETA_SUM"
] | 3 | 0.002 | 2026-02-08T08:47:47.293623Z | {
"verified": true,
"answer": 38685,
"timestamp": "2026-02-08T08:47:47.296070Z"
} | b47e66 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 233,
"completion_tokens": 6335
},
"timestamp": "2026-02-13T21:38:14.946Z",
"answer": 38685
},
... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "K2",
"status": "ok"
},
{
"lemma": "K3",
"status": "ok_later"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma... | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} |
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