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305627
lin_form_endings_v1_48377204_283
Let $a = 24$, $b = 40$, and $k = 43$. Let $s = \gcd(a, b)$. Compute $\left\lfloor \frac{k}{\gcd(k, s)} \right\rfloor$, multiply the result by $13524$, and then take the remainder when divided by $56955$.
11,982
graphs = [ Graph( let={ "a_coeff": Const(24), "b_coeff": Const(40), "k_val": Const(43), "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(13...
COMB
NT
COMPUTE
sympy
LIN_FORM
[ "LIN_FORM" ]
7b2633
lin_form_endings_v1
null
3
null
[ "LIN_FORM" ]
1
0.001
2026-02-08T15:20:03.403783Z
{ "verified": true, "answer": 11982, "timestamp": "2026-02-08T15:20:03.404684Z" }
b721f2
CC BY 4.0
[ { "id": 5, "model": "deepseek-ai/DeepSeek-V3.2", "score": 3, "correct": { "strict": true, "boxed": true, "relaxed": true }, "usage": { "prompt_tokens": 116, "completion_tokens": 458 }, "timestamp": "2026-02-16T03:07:22.907Z", "answer": 11982 }, {...
1
[ { "lemma": "COUNT_CARTESIAN", "status": "no" }, { "lemma": "COUNT_COPRIME_GRID", "status": "no" }, { "lemma": "COUNT_INTEGER_RANGE", "status": "no" }, { "lemma": "LIN_FORM", "status": "ok" }, { "lemma": "V7", "status": "no" }, { "lemma": "V8_SUM", ...
{ "lo": -7.08, "mid": -0.29, "hi": 6.49 }
4dc1a6
sequence_count_fib_divisible_v1_1439011603_1515
Let $d_1$ be a positive integer divisor of 769113 such that $1 \leq d_1 \leq 873$. Define $u$ to be the largest such $d_1$. Let $d = 20$. Consider the set of all positive integers $n$ such that $1 \leq n \leq u$ and $d$ divides the $n$-th Fibonacci number. Compute the number of elements in this set.
29
graphs = [ Graph( let={ "upper": MaxOverSet(set=SolutionsSet(var=Var("d1"), condition=And(Geq(Var("d1"), Const(1)), Leq(Var("d1"), Const(873)), Divides(divisor=Var("d1"), dividend=Const(769113))))), "d": Const(20), "result": CountOverSet(set=SolutionsSet(var=Var("n"), con...
NT
null
COUNT
sympy
B3
[ "MAX_DIVISOR" ]
51757e
sequence_count_fib_divisible_v1
null
5
0
[ "B3", "MAX_DIVISOR" ]
2
0.09
2026-02-08T16:09:19.290612Z
{ "verified": true, "answer": 29, "timestamp": "2026-02-08T16:09:19.380794Z" }
a89f64
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": 2080 }, "timestamp": "2026-02-16T21:29:54.412Z", "answer": 29 }, { ...
1
[ { "lemma": "K13", "status": "no" }, { "lemma": "LTE_DIFF", "status": "no" }, { "lemma": "LTE_DIFF_P2", "status": "no" }, { "lemma": "MAX_DIVISOR", "status": "ok" }, { "lemma": "MOD_ADD", "status": "no" }, { "lemma": "VAL_SUM_EQ", "status": "no" }...
{ "lo": -7.08, "mid": -0.29, "hi": 6.49 }
656b2f
antilemma_cartesian_v1_655260480_5732
Let $x$ be the number of ordered pairs $(a, b)$ such that $1 \leq a \leq 12$ and $1 \leq b \leq 15$. Compute the smallest positive integer $k$ such that the $k$th Fibonacci number is divisible by $x + 2$.
168
graphs = [ Graph( let={ "x": CountOverSet(set=CartesianProduct(left=IntegerRange(start=Const(1), end=Const(12)), right=IntegerRange(start=Const(1), end=Const(15)))), "Q": FibonacciEntryPoint(modulus=Sum(Abs(arg=Ref(name='x')), Const(value=2))), }, goal=Ref("Q"), )...
COMB
GEOM
COMPUTE
sympy
COUNT_CARTESIAN
[ "COUNT_CARTESIAN" ]
409d7d
antilemma_cartesian_v1
null
2
0
[ "COUNT_CARTESIAN" ]
1
0.001
2026-02-08T18:38:37.282870Z
{ "verified": true, "answer": 168, "timestamp": "2026-02-08T18:38:37.283425Z" }
8b59d5
CC BY 4.0
[ { "id": 5, "model": "deepseek-ai/DeepSeek-V3.2", "score": 3, "correct": { "strict": true, "boxed": true, "relaxed": true }, "usage": { "prompt_tokens": 111, "completion_tokens": 1577 }, "timestamp": "2026-02-18T18:14:45.641Z", "answer": 168 }, { ...
1
[ { "lemma": "C2", "status": "no" }, { "lemma": "COUNT_CARTESIAN", "status": "ok" }, { "lemma": "COUNT_COPRIME_GRID", "status": "no" }, { "lemma": "COUNT_INTEGER_RANGE", "status": "no" }, { "lemma": "V7", "status": "no" }, { "lemma": "V8_SUM", "statu...
{ "lo": -3.12, "mid": 1.47, "hi": 6.57 }
94a11e_n
comb_count_derangements_v1_1218484723_56
A theater group has $n$ actors, each assigned a unique role. On opening night, due to a mix-up, every actor takes a role that isn't their own—an arrangement called a derangement. The value $n$ is computed as $2^0 + 2^1 + 2^2 = 7$. Let $R$ be the number of such possible mix-ups. Compute the remainder when $96031 \cdot R...
7,354
COMB
null
COUNT
sympy
SUM_GEOM
[ "SUM_GEOM", "ZERO_BINOM_N" ]
4e18d8
comb_count_derangements_v1
null
4
null
[ "SUM_GEOM", "ZERO_BINOM_N" ]
2
0.002
2026-02-25T01:45:38.643646Z
null
c50dc1
94a11e
narrative
CC BY 4.0
[ { "id": 1, "model": "openai/gpt-oss-20b", "score": 3, "correct": { "strict": true, "boxed": true, "relaxed": true }, "usage": { "prompt_tokens": 210, "completion_tokens": 2314 }, "timestamp": "2026-03-30T14:41:25.648Z", "answer": 7354 }, { "i...
1
[ { "lemma": "COUNT_CARTESIAN", "status": "no" }, { "lemma": "COUNT_COPRIME_GRID", "status": "no" }, { "lemma": "COUNT_SUM_EQUALS", "status": "no" }, { "lemma": "SUM_GEOM", "status": "ok" }, { "lemma": "V8", "status": "no" }, { "lemma": "V8_SUM", "st...
{ "lo": -5.37, "mid": 0.23, "hi": 5.22 }
c4f953
comb_factorial_compute_v1_1218484723_2537
Find the number of ordered pairs $(a, b)$ of positive integers with $1 \leq a \leq b \leq 15$ such that $2a^2 - 4ab + 2b^2 = 128$. Let $Q$ be the factorial of this number. Compute $Q$.
5,040
graphs = [ Graph( let={ "_m": Const(2), "_n": Const(2), "n": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("a"), Var("b")]), condition=And(Geq(Var("a"), Const(1)), Leq(Var("a"), CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("a1"), Var("b1")]), condition=An...
COMB
null
COMPUTE
sympy
QF_PSD_ORBIT
[ "QF_PSD_ORBIT/QF_PSD_ORBIT", "B3/QF_PSD_ORBIT" ]
0242d3
comb_factorial_compute_v1
null
5
0
[ "B3", "QF_PSD_ORBIT" ]
2
0.009
2026-02-25T04:16:56.198405Z
{ "verified": true, "answer": 5040, "timestamp": "2026-02-25T04:16:56.207385Z" }
2b0e4f
CC BY 4.0
[ { "id": 1, "model": "openai/gpt-oss-20b", "score": 3, "correct": { "strict": true, "boxed": true, "relaxed": true }, "usage": { "prompt_tokens": 177, "completion_tokens": 652 }, "timestamp": "2026-03-29T05:16:17.193Z", "answer": 5040 }, { "id...
2
[ { "lemma": "B3", "status": "ok" }, { "lemma": "COUNT_CARTESIAN", "status": "no" }, { "lemma": "COUNT_COPRIME_GRID", "status": "no" }, { "lemma": "COUNT_INTEGER_RANGE", "status": "no" }, { "lemma": "COUNT_SUM_EQUALS", "status": "no" }, { "lemma": "QF_PS...
{ "lo": -10, "mid": -6.41, "hi": -2.82 }
b48b53
diophantine_fbi2_min_v1_124444284_2712
Let $n$ range over the positive integers from 1 to 154 such that $$ n \equiv \left\lfloor \frac{n}{2} \right\rfloor \pmod{7}. $$ Let $k$ be the number of such integers. Find the smallest divisor $d \ge 2$ of $k$ for which $\frac{k}{d} \ge 7$ and $d \le 32$. Compute the remainder when $72774$ times this divisor is divid...
31,342
graphs = [ Graph( let={ "_n": Const(57103), "k": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Const(154)), Congruent(a=Var(name='n'), b=Floor(arg=Div(left=Var(name='n'), right=Const(value=2))), modulus=Const(value=7))))), ...
NT
null
EXTREMUM
sympy
SUM_ARITHMETIC
[ "SUM_ARITHMETIC", "L3C" ]
22c5b7
diophantine_fbi2_min_v1
null
6
0
[ "L3C", "SUM_ARITHMETIC" ]
2
0.005
2026-02-08T04:53:57.660661Z
{ "verified": true, "answer": 31342, "timestamp": "2026-02-08T04:53:57.665452Z" }
30716a
CC BY 4.0
[ { "id": 2, "model": "openai/gpt-oss-120b", "score": 3, "correct": { "strict": true, "boxed": true, "relaxed": true }, "usage": { "prompt_tokens": 221, "completion_tokens": 1342 }, "timestamp": "2026-02-11T22:42:06.301Z", "answer": 31342 }, { ...
1
[ { "lemma": "C2", "status": "no" }, { "lemma": "COUNT_PRIMES", "status": "no" }, { "lemma": "K16", "status": "no" }, { "lemma": "L3C", "status": "ok" }, { "lemma": "SUM_ARITHMETIC", "status": "ok" }, { "lemma": "V3", "status": "no" }, { "lem...
{ "lo": -3.42, "mid": 1.86, "hi": 7.55 }
fbc7a3
diophantine_fbi2_count_v1_1915831931_3405
Let $B$ be the set of all positive integers $p$ for which there exists a positive integer $q$ such that $p < q$, $pq = 6$, and $\gcd(p, q) = 1$. Let $t$ be the number of elements in $B$. Define $S$ as the set of all positive integers $d$ such that $t \le d \le 89$, $d$ divides 720, $\frac{720}{d} \ge 2$, and $\frac{720...
16
graphs = [ Graph( let={ "k": Const(720), "result": CountOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), 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(n...
NT
null
COUNT
sympy
COPRIME_PAIRS
[ "COPRIME_PAIRS" ]
2bb3aa
diophantine_fbi2_count_v1
null
5
0
[ "COPRIME_PAIRS" ]
1
0.008
2026-02-08T17:38:30.927916Z
{ "verified": true, "answer": 16, "timestamp": "2026-02-08T17:38:30.935941Z" }
c0d9b4
CC BY 4.0
[ { "id": 5, "model": "deepseek-ai/DeepSeek-V3.2", "score": 3, "correct": { "strict": true, "boxed": true, "relaxed": true }, "usage": { "prompt_tokens": 175, "completion_tokens": 1101 }, "timestamp": "2026-02-18T05:36:56.724Z", "answer": 16 }, { ...
1
[ { "lemma": "C2", "status": "no" }, { "lemma": "COPRIME_PAIRS", "status": "ok" }, { "lemma": "K18", "status": "no" }, { "lemma": "K5", "status": "no" }, { "lemma": "LTE_SUM", "status": "no" }, { "lemma": "V5", "status": "no" } ]
{ "lo": -7.08, "mid": -0.29, "hi": 6.49 }
c55962
nt_sum_divisors_compute_v1_2080023795_57
Let $c = \mu(47)^k$, where $\mu$ denotes the M\"obius function and $k$ is the number of unordered pairs of coprime positive integers $(p,q)$ such that $p < q$ and $pq = 12$. Let $u = \lambda(3) + 1$, where $\lambda$ denotes the Liouville function. Define $n = 44521 + u$. Let $\sigma(n)$ denote the sum of the positive d...
35,923
graphs = [ Graph( let={ "n2": Const(47), "c": Pow(MoebiusMu(n=Ref(name='n2')), 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=12)), Eq(left=G...
NT
null
COMPUTE
sympy
COPRIME_PAIRS
[ "COPRIME_PAIRS/MOBIUS_SQUAREFREE", "LIOUVILLE_MINUS_ONE" ]
6b62be
nt_sum_divisors_compute_v1
null
5
2
[ "COPRIME_PAIRS", "LIOUVILLE_MINUS_ONE", "MOBIUS_SQUAREFREE" ]
3
0.003
2026-02-08T11:30:51.924549Z
{ "verified": true, "answer": 35923, "timestamp": "2026-02-08T11:30:51.927964Z" }
ed8b76
CC BY 4.0
[ { "id": 1, "model": "openai/gpt-oss-20b", "score": 3, "correct": { "strict": true, "boxed": true, "relaxed": true }, "usage": { "prompt_tokens": 235, "completion_tokens": 2382 }, "timestamp": "2026-02-08T20:38:56.704Z", "answer": 35923 }, { "...
1
[ { "lemma": "COPRIME_PAIRS", "status": "ok" }, { "lemma": "K15", "status": "no" }, { "lemma": "K18", "status": "no" }, { "lemma": "K5", "status": "no" }, { "lemma": "LIOUVILLE_MINUS_ONE", "status": "ok" }, { "lemma": "LTE_DIFF", "status": "no" }, ...
{ "lo": -6.69, "mid": -2.4, "hi": 1.76 }
7786a1
comb_catalan_compute_v1_1915831931_3466
Let $w = \sum_{k=0}^{10} (-1)^k \binom{10}{k}$ and $t = \sum_{k_1=0}^{0} (-1)^{k_1} \binom{0}{k_1}$. Let $C_{10}$ denote the 10th Catalan number. Let $Q$ be the remainder when $ (41383 + w) \cdot t \cdot C_{10} $ is divided by $80559$. Compute the value of $Q$.
5,816
graphs = [ Graph( let={ "n2": Const(10), "w": Summation(var="k", start=Const(0), end=Ref("n2"), expr=Mul(Pow(Const(-1), Var("k")), Binom(n=Ref("n2"), k=Var("k")))), "n1": Const(0), "t": Summation(var="k1", start=Const(0), end=Ref("n1"), expr=Mul(Pow(Const(-1),...
COMB
null
COMPUTE
sympy
BINOMIAL_ALTERNATING
[ "BINOMIAL_ALTERNATING" ]
c21569
comb_catalan_compute_v1
null
3
2
[ "BINOMIAL_ALTERNATING" ]
1
0.003
2026-02-08T17:41:32.445124Z
{ "verified": true, "answer": 5816, "timestamp": "2026-02-08T17:41:32.447641Z" }
aae825
CC BY 4.0
[ { "id": 5, "model": "deepseek-ai/DeepSeek-V3.2", "score": 3, "correct": { "strict": true, "boxed": true, "relaxed": true }, "usage": { "prompt_tokens": 155, "completion_tokens": 1430 }, "timestamp": "2026-02-18T05:43:51.040Z", "answer": 5816 }, {...
1
[ { "lemma": "BINOMIAL_ALTERNATING", "status": "ok" }, { "lemma": "COUNT_CARTESIAN", "status": "no" }, { "lemma": "COUNT_COPRIME_GRID", "status": "no" }, { "lemma": "COUNT_INTEGER_RANGE", "status": "no" }, { "lemma": "COUNT_SUM_EQUALS", "status": "no" }, { ...
{ "lo": -2.38, "mid": 1.74, "hi": 6.59 }
b97aca
comb_count_surjections_v1_1520064083_3198
Let $n$ be the number of ordered pairs $(x_1, x_2)$ of positive odd integers such that $x_1 + x_2$ equals the number of integers $t$ in the range $22 \leq t \leq 61$ for which there exist integers $a$ and $b$ satisfying $1 \leq a \leq 5$, $1 \leq b \leq 2$, and $t = 6a + 15b + 1$. Let $k = 4$. Compute $k! \cdot S(n, k)...
240
graphs = [ Graph( let={ "n": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x1"), Var("x2")]), condition=And(IsPositive(arg=Var(name='x1')), IsPositive(arg=Var(name='x2')), IsOdd(arg=Var(name='x1')), IsOdd(arg=Var(name='x2')), Eq(Sum(Var("x1"), Var("x2")), CountOverSet(set=SolutionsSet(v...
COMB
null
COUNT
sympy
LIN_FORM
[ "LIN_FORM/COMB1" ]
268a62
comb_count_surjections_v1
null
6
0
[ "COMB1", "LIN_FORM" ]
2
0.004
2026-02-08T05:30:43.662437Z
{ "verified": true, "answer": 240, "timestamp": "2026-02-08T05:30:43.666745Z" }
cd0542
CC BY 4.0
[ { "id": 1, "model": "openai/gpt-oss-20b", "score": 3, "correct": { "strict": true, "boxed": true, "relaxed": true }, "usage": { "prompt_tokens": 256, "completion_tokens": 1259 }, "timestamp": "2026-02-24T03:51:43.407Z", "answer": 240 }, { "id...
1
[ { "lemma": "C2", "status": "no" }, { "lemma": "COMB1", "status": "ok_later" }, { "lemma": "COUNT_COPRIME_GRID", "status": "no" }, { "lemma": "COUNT_INTEGER_RANGE", "status": "no" }, { "lemma": "COUNT_SUM_EQUALS", "status": "no" }, { "lemma": "LIN_FORM"...
{ "lo": -3.84, "mid": -1.69, "hi": 1.09 }
656087
comb_sum_binomial_row_v1_1520064083_534
Let $n$ be the number of positive integers less than or equal to 47 that are relatively prime to 12. Find the value of $2^n$.
65,536
graphs = [ Graph( let={ "_n": Const(12), "n": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Const(47)), Eq(GCD(a=Var("n"), b=Ref("_n")), Const(1))))), "result": Pow(Const(2), Ref("n")), }, goal=Ref("result...
NT
null
SUM
sympy
C4
[ "C4" ]
08d162
comb_sum_binomial_row_v1
null
4
0
[ "C4" ]
1
0.001
2026-02-08T03:28:00.125641Z
{ "verified": true, "answer": 65536, "timestamp": "2026-02-08T03:28:00.126777Z" }
c93a12
CC BY 4.0
[ { "id": 1, "model": "openai/gpt-oss-20b", "score": 3, "correct": { "strict": true, "boxed": true, "relaxed": true }, "usage": { "prompt_tokens": 144, "completion_tokens": 581 }, "timestamp": "2026-02-10T14:27:28.619Z", "answer": 65536 }, { "i...
1
[ { "lemma": "C4", "status": "ok" }, { "lemma": "K15", "status": "no" }, { "lemma": "K5", "status": "no" }, { "lemma": "MOD_FACTORIAL", "status": "no" }, { "lemma": "MOD_SUB", "status": "no" }, { "lemma": "V7", "status": "no" } ]
{ "lo": -5.55, "mid": -3.02, "hi": 0.31 }
720c62
nt_num_divisors_compute_v1_124444284_6122
Let $m$ be the sum of all integers $x$ satisfying $$x^2-2936x-201201=0.$$ Let $n$ be the number of nonnegative integers $j$ such that $$0\le j\le M\quad\text{and}\quad\binom{m}{j}\equiv1\pmod{2},$$ where $M$ is the minimum value of $x+y$ over all ordered pairs $(x,y)$ of positive integers satisfying $xy=2155024$. Let $...
8
graphs = [ Graph( let={ "_c": Const(2), "_m": SumOverSet(set=SolutionsSet(var=Var("x"), condition=Eq(Sum(Pow(Var("x"), Ref("_c")), Mul(Const(-2936), Var("x")), Const(-201201)), Const(0)))), "_n": Const(2), "n": CountOverSet(set=SolutionsSet(var=Var("j"), condi...
NT
null
COMPUTE
sympy
VIETA_SUM
[ "VIETA_SUM/B3/V8" ]
4734d2
nt_num_divisors_compute_v1
null
8
0
[ "B3", "V8", "VIETA_SUM" ]
3
0.003
2026-02-08T08:08:37.763486Z
{ "verified": true, "answer": 8, "timestamp": "2026-02-08T08:08:37.766942Z" }
8adece
CC BY 4.0
[ { "id": 5, "model": "deepseek-ai/DeepSeek-V3.2", "score": 3, "correct": { "strict": true, "boxed": true, "relaxed": true }, "usage": { "prompt_tokens": 173, "completion_tokens": 1438 }, "timestamp": "2026-02-13T15:24:51.202Z", "answer": 8 }, { ...
1
[ { "lemma": "B3", "status": "ok_later" }, { "lemma": "C2", "status": "no" }, { "lemma": "COUNT_COPRIME_GRID", "status": "no" }, { "lemma": "K14", "status": "no" }, { "lemma": "K17", "status": "no" }, { "lemma": "V5", "status": "no" }, { "lem...
{ "lo": -3.44, "mid": 1.34, "hi": 6.56 }
54dc97
nt_count_with_divisor_count_v1_124444284_7971
Let $m = 15$ and $n = 2$. Define $T$ to be the set of all integers $t$ such that $21 \leq t \leq 28383$ and there exist positive integers $a$ and $b$ with $1 \leq a \leq 3343$, $1 \leq b \leq 555$, and $t = 6a + 15b$. Let $U$ be the number of positive integers $n$ such that $1 \leq n \leq U'$ and $\gcd(n, m) = 1$, wher...
1,034
graphs = [ Graph( let={ "_m": Const(15), "_n": Const(2), "upper": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), CountOverSet(set=SolutionsSet(var=Var("t"), condition=Exists(var=Var(name='a'), condition=Exists(var=Var(name...
NT
null
COUNT
sympy
COUNT_PRIMES
[ "LIN_FORM/C4" ]
067e5d
nt_count_with_divisor_count_v1
null
6
0
[ "C4", "COUNT_PRIMES", "LIN_FORM" ]
3
14.822
2026-02-08T09:29:18.038018Z
{ "verified": true, "answer": 1034, "timestamp": "2026-02-08T09:29:32.860045Z" }
fdcb01
CC BY 4.0
[ { "id": 5, "model": "deepseek-ai/DeepSeek-V3.2", "score": 3, "correct": { "strict": true, "boxed": true, "relaxed": true }, "usage": { "prompt_tokens": 262, "completion_tokens": 4851 }, "timestamp": "2026-02-14T04:19:54.108Z", "answer": 1034 }, {...
1
[ { "lemma": "C4", "status": "ok_later" }, { "lemma": "COUNT_FIB_DIVISIBLE", "status": "no" }, { "lemma": "LIN_FORM", "status": "ok" }, { "lemma": "MOD_SUB", "status": "no" }, { "lemma": "V1", "status": "no" }, { "lemma": "V5", "status": "no" }, ...
{ "lo": -5.14, "mid": 0.32, "hi": 6.51 }
f2f68f
sequence_fibonacci_compute_v1_168721529_257
Let $n$ be the largest prime number such that $2 \leq n \leq 25$. Compute the $n$-th Fibonacci number, where the Fibonacci sequence is defined by $F_1 = 1$, $F_2 = 1$, and $F_k = F_{k-1} + F_{k-2}$ for all $k \geq 3$. Find the value of this result.
28,657
graphs = [ Graph( let={ "_n": Const(25), "n": MaxOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(2)), Leq(Var("n"), Ref("_n")), IsPrime(Var("n"))))), "result": Fibonacci(arg=Ref(name='n')), }, goal=Ref("result"), ) ]
NT
null
COMPUTE
sympy
MAX_PRIME_BELOW
[ "MAX_PRIME_BELOW" ]
dc3ad3
sequence_fibonacci_compute_v1
null
4
0
[ "MAX_PRIME_BELOW" ]
1
0.001
2026-02-08T12:56:11.575733Z
{ "verified": true, "answer": 28657, "timestamp": "2026-02-08T12:56:11.576493Z" }
c02872
CC BY 4.0
[ { "id": 1, "model": "openai/gpt-oss-20b", "score": 3, "correct": { "strict": true, "boxed": true, "relaxed": true }, "usage": { "prompt_tokens": 207, "completion_tokens": 439 }, "timestamp": "2026-02-09T02:57:41.133Z", "answer": 28657 }, { "i...
1
[ { "lemma": "COUNT_FIB_DIVISIBLE", "status": "no" }, { "lemma": "K13", "status": "no" }, { "lemma": "LTE_SUM", "status": "no" }, { "lemma": "MAX_PRIME_BELOW", "status": "ok" }, { "lemma": "MAX_VAL", "status": "no" }, { "lemma": "MOD_SUB", "status": ...
{ "lo": -5.3, "mid": -2.05, "hi": 1.82 }
004236
antilemma_sum_equals_v1_865884756_4577
Let $n = 24$. Let $x$ be the number of ordered pairs $(i, j)$ of positive integers such that $1 \leq i \leq 23$, $1 \leq j \leq 23$, and $i + j = n$. Compute the remainder when $44121 \cdot x$ is divided by $64574$.
46,173
graphs = [ Graph( let={ "_n": Const(24), "x": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("i"), Var("j")]), condition=Eq(Sum(Var("i"), Var("j")), Ref("_n")), domain=CartesianProduct(left=IntegerRange(start=Const(1), end=Const(23)), right=IntegerRange(start=Const(1), end=Con...
COMB
GEOM
COMPUTE
sympy
LIN_FORM
[ "COUNT_SUM_EQUALS" ]
75ab0f
antilemma_sum_equals_v1
null
3
0
[ "COUNT_SUM_EQUALS", "LIN_FORM" ]
2
0.047
2026-02-08T17:59:42.167600Z
{ "verified": true, "answer": 46173, "timestamp": "2026-02-08T17:59:42.214365Z" }
db5628
CC BY 4.0
[ { "id": 5, "model": "deepseek-ai/DeepSeek-V3.2", "score": 3, "correct": { "strict": true, "boxed": true, "relaxed": true }, "usage": { "prompt_tokens": 120, "completion_tokens": 781 }, "timestamp": "2026-02-18T11:49:36.136Z", "answer": 46173 }, {...
1
[ { "lemma": "COUNT_CARTESIAN", "status": "no" }, { "lemma": "COUNT_COPRIME_GRID", "status": "no" }, { "lemma": "COUNT_INTEGER_RANGE", "status": "no" }, { "lemma": "COUNT_SUM_EQUALS", "status": "ok" }, { "lemma": "V7", "status": "no" }, { "lemma": "V8_SU...
{ "lo": -2.38, "mid": 1.74, "hi": 6.59 }
41d17b
sequence_count_fib_divisible_v1_1742523217_3349
Let $t$ be an integer. Determine the number of values of $t$ such that $24 \leq t \leq 541$ and there exist positive integers $a \leq 132$ and $b \leq 52$ satisfying $t = 2a + 5b + 17$. Let this number be $u$. Now, let $F_n$ denote the $n$th Fibonacci number, with $F_1 = F_2 = 1$ and $F_n = F_{n-1} + F_{n-2}$ for $n \g...
77,169
graphs = [ Graph( let={ "_n": Const(77230), "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=132)), Geq(l...
NT
null
COUNT
sympy
LIN_FORM
[ "LIN_FORM" ]
7b2633
sequence_count_fib_divisible_v1
null
7
0
[ "LIN_FORM" ]
1
0.024
2026-02-08T05:48:35.673858Z
{ "verified": true, "answer": 77169, "timestamp": "2026-02-08T05:48:35.698017Z" }
205899
CC BY 4.0
[ { "id": 5, "model": "deepseek-ai/DeepSeek-V3.2", "score": 3, "correct": { "strict": true, "boxed": true, "relaxed": true }, "usage": { "prompt_tokens": 227, "completion_tokens": 3306 }, "timestamp": "2026-02-12T14:53:27.810Z", "answer": 77169 }, ...
1
[ { "lemma": "K13", "status": "no" }, { "lemma": "LIN_FORM", "status": "ok" }, { "lemma": "LTE_DIFF", "status": "no" }, { "lemma": "MAX_VAL", "status": "no" }, { "lemma": "MOD_ADD", "status": "no" }, { "lemma": "V5", "status": "no" } ]
{ "lo": -3.51, "mid": 1.33, "hi": 6.56 }
740a4c
nt_lcm_compute_v1_1978505735_3538
Let $S$ be the set of all ordered pairs $(x, y)$ of positive integers such that $xy = 186624$. For each such pair, compute $x + y$. Let $b$ be the minimum value among all such sums. Let $a = 1103$. Define $c = \operatorname{lcm}(a, b)$. Find the remainder when $17950 \cdot c$ is divided by $68789$.
33,036
graphs = [ Graph( let={ "a": Const(1103), "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(186624)))), expr=Sum(Var("x"), Var("y"))))...
NT
null
COMPUTE
sympy
B3
[ "B3" ]
0cd20d
nt_lcm_compute_v1
null
4
0
[ "B3" ]
1
0.001
2026-02-08T17:42:39.391127Z
{ "verified": true, "answer": 33036, "timestamp": "2026-02-08T17:42:39.392450Z" }
0198fa
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": 5301 }, "timestamp": "2026-02-18T06:21:57.047Z", "answer": 33036 }, ...
1
[ { "lemma": "B3", "status": "ok" }, { "lemma": "C2", "status": "no" }, { "lemma": "COUNT_DIVISOR_COUNT", "status": "no" }, { "lemma": "K14", "status": "no" }, { "lemma": "K16", "status": "no" }, { "lemma": "L3b", "status": "no" } ]
{ "lo": -7.08, "mid": -0.29, "hi": 6.49 }
60ec0f
modular_min_modexp_v1_1915831931_2183
Let $N$ be the number of positive integers $n_1$ such that $1 \leq n_1 \leq 4075$ and $5$ divides the $n_1$-th Fibonacci number. Let $m$ be the largest prime number $n$ such that $2 \leq n \leq N$. Let $x$ be the smallest positive integer such that $1 \leq x \leq 405$ and $11^x \equiv 30 \pmod{m}$. Compute the remainde...
44,204
graphs = [ Graph( let={ "_n": Const(4075), "a": Const(11), "b": Const(30), "m": MaxOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(2)), Leq(Var("n"), CountOverSet(set=SolutionsSet(var=Var("n1"), condition=And(Geq(Var("n1"), Const(1)), ...
NT
null
EXTREMUM
sympy
COUNT_FIB_DIVISIBLE
[ "COUNT_FIB_DIVISIBLE/MAX_PRIME_BELOW" ]
c3fe6d
modular_min_modexp_v1
null
7
0
[ "COUNT_FIB_DIVISIBLE", "MAX_PRIME_BELOW" ]
2
0.033
2026-02-08T16:39:32.209718Z
{ "verified": true, "answer": 44204, "timestamp": "2026-02-08T16:39:32.242641Z" }
be7ac2
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": 2243 }, "timestamp": "2026-02-17T09:01:22.591Z", "answer": 44204 }, ...
1
[ { "lemma": "COUNT_FIB_DIVISIBLE", "status": "ok" }, { "lemma": "COUNT_PRIMES", "status": "no" }, { "lemma": "K17", "status": "no" }, { "lemma": "K18", "status": "no" }, { "lemma": "LTE_DIFF", "status": "no" }, { "lemma": "MAX_PRIME_BELOW", "status"...
{ "lo": -7.08, "mid": -0.29, "hi": 6.49 }
8c05ec
antilemma_sum_factor_cartesian_v1_677425708_1617
Let $T$ be the set of all integers $t$ such that $21 \leq t \leq 43$ and there exist positive integers $a$, $b$ with $1 \leq a \leq 5$, $1 \leq b \leq 3$, satisfying $t = 3a + 5b + 13$. Let $g = \gcd(8, |T|)$. Let $D$ be the set of positive divisors of $g$. Define $\mu(d)$ as the M\"obius function. Let $S$ be the set o...
29,484
graphs = [ Graph( let={ "_n": Const(8), "x": SumOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("i"), Var("j")]), condition=SumOverDivisors(n=GCD(a=Ref(name='_n'), b=CountOverSet(set=SolutionsSet(var=Var(name='t'), condition=Exists(var=Var(name='a'), condition=Exists(...
NT
null
COMPUTE
sympy
LIN_FORM
[ "LIN_FORM/MOBIUS_COPRIME/SUM_FACTOR_CARTESIAN", "SUM_FACTOR_CARTESIAN" ]
a038a8
antilemma_sum_factor_cartesian_v1
null
6
0
[ "LIN_FORM", "MOBIUS_COPRIME", "SUM_FACTOR_CARTESIAN" ]
3
0.001
2026-02-08T04:18:51.039791Z
{ "verified": true, "answer": 29484, "timestamp": "2026-02-08T04:18:51.041207Z" }
614359
CC BY 4.0
[ { "id": 1, "model": "openai/gpt-oss-20b", "score": 0, "correct": { "strict": false, "boxed": false, "relaxed": false }, "usage": { "prompt_tokens": 312, "completion_tokens": 1236 }, "timestamp": "2026-02-09T22:23:15.070Z", "answer": 0 }, { "i...
0
[ { "lemma": "COUNT_DIVISOR_COUNT", "status": "no" }, { "lemma": "K13", "status": "no" }, { "lemma": "K14", "status": "no" }, { "lemma": "K15", "status": "no" }, { "lemma": "LIN_FORM", "status": "ok" }, { "lemma": "MOBIUS_COPRIME", "status": "ok_late...
{ "lo": 2.2, "mid": 6.06, "hi": 9.93 }
80f728
diophantine_fbi2_count_v1_1470522791_977
Let $k$ be the minimum value of $x + y$ over all ordered pairs $(x, y)$ of positive integers such that $x \cdot y = 176400$. Determine the number of positive integers $d$ such that $6 \leq d \leq 172$, $d$ divides $k$, and $\frac{k}{d}$ is at least $4$ and at most the sum of the solutions to the equation $x^2 - 170x + ...
23
graphs = [ Graph( let={ "_n": Const(5704), "k": MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(Mul(Var("x"), Var("y")), Const(176400)))), expr=Sum(Var("x"), Var("y")))...
NT
null
COUNT
sympy
V1
[ "VIETA_SUM", "B3" ]
018050
diophantine_fbi2_count_v1
null
6
0
[ "B3", "V1", "VIETA_SUM" ]
3
0.124
2026-02-08T13:21:31.189710Z
{ "verified": true, "answer": 23, "timestamp": "2026-02-08T13:21:31.313214Z" }
d1bb1f
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": 2029 }, "timestamp": "2026-02-15T14:04:28.305Z", "answer": 23 }, { ...
1
[ { "lemma": "B3", "status": "ok" }, { "lemma": "K14", "status": "no" }, { "lemma": "K5", "status": "no" }, { "lemma": "L3b", "status": "no" }, { "lemma": "LTE_DIFF", "status": "no" }, { "lemma": "POLY_PADIC_VAL_CONST", "status": "no" }, { "l...
{ "lo": -5.14, "mid": 0.32, "hi": 6.51 }
261ebe
nt_min_coprime_above_v1_1439011603_1943
Let $P$ be the set of all ordered pairs of positive integers $(x, y)$ such that $xy = 17842176$. For each such pair, compute $x + y$, and let $s$ be the minimum value of $x + y$ over all such pairs. Let $n$ be the smallest integer greater than $8192$ and at most $s$ that is relatively prime to $246$. Determine the valu...
8,195
graphs = [ Graph( let={ "start": Const(8192), "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(17842176)))), expr=Sum(Var("x"), V...
NT
null
EXTREMUM
sympy
B3
[ "B3" ]
0cd20d
nt_min_coprime_above_v1
null
5
0
[ "B3" ]
1
0.043
2026-02-08T16:23:29.115139Z
{ "verified": true, "answer": 8195, "timestamp": "2026-02-08T16:23:29.158083Z" }
55eb52
CC BY 4.0
[ { "id": 5, "model": "deepseek-ai/DeepSeek-V3.2", "score": 3, "correct": { "strict": true, "boxed": true, "relaxed": true }, "usage": { "prompt_tokens": 142, "completion_tokens": 1497 }, "timestamp": "2026-02-17T03:53:50.496Z", "answer": 8195 }, {...
1
[ { "lemma": "B3", "status": "ok" }, { "lemma": "C2", "status": "no" }, { "lemma": "COUNT_PRIMES", "status": "no" }, { "lemma": "K16", "status": "no" }, { "lemma": "MOD_FACTORIAL", "status": "no" }, { "lemma": "V3", "status": "no" } ]
{ "lo": -7.08, "mid": -0.29, "hi": 6.49 }
d49ad2
nt_num_divisors_compute_v1_153355830_2927
Let $n = 169$. Define $r$ to be the number of positive divisors of $n$. Let $s = \sum_{k=1}^{87} k$. Compute $r^2 + 7r + s$.
3,858
graphs = [ Graph( let={ "_n": Const(7), "n": Const(169), "result": NumDivisors(n=Ref("n")), "_c": Summation(var="k", start=Const(1), end=Const(87), expr=Var("k")), "Q": Sum(Pow(Ref("result"), Const(2)), Mul(Ref("_n"), Ref("result")), Ref("_c")), ...
NT
null
COMPUTE
sympy
MAX_PRIME_BELOW
[ "SUM_ARITHMETIC" ]
609463
nt_num_divisors_compute_v1
quadratic_mod
3
0
[ "MAX_PRIME_BELOW", "SUM_ARITHMETIC" ]
2
0.03
2026-02-08T07:28:50.045632Z
{ "verified": true, "answer": 3858, "timestamp": "2026-02-08T07:28:50.075740Z" }
86d9b3
CC BY 4.0
[ { "id": 8, "model": "mathstral", "score": 0, "correct": { "strict": false, "boxed": false, "relaxed": false }, "usage": { "prompt_tokens": 108, "completion_tokens": 243 }, "timestamp": "2026-02-15T18:59:39.110Z", "answer": 3954 }, { "id": 11,...
1
[ { "lemma": "K18", "status": "no" }, { "lemma": "L3b", "status": "no" }, { "lemma": "LTE_DIFF", "status": "no" }, { "lemma": "SUM_ARITHMETIC", "status": "ok" }, { "lemma": "V7", "status": "no" }, { "lemma": "V8", "status": "no" } ]
{ "lo": -9.14, "mid": -6.05, "hi": -3.73 }
11815a
sequence_count_fib_divisible_v1_168721529_1527
Let $n$ be a positive integer. Define $\text{upper}$ to be the minimum value of $x + y$ over all ordered pairs $(x, y)$ of positive integers such that $xy = 97344$. Define $d$ to be the maximum value of $xy$ over all ordered pairs $(x, y)$ of positive integers such that $x + y = 6$. Determine the value of the number of...
52
graphs = [ Graph( let={ "_m": Const(6), "_n": Const(97344), "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
MIN_PRIME_FACTOR
[ "B3", "B1" ]
655d51
sequence_count_fib_divisible_v1
null
6
0
[ "B1", "B3", "MIN_PRIME_FACTOR" ]
3
0.132
2026-02-08T13:44:47.407270Z
{ "verified": true, "answer": 52, "timestamp": "2026-02-08T13:44:47.539503Z" }
042222
CC BY 4.0
[ { "id": 1, "model": "openai/gpt-oss-20b", "score": 3, "correct": { "strict": true, "boxed": true, "relaxed": true }, "usage": { "prompt_tokens": 234, "completion_tokens": 3242 }, "timestamp": "2026-02-09T18:36:52.115Z", "answer": 52 }, { "id"...
1
[ { "lemma": "B1", "status": "ok" }, { "lemma": "B3", "status": "ok" }, { "lemma": "DS2", "status": "no" }, { "lemma": "K13", "status": "no" }, { "lemma": "L3c", "status": "no" }, { "lemma": "MOD_MUL", "status": "no" }, { "lemma": "VAL_SUM_EQ...
{ "lo": -5.49, "mid": 0.03, "hi": 6.12 }
f5ba92
antilemma_sum_equals_v1_124444284_5679
Compute the number of ordered pairs $(i, j)$ of integers such that $1 \le i \le 41$, $1 \le j \le 41$, and $i + j = 42$.
41
graphs = [ Graph( let={ "_n": Const(42), "x": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("i"), Var("j")]), condition=Eq(Sum(Var("i"), Var("j")), Ref("_n")), domain=CartesianProduct(left=IntegerRange(start=Const(1), end=Const(41)), right=IntegerRange(start=Const(1), end=Con...
COMB
GEOM
COMPUTE
sympy
COUNT_SUM_EQUALS
[ "COUNT_SUM_EQUALS" ]
75ab0f
antilemma_sum_equals_v1
null
3
0
[ "COUNT_SUM_EQUALS" ]
1
0.013
2026-02-08T06:46:18.088342Z
{ "verified": true, "answer": 41, "timestamp": "2026-02-08T06:46:18.101601Z" }
3fbc4b
CC BY 4.0
[ { "id": 1, "model": "openai/gpt-oss-20b", "score": 3, "correct": { "strict": true, "boxed": true, "relaxed": true }, "usage": { "prompt_tokens": 154, "completion_tokens": 231 }, "timestamp": "2026-02-24T07:00:01.636Z", "answer": 41 }, { "id":...
2
[ { "lemma": "C2", "status": "no" }, { "lemma": "COUNT_CARTESIAN", "status": "no" }, { "lemma": "COUNT_COPRIME_GRID", "status": "no" }, { "lemma": "COUNT_INTEGER_RANGE", "status": "no" }, { "lemma": "COUNT_SUM_EQUALS", "status": "ok" }, { "lemma": "V8", ...
{ "lo": -10, "mid": -7.79, "hi": -5.57 }
9649c1
nt_max_prime_below_v1_865884756_6709
Let $p$ be the largest prime number less than or equal to $63001$. Compute the Bell number $B_r$, where $r$ is the remainder when $p$ is divided by $11$.
5
graphs = [ Graph( let={ "upper": Const(63001), "result": MaxOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(2)), Leq(Var("n"), Ref("upper")), IsPrime(Var("n"))))), "Q": Bell(Mod(value=Abs(arg=Ref(name='result')), modulus=Const(11))), }, ...
NT
COMB
EXTREMUM
sympy
MAX_PRIME_BELOW
[ "MAX_PRIME_BELOW" ]
88ea9c
nt_max_prime_below_v1
bell_mod
2
0
[ "MAX_PRIME_BELOW" ]
1
2.743
2026-02-08T19:21:38.629698Z
{ "verified": true, "answer": 5, "timestamp": "2026-02-08T19:21:41.373078Z" }
2319f3
CC BY 4.0
[ { "id": 5, "model": "deepseek-ai/DeepSeek-V3.2", "score": 3, "correct": { "strict": true, "boxed": true, "relaxed": true }, "usage": { "prompt_tokens": 90, "completion_tokens": 4302 }, "timestamp": "2026-02-18T22:04:16.181Z", "answer": 5 }, { ...
1
[ { "lemma": "K17", "status": "no" }, { "lemma": "MAX_PRIME_BELOW", "status": "ok" }, { "lemma": "V3", "status": "no" }, { "lemma": "V5", "status": "no" }, { "lemma": "V7", "status": "no" }, { "lemma": "VAL_SUM_EQ", "status": "no" } ]
{ "lo": -7.08, "mid": -0.29, "hi": 6.49 }
535019
comb_catalan_compute_v1_153355830_935
Let $ n = 10 $ and let $ C_n $ denote the $ n $-th Catalan number. Define $$ S = \sum_{i=a}^{b} d_i (i+1)^2, $$ where $ d_i $ is the $ i $-th decimal digit of $ |C_n| $ (starting from the units digit at $ i = 0 $), $$ a = \sum_{k=0}^{8} (-1)^k \binom{8}{k}, $$ and $ b = \text{number of digits of } |C_n| - 0! $. Let $ Q...
50,226
graphs = [ Graph( let={ "n": Const(10), "result": Catalan(Ref("n")), "_c": Const(50000), "Q": Sum(Summation(var="i", start=Summation(var="k", start=Const(0), end=Const(8), expr=Mul(Pow(Const(-1), Var("k")), Binom(n=Const(8), k=Var("k")))), end=Sub(NumDigits(x=...
COMB
null
COMPUTE
sympy
BINOMIAL_ALTERNATING
[ "BINOMIAL_ALTERNATING", "ONE_FACTORIAL_0" ]
8794cb
comb_catalan_compute_v1
null
4
0
[ "BINOMIAL_ALTERNATING", "ONE_FACTORIAL_0" ]
2
0.002
2026-02-08T04:16:39.842941Z
{ "verified": true, "answer": 50226, "timestamp": "2026-02-08T04:16:39.845047Z" }
088d22
CC BY 4.0
[ { "id": 1, "model": "openai/gpt-oss-20b", "score": 3, "correct": { "strict": true, "boxed": true, "relaxed": true }, "usage": { "prompt_tokens": 258, "completion_tokens": 805 }, "timestamp": "2026-02-24T00:08:57.233Z", "answer": 50226 }, { "i...
1
[ { "lemma": "BINOMIAL_ALTERNATING", "status": "ok" }, { "lemma": "COUNT_CARTESIAN", "status": "no" }, { "lemma": "COUNT_COPRIME_GRID", "status": "no" }, { "lemma": "COUNT_SUM_EQUALS", "status": "no" }, { "lemma": "ONE_FACTORIAL_0", "status": "ok" }, { "...
{ "lo": -2.46, "mid": 0.47, "hi": 3.59 }
d3fc82
sequence_fibonacci_compute_v1_1742523217_902
Let $n$ be the number of ordered pairs $(i,j)$ of positive integers such that $1 \leq i \leq 3$, $1 \leq j \leq 10$, and $\gcd(i,j) = 1$. Let $a = F_n$, where $F_n$ denotes the $n$th Fibonacci number. Compute $$a + \varphi(|a| + 1) + \tau(|a| + 1),$$ where $\varphi(k)$ denotes Euler's totient function and $\tau(k)$ den...
23,511
graphs = [ Graph( let={ "n": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("i"), Var("j")]), condition=Eq(GCD(a=Var("i"), b=Var("j")), Const(1)), domain=CartesianProduct(left=IntegerRange(start=Const(1), end=Const(3)), right=IntegerRange(start=Const(1), end=Const(10))))), "re...
NT
null
COMPUTE
sympy
COUNT_COPRIME_GRID
[ "COUNT_COPRIME_GRID" ]
20ec03
sequence_fibonacci_compute_v1
null
4
0
[ "COUNT_COPRIME_GRID" ]
1
0.002
2026-02-08T03:21:12.467862Z
{ "verified": true, "answer": 23511, "timestamp": "2026-02-08T03:21:12.469552Z" }
5e6bb6
CC BY 4.0
[ { "id": 1, "model": "openai/gpt-oss-20b", "score": 3, "correct": { "strict": true, "boxed": true, "relaxed": true }, "usage": { "prompt_tokens": 245, "completion_tokens": 1146 }, "timestamp": "2026-02-10T00:20:09.393Z", "answer": 23511 }, { "...
1
[ { "lemma": "COUNT_COPRIME_GRID", "status": "ok" }, { "lemma": "COUNT_PRIMES", "status": "no" }, { "lemma": "COUNT_SUM_EQUALS", "status": "no" }, { "lemma": "L3c", "status": "no" }, { "lemma": "MOD_ADD", "status": "no" }, { "lemma": "V5", "status": ...
{ "lo": -3.46, "mid": 1.03, "hi": 5.49 }
89ab46
alg_sum_powers_v1_1218484723_74
Find the remainder when $\sum_{k=1}^{1084} k^2$ is divided by $\left|\left\{ x : 1 \le x \le 7885,\ |4x - 15600| \le 15596 \right\}\right|$.
4,326
graphs = [ Graph( let={ "_n": Const(7885), "result": Mod(value=Summation(var="k", start=Const(1), end=Const(1084), expr=Pow(Var("k"), Const(2))), modulus=CountOverSet(set=SolutionsSet(var=Var("x"), condition=And(Geq(Var("x"), Const(1)), Leq(Var("x"), Ref("_n")), Leq(Abs(arg=Sub(left=...
ALG
null
COMPUTE
sympy
ABS_INEQ
[ "ABS_INEQ" ]
1c5bb8
alg_sum_powers_v1
null
4
0
[ "ABS_INEQ" ]
1
0.052
2026-02-25T01:46:50.932452Z
{ "verified": true, "answer": 4326, "timestamp": "2026-02-25T01:46:50.984187Z" }
e26dd3
CC BY 4.0
[ { "id": 1, "model": "openai/gpt-oss-20b", "score": 3, "correct": { "strict": true, "boxed": true, "relaxed": true }, "usage": { "prompt_tokens": 171, "completion_tokens": 2260 }, "timestamp": "2026-03-10T08:01:15.798Z", "answer": 4326 }, { "i...
1
[ { "lemma": "ABS_INEQ", "status": "ok" }, { "lemma": "POLY_PADIC_VAL_CONST", "status": "no" } ]
{ "lo": -0.93, "mid": 2.04, "hi": 4.6 }
0371e3
algebra_poly_eval_v1_458359167_5108
Let $x = 12$. Define $e$ to be the number of positive integers $p$ for which there exists a positive integer $q$ such that: - $p \cdot q = 54$, - $\gcd(p, q) = 1$, - $p < q$. Let $r = 6x^e - 4x + 3$. Let $Q = (34843 \cdot r) \mod 58087$. Find the value of $Q$.
15,700
graphs = [ Graph( let={ "x": Const(12), "result": Sum(Mul(Const(6), Pow(Ref("x"), CountOverSet(set=SolutionsSet(var=Var("p"), condition=And(IsPositive(arg=Var(name='p')), Exists(var=Var(name='q'), condition=And(Eq(left=Mul(Var(name='p'), Var(name='q')), right=Const(value=54)), Eq(lef...
NT
null
COMPUTE
sympy
COPRIME_PAIRS
[ "COPRIME_PAIRS" ]
2bb3aa
algebra_poly_eval_v1
null
4
0
[ "COPRIME_PAIRS" ]
1
0.002
2026-02-08T12:16:59.665777Z
{ "verified": true, "answer": 15700, "timestamp": "2026-02-08T12:16:59.667705Z" }
1b7439
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": 1355 }, "timestamp": "2026-02-14T23:56:17.255Z", "answer": 15700 }, ...
1
[ { "lemma": "COPRIME_PAIRS", "status": "ok" }, { "lemma": "COUNT_FIB_DIVISIBLE", "status": "no" }, { "lemma": "K14", "status": "no" }, { "lemma": "L3b", "status": "no" }, { "lemma": "MOD_FACTORIAL", "status": "no" }, { "lemma": "POLY_PADIC_VAL_CONST", ...
{ "lo": -5.49, "mid": 0.22, "hi": 6.51 }
6f86f2
comb_binomial_compute_v1_1520064083_9107
Let $m = 72250$ and $n = 88187$. Define $k$ to be the largest prime number $p$ such that $$2 \le p \le \sum_{k=1}^{3} \varphi(k) \left\lfloor \frac{3}{k} \right\rfloor,$$ where $\varphi$ denotes Euler's totient function. Let $r = \binom{12}{k}$. Compute the remainder when $n \cdot r$ is divided by $m$.
50,604
graphs = [ Graph( let={ "_m": Const(72250), "_n": Const(88187), "n": Const(12), "k": MaxOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(2)), Leq(Var("n"), Summation(var="k", start=Const(1), end=Const(3), expr=Mul(EulerPhi(n=Var("k")), ...
NT
null
COMPUTE
sympy
K2
[ "K2/MAX_PRIME_BELOW" ]
f058da
comb_binomial_compute_v1
null
5
0
[ "K2", "MAX_PRIME_BELOW" ]
2
0.005
2026-02-08T10:32:53.577235Z
{ "verified": true, "answer": 50604, "timestamp": "2026-02-08T10:32:53.581765Z" }
4dc9c1
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": 1567 }, "timestamp": "2026-02-14T07:40:31.537Z", "answer": 50604 }, ...
1
[ { "lemma": "C2", "status": "no" }, { "lemma": "COUNT_PRIMES", "status": "no" }, { "lemma": "K2", "status": "ok" }, { "lemma": "LTE_SUM", "status": "no" }, { "lemma": "MAX_PRIME_BELOW", "status": "ok_later" }, { "lemma": "V1", "status": "no" }, ...
{ "lo": -5.14, "mid": 0.32, "hi": 6.51 }
f9e80a
nt_gcd_compute_v1_677425708_1505
Let $a_1 = 1591$ and let $b_1$ be the smallest divisor of $212341$ that is at least $2$. Let $w = \sum_{d \mid \gcd(a_1, b_1)} \mu(d)$, where $\mu$ is the M\"obius function. Let $m = \mu(23)^2$. Define $a = 318535$ and $b = 591565 \cdot w \cdot m$. Compute $\gcd(a, b)$.
45,505
graphs = [ Graph( let={ "_n": Const(2), "a1": Const(1591), "b1": MinOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Ref("_n")), Divides(divisor=Var("d"), dividend=Const(212341))))), "w": SumOverDivisors(n=GCD(a=Ref(name='a1'), b=Ref(name='b1...
NT
null
COMPUTE
sympy
MIN_PRIME_FACTOR
[ "MIN_PRIME_FACTOR/MOBIUS_COPRIME", "MOBIUS_SQUAREFREE" ]
931c50
nt_gcd_compute_v1
null
6
2
[ "MIN_PRIME_FACTOR", "MOBIUS_COPRIME", "MOBIUS_SQUAREFREE" ]
3
0.002
2026-02-08T04:14:01.536681Z
{ "verified": true, "answer": 45505, "timestamp": "2026-02-08T04:14:01.538446Z" }
bdabae
CC BY 4.0
[ { "id": 1, "model": "openai/gpt-oss-20b", "score": 3, "correct": { "strict": true, "boxed": true, "relaxed": true }, "usage": { "prompt_tokens": 225, "completion_tokens": 7015 }, "timestamp": "2026-02-09T20:48:47.117Z", "answer": 45505 }, { "...
1
[ { "lemma": "C2", "status": "no" }, { "lemma": "COUNT_DIVISOR_COUNT", "status": "no" }, { "lemma": "L3b", "status": "no" }, { "lemma": "MIN_PRIME_FACTOR", "status": "ok" }, { "lemma": "MOBIUS_COPRIME", "status": "ok_later" }, { "lemma": "MOBIUS_SQUAREFR...
{ "lo": -6.5, "mid": -0.2, "hi": 6.11 }
96e4a9
comb_catalan_compute_v1_1520064083_5852
Let $k$ be the number of ordered pairs $(x_1, x_2)$ of positive odd integers such that $x_1 + x_2 = 44$. Let $n$ be the number of ordered pairs $(x_1, x_2)$ of positive odd integers such that $x_1 + x_2 = k$. Let $C_n$ denote the $n$-th Catalan number. Compute $94249 - C_n$.
35,463
graphs = [ Graph( let={ "n": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x1"), Var("x2")]), condition=And(IsPositive(arg=Var(name='x1')), IsPositive(arg=Var(name='x2')), IsOdd(arg=Var(name='x1')), IsOdd(arg=Var(name='x2')), Eq(Sum(Var("x1"), Var("x2")), CountOverSet(set=SolutionsSet(v...
COMB
null
COMPUTE
sympy
COMB1
[ "COMB1/COMB1" ]
b2c526
comb_catalan_compute_v1
null
5
0
[ "COMB1" ]
1
0.002
2026-02-08T07:40:55.064687Z
{ "verified": true, "answer": 35463, "timestamp": "2026-02-08T07:40:55.066940Z" }
918e9e
CC BY 4.0
[ { "id": 1, "model": "openai/gpt-oss-20b", "score": 3, "correct": { "strict": true, "boxed": true, "relaxed": true }, "usage": { "prompt_tokens": 207, "completion_tokens": 2842 }, "timestamp": "2026-02-24T08:19:34.725Z", "answer": 35463 }, { "...
1
[ { "lemma": "C2", "status": "no" }, { "lemma": "COMB1", "status": "ok" }, { "lemma": "COUNT_COPRIME_GRID", "status": "no" }, { "lemma": "V7", "status": "no" }, { "lemma": "V8", "status": "no" }, { "lemma": "V8_SUM", "status": "no" } ]
{ "lo": -4.92, "mid": -2.91, "hi": -0.68 }
09f2c8
nt_count_divisible_and_v1_1978505735_5990
Let $A$ be the number of positive integers $n$ such that $n \leq 110304$, $n$ is divisible by 9, and $n$ is divisible by 12. Let $S$ be the set of all ordered pairs $(a,b)$ of positive integers such that $1 \leq a \leq 11$, $1 \leq b \leq 4$, and $t = 8a + 10b + 7$ satisfies $25 \leq t \leq 135$. Let $m = |S|$. Let $P$...
50,165
graphs = [ Graph( let={ "_n": Const(52745), "upper": Const(110304), "d1": Const(9), "d2": Const(12), "result": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Ref("upper")), Eq(Mod(value=Var("n"), mo...
NT
null
COUNT
sympy
LIN_FORM
[ "LIN_FORM/B1" ]
36d1f4
nt_count_divisible_and_v1
negation_mod
6
0
[ "B1", "LIN_FORM" ]
2
3.465
2026-02-08T19:21:51.317287Z
{ "verified": true, "answer": 50165, "timestamp": "2026-02-08T19:21:54.782493Z" }
92a18d
CC BY 4.0
[ { "id": 5, "model": "deepseek-ai/DeepSeek-V3.2", "score": 3, "correct": { "strict": true, "boxed": true, "relaxed": true }, "usage": { "prompt_tokens": 223, "completion_tokens": 1556 }, "timestamp": "2026-02-18T22:04:16.746Z", "answer": 50165 }, ...
1
[ { "lemma": "B1", "status": "ok_later" }, { "lemma": "COUNT_PRIMES", "status": "no" }, { "lemma": "DS2", "status": "no" }, { "lemma": "L3b", "status": "no" }, { "lemma": "LIN_FORM", "status": "ok" }, { "lemma": "LTE_DIFF_P2", "status": "no" }, {...
{ "lo": -7.08, "mid": -0.29, "hi": 6.49 }
ebba60_n
alg_qf_psd_count_v1_1218484723_6873
A shipping company numbers its containers from $1$ to $112112$. A container is marked "bulk" if its number is divisible by $44$. Let $M$ be the total number of bulk containers. An engineer studies the set of values $v$ between $13$ and $M$ for which there exist dimensions $a$ and $b$ (in meters) with $1 \le a \le 14$ a...
10
ALG
null
COUNT
sympy
POLY3_COUNT
[ "C2/QF_PSD_DISTINCT" ]
389a25
alg_qf_psd_count_v1
null
7
null
[ "C2", "POLY3_COUNT", "QF_PSD_DISTINCT" ]
3
3.825
2026-02-25T08:19:51.596019Z
null
729fd4
ebba60
narrative
CC BY 4.0
[ { "id": 1, "model": "openai/gpt-oss-20b", "score": 1, "correct": { "strict": false, "boxed": false, "relaxed": true }, "usage": { "prompt_tokens": 322, "completion_tokens": 32768 }, "timestamp": "2026-03-31T01:56:04.291Z", "answer": null }, { ...
1
[ { "lemma": "C2", "status": "ok" }, { "lemma": "COUNT_PRIMES", "status": "no" }, { "lemma": "K13", "status": "no" }, { "lemma": "MOD_SUB", "status": "no" }, { "lemma": "QF_PSD_DISTINCT", "status": "ok_later" }, { "lemma": "V5", "status": "no" }, ...
{ "lo": 1.5, "mid": 4.69, "hi": 7.23 }
02a01d
nt_count_gcd_equals_v1_1520064083_4237
Let $k$ be the minimum value of $x + y$ over all pairs of positive integers $(x, y)$ such that $xy = 10201$. Let $d$ be the number of positive integers $n$ such that $1 \leq n \leq 40320$ and $\gcd(n, k) = 2$. Compute the remainder when $31447 \cdot d$ is divided by $59200$.
15,967
graphs = [ Graph( let={ "_n": Const(59200), "upper": Const(40320), "k": MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(Mul(Var("x"), Var("y")), Const(10201...
NT
null
COUNT
sympy
B3
[ "B3" ]
0cd20d
nt_count_gcd_equals_v1
null
5
0
[ "B3" ]
1
3.219
2026-02-08T06:10:11.348601Z
{ "verified": true, "answer": 15967, "timestamp": "2026-02-08T06:10:14.567478Z" }
e92493
CC BY 4.0
[ { "id": 5, "model": "deepseek-ai/DeepSeek-V3.2", "score": 3, "correct": { "strict": true, "boxed": true, "relaxed": true }, "usage": { "prompt_tokens": 136, "completion_tokens": 2356 }, "timestamp": "2026-02-12T20:18:32.058Z", "answer": 15967 }, ...
1
[ { "lemma": "B3", "status": "ok" }, { "lemma": "K16", "status": "no" }, { "lemma": "MOD_ADD", "status": "no" }, { "lemma": "MOD_MUL", "status": "no" }, { "lemma": "MOD_SUB", "status": "no" }, { "lemma": "VAL_SUM_EQ", "status": "no" } ]
{ "lo": -3.44, "mid": 1.34, "hi": 6.56 }
c6608f
sequence_count_fib_divisible_v1_784195855_6411
Let $u$ be the number of positive integers $n$ such that $1 \leq n \leq 6454$ and $13$ divides the $n$-th Fibonacci number. Let $d = 5$. Compute the number of positive integers $n$ such that $1 \leq n \leq u$ and $d$ divides the $n$-th Fibonacci number.
184
graphs = [ Graph( let={ "_n": Const(13), "upper": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Const(6454)), Divides(divisor=Ref("_n"), dividend=Fibonacci(arg=Var(name='n')))))), "d": Const(5), "result": Coun...
NT
null
COUNT
sympy
L3B
[ "COUNT_FIB_DIVISIBLE" ]
66de3c
sequence_count_fib_divisible_v1
null
6
0
[ "COUNT_FIB_DIVISIBLE", "L3B" ]
2
0.098
2026-02-08T08:39:02.252260Z
{ "verified": true, "answer": 184, "timestamp": "2026-02-08T08:39:02.350607Z" }
f157a7
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": 1751 }, "timestamp": "2026-02-13T20:07:16.775Z", "answer": 184 }, { ...
1
[ { "lemma": "C2", "status": "no" }, { "lemma": "COUNT_FIB_DIVISIBLE", "status": "ok" }, { "lemma": "DS2", "status": "no" }, { "lemma": "K18", "status": "no" }, { "lemma": "LTE_DIFF", "status": "no" }, { "lemma": "MAX_PRIME_BELOW", "status": "no" }...
{ "lo": -3.44, "mid": 1.34, "hi": 6.56 }
3c2000
algebra_poly_eval_v1_784195855_1699
Let $n$ be an integer. Define $b$ to be the largest prime number $n$ such that $2 \leq n \leq 17$. Compute the value of $$ \frac{b^5 + 11b^4 - 30b^3 - 61b^2 - 123b - 78}{30}. $$Then let $Q$ be the remainder when $32881$ times this value is divided by $95006$. Find the value of $Q$.
26,480
graphs = [ Graph( let={ "_n": Const(17), "b": MaxOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(2)), Leq(Var("n"), Ref("_n")), IsPrime(Var("n"))))), "result": Div(Sum(Pow(Ref("b"), Const(5)), Mul(Const(11), Pow(Ref("b"), Const(4))), Mul(Const(-30...
NT
null
COMPUTE
sympy
MAX_PRIME_BELOW
[ "MAX_PRIME_BELOW" ]
dc3ad3
algebra_poly_eval_v1
null
6
0
[ "MAX_PRIME_BELOW" ]
1
0.003
2026-02-08T05:13:53.757071Z
{ "verified": true, "answer": 26480, "timestamp": "2026-02-08T05:13:53.760556Z" }
b118b3
CC BY 4.0
[ { "id": 5, "model": "deepseek-ai/DeepSeek-V3.2", "score": 3, "correct": { "strict": true, "boxed": true, "relaxed": true }, "usage": { "prompt_tokens": 149, "completion_tokens": 1360 }, "timestamp": "2026-02-12T06:09:11.524Z", "answer": 26480 }, ...
1
[ { "lemma": "COUNT_FIB_DIVISIBLE", "status": "no" }, { "lemma": "K5", "status": "no" }, { "lemma": "MAX_PRIME_BELOW", "status": "ok" }, { "lemma": "POLY_PADIC_VAL_CONST", "status": "no" }, { "lemma": "V3", "status": "no" }, { "lemma": "V8", "status"...
{ "lo": -3.51, "mid": 1.33, "hi": 6.56 }
ffe56e
geo_visible_lattice_v1_1520064083_1618
Let $n = 55$. Define $\text{result}$ to be the number of ordered pairs $(x, y)$ of positive integers such that $1 \leq x, y \leq n$ and $\gcd(x, y) = 1$. Let $Q$ be the remainder when $44121 \cdot \text{result}$ is divided by $52825$. Compute $Q$.
20,934
graphs = [ Graph( let={ "n": Const(55), "result": VisibleLatticePoints(n=Ref(name='n')), "Q": Mod(value=Mul(Const(44121), Ref("result")), modulus=Const(52825)), }, goal=Ref("Q"), ) ]
GEOM
null
COUNT
sympy
[]
geo_visible_lattice_v1
null
4
0
null
null
1.687
2026-02-08T04:08:23.856248Z
{ "verified": true, "answer": 20934, "timestamp": "2026-02-08T04:08:25.542765Z" }
edeec9
CC BY 4.0
[ { "id": 1, "model": "openai/gpt-oss-20b", "score": 3, "correct": { "strict": true, "boxed": true, "relaxed": true }, "usage": { "prompt_tokens": 195, "completion_tokens": 30246 }, "timestamp": "2026-02-23T23:46:25.976Z", "answer": 20934 }, { ...
1
[]
{ "lo": 1.97, "mid": 4.36, "hi": 6.69 }
ff56ed
sequence_fibonacci_compute_v1_1520064083_7110
Let $n$ be the number of integers $t$ such that $24 \le t \le 108$ and there exist integers $a$ and $b$ with $1 \le a \le 7$, $1 \le b \le 3$, and $t = 9a + 15b$. Let $F_n$ denote the $n$th Fibonacci number, where $F_1 = F_2 = 1$ and $F_k = F_{k-1} + F_{k-2}$ for $k \ge 3$. Compute the remainder when $75433 \cdot F_n$ ...
10,544
graphs = [ Graph( let={ "_n": Const(75433), "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=7)), Geq(left=Va...
NT
null
COMPUTE
sympy
LIN_FORM
[ "LIN_FORM" ]
7b2633
sequence_fibonacci_compute_v1
null
5
0
[ "LIN_FORM" ]
1
0.001
2026-02-08T08:45:59.489076Z
{ "verified": true, "answer": 10544, "timestamp": "2026-02-08T08:45:59.490163Z" }
81e5e2
CC BY 4.0
[ { "id": 5, "model": "deepseek-ai/DeepSeek-V3.2", "score": 3, "correct": { "strict": true, "boxed": true, "relaxed": true }, "usage": { "prompt_tokens": 187, "completion_tokens": 2625 }, "timestamp": "2026-02-13T21:31:01.156Z", "answer": 10544 }, ...
1
[ { "lemma": "COUNT_PRIMES", "status": "no" }, { "lemma": "LIN_FORM", "status": "ok" }, { "lemma": "MOD_ADD", "status": "no" }, { "lemma": "MOD_MUL", "status": "no" }, { "lemma": "V7", "status": "no" }, { "lemma": "V8_SUM", "status": "no" } ]
{ "lo": -3.44, "mid": 1.34, "hi": 6.56 }
55c3cd
algebra_poly_eval_v1_677425708_1238
Let $m = 16908$ and $n = 67375$. Define $t$ to be the number of nonnegative integers $j$ such that $0 \le j \le m$ and $\binom{m}{j}$ is odd. Let $d_0$ be the smallest divisor of $n$ that is at least $2$. Compute the value of $t^4 + d_0 \cdot t^3 + 3t^2 - 10t + 8$.
86,632
graphs = [ Graph( let={ "_m": Const(16908), "_n": Const(67375), "t": CountOverSet(set=SolutionsSet(var=Var("j"), condition=And(Geq(Var("j"), Const(0)), Leq(Var("j"), Const(16908)), Eq(Mod(value=Binom(n=Ref("_m"), k=Var("j")), modulus=Const(2)), Const(1))), domain='nonnega...
NT
null
COMPUTE
sympy
MIN_PRIME_FACTOR
[ "MIN_PRIME_FACTOR", "V8" ]
aeb95e
algebra_poly_eval_v1
null
6
0
[ "MIN_PRIME_FACTOR", "V8" ]
2
0.003
2026-02-08T04:02:52.877966Z
{ "verified": true, "answer": 86632, "timestamp": "2026-02-08T04:02:52.881000Z" }
0c2476
CC BY 4.0
[ { "id": 1, "model": "openai/gpt-oss-20b", "score": 3, "correct": { "strict": true, "boxed": true, "relaxed": true }, "usage": { "prompt_tokens": 217, "completion_tokens": 2329 }, "timestamp": "2026-02-09T17:23:36.489Z", "answer": 86632 }, { "...
1
[ { "lemma": "COUNT_DIVISOR_COUNT", "status": "no" }, { "lemma": "COUNT_PRIMES", "status": "no" }, { "lemma": "DS2", "status": "no" }, { "lemma": "MIN_PRIME_FACTOR", "status": "ok" }, { "lemma": "MOD_FACTORIAL", "status": "no" }, { "lemma": "MOD_SUB", ...
{ "lo": -3.46, "mid": 1.03, "hi": 5.49 }
eaf96b
antilemma_k3_v1_1520064083_5631
Compute the sum of $\phi(d)$ over all positive divisors $d$ of $46583$, where $\phi$ is Euler's totient function.
46,583
graphs = [ Graph( let={ "_n": Const(46583), "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
2026-02-08T07:30:16.846917Z
{ "verified": true, "answer": 46583, "timestamp": "2026-02-08T07:30:16.847470Z" }
6c83d0
CC BY 4.0
[ { "id": 5, "model": "deepseek-ai/DeepSeek-V3.2", "score": 3, "correct": { "strict": true, "boxed": true, "relaxed": true }, "usage": { "prompt_tokens": 77, "completion_tokens": 4072 }, "timestamp": "2026-02-13T10:48:11.400Z", "answer": 46583 }, {...
1
[ { "lemma": "COUNT_DIVISOR_COUNT", "status": "no" }, { "lemma": "COUNT_PRIMES", "status": "no" }, { "lemma": "K3", "status": "ok" }, { "lemma": "L3b", "status": "no" }, { "lemma": "LTE_DIFF_P2", "status": "no" }, { "lemma": "MAX_VAL", "status": "no"...
{ "lo": -3.51, "mid": 1.33, "hi": 6.56 }
de2998
antilemma_k2_v1_1125832087_2027
Let $x = \sum_{k=1}^{61} \phi(k) \left\lfloor \frac{61}{k} \right\rfloor$, where $\phi(k)$ denotes Euler's totient function. Let $Q$ be the remainder when $2676x$ is divided by $99991$. Compute $Q$.
60,766
graphs = [ Graph( let={ "x": Summation(var="k", start=Const(1), end=Const(61), expr=Mul(EulerPhi(n=Var("k")), Floor(Div(Const(61), Var("k"))))), "Q": Mod(value=Mul(Const(2676), Ref("x")), modulus=Const(99991)), }, goal=Ref("Q"), ) ]
NT
COMB
COMPUTE
sympy
K2
[ "K2" ]
6897ab
antilemma_k2_v1
null
5
0
[ "K2" ]
1
0.001
2026-02-08T04:17:30.130980Z
{ "verified": true, "answer": 60766, "timestamp": "2026-02-08T04:17:30.132071Z" }
0d6557
CC BY 4.0
[ { "id": 2, "model": "openai/gpt-oss-120b", "score": 3, "correct": { "strict": true, "boxed": true, "relaxed": true }, "usage": { "prompt_tokens": 181, "completion_tokens": 912 }, "timestamp": "2026-02-10T16:05:23.664Z", "answer": 60766 }, { "...
1
[ { "lemma": "DS2", "status": "no" }, { "lemma": "K16", "status": "no" }, { "lemma": "K2", "status": "ok" }, { "lemma": "K5", "status": "no" }, { "lemma": "LTE_DIFF", "status": "no" }, { "lemma": "V7", "status": "no" } ]
{ "lo": -3.42, "mid": 1.86, "hi": 7.55 }
9ad3e8
nt_count_divisors_in_range_v1_1742523217_4707
Determine the number of positive divisors $d$ of 5040 such that $34 \leq d \leq 5042$. Let this number be $r$. Compute $r^2 + 19r + 76^2$.
8,136
graphs = [ Graph( let={ "_n": Const(2), "n": Const(5040), "a": Const(34), "b": Const(5042), "result": CountOverSet(set=SolutionsSet(var=Var("d"), condition=And(Divides(divisor=Var("d"), dividend=Ref("n")), Geq(Var("d"), Ref("a")), Leq(Var("d"), Ref...
NT
null
COUNT
sympy
COUNT_CARTESIAN
[ "COUNT_CARTESIAN" ]
a1d5cf
nt_count_divisors_in_range_v1
quadratic_mod
3
0
[ "COUNT_CARTESIAN" ]
1
0.046
2026-02-08T09:05:52.079922Z
{ "verified": true, "answer": 8136, "timestamp": "2026-02-08T09:05:52.125699Z" }
7fdb8e
CC BY 4.0
[ { "id": 5, "model": "deepseek-ai/DeepSeek-V3.2", "score": 3, "correct": { "strict": true, "boxed": true, "relaxed": true }, "usage": { "prompt_tokens": 95, "completion_tokens": 2091 }, "timestamp": "2026-02-14T00:19:44.063Z", "answer": 8136 }, { ...
1
[ { "lemma": "COUNT_CARTESIAN", "status": "ok" }, { "lemma": "COUNT_DIVISOR_COUNT", "status": "no" }, { "lemma": "L3b", "status": "no" }, { "lemma": "MOD_MUL", "status": "no" }, { "lemma": "POLY_PADIC_VAL_CONST", "status": "no" }, { "lemma": "V5", "s...
{ "lo": -3.44, "mid": 1.34, "hi": 6.56 }
abba56_n
alg_qf_psd_orbit_v1_1419126231_319
A game board consists of tiles arranged in rectangular grids, each with dimensions $a \times b$ where $1 \le a \le b \le 191$. A tile configuration is valid if $16a^2 + 16b^2 = 442000$. How many valid configurations exist?
8
ALG
null
COUNT
sympy
MAX_PRIME_BELOW
[ "MAX_PRIME_BELOW" ]
dc3ad3
alg_qf_psd_orbit_v1
null
4
null
[ "MAX_PRIME_BELOW" ]
1
0.057
2026-02-25T09:50:08.682072Z
null
db2825
abba56
narrative
CC BY 4.0
[ { "id": 1, "model": "openai/gpt-oss-20b", "score": 3, "correct": { "strict": true, "boxed": true, "relaxed": true }, "usage": { "prompt_tokens": 172, "completion_tokens": 21413 }, "timestamp": "2026-03-31T03:33:39.394Z", "answer": 8 }, { "id"...
1
[ { "lemma": "K17", "status": "no" }, { "lemma": "LTE_SUM", "status": "no" }, { "lemma": "MAX_PRIME_BELOW", "status": "ok" }, { "lemma": "MOD_ADD", "status": "no" }, { "lemma": "V1", "status": "no" }, { "lemma": "V7", "status": "no" } ]
{ "lo": -5.37, "mid": 0.23, "hi": 5.22 }
857ea3
modular_modexp_compute_v1_1915831931_2056
Let $e$ be the minimum value of $x + y$ over all ordered pairs $(x,y)$ of positive integers such that $xy = 197136$. Compute the remainder when $13^e$ is divided by $81225$.
59,671
graphs = [ Graph( let={ "a": Const(13), "e": MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(Mul(Var("x"), Var("y")), Const(197136)))), expr=Sum(Var("x"), Var("y")))), ...
NT
null
COMPUTE
sympy
B3
[ "B3" ]
0cd20d
modular_modexp_compute_v1
null
4
0
[ "B3" ]
1
0.001
2026-02-08T16:36:14.841326Z
{ "verified": true, "answer": 59671, "timestamp": "2026-02-08T16:36:14.842325Z" }
b5f170
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": 3612 }, "timestamp": "2026-02-17T07:37:50.065Z", "answer": 59671 }, {...
1
[ { "lemma": "B3", "status": "ok" }, { "lemma": "K16", "status": "no" }, { "lemma": "K5", "status": "no" }, { "lemma": "MOD_FACTORIAL", "status": "no" }, { "lemma": "POLY_PADIC_VAL_CONST", "status": "no" }, { "lemma": "VAL_SUM_EQ", "status": "no" }...
{ "lo": -7.08, "mid": -0.29, "hi": 6.49 }
bbd883
antilemma_v7_kummer_458359167_278
Let $S$ be the set of all ordered pairs $(x, y)$ of positive integers such that $xy = 2500$. Let $n$ be the minimum value of $x + y$ over all such pairs. Let $m = 2$, and let $k$ be the largest integer such that $m^k$ divides $\binom{n}{40}$. Compute the remainder when $44121 \cdot k$ is divided by $95855$.
36,508
graphs = [ Graph( let={ "_m": Const(2), "_n": MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(Mul(Var("x"), Var("y")), Const(2500)))), expr=Sum(Var("x"), Var("y")))), ...
NT
null
COMPUTE
sympy
B3
[ "B3/V7", "V7" ]
664b43
antilemma_v7_kummer
null
6
0
[ "B3", "V7" ]
2
0.001
2026-02-08T03:09:46.131797Z
{ "verified": true, "answer": 36508, "timestamp": "2026-02-08T03:09:46.132864Z" }
503c7f
CC BY 4.0
[ { "id": 8, "model": "mathstral", "score": 3, "correct": { "strict": true, "boxed": true, "relaxed": true }, "usage": { "prompt_tokens": 205, "completion_tokens": 1047 }, "timestamp": "2026-02-17T20:18:03.268Z", "answer": 36508 } ]
2
[ { "lemma": "B3", "status": "ok" }, { "lemma": "COUNT_CARTESIAN", "status": "no" }, { "lemma": "K14", "status": "no" }, { "lemma": "L3c", "status": "no" }, { "lemma": "V7", "status": "ok" }, { "lemma": "V8", "status": "no" }, { "lemma": "V8_...
{ "lo": -10, "mid": -6.47, "hi": -2.95 }
776f1c
antilemma_count_primes_v1_677425708_1686
Compute the number of prime numbers $ n $ such that $ 2 \leq n \leq 1117 $.
187
graphs = [ Graph( let={ "x": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(2)), Leq(Var("n"), Const(1117)), IsPrime(Var("n"))))), }, goal=Ref("x"), ) ]
NT
null
COMPUTE
sympy
COUNT_PRIMES
[ "COUNT_PRIMES" ]
07c874
antilemma_count_primes_v1
null
4
0
[ "COUNT_PRIMES" ]
1
0.001
2026-02-08T04:22:25.791153Z
{ "verified": true, "answer": 187, "timestamp": "2026-02-08T04:22:25.791829Z" }
7c70b7
CC BY 4.0
[ { "id": 1, "model": "openai/gpt-oss-20b", "score": 3, "correct": { "strict": true, "boxed": true, "relaxed": true }, "usage": { "prompt_tokens": 136, "completion_tokens": 7378 }, "timestamp": "2026-02-09T23:30:29.081Z", "answer": 187 }, { "id...
1
[ { "lemma": "COUNT_PRIMES", "status": "ok" }, { "lemma": "K13", "status": "no" }, { "lemma": "LTE_DIFF", "status": "no" }, { "lemma": "MOD_FACTORIAL", "status": "no" }, { "lemma": "MOD_SUB", "status": "no" }, { "lemma": "V8_SUM", "status": "no" } ...
{ "lo": -6.5, "mid": -0.2, "hi": 6.11 }
f4f382
algebra_poly_eval_v1_865884756_2404
Let $m = 6$. Define $p$ to be the number of positive integers $a$ for which there exists a positive integer $b$ such that $a \cdot b = 4410$, $\gcd(a, b) = 1$, and $a < b$. Compute the value of $$ p \cdot m^3 - 10m^2 - 3m + 1. $$
1,351
graphs = [ Graph( let={ "m": Const(6), "result": Sum(Mul(CountOverSet(set=SolutionsSet(var=Var("p"), condition=And(IsPositive(arg=Var(name='p')), Exists(var=Var(name='q'), condition=And(Eq(left=Mul(Var(name='p'), Var(name='q')), right=Const(value=4410)), Eq(left=GCD(a=Var(name='p'), ...
NT
null
COMPUTE
sympy
COPRIME_PAIRS
[ "COPRIME_PAIRS" ]
2bb3aa
algebra_poly_eval_v1
null
5
0
[ "COPRIME_PAIRS" ]
1
0.003
2026-02-08T16:45:57.339322Z
{ "verified": true, "answer": 1351, "timestamp": "2026-02-08T16:45:57.342541Z" }
b133a3
CC BY 4.0
[ { "id": 5, "model": "deepseek-ai/DeepSeek-V3.2", "score": 3, "correct": { "strict": true, "boxed": true, "relaxed": true }, "usage": { "prompt_tokens": 133, "completion_tokens": 1314 }, "timestamp": "2026-02-17T11:04:48.895Z", "answer": 1351 }, {...
1
[ { "lemma": "COPRIME_PAIRS", "status": "ok" }, { "lemma": "COUNT_COPRIME_GRID", "status": "no" }, { "lemma": "L3b", "status": "no" }, { "lemma": "L3c", "status": "no" }, { "lemma": "MAX_VAL", "status": "no" }, { "lemma": "V5", "status": "no" } ]
{ "lo": -7.08, "mid": -0.29, "hi": 6.49 }
be52fd
alg_telescope_v1_1419126231_59
Find the remainder when $$\sum_{k=0}^{m} (3k^2 + 3k + 1)$$ is divided by $5148$, where $m = \min\{x + y \mid x, y > 0,\ xy = 727609\}$.
4,419
graphs = [ Graph( let={ "_n": Const(5148), "result": Mod(value=Summation(var="k", start=Const(0), end=MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(Mul(Var("x"), Var(...
ALG
null
COMPUTE
sympy
B3
[ "B3" ]
0cd20d
alg_telescope_v1
null
5
0
[ "B3" ]
1
0.108
2026-02-25T09:36:54.622245Z
{ "verified": true, "answer": 4419, "timestamp": "2026-02-25T09:36:54.730025Z" }
67a283
CC BY 4.0
[ { "id": 1, "model": "openai/gpt-oss-20b", "score": 3, "correct": { "strict": true, "boxed": true, "relaxed": true }, "usage": { "prompt_tokens": 173, "completion_tokens": 10388 }, "timestamp": "2026-03-30T06:46:31.363Z", "answer": 4419 }, { "...
1
[ { "lemma": "B3", "status": "ok" }, { "lemma": "POLY_PADIC_VAL_CONST", "status": "no" } ]
{ "lo": -3.33, "mid": 1.03, "hi": 5.26 }
033d28
comb_catalan_compute_v1_153355830_1968
Let $n$ be the number of integers $t$ in the range $21 \leq t \leq 60$ for which there exist integers $a$ and $b$ with $1 \leq a \leq 2$, $1 \leq b \leq 5$, and $t = 15a + 6b$. Compute the remainder when $44121$ times the $n$-th Catalan number is divided by $85555$.
64,461
graphs = [ Graph( let={ "_n": Const(85555), "n": CountOverSet(set=SolutionsSet(var=Var("t"), condition=Exists(var=Var(name='a'), condition=Exists(var=Var(name='b'), condition=And(Geq(left=Var(name='a'), right=Const(value=1)), Leq(left=Var(name='a'), right=Const(value=2)), Geq(left=Va...
COMB
null
COMPUTE
sympy
LIN_FORM
[ "LIN_FORM" ]
7b2633
comb_catalan_compute_v1
null
5
0
[ "LIN_FORM" ]
1
0.003
2026-02-08T06:49:53.088098Z
{ "verified": true, "answer": 64461, "timestamp": "2026-02-08T06:49:53.091281Z" }
a881b0
CC BY 4.0
[ { "id": 1, "model": "openai/gpt-oss-20b", "score": 3, "correct": { "strict": true, "boxed": true, "relaxed": true }, "usage": { "prompt_tokens": 211, "completion_tokens": 2434 }, "timestamp": "2026-02-24T07:07:33.640Z", "answer": 64461 }, { "...
1
[ { "lemma": "COUNT_CARTESIAN", "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": -2.46, "mid": 0.47, "hi": 3.59 }
6a2a21
sequence_count_fib_divisible_v1_1915831931_3199
Let $S$ be the set of all positive integers $n$ such that $n \leq \sum_{k=1}^{30} k$ and $6$ divides the $n$-th Fibonacci number $F_n$. Compute the number of elements in $S$.
38
graphs = [ Graph( let={ "upper": Summation(var="k", start=Const(1), end=Const(30), expr=Var("k")), "d": Const(6), "result": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Ref("upper")), Divides(divisor=Ref("d"), dividend=F...
NT
null
COUNT
sympy
SUM_ARITHMETIC
[ "SUM_ARITHMETIC" ]
eb34f0
sequence_count_fib_divisible_v1
null
4
0
[ "SUM_ARITHMETIC" ]
1
0.021
2026-02-08T17:24:57.064414Z
{ "verified": true, "answer": 38, "timestamp": "2026-02-08T17:24:57.085816Z" }
a3822c
CC BY 4.0
[ { "id": 5, "model": "deepseek-ai/DeepSeek-V3.2", "score": 3, "correct": { "strict": true, "boxed": true, "relaxed": true }, "usage": { "prompt_tokens": 103, "completion_tokens": 1172 }, "timestamp": "2026-02-18T02:53:56.783Z", "answer": 38 }, { ...
1
[ { "lemma": "COUNT_DIVISOR_COUNT", "status": "no" }, { "lemma": "COUNT_PRIMES", "status": "no" }, { "lemma": "K13", "status": "no" }, { "lemma": "K15", "status": "no" }, { "lemma": "MOD_SUB", "status": "no" }, { "lemma": "SUM_ARITHMETIC", "status": ...
{ "lo": -7.08, "mid": -0.29, "hi": 6.49 }
8d5069
nt_count_coprime_and_v1_124444284_6017
Let $n = 5$. Let $U$ be the number of ordered pairs $(a,b)$ such that $1 \leq a \leq 16$ and $1 \leq b \leq 577$. Let $k_1 = 8$ and $k_2 = \sum_{i=1}^{n} i$. Compute the number of positive integers $m$ such that $1 \leq m \leq U$, $\gcd(m, k_1) = 1$, and $\gcd(m, k_2) = 1$.
2,462
graphs = [ Graph( let={ "_n": Const(5), "upper": CountOverSet(set=CartesianProduct(left=IntegerRange(start=Const(1), end=Const(16)), right=IntegerRange(start=Const(1), end=Const(577)))), "k1": Const(8), "k2": Summation(var="k", start=Const(1), end=Ref("_n"), e...
NT
null
COUNT
sympy
COUNT_CARTESIAN
[ "COUNT_CARTESIAN", "SUM_ARITHMETIC" ]
b1d095
nt_count_coprime_and_v1
null
5
0
[ "COUNT_CARTESIAN", "SUM_ARITHMETIC" ]
2
1.666
2026-02-08T06:59:05.062832Z
{ "verified": true, "answer": 2462, "timestamp": "2026-02-08T06:59:06.728788Z" }
1ae422
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": 1307 }, "timestamp": "2026-02-13T14:35:33.419Z", "answer": 2462 }, {...
1
[ { "lemma": "COUNT_CARTESIAN", "status": "ok" }, { "lemma": "COUNT_FIB_DIVISIBLE", "status": "no" }, { "lemma": "K14", "status": "no" }, { "lemma": "SUM_ARITHMETIC", "status": "ok" }, { "lemma": "V1", "status": "no" }, { "lemma": "V3", "status": "no...
{ "lo": -3.44, "mid": 1.34, "hi": 6.56 }
fcdbe8
alg_poly3_min_v1_601307018_5928
Find the remainder when the minimum value of $-375a^2b - 375ab^2 - 133a^3 - 125b^3$, taken over all integers $a, b$ such that $1 \leq a \leq 70$ and $1 \leq b \leq \min\{ |x - y| : x > 0, y > 0, xy = 10011 \}$, is divided by $77456$.
19,584
graphs = [ Graph( let={ "_n": Const(3), "result": Mod(value=MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("a"), Var("b")]), condition=And(Geq(Var("a"), Const(1)), Leq(Var("a"), Const(70)), Geq(Var("b"), Const(1)), Leq(Var("b"), MinOverSet(set=MapOverSet(set=Solut...
ALG
null
COMPUTE
sympy
B3_DIFF
[ "B3_DIFF" ]
b47ea7
alg_poly3_min_v1
null
4
0
[ "B3_DIFF" ]
1
0.02
2026-03-10T06:30:02.304639Z
{ "verified": true, "answer": 19584, "timestamp": "2026-03-10T06:30:02.324193Z" }
87f500
CC BY 4.0
[ { "id": 2, "model": "openai/gpt-oss-120b", "score": 3, "correct": { "strict": true, "boxed": true, "relaxed": true }, "usage": { "prompt_tokens": 212, "completion_tokens": 2782 }, "timestamp": "2026-04-19T03:11:59.011Z", "answer": 19584 }, { ...
1
[ { "lemma": "B3_DIFF", "status": "ok" }, { "lemma": "POLY_PADIC_VAL_CONST", "status": "no" } ]
{ "lo": -5.35, "mid": 0.52, "hi": 5.84 }
ca0705
geo_count_lattice_triangle_v1_153355830_610
Let $m = 233$ and $n = 233$. Define $A$ to be twice the area of the polygon with vertices at $(0,0)$, $(m,0)$, and $(276,-240)$, adjusted by the number of interior lattice points along certain diagonals generated by linear combinations $t = 7a + 4b$ where $a$ and $b$ are integers satisfying $1 \le a \le 40$, $1 \le b \...
8,814
graphs = [ Graph( let={ "_m": Const(233), "_n": Const(233), "area_2x": Abs(arg=Sum(Mul(Ref(name='_m'), CountOverSet(set=SolutionsSet(var=Var(name='t'), condition=Exists(var=Var(name='a'), condition=Exists(var=Var(name='b'), condition=And(Geq(left=Var(name='a'), right=Cons...
NT
null
COUNT
sympy
SUM_ARITHMETIC
[ "SUM_ARITHMETIC", "LIN_FORM" ]
7209d0
geo_count_lattice_triangle_v1
null
6
0
[ "LIN_FORM", "SUM_ARITHMETIC" ]
2
0.013
2026-02-08T04:05:09.138178Z
{ "verified": true, "answer": 8814, "timestamp": "2026-02-08T04:05:09.151017Z" }
97ba0c
CC BY 4.0
[ { "id": 2, "model": "openai/gpt-oss-120b", "score": 3, "correct": { "strict": true, "boxed": true, "relaxed": true }, "usage": { "prompt_tokens": 449, "completion_tokens": 7029 }, "timestamp": "2026-02-10T15:15:36.904Z", "answer": 8814 }, { "...
1
[ { "lemma": "COUNT_DIVISOR_COUNT", "status": "no" }, { "lemma": "K15", "status": "no" }, { "lemma": "K17", "status": "no" }, { "lemma": "LIN_FORM", "status": "ok" }, { "lemma": "SUM_ARITHMETIC", "status": "ok" }, { "lemma": "V1", "status": "no" },...
{ "lo": -3.42, "mid": 1.86, "hi": 7.55 }
8012b4
comb_count_surjections_v1_124444284_6697
Let $m = 15$. Define $\ell$ to be the number of ordered pairs $(i, j)$ of positive integers such that $i + j = m$ and $1 \leq i, j \leq 15$. Let $n$ be the number of ordered pairs $(x_1, x_2)$ of positive odd integers such that $x_1 + x_2 = \ell$. Let $k = 5$. Define $r = k! \cdot S(n, k)$, where $S(n, k)$ denotes the ...
270
graphs = [ Graph( let={ "_m": Const(15), "_n": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("i"), Var("j")]), condition=Eq(Sum(Var("i"), Var("j")), Ref("_m")), domain=CartesianProduct(left=IntegerRange(start=Const(1), end=Const(15)), right=IntegerRange(start=Const(1), end=Co...
COMB
NT
COUNT
sympy
LIN_FORM
[ "COUNT_SUM_EQUALS/COMB1" ]
5b2e59
comb_count_surjections_v1
null
7
0
[ "COMB1", "COUNT_SUM_EQUALS", "LIN_FORM" ]
3
0.068
2026-02-08T08:35:26.668779Z
{ "verified": true, "answer": 270, "timestamp": "2026-02-08T08:35:26.736524Z" }
4b02ea
CC BY 4.0
[ { "id": 1, "model": "openai/gpt-oss-20b", "score": 3, "correct": { "strict": true, "boxed": true, "relaxed": true }, "usage": { "prompt_tokens": 275, "completion_tokens": 9063 }, "timestamp": "2026-02-24T09:41:25.969Z", "answer": 270 }, { "id...
1
[ { "lemma": "C2", "status": "no" }, { "lemma": "COMB1", "status": "ok_later" }, { "lemma": "COUNT_CARTESIAN", "status": "no" }, { "lemma": "COUNT_INTEGER_RANGE", "status": "no" }, { "lemma": "COUNT_SUM_EQUALS", "status": "ok" }, { "lemma": "V7", "st...
{ "lo": -2.35, "mid": 1.22, "hi": 4.84 }
2caa26
nt_num_divisors_compute_v1_153355830_921
Let $p_1 = 67$, $q_1 = 29$, and $r = 47$. Let $n_2 = p_1 q_1 r$. Let $h = \mu(n_2)^2$, where $\mu$ denotes the M\"obius function. Let $p = 37$ and $q = 13$, and let $n_1 = p q$. Let $w = \mu(n_1)^{2h}$. Let $n = 31 \cdot w$. Determine the number of positive divisors of $n$.
2
graphs = [ Graph( let={ "p1": Const(67), "q1": Const(29), "r": Const(47), "n2": Mul(Ref("p1"), Ref("q1"), Ref("r")), "h": Pow(MoebiusMu(n=Ref(name='n2')), Const(2)), "p": Const(37), "q": Const(13), "n1": Mul(Ref(...
NT
null
COMPUTE
sympy
MOBIUS_SQUAREFREE
[ "MOBIUS_SQUAREFREE" ]
6fcd31
nt_num_divisors_compute_v1
null
3
2
[ "MOBIUS_SQUAREFREE" ]
1
0.001
2026-02-08T04:15:23.853200Z
{ "verified": true, "answer": 2, "timestamp": "2026-02-08T04:15:23.854648Z" }
14b474
CC BY 4.0
[ { "id": 8, "model": "mathstral", "score": 3, "correct": { "strict": true, "boxed": true, "relaxed": true }, "usage": { "prompt_tokens": 220, "completion_tokens": 430 }, "timestamp": "2026-02-18T10:19:10.357Z", "answer": 2 } ]
2
[ { "lemma": "COUNT_DIVISOR_COUNT", "status": "no" }, { "lemma": "K17", "status": "no" }, { "lemma": "LTE_DIFF", "status": "no" }, { "lemma": "MOBIUS_SQUAREFREE", "status": "ok" }, { "lemma": "V1", "status": "no" }, { "lemma": "V3", "status": "no" ...
{ "lo": -10, "mid": -6.47, "hi": -2.95 }
87a018
diophantine_fbi2_count_v1_784195855_2972
Let $n = 66$. Let $k = 180$. Compute the number of integers $d$ such that $d \ge 3$, $d$ divides $k$, $\frac{k}{d} \ge 3$, $\frac{k}{d} \le n$, and $d \le 1 + 2 + \cdots + 11$.
14
graphs = [ Graph( let={ "_n": Const(66), "k": Const(180), "result": CountOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Const(3)), Leq(Var("d"), Summation(var="k", start=Const(1), end=Const(11), expr=Var("k"))), Divides(divisor=Var("d"), dividend=Ref("...
NT
null
COUNT
sympy
COUNT_COPRIME_GRID
[ "SUM_ARITHMETIC" ]
eb34f0
diophantine_fbi2_count_v1
null
4
0
[ "COUNT_COPRIME_GRID", "SUM_ARITHMETIC" ]
2
0.052
2026-02-08T06:09:33.885967Z
{ "verified": true, "answer": 14, "timestamp": "2026-02-08T06:09:33.937999Z" }
ba35ae
CC BY 4.0
[ { "id": 5, "model": "deepseek-ai/DeepSeek-V3.2", "score": 3, "correct": { "strict": true, "boxed": true, "relaxed": true }, "usage": { "prompt_tokens": 123, "completion_tokens": 1136 }, "timestamp": "2026-02-12T20:52:12.474Z", "answer": 14 }, { ...
1
[ { "lemma": "C2", "status": "no" }, { "lemma": "COUNT_PRIMES", "status": "no" }, { "lemma": "MOD_ADD", "status": "no" }, { "lemma": "MOD_MUL", "status": "no" }, { "lemma": "SUM_ARITHMETIC", "status": "ok" }, { "lemma": "VAL_SUM_EQ", "status": "no" ...
{ "lo": -7.01, "mid": -4.68, "hi": -2.15 }
f62d77
nt_sum_divisors_range_v1_865884756_4417
Let $m = 27447$. Define $N$ as the number of integers $t$ such that $20 \leq t \leq 12042$ and there exist integers $a$, $b$ with $1 \leq a \leq 426$, $1 \leq b \leq 1013$, and $t = 14a + 6b$. Let $D$ be the largest positive divisor of $36066000$ that is at most $N$. Define $S$ as the sum of the number of positive divi...
10,625
graphs = [ Graph( let={ "_m": Const(27447), "_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=426)), Geq(left...
NT
null
SUM
sympy
LIN_FORM
[ "LIN_FORM/MAX_DIVISOR" ]
8c55ae
nt_sum_divisors_range_v1
null
6
0
[ "LIN_FORM", "MAX_DIVISOR" ]
2
0.214
2026-02-08T17:55:33.115302Z
{ "verified": true, "answer": 10625, "timestamp": "2026-02-08T17:55:33.329570Z" }
7a36b1
CC BY 4.0
[ { "id": 5, "model": "deepseek-ai/DeepSeek-V3.2", "score": 3, "correct": { "strict": true, "boxed": true, "relaxed": true }, "usage": { "prompt_tokens": 188, "completion_tokens": 6976 }, "timestamp": "2026-02-18T09:51:39.607Z", "answer": 10625 }, ...
1
[ { "lemma": "COUNT_DIVISOR_COUNT", "status": "no" }, { "lemma": "K5", "status": "no" }, { "lemma": "LIN_FORM", "status": "ok" }, { "lemma": "LTE_DIFF_P2", "status": "no" }, { "lemma": "MAX_DIVISOR", "status": "ok_later" }, { "lemma": "MOD_MUL", "sta...
{ "lo": -7.08, "mid": -0.29, "hi": 6.49 }
ae2a89
nt_count_gcd_equals_v1_48377204_1937
Let $d$ be the number of positive integers $n$ such that $1 \leq n \leq 641$ and $\gcd(n, 10) = 1$. Compute the number of positive integers $n_1$ such that $1 \leq n_1 \leq 41616$ and $\gcd(n_1, 257) = d$.
161
graphs = [ Graph( let={ "upper": Const(41616), "k": Const(257), "d": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Const(641)), Eq(GCD(a=Var("n"), b=Const(10)), Const(1))))), "result": CountOverSet(set=Solutio...
NT
null
COUNT
sympy
MIN_PRIME_FACTOR
[ "C4" ]
08d162
nt_count_gcd_equals_v1
null
6
0
[ "C4", "MIN_PRIME_FACTOR" ]
2
8.405
2026-02-08T16:30:57.779275Z
{ "verified": true, "answer": 161, "timestamp": "2026-02-08T16:31:06.184620Z" }
e82dcc
CC BY 4.0
[ { "id": 5, "model": "deepseek-ai/DeepSeek-V3.2", "score": 3, "correct": { "strict": true, "boxed": true, "relaxed": true }, "usage": { "prompt_tokens": 123, "completion_tokens": 1684 }, "timestamp": "2026-02-17T06:19:05.776Z", "answer": 161 }, { ...
1
[ { "lemma": "C4", "status": "ok" }, { "lemma": "COUNT_FIB_DIVISIBLE", "status": "no" }, { "lemma": "K18", "status": "no" }, { "lemma": "L3b", "status": "no" }, { "lemma": "MOD_ADD", "status": "no" }, { "lemma": "V1", "status": "no" } ]
{ "lo": -7.08, "mid": -0.29, "hi": 6.49 }
357d75
comb_factorial_compute_v1_1874849503_1673
Let $S$ be the set of all integers $t$ such that there exist positive integers $a$ and $b$ with $1 \le a \le 3611$, $1 \le b \le 204$, $15 \le t \le 8250$, and $t = 2a + 5b + 8$. For each nonnegative integer $j$, let $\alpha_j = 1$ if $\binom{|S|}{j}$ is odd, and $\alpha_j = 0$ otherwise. Let $n$ be the number of nonne...
33,284
graphs = [ Graph( let={ "_m": Const(8232), "_n": Const(60325), "n": CountOverSet(set=SolutionsSet(var=Var("j"), condition=And(Geq(Var("j"), Const(0)), Leq(Var("j"), Ref("_m")), Eq(Mod(value=Binom(n=CountOverSet(set=SolutionsSet(var=Var("t"), condition=Exists(var=Var(name=...
ALG
COMB
COMPUTE
sympy
LIN_FORM
[ "LIN_FORM/V8" ]
654a7e
comb_factorial_compute_v1
null
7
0
[ "LIN_FORM", "V8" ]
2
0.004
2026-02-08T14:01:54.047585Z
{ "verified": true, "answer": 33284, "timestamp": "2026-02-08T14:01:54.051478Z" }
ef04b4
CC BY 4.0
[ { "id": 1, "model": "openai/gpt-oss-20b", "score": 3, "correct": { "strict": true, "boxed": true, "relaxed": true }, "usage": { "prompt_tokens": 277, "completion_tokens": 13444 }, "timestamp": "2026-02-24T19:35:18.017Z", "answer": 33284 }, { ...
1
[ { "lemma": "LIN_FORM", "status": "ok" }, { "lemma": "POLY_PADIC_VAL_CONST", "status": "no" }, { "lemma": "V8", "status": "ok_later" } ]
{ "lo": 1.15, "mid": 4.18, "hi": 6.61 }
cc740b
geo_count_lattice_rect_v1_458359167_2366
Compute the number of lattice points $(x, y)$ such that $0 \leq x \leq 169$ and $0 \leq y \leq 497$.
84,660
graphs = [ Graph( let={ "a": Const(169), "b": Const(497), "result": LatticePointsRect(a=Ref(name='a'), b=Ref(name='b')), }, goal=Ref("result"), ) ]
GEOM
null
COUNT
sympy
[]
geo_count_lattice_rect_v1
null
2
0
null
null
0
2026-02-08T05:20:01.829127Z
{ "verified": true, "answer": 84660, "timestamp": "2026-02-08T05:20:01.829465Z" }
8221dd
CC BY 4.0
[ { "id": 1, "model": "openai/gpt-oss-20b", "score": 3, "correct": { "strict": true, "boxed": true, "relaxed": true }, "usage": { "prompt_tokens": 148, "completion_tokens": 232 }, "timestamp": "2026-02-24T03:24:45.668Z", "answer": 84660 }, { "i...
1
[]
{ "lo": -5.98, "mid": -3.97, "hi": -1.94 }
c2482b
antilemma_cartesian_v1_2051736721_3301
Let $x$ be the number of ordered pairs $(a, b)$ where $a$ is an integer satisfying $1 \leq a \leq 25$ and $b$ is an integer satisfying $1 \leq b \leq 40$. Let $S$ be the set of all integers $t$ such that $15 \leq t \leq 51$ and there exist integers $a$ and $b$ with $1 \leq a \leq 4$, $1 \leq b \leq 3$, and $t = 6a + 9b...
14,139
graphs = [ Graph( let={ "_n": Const(50918), "x": CountOverSet(set=CartesianProduct(left=IntegerRange(start=Const(1), end=Const(25)), right=IntegerRange(start=Const(1), end=Const(40)))), "Q": Mod(value=Bell(Mod(value=Abs(arg=Ref(name='x')), modulus=CountOverSet(set=Solutio...
COMB
GEOM
COMPUTE
sympy
LIN_FORM
[ "LIN_FORM", "COUNT_CARTESIAN" ]
6e491f
antilemma_cartesian_v1
bell_mod
5
0
[ "COUNT_CARTESIAN", "LIN_FORM" ]
2
0.015
2026-02-08T17:14:29.630007Z
{ "verified": true, "answer": 14139, "timestamp": "2026-02-08T17:14:29.645410Z" }
4cf909
CC BY 4.0
[ { "id": 5, "model": "deepseek-ai/DeepSeek-V3.2", "score": 3, "correct": { "strict": true, "boxed": true, "relaxed": true }, "usage": { "prompt_tokens": 204, "completion_tokens": 1252 }, "timestamp": "2026-02-17T22:26:04.162Z", "answer": 14139 }, ...
1
[ { "lemma": "COUNT_CARTESIAN", "status": "ok" }, { "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": -2.38, "mid": 1.74, "hi": 6.59 }
249ac6
geo_count_lattice_triangle_v1_124444284_8085
Let $c=180$, and consider the quadratic polynomial $$f(x) = x^2 - 121x + K,$$ where $$K = \min (x+y),$$ with the minimum taken over all ordered pairs $(x,y)$ of positive integers such that $xy = 1610361$. Let $S$ be the set of all integers $x$ such that $f(x)=0$. Let $n=180$ and define $$A = \left|\, n\sum_{x\in S} x +...
9,444
graphs = [ Graph( let={ "_c": Const(180), "_m": Const(10), "_n": Const(180), "area_2x": Abs(arg=Sum(Mul(SumOverSet(set=SolutionsSet(var=Var(name='x'), condition=Eq(left=Sum(Pow(base=Var(name='x'), exp=Const(value=2)), Mul(Const(value=-121), Var(name='x')), Min...
NT
null
COUNT
sympy
B3
[ "B3/VIETA_SUM", "LIN_FORM" ]
46452c
geo_count_lattice_triangle_v1
null
8
0
[ "B3", "LIN_FORM", "VIETA_SUM" ]
3
0.012
2026-02-08T09:33:34.468852Z
{ "verified": true, "answer": 9444, "timestamp": "2026-02-08T09:33:34.480732Z" }
8a2bf0
CC BY 4.0
[ { "id": 5, "model": "deepseek-ai/DeepSeek-V3.2", "score": 3, "correct": { "strict": true, "boxed": true, "relaxed": true }, "usage": { "prompt_tokens": 322, "completion_tokens": 6481 }, "timestamp": "2026-02-14T04:46:51.602Z", "answer": 9444 }, {...
1
[ { "lemma": "B3", "status": "ok" }, { "lemma": "LIN_FORM", "status": "ok" }, { "lemma": "LTE_SUM", "status": "no" }, { "lemma": "MAX_VAL", "status": "no" }, { "lemma": "MOD_MUL", "status": "no" }, { "lemma": "POLY_PADIC_VAL_CONST", "status": "no" ...
{ "lo": -5.14, "mid": 0.32, "hi": 6.51 }
296457
sequence_count_fib_divisible_v1_971394319_229
Let $n = 56390$ and $\text{upper} = 175$. Define $$ d = \sum_{k=1}^{3} \varphi(k) \left\lfloor \frac{3}{k} \right\rfloor. $$ Let $\text{result}$ be the number of positive integers $n$ with $1 \leq n \leq \text{upper}$ such that $d$ divides the $n$-th Fibonacci number. Let $Q$ be the remainder when $44121 \cdot \text{re...
53,794
graphs = [ Graph( let={ "_n": Const(56390), "upper": Const(175), "d": Summation(var="k", start=Const(1), end=Const(3), expr=Mul(EulerPhi(n=Var("k")), Floor(Div(Const(3), Var("k"))))), "result": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var(...
NT
null
COUNT
sympy
K2
[ "K2" ]
6897ab
sequence_count_fib_divisible_v1
null
5
0
[ "K2" ]
1
0.012
2026-02-08T12:54:24.167923Z
{ "verified": true, "answer": 53794, "timestamp": "2026-02-08T12:54:24.179575Z" }
0bd412
CC BY 4.0
[ { "id": 5, "model": "deepseek-ai/DeepSeek-V3.2", "score": 3, "correct": { "strict": true, "boxed": true, "relaxed": true }, "usage": { "prompt_tokens": 170, "completion_tokens": 1400 }, "timestamp": "2026-02-15T08:01:26.591Z", "answer": 53794 }, ...
1
[ { "lemma": "K13", "status": "no" }, { "lemma": "K14", "status": "no" }, { "lemma": "K17", "status": "no" }, { "lemma": "K2", "status": "ok" }, { "lemma": "MOD_FACTORIAL", "status": "no" }, { "lemma": "POLY_PADIC_VAL_CONST", "status": "no" } ]
{ "lo": -5.14, "mid": 0.32, "hi": 6.51 }
e563b3
antilemma_cartesian_v1_1742523217_1493
Let $x$ be the number of ordered pairs $(a,b)$ where $a$ is an integer between 1 and 25, inclusive, and $b$ is an integer between 1 and 32, inclusive. Compute the remainder when $10877 \cdot x$ is divided by 53151.
37,987
graphs = [ Graph( let={ "x": CountOverSet(set=CartesianProduct(left=IntegerRange(start=Const(1), end=Const(25)), right=IntegerRange(start=Const(1), end=Const(32)))), "_c": Const(10877), "Q": Mod(value=Mul(Ref("_c"), Ref("x")), modulus=Const(53151)), }, goa...
COMB
GEOM
COMPUTE
sympy
COUNT_CARTESIAN
[ "COUNT_CARTESIAN" ]
409d7d
antilemma_cartesian_v1
null
2
0
[ "COUNT_CARTESIAN" ]
1
0.001
2026-02-08T04:01:58.555184Z
{ "verified": true, "answer": 37987, "timestamp": "2026-02-08T04:01:58.555843Z" }
bb6ccb
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": 2962 }, "timestamp": "2026-02-10T16:33:49.916Z", "answer": 37987 }, { "...
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": "V7", ...
{ "lo": -0.05, "mid": 2.89, "hi": 5.27 }
eee24b
nt_max_prime_below_v1_677425708_4187
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 $m$ be the number of elements in $S$. Determine the largest prime number $n$ such that $m \leq n \leq 30276$.
30,271
graphs = [ Graph( let={ "upper": Const(30276), "result": MaxOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), CountOverSet(set=SolutionsSet(var=Var("p"), condition=And(IsPositive(arg=Var(name='p')), Exists(var=Var(name='q'), condition=And(Eq(left=Mul(Var(name='p'), V...
NT
null
EXTREMUM
sympy
COPRIME_PAIRS
[ "COPRIME_PAIRS" ]
2bb3aa
nt_max_prime_below_v1
null
4
0
[ "COPRIME_PAIRS" ]
1
0.708
2026-02-08T06:29:15.456784Z
{ "verified": true, "answer": 30271, "timestamp": "2026-02-08T06:29:16.164617Z" }
e97611
CC BY 4.0
[ { "id": 5, "model": "deepseek-ai/DeepSeek-V3.2", "score": 3, "correct": { "strict": true, "boxed": true, "relaxed": true }, "usage": { "prompt_tokens": 129, "completion_tokens": 1565 }, "timestamp": "2026-02-13T00:32:55.463Z", "answer": 30271 }, ...
1
[ { "lemma": "COPRIME_PAIRS", "status": "ok" }, { "lemma": "COUNT_PRIMES", "status": "no" }, { "lemma": "K14", "status": "no" }, { "lemma": "LTE_DIFF", "status": "no" }, { "lemma": "POLY_PADIC_VAL_CONST", "status": "no" }, { "lemma": "V1", "status": ...
{ "lo": -3.44, "mid": 1.34, "hi": 6.56 }
feaf2d_n
alg_linear_system_2x2_v1_1218484723_1221
A cryptographer uses a system of linear combinations: values $t = 6a + 4b$ (with $1 \leq a \leq 3$, $1 \leq b \leq 4$) form a codebook of size $d$. From a matrix equation, they compute $R = \frac{N}{\det} + \frac{M}{\det}$ using given constants, then set $k = |R| \bmod d$. The security level is the $k$-th Bell number. ...
5
ALG
COMB
COMPUTE
sympy
LIN_FORM
[ "LIN_FORM" ]
1ae498
alg_linear_system_2x2_v1
bell_mod
3
null
[ "LIN_FORM" ]
1
0.002
2026-02-25T02:59:39.312006Z
null
c7ecd3
feaf2d
narrative
CC BY 4.0
[ { "id": 1, "model": "openai/gpt-oss-20b", "score": 1, "correct": { "strict": false, "boxed": false, "relaxed": true }, "usage": { "prompt_tokens": 230, "completion_tokens": 2700 }, "timestamp": "2026-03-30T16:31:58.985Z", "answer": 52 }, { "i...
1
[ { "lemma": "LIN_FORM", "status": "ok" }, { "lemma": "POLY_PADIC_VAL_CONST", "status": "no" } ]
{ "lo": 3.8, "mid": 6.33, "hi": 9.49 }
d6d70d
algebra_quadratic_discriminant_v1_865884756_1740
Let $a = -2$, $b = 16$, and $c = 0$. Define $\Delta = b^2 - 4ac$. Compute the remainder when $44121 \cdot \Delta$ is divided by $58390$.
25,706
graphs = [ Graph( let={ "a": Const(-2), "b": Const(16), "c": Const(0), "result": Sub(Pow(Ref("b"), Const(2)), Mul(Const(4), Ref("a"), Ref("c"))), "Q": Mod(value=Mul(Const(44121), Ref("result")), modulus=Const(58390)), }, goal=Ref("Q...
NT
null
COMPUTE
sympy
COPRIME_PAIRS
[ "COPRIME_PAIRS" ]
2bb3aa
algebra_quadratic_discriminant_v1
null
2
0
[ "COPRIME_PAIRS" ]
1
0.019
2026-02-08T16:15:02.139586Z
{ "verified": true, "answer": 25706, "timestamp": "2026-02-08T16:15:02.158370Z" }
cf5727
CC BY 4.0
[ { "id": 5, "model": "deepseek-ai/DeepSeek-V3.2", "score": 3, "correct": { "strict": true, "boxed": true, "relaxed": true }, "usage": { "prompt_tokens": 98, "completion_tokens": 678 }, "timestamp": "2026-02-17T00:17:51.905Z", "answer": 25706 }, { ...
1
[ { "lemma": "C2", "status": "no" }, { "lemma": "COPRIME_PAIRS", "status": "ok" }, { "lemma": "MOD_FACTORIAL", "status": "no" }, { "lemma": "MOD_MUL", "status": "no" }, { "lemma": "POLY_PADIC_VAL_CONST", "status": "no" }, { "lemma": "V7", "status": "...
{ "lo": -7.08, "mid": -0.29, "hi": 6.49 }
673b2c
comb_count_surjections_v1_124444284_7723
Let $k$ be the number of integers $t$ with $5 \leq t \leq 12$ for which there exist integers $a$ and $b$ such that $1 \leq a \leq 2$, $1 \leq b \leq 3$, and $t = 3a + 2b$. Define $r = k! \cdot S(6, k)$, where $S(6, k)$ denotes the Stirling number of the second kind. Compute the remainder when $18847 \cdot r$ is divided...
4,302
graphs = [ Graph( let={ "n": Const(6), "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=2)), Geq(left=Var(nam...
COMB
null
COUNT
sympy
LIN_FORM
[ "LIN_FORM" ]
7b2633
comb_count_surjections_v1
null
5
0
[ "LIN_FORM" ]
1
0.003
2026-02-08T09:20:07.278235Z
{ "verified": true, "answer": 4302, "timestamp": "2026-02-08T09:20:07.280884Z" }
070754
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": 1670 }, "timestamp": "2026-02-24T11:02:44.266Z", "answer": 4302 }, { "i...
1
[ { "lemma": "C2", "status": "no" }, { "lemma": "COUNT_CARTESIAN", "status": "no" }, { "lemma": "COUNT_INTEGER_RANGE", "status": "no" }, { "lemma": "COUNT_SUM_EQUALS", "status": "no" }, { "lemma": "LIN_FORM", "status": "ok" }, { "lemma": "V7", "statu...
{ "lo": -2.35, "mid": 1.22, "hi": 4.84 }
0e934e
comb_factorial_compute_v1_1520064083_7042
Let $n$ be the number of positive integers $p$ for which there exists a positive integer $q$ such that $p \cdot q = 9450$, $\gcd(p, q) = 1$, and $p < q$. Compute $n!$.
40,320
graphs = [ Graph( let={ "n": CountOverSet(set=SolutionsSet(var=Var("p"), condition=And(IsPositive(arg=Var(name='p')), Exists(var=Var(name='q'), condition=And(Eq(left=Mul(Var(name='p'), Var(name='q')), right=Const(value=9450)), Eq(left=GCD(a=Var(name='p'), b=Var(name='q')), right=Const(value=1)),...
NT
null
COMPUTE
sympy
COPRIME_PAIRS
[ "COPRIME_PAIRS" ]
2bb3aa
comb_factorial_compute_v1
null
5
0
[ "COPRIME_PAIRS" ]
1
0.003
2026-02-08T08:43:25.941090Z
{ "verified": true, "answer": 40320, "timestamp": "2026-02-08T08:43:25.944169Z" }
8fd120
CC BY 4.0
[ { "id": 5, "model": "deepseek-ai/DeepSeek-V3.2", "score": 3, "correct": { "strict": true, "boxed": true, "relaxed": true }, "usage": { "prompt_tokens": 103, "completion_tokens": 1198 }, "timestamp": "2026-02-13T20:56:00.009Z", "answer": 40320 }, ...
1
[ { "lemma": "COPRIME_PAIRS", "status": "ok" }, { "lemma": "COUNT_FIB_DIVISIBLE", "status": "no" }, { "lemma": "K14", "status": "no" }, { "lemma": "V3", "status": "no" }, { "lemma": "V5", "status": "no" }, { "lemma": "V8", "status": "no" } ]
{ "lo": -3.44, "mid": 1.34, "hi": 6.56 }
a5f9aa
comb_bell_compute_v1_784195855_5792
Let $n$ be the number of integers $t$ with $15 \leq t \leq 45$ such that $t = 6a + 9b$ for some integers $a$ and $b$ satisfying $1 \leq a \leq 3$ and $1 \leq b \leq 3$. Let $B_n$ denote the $n$-th Bell number, which counts the number of partitions of a set of $n$ elements. Compute $46656 - B_n$.
25,509
graphs = [ Graph( let={ "_n": Const(46656), "n": CountOverSet(set=SolutionsSet(var=Var("t"), condition=Exists(var=Var(name='a'), condition=Exists(var=Var(name='b'), condition=And(Geq(left=Var(name='a'), right=Const(value=1)), Leq(left=Var(name='a'), right=Const(value=3)), Geq(left=Va...
COMB
null
COMPUTE
sympy
LIN_FORM
[ "LIN_FORM" ]
7b2633
comb_bell_compute_v1
null
6
0
[ "LIN_FORM" ]
1
0.002
2026-02-08T08:06:53.904897Z
{ "verified": true, "answer": 25509, "timestamp": "2026-02-08T08:06:53.906455Z" }
d164fa
CC BY 4.0
[ { "id": 1, "model": "openai/gpt-oss-20b", "score": 3, "correct": { "strict": true, "boxed": true, "relaxed": true }, "usage": { "prompt_tokens": 222, "completion_tokens": 1573 }, "timestamp": "2026-02-24T08:50:58.683Z", "answer": 25509 }, { "...
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": -3.84, "mid": -1.67, "hi": 1.32 }
3f4016
comb_count_partitions_v1_784195855_8373
Let $m = 2$. Define $s$ to be the sum of all positive integers $n$ such that $1 \leq n \leq 2$ and $n$ is even. Let $n$ be the largest positive integer $k$ such that $s^k \leq 1086369939509$. Compute the number of integer partitions of $n$.
31,185
graphs = [ Graph( let={ "_m": Const(2), "_n": SumOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Const(2)), Eq(Mod(value=Var("n"), modulus=Ref("_m")), Const(0))))), "n": MaxOverSet(set=SolutionsSet(var=Var("k"), condition=Leq(Po...
COMB
null
COUNT
sympy
SUM_DIVISIBLE
[ "SUM_DIVISIBLE/MAX_VAL" ]
622ecb
comb_count_partitions_v1
null
5
0
[ "MAX_VAL", "SUM_DIVISIBLE" ]
2
0.002
2026-02-08T16:02:19.547249Z
{ "verified": true, "answer": 31185, "timestamp": "2026-02-08T16:02:19.549448Z" }
a15efa
CC BY 4.0
[ { "id": 2, "model": "openai/gpt-oss-120b", "score": 3, "correct": { "strict": true, "boxed": true, "relaxed": true }, "usage": { "prompt_tokens": 191, "completion_tokens": 1003 }, "timestamp": "2026-02-24T19:31:29.996Z", "answer": 31185 }, { ...
1
[ { "lemma": "COUNT_INTEGER_RANGE", "status": "no" }, { "lemma": "COUNT_SUM_EQUALS", "status": "no" }, { "lemma": "MAX_VAL", "status": "ok_later" }, { "lemma": "SUM_DIVISIBLE", "status": "ok" }, { "lemma": "V7", "status": "no" }, { "lemma": "V8", "st...
{ "lo": -2.4, "mid": 1.57, "hi": 5.75 }
5daab2
geo_count_lattice_triangle_v1_601307018_9316
Let $N = \left|111 \cdot 100 + 8 \cdot (0 - 77)\right|$ and let $$M = \gcd(111, 77) + \gcd(|8 - 111|, |100 - 77|) + \gcd(|0 - 8|, |0 - 100|).$$ Compute $\frac{N + 2 - M}{2}$.
5,240
graphs = [ Graph( let={ "area_2x": Abs(arg=Sum(Mul(Const(value=111), Const(value=100)), Mul(Const(value=8), Sub(left=Const(value=0), right=Const(value=77))))), "boundary": Sum(GCD(a=Abs(arg=Const(value=111)), b=Abs(arg=Const(value=77))), GCD(a=Abs(arg=Sub(left=Const(value=8), right=C...
GEOM
NT
COUNT
sympy
[]
geo_count_lattice_triangle_v1
null
4
0
null
null
0.003
2026-03-10T09:43:55.733542Z
{ "verified": true, "answer": 5240, "timestamp": "2026-03-10T09:43:55.736728Z" }
b5fe69
CC BY 4.0
[ { "id": 2, "model": "openai/gpt-oss-120b", "score": 3, "correct": { "strict": true, "boxed": true, "relaxed": true }, "usage": { "prompt_tokens": 203, "completion_tokens": 563 }, "timestamp": "2026-04-19T11:05:43.746Z", "answer": 5240 }, { "i...
1
[]
{ "lo": -5.34, "mid": 1.1, "hi": 7.53 }
2aba2f
comb_count_derangements_v1_1915831931_3688
Let $n$ be the sum of all positive integers from 1 to 7 that are divisible by 7. Let $!n$ denote the subfactorial of $n$, the number of derangements of $n$ elements. Compute the remainder when $85151 \cdot (!n)$ is divided by $52040$.
32,634
graphs = [ Graph( let={ "_n": Const(85151), "n": SumOverSet(set=SolutionsSet(var=Var("n1"), condition=And(Geq(Var("n1"), Const(1)), Leq(Var("n1"), Const(7)), Eq(Mod(value=Var("n1"), modulus=Const(7)), Const(0))))), "result": Subfactorial(arg=Ref(name='n')), "Q...
COMB
null
COUNT
sympy
SUM_DIVISIBLE
[ "SUM_DIVISIBLE" ]
02dbe3
comb_count_derangements_v1
null
3
0
[ "SUM_DIVISIBLE" ]
1
0.002
2026-02-08T17:49:23.425787Z
{ "verified": true, "answer": 32634, "timestamp": "2026-02-08T17:49:23.427580Z" }
2a1f34
CC BY 4.0
[ { "id": 5, "model": "deepseek-ai/DeepSeek-V3.2", "score": 3, "correct": { "strict": true, "boxed": true, "relaxed": true }, "usage": { "prompt_tokens": 115, "completion_tokens": 2183 }, "timestamp": "2026-02-18T08:11:00.262Z", "answer": 32634 }, ...
1
[ { "lemma": "COUNT_CARTESIAN", "status": "no" }, { "lemma": "COUNT_COPRIME_GRID", "status": "no" }, { "lemma": "COUNT_SUM_EQUALS", "status": "no" }, { "lemma": "SUM_DIVISIBLE", "status": "ok" }, { "lemma": "V7", "status": "no" }, { "lemma": "V8_SUM", ...
{ "lo": -2.38, "mid": 1.74, "hi": 6.59 }
8a60ca
nt_sum_divisors_mod_v1_1978505735_3066
Let $n = \sum_{k=1}^{15} k$. Let $M = 10687$. Define $\sigma(n)$ to be the sum of the positive divisors of $n$. Let $r$ be the remainder when $\sigma(n)$ is divided by $M$. Compute the value of $7^{|r|} + 13924$ modulo $99991$.
63,047
graphs = [ Graph( let={ "n": Summation(var="k", start=Const(1), end=Const(15), expr=Var("k")), "M": Const(10687), "sigma": SumDivisors(n=Ref("n")), "result": Mod(value=Ref("sigma"), modulus=Ref("M")), "Q": Sum(ModExp(base=Const(7), exp=Abs(arg=Ref(...
NT
null
COMPUTE
sympy
SUM_ARITHMETIC
[ "SUM_ARITHMETIC" ]
eb34f0
nt_sum_divisors_mod_v1
null
3
0
[ "SUM_ARITHMETIC" ]
1
0.003
2026-02-08T17:19:02.637257Z
{ "verified": true, "answer": 63047, "timestamp": "2026-02-08T17:19:02.640450Z" }
fc4e9f
CC BY 4.0
[ { "id": 5, "model": "deepseek-ai/DeepSeek-V3.2", "score": 3, "correct": { "strict": true, "boxed": true, "relaxed": true }, "usage": { "prompt_tokens": 125, "completion_tokens": 5361 }, "timestamp": "2026-02-18T00:40:29.819Z", "answer": 63047 }, ...
1
[ { "lemma": "COUNT_COPRIME_GRID", "status": "no" }, { "lemma": "DS2", "status": "no" }, { "lemma": "POLY_PADIC_VAL_CONST", "status": "no" }, { "lemma": "SUM_ARITHMETIC", "status": "ok" }, { "lemma": "V8", "status": "no" }, { "lemma": "VAL_SUM_EQ", "...
{ "lo": -7.08, "mid": -0.29, "hi": 6.49 }
af5cce
nt_count_intersection_v1_784195855_9943
Let $N$ be the minimum value of $x + y$ over all ordered pairs $(x, y)$ of positive integers such that $xy = 6250000$. Determine the value of the number of positive integers $n$ such that $1 \leq n \leq N$, $7$ divides $n$, and $\gcd(n, 6) = 1$.
238
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(6250000)))), expr=Sum(Var("x"), Var("y")))), "a": Const(7), ...
NT
null
COUNT
sympy
B3
[ "B3" ]
0cd20d
nt_count_intersection_v1
null
5
0
[ "B3" ]
1
0.177
2026-02-08T17:20:21.664869Z
{ "verified": true, "answer": 238, "timestamp": "2026-02-08T17:20:21.841530Z" }
95f00d
CC BY 4.0
[ { "id": 5, "model": "deepseek-ai/DeepSeek-V3.2", "score": 3, "correct": { "strict": true, "boxed": true, "relaxed": true }, "usage": { "prompt_tokens": 125, "completion_tokens": 1440 }, "timestamp": "2026-02-18T00:17:45.949Z", "answer": 238 }, { ...
1
[ { "lemma": "B3", "status": "ok" }, { "lemma": "K16", "status": "no" }, { "lemma": "MAX_PRIME_BELOW", "status": "no" }, { "lemma": "POLY_PADIC_VAL_CONST", "status": "no" }, { "lemma": "V3", "status": "no" }, { "lemma": "V5", "status": "no" } ]
{ "lo": -7.08, "mid": -0.29, "hi": 6.49 }
20fa0f
nt_count_coprime_and_v1_677425708_1666
Let $u = 13950$. Compute the number of positive integers $n$ such that $1 \leq n \leq u$, $\gcd(n, 8) = \phi(2)$, and $\gcd(n, 9) = 1$. Multiply this number by 69316 and find the remainder when the result is divided by 89707.
2,149
graphs = [ Graph( let={ "upper": Const(13950), "k1": Const(8), "k2": Const(9), "result": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Ref("upper")), Eq(GCD(a=Var("n"), b=Ref("k1")), EulerPhi(n=Const(2))), Eq(...
NT
null
COUNT
sympy
ONE_PHI_2
[ "ONE_PHI_2" ]
e19278
nt_count_coprime_and_v1
null
5
0
[ "ONE_PHI_2" ]
1
6.676
2026-02-08T04:21:57.003478Z
{ "verified": true, "answer": 2149, "timestamp": "2026-02-08T04:22:03.679761Z" }
d6a86e
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": 3355 }, "timestamp": "2026-02-09T23:05:58.013Z", "answer": 2149 }, { "i...
1
[ { "lemma": "COUNT_DIVISOR_COUNT", "status": "no" }, { "lemma": "COUNT_FIB_DIVISIBLE", "status": "no" }, { "lemma": "K15", "status": "no" }, { "lemma": "LTE_SUM", "status": "no" }, { "lemma": "MOD_SUB", "status": "no" }, { "lemma": "ONE_PHI_2", "sta...
{ "lo": -6.5, "mid": -0.2, "hi": 6.11 }
5f3471
lin_form_endings_v1_124444284_9854
Let $a = 30$ and $b = 70$. Compute the remainder when $6790 \left\lfloor \frac{70}{\gcd(a,b)} \right\rfloor$ is divided by $90287$.
47,530
graphs = [ Graph( let={ "a_coeff": Const(30), "b_coeff": Const(70), "_inner_result": Floor(Div(Const(70), GCD(a=Ref("a_coeff"), b=Ref("b_coeff")))), "_scale_k": Const(6790), "_scaled": Mul(Ref("_scale_k"), Ref("_inner_result")), "_mod_M...
COMB
NT
COMPUTE
sympy
LIN_FORM
[ "LIN_FORM" ]
7b2633
lin_form_endings_v1
null
2
null
[ "LIN_FORM" ]
1
0
2026-02-08T12:42:15.404533Z
{ "verified": true, "answer": 47530, "timestamp": "2026-02-08T12:42:15.405013Z" }
193f4a
CC BY 4.0
[ { "id": 8, "model": "mathstral", "score": 3, "correct": { "strict": true, "boxed": true, "relaxed": true }, "usage": { "prompt_tokens": 114, "completion_tokens": 297 }, "timestamp": "2026-02-16T04:02:27.158Z", "answer": 47530 }, { "id": 11, ...
2
[ { "lemma": "C2", "status": "no" }, { "lemma": "COUNT_CARTESIAN", "status": "no" }, { "lemma": "COUNT_SUM_EQUALS", "status": "no" }, { "lemma": "LIN_FORM", "status": "ok" }, { "lemma": "V7", "status": "no" }, { "lemma": "V8", "status": "no" } ]
{ "lo": -9.12, "mid": -6.02, "hi": -3.62 }
ee94e8
nt_max_prime_below_v1_1918700295_4120
Let $p$ and $q$ be positive integers such that $pq = 18$, $\gcd(p, q) = 1$, and $p < q$. Let $A$ be the set of all such integers $p$. Let $m$ be the number of elements in $A$. Let $S$ be the set of all prime numbers $n$ such that $m \leq n \leq 37401$. Let $r$ be the largest element of $S$. Compute the remainder when $...
5,449
graphs = [ Graph( let={ "_n": Const(68340), "upper": Const(37401), "result": MaxOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), CountOverSet(set=SolutionsSet(var=Var("p"), condition=And(IsPositive(arg=Var(name='p')), Exists(var=Var(name='q'), condition=...
NT
null
EXTREMUM
sympy
COPRIME_PAIRS
[ "COPRIME_PAIRS" ]
2bb3aa
nt_max_prime_below_v1
null
4
0
[ "COPRIME_PAIRS" ]
1
2.804
2026-02-08T09:09:06.929111Z
{ "verified": true, "answer": 5449, "timestamp": "2026-02-08T09:09:09.733248Z" }
49ac5f
CC BY 4.0
[ { "id": 5, "model": "deepseek-ai/DeepSeek-V3.2", "score": 3, "correct": { "strict": true, "boxed": true, "relaxed": true }, "usage": { "prompt_tokens": 166, "completion_tokens": 5544 }, "timestamp": "2026-02-14T00:52:43.604Z", "answer": 5449 }, {...
1
[ { "lemma": "C2", "status": "no" }, { "lemma": "COPRIME_PAIRS", "status": "ok" }, { "lemma": "COUNT_FIB_DIVISIBLE", "status": "no" }, { "lemma": "L3b", "status": "no" }, { "lemma": "LTE_DIFF", "status": "no" }, { "lemma": "VAL_SUM_EQ", "status": "no...
{ "lo": -3.44, "mid": 1.34, "hi": 6.56 }
4ee3cd
nt_count_divisors_in_range_v1_809748730_331
Let $n = 5040$, $a = 10$, and $b = 321$. Determine the number of positive divisors $d$ of $n$ such that $a \leq d \leq b$.
38
graphs = [ Graph( let={ "n": Const(5040), "a": Const(10), "b": Const(321), "result": CountOverSet(set=SolutionsSet(var=Var("d"), condition=And(Divides(divisor=Var("d"), dividend=Ref("n")), Geq(Var("d"), Ref("a")), Leq(Var("d"), Ref("b"))))), }, ...
NT
null
COUNT
sympy
C3
[ "C3/SUM_INDEPENDENT/SUM_ARITHMETIC" ]
03a60c
nt_count_divisors_in_range_v1
null
3
0
[ "C3", "SUM_ARITHMETIC", "SUM_INDEPENDENT" ]
3
0.214
2026-02-08T11:28:29.526671Z
{ "verified": true, "answer": 38, "timestamp": "2026-02-08T11:28:29.740747Z" }
8eafc2
CC BY 4.0
[ { "id": 5, "model": "deepseek-ai/DeepSeek-V3.2", "score": 3, "correct": { "strict": true, "boxed": true, "relaxed": true }, "usage": { "prompt_tokens": 92, "completion_tokens": 1973 }, "timestamp": "2026-02-14T14:56:33.033Z", "answer": 38 }, { ...
1
[ { "lemma": "C3", "status": "ok" }, { "lemma": "COUNT_DIVISOR_COUNT", "status": "no" }, { "lemma": "L3b", "status": "no" }, { "lemma": "LTE_DIFF", "status": "no" }, { "lemma": "MOD_MUL", "status": "no" }, { "lemma": "SUM_ARITHMETIC", "status": "ok_l...
{ "lo": -5.14, "mid": 0.3, "hi": 6.27 }
61ac4f
comb_catalan_compute_v1_1520064083_9193
Let $T$ be the set of all integers $t$ such that $21 \leq t \leq 60$ and there exist positive integers $a \leq 5$ and $b \leq 2$ satisfying $t = 6a + 15b$. Let $n$ be the number of elements in $T$. Let $C_n$ denote the $n$-th Catalan number. Compute the remainder when $44121 \cdot C_n$ is divided by $76540$.
72,576
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=5)), Geq(left=Va...
COMB
null
COMPUTE
sympy
LIN_FORM
[ "LIN_FORM" ]
7b2633
comb_catalan_compute_v1
null
4
0
[ "LIN_FORM" ]
1
0.003
2026-02-08T10:35:39.472641Z
{ "verified": true, "answer": 72576, "timestamp": "2026-02-08T10:35:39.475648Z" }
36d959
CC BY 4.0
[ { "id": 1, "model": "openai/gpt-oss-20b", "score": 3, "correct": { "strict": true, "boxed": true, "relaxed": true }, "usage": { "prompt_tokens": 220, "completion_tokens": 6978 }, "timestamp": "2026-02-24T12:09:55.386Z", "answer": 72576 }, { "...
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": -2.35, "mid": 1.22, "hi": 4.84 }
c3fbe8
algebra_poly_eval_v1_124444284_5231
Let $m = 6$. Compute $-m^2 + 8m + \max\{n \mid n \text{ is a prime and } 2 \le n \le 9\}$.
19
graphs = [ Graph( let={ "_n": Const(2), "m": Const(6), "result": Sum(Mul(Const(-1), Pow(Ref("m"), Ref("_n"))), Mul(Const(8), Ref("m")), MaxOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(2)), Leq(Var("n"), Const(9)), IsPrime(Var("n")))))), ...
NT
null
COMPUTE
sympy
MAX_PRIME_BELOW
[ "MAX_PRIME_BELOW" ]
dc3ad3
algebra_poly_eval_v1
null
3
0
[ "MAX_PRIME_BELOW" ]
1
0.001
2026-02-08T06:27:15.176037Z
{ "verified": true, "answer": 19, "timestamp": "2026-02-08T06:27:15.177369Z" }
64df72
CC BY 4.0
[ { "id": 8, "model": "mathstral", "score": 3, "correct": { "strict": true, "boxed": true, "relaxed": true }, "usage": { "prompt_tokens": 98, "completion_tokens": 225 }, "timestamp": "2026-02-15T17:33:06.320Z", "answer": 19 }, { "id": 11, "...
2
[ { "lemma": "COUNT_COPRIME_GRID", "status": "no" }, { "lemma": "COUNT_DIVISOR_COUNT", "status": "no" }, { "lemma": "K14", "status": "no" }, { "lemma": "K17", "status": "no" }, { "lemma": "MAX_PRIME_BELOW", "status": "ok" }, { "lemma": "MOD_FACTORIAL", ...
{ "lo": -10, "mid": -7.73, "hi": -5.46 }
b64e4e
nt_count_divisible_and_v1_717093673_1136
Let $d_1$ be the number of integers $t$ such that $7 \leq t \leq 24$ and there exist integers $a$ and $b$ with $1 \leq a \leq 3$, $1 \leq b \leq 4$, and $t = 4a + 3b$. Let $d_2 = 15$. Define $S$ as the set of all positive integers $n$ such that $n \leq 233340$, $n$ is divisible by $d_1$, and $n$ is divisible by $d_2$. ...
59,408
graphs = [ Graph( let={ "upper": Const(233340), "d1": CountOverSet(set=SolutionsSet(var=Var("t"), condition=Exists(var=Var(name='a'), condition=Exists(var=Var(name='b'), condition=And(Geq(left=Var(name='a'), right=Const(value=1)), Leq(left=Var(name='a'), right=Const(value=3)), Geq(le...
NT
null
COUNT
sympy
LIN_FORM
[ "LIN_FORM" ]
7b2633
nt_count_divisible_and_v1
null
3
0
[ "LIN_FORM" ]
1
27.81
2026-02-08T15:52:17.925678Z
{ "verified": true, "answer": 59408, "timestamp": "2026-02-08T15:52:45.735265Z" }
673fdf
CC BY 4.0
[ { "id": 5, "model": "deepseek-ai/DeepSeek-V3.2", "score": 3, "correct": { "strict": true, "boxed": true, "relaxed": true }, "usage": { "prompt_tokens": 212, "completion_tokens": 2452 }, "timestamp": "2026-02-16T15:23:50.371Z", "answer": 59408 }, ...
1
[ { "lemma": "COUNT_DIVISOR_COUNT", "status": "no" }, { "lemma": "K14", "status": "no" }, { "lemma": "LIN_FORM", "status": "ok" }, { "lemma": "MOD_FACTORIAL", "status": "no" }, { "lemma": "POLY_PADIC_VAL_CONST", "status": "no" }, { "lemma": "V7", "st...
{ "lo": -7.08, "mid": -0.29, "hi": 6.49 }
aa6329
lte_diff_endings_v1_151522320_63
Let $a = 121$, $b = 9$, $n = 24$, $m = 30$, and $p = 2$. Define $d_n = a^n - b^n$ and $d_m = a^m - b^m$. Let $G = \gcd(d_n, d_m)$. Determine the largest integer $k$ such that $p^k$ divides $G$. Multiply this $k$ by $13033$, and find the remainder when the result is divided by $96913$.
65,165
graphs = [ Graph( let={ "a_val": Const(121), "b_val": Const(9), "n_val": Const(24), "m_val": Const(30), "p_val": Const(2), "a_pow_n": Pow(Ref("a_val"), Ref("n_val")), "b_pow_n": Pow(Ref("b_val"), Ref("n_val")), "...
NT
null
COMPUTE
sympy
LTE_DIFF
[ "LTE_DIFF" ]
cf8260
lte_diff_endings_v1
null
6
null
[ "LTE_DIFF" ]
1
0.001
2026-02-08T02:56:29.470386Z
{ "verified": true, "answer": 65165, "timestamp": "2026-02-08T02:56:29.471680Z" }
e79ed2
CC BY 4.0
[ { "id": 2, "model": "openai/gpt-oss-120b", "score": 3, "correct": { "strict": true, "boxed": true, "relaxed": true }, "usage": { "prompt_tokens": 228, "completion_tokens": 787 }, "timestamp": "2026-02-08T22:25:00.216Z", "answer": 65165 }, { "...
1
[ { "lemma": "COUNT_DIVISOR_COUNT", "status": "no" }, { "lemma": "LTE_DIFF", "status": "ok" }, { "lemma": "LTE_SUM", "status": "no" }, { "lemma": "MAX_VAL", "status": "no" }, { "lemma": "MOD_MUL", "status": "no" }, { "lemma": "V1", "status": "no" }...
{ "lo": -6.49, "mid": 0.51, "hi": 7.52 }
6eff3b
antilemma_sum_primes_v1_1520064083_1121
Let $m = 4$. Let $n_0$ be the smallest positive integer $n$ such that the largest power of 2 dividing $n!$ is at least $1$. Let $x$ be the sum of all prime numbers $n$ satisfying $n_0 \leq n \leq m$. Compute $x$.
5
graphs = [ Graph( let={ "_m": Const(4), "_n": MinOverSet(set=SolutionsSet(var=Var("n"), condition=Geq(MaxKDivides(target=Factorial(Var("n")), base=Const(2)), Const(1)), domain='Z_{>0}')), "x": SumOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Ref("_n")...
NT
null
COMPUTE
sympy
COPRIME_PAIRS
[ "V5/SUM_PRIMES", "SUM_PRIMES" ]
3729fd
antilemma_sum_primes_v1
null
4
0
[ "COPRIME_PAIRS", "SUM_PRIMES", "V5" ]
3
0.008
2026-02-08T03:48:08.483369Z
{ "verified": true, "answer": 5, "timestamp": "2026-02-08T03:48:08.491135Z" }
ecd3bd
CC BY 4.0
[ { "id": 8, "model": "mathstral", "score": 3, "correct": { "strict": true, "boxed": true, "relaxed": true }, "usage": { "prompt_tokens": 163, "completion_tokens": 376 }, "timestamp": "2026-02-18T06:18:00.236Z", "answer": 5 } ]
2
[ { "lemma": "COUNT_COPRIME_GRID", "status": "no" }, { "lemma": "COUNT_FIB_DIVISIBLE", "status": "no" }, { "lemma": "LTE_DIFF_P2", "status": "no" }, { "lemma": "MOD_ADD", "status": "no" }, { "lemma": "MOD_SUB", "status": "no" }, { "lemma": "SUM_PRIMES", ...
{ "lo": -10, "mid": -6.47, "hi": -2.95 }
501b60
comb_binomial_compute_v1_2051736721_2378
Let $n$ be the number of positive integers $p$ for which there exists a positive integer $q$ such that $pq = 1956570$, $\gcd(p, q) = 1$, and $p < q$. Let $k$ be the largest prime number satisfying $2 \leq k \leq 9$. 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=1956570)), 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
4
0
[ "COPRIME_PAIRS", "MAX_PRIME_BELOW" ]
2
0.005
2026-02-08T16:37:55.447361Z
{ "verified": true, "answer": 11440, "timestamp": "2026-02-08T16:37:55.452233Z" }
924532
CC BY 4.0
[ { "id": 5, "model": "deepseek-ai/DeepSeek-V3.2", "score": 3, "correct": { "strict": true, "boxed": true, "relaxed": true }, "usage": { "prompt_tokens": 123, "completion_tokens": 1854 }, "timestamp": "2026-02-17T08:43:20.084Z", "answer": 11440 }, ...
1
[ { "lemma": "COPRIME_PAIRS", "status": "ok" }, { "lemma": "K13", "status": "no" }, { "lemma": "K16", "status": "no" }, { "lemma": "MAX_PRIME_BELOW", "status": "ok" }, { "lemma": "MOD_SUB", "status": "no" }, { "lemma": "V7", "status": "no" }, { ...
{ "lo": -7.08, "mid": -0.29, "hi": 6.49 }
feb6de
modular_mod_compute_v1_1978505735_4773
Let $n = 96631$. Let $a$ be the largest positive divisor of $538731$ that is at most $729$. Let $m = 12996$. Define $r$ to be the remainder when $a$ is divided by $m$, and let $Q$ be the remainder when $n \cdot r$ is divided by $57635$. Find the value of $Q$.
14,029
graphs = [ Graph( let={ "_n": Const(96631), "a": MaxOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Const(1)), Leq(Var("d"), Const(729)), Divides(divisor=Var("d"), dividend=Const(538731))))), "m": Const(12996), "result": Mod(value=Ref("a"), ...
NT
null
COMPUTE
sympy
MAX_DIVISOR
[ "MAX_DIVISOR" ]
51757e
modular_mod_compute_v1
null
3
0
[ "MAX_DIVISOR" ]
1
0.002
2026-02-08T18:30:28.113161Z
{ "verified": true, "answer": 14029, "timestamp": "2026-02-08T18:30:28.115219Z" }
5ffe34
CC BY 4.0
[ { "id": 5, "model": "deepseek-ai/DeepSeek-V3.2", "score": 3, "correct": { "strict": true, "boxed": true, "relaxed": true }, "usage": { "prompt_tokens": 131, "completion_tokens": 1644 }, "timestamp": "2026-02-18T17:43:12.908Z", "answer": 14029 }, ...
1
[ { "lemma": "C2", "status": "no" }, { "lemma": "COUNT_COPRIME_GRID", "status": "no" }, { "lemma": "K15", "status": "no" }, { "lemma": "K18", "status": "no" }, { "lemma": "MAX_DIVISOR", "status": "ok" }, { "lemma": "MOD_FACTORIAL", "status": "no" }...
{ "lo": -7.08, "mid": -0.29, "hi": 6.49 }
5274e7
nt_min_coprime_above_v1_2051736721_1289
Let $\text{start}$ be the largest prime number $n$ such that $2 \leq n \leq 1018$. Let $T$ be the set of all ordered pairs $(x, y)$ of positive integers such that $x \cdot y = 549081$. Let $\text{upper}$ be the minimum value of $x + y$ as $(x, y)$ ranges over $T$. Define $\text{result}$ to be the smallest integer $n_1$...
1,015
graphs = [ Graph( let={ "_n": Const(1018), "start": MaxOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(2)), Leq(Var("n"), Ref("_n")), IsPrime(Var("n"))))), "upper": MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]...
NT
null
EXTREMUM
sympy
MAX_PRIME_BELOW
[ "MAX_PRIME_BELOW", "B3" ]
78ed98
nt_min_coprime_above_v1
null
5
0
[ "B3", "MAX_PRIME_BELOW" ]
2
0.181
2026-02-08T15:55:58.530874Z
{ "verified": true, "answer": 1015, "timestamp": "2026-02-08T15:55:58.712124Z" }
2ffba3
CC BY 4.0
[ { "id": 5, "model": "deepseek-ai/DeepSeek-V3.2", "score": 3, "correct": { "strict": true, "boxed": true, "relaxed": true }, "usage": { "prompt_tokens": 186, "completion_tokens": 1847 }, "timestamp": "2026-02-16T18:13:40.095Z", "answer": 1015 }, {...
1
[ { "lemma": "B3", "status": "ok" }, { "lemma": "COUNT_COPRIME_GRID", "status": "no" }, { "lemma": "COUNT_DIVISOR_COUNT", "status": "no" }, { "lemma": "L3b", "status": "no" }, { "lemma": "MAX_PRIME_BELOW", "status": "ok" }, { "lemma": "MOD_SUB", "sta...
{ "lo": -7.08, "mid": -0.29, "hi": 6.49 }
62c2e1
comb_count_surjections_v1_153355830_1285
Let $n$ 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 = 7$. Let $k = 4$. Compute $k! \cdot S(n, k)$, where $S(n, k)$ denotes the number of ways to partition a set of $n$ elements into $k$ nonempty unlabeled subsets.
1,560
graphs = [ Graph( let={ "_n": Const(7), "n": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("i"), Var("j")]), condition=Eq(Sum(Var("i"), Var("j")), Ref("_n")), domain=CartesianProduct(left=IntegerRange(start=Const(1), end=Const(6)), right=IntegerRange(start=Const(1), end=Const...
COMB
null
COUNT
sympy
COUNT_SUM_EQUALS
[ "COUNT_SUM_EQUALS" ]
75ab0f
comb_count_surjections_v1
null
5
0
[ "COUNT_SUM_EQUALS" ]
1
0.011
2026-02-08T06:16:54.712477Z
{ "verified": true, "answer": 1560, "timestamp": "2026-02-08T06:16:54.723375Z" }
801e6e
CC BY 4.0
[ { "id": 1, "model": "openai/gpt-oss-20b", "score": 3, "correct": { "strict": true, "boxed": true, "relaxed": true }, "usage": { "prompt_tokens": 209, "completion_tokens": 919 }, "timestamp": "2026-02-24T05:43:09.754Z", "answer": 1560 }, { "id...
1
[ { "lemma": "C2", "status": "no" }, { "lemma": "COUNT_COPRIME_GRID", "status": "no" }, { "lemma": "COUNT_INTEGER_RANGE", "status": "no" }, { "lemma": "COUNT_SUM_EQUALS", "status": "ok" }, { "lemma": "V7", "status": "no" }, { "lemma": "V8_SUM", "stat...
{ "lo": -4.93, "mid": -2.91, "hi": -0.71 }
576eb0
geo_count_lattice_rect_v1_784195855_7122
Let $R$ be the number of lattice points $(x, y)$ such that $0 \leq x \leq 105$ and $0 \leq y \leq 43$. Compute the remainder when $44121 \cdot R$ is divided by $65071$.
25,842
graphs = [ Graph( let={ "a": Const(105), "b": Const(43), "result": LatticePointsRect(a=Ref(name='a'), b=Ref(name='b')), "Q": Mod(value=Mul(Const(44121), Ref("result")), modulus=Const(65071)), }, goal=Ref("Q"), ) ]
GEOM
null
COUNT
sympy
[]
geo_count_lattice_rect_v1
null
2
0
null
null
0.001
2026-02-08T09:06:11.432911Z
{ "verified": true, "answer": 25842, "timestamp": "2026-02-08T09:06:11.434062Z" }
daaba8
CC BY 4.0
[ { "id": 1, "model": "openai/gpt-oss-20b", "score": 3, "correct": { "strict": true, "boxed": true, "relaxed": true }, "usage": { "prompt_tokens": 171, "completion_tokens": 1433 }, "timestamp": "2026-02-24T10:27:21.746Z", "answer": 25842 }, { "...
1
[]
{ "lo": 1.15, "mid": 4.18, "hi": 6.61 }
ad91a2
antilemma_v7_kummer_784195855_3291
Let $x$ be the largest integer $k$ such that $7^k$ divides $\binom{160}{64}$. Compute $73663x$.
73,663
graphs = [ Graph( let={ "_n": Const(7), "x": MaxKDivides(target=Binom(n=Const(160), k=Const(64)), base=Ref("_n")), "Q": Mul(Const(73663), Ref("x")), }, goal=Ref("Q"), ) ]
NT
null
COMPUTE
sympy
C2
[ "V7" ]
0672d4
antilemma_v7_kummer
null
5
0
[ "C2", "V7" ]
2
0.007
2026-02-08T06:19:33.403153Z
{ "verified": true, "answer": 73663, "timestamp": "2026-02-08T06:19:33.410545Z" }
fa7f76
CC BY 4.0
[ { "id": 8, "model": "mathstral", "score": 3, "correct": { "strict": true, "boxed": true, "relaxed": true }, "usage": { "prompt_tokens": 132, "completion_tokens": 669 }, "timestamp": "2026-02-19T05:02:21.915Z", "answer": 73663 } ]
2
[ { "lemma": "COUNT_DIVISOR_COUNT", "status": "no" }, { "lemma": "COUNT_INTEGER_RANGE", "status": "no" }, { "lemma": "K18", "status": "no" }, { "lemma": "MAX_VAL", "status": "no" }, { "lemma": "MOD_ADD", "status": "no" }, { "lemma": "V7", "status": "...
{ "lo": -10, "mid": -6.47, "hi": -2.95 }
53a82d
nt_count_digit_sum_v1_1431428450_1040
Let $T$ be the set of all integers $t$ such that $21 \le t \le 108$ and there exist integers $a$ and $b$ with $1 \le a \le 2$, $1 \le b \le 13$, and $t = 15a + 6b$. Let $s = |T|$. Let $N$ be the number of integers $n$ with $1 \le n \le 68644$ such that the sum of the decimal digits of $n$ is equal to $s$. Compute the r...
3,204
graphs = [ Graph( let={ "_n": Const(67249), "upper": Const(68644), "target_sum": CountOverSet(set=SolutionsSet(var=Var("t"), condition=Exists(var=Var(name='a'), condition=Exists(var=Var(name='b'), condition=And(Geq(left=Var(name='a'), right=Const(value=1)), Leq(left=Var(n...
NT
null
COUNT
sympy
LIN_FORM
[ "LIN_FORM" ]
7b2633
nt_count_digit_sum_v1
null
4
0
[ "LIN_FORM" ]
1
3.055
2026-02-08T13:51:59.547371Z
{ "verified": true, "answer": 3204, "timestamp": "2026-02-08T13:52:02.602135Z" }
44d0e4
CC BY 4.0
[ { "id": 5, "model": "deepseek-ai/DeepSeek-V3.2", "score": 3, "correct": { "strict": true, "boxed": true, "relaxed": true }, "usage": { "prompt_tokens": 180, "completion_tokens": 4920 }, "timestamp": "2026-02-15T21:35:05.527Z", "answer": 3204 }, {...
1
[ { "lemma": "C2", "status": "no" }, { "lemma": "COUNT_FIB_DIVISIBLE", "status": "no" }, { "lemma": "K13", "status": "no" }, { "lemma": "K15", "status": "no" }, { "lemma": "LIN_FORM", "status": "ok" }, { "lemma": "V1", "status": "no" } ]
{ "lo": -5.49, "mid": 0.22, "hi": 6.51 }
260ad4
comb_catalan_compute_v1_601307018_7311
Let $B_n$ denote the $n$-th Bell number and $C_n$ the $n$-th Catalan number. Let $N = C_{10}$. Find the remainder when $B_{N \bmod 11}$ is divided by $95215$.
20,760
graphs = [ Graph( let={ "n": Const(10), "result": Catalan(Ref("n")), "Q": Mod(value=Bell(Mod(value=Abs(arg=Ref(name='result')), modulus=Const(11))), modulus=Const(95215)), }, goal=Ref("Q"), ) ]
COMB
null
COMPUTE
sympy
LIN_FORM
[ "LIN_FORM", "K3" ]
2db00f
comb_catalan_compute_v1
bell_mod
3
0
[ "K3", "LIN_FORM" ]
2
0.035
2026-03-10T07:54:33.937798Z
{ "verified": true, "answer": 20760, "timestamp": "2026-03-10T07:54:33.972969Z" }
ebb0b1
CC BY 4.0
[ { "id": 2, "model": "openai/gpt-oss-120b", "score": 3, "correct": { "strict": true, "boxed": true, "relaxed": true }, "usage": { "prompt_tokens": 169, "completion_tokens": 475 }, "timestamp": "2026-04-19T06:23:49.876Z", "answer": 20760 }, { "...
1
[ { "lemma": "C2", "status": "no" }, { "lemma": "COUNT_CARTESIAN", "status": "no" }, { "lemma": "COUNT_COPRIME_GRID", "status": "no" }, { "lemma": "K3", "status": "ok" }, { "lemma": "LIN_FORM", "status": "ok" }, { "lemma": "V8", "status": "no" }, ...
{ "lo": -5.34, "mid": 1.1, "hi": 7.53 }
c96f75
alg_qf_psd_min_v1_601307018_8935
Let $Q$ be the minimum value of $$ 37220a^2 - 89328ab - 119104ac - 89328ad + 119104b^2 + 89328bc + 119104bd + 126548c^2 + 141436cd + 93050d^2 $$ over all ordered quadruples $(a, b, c, d)$ of positive integers satisfying $1 \le a, b, d \le 4$ and $1 \le c \le \min\{x + y : x, y > 0,\, xy = 4,\, x \le y\}$. Find $Q$.
93,050
graphs = [ Graph( let={ "_n": Const(2), "result": MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("a"), Var("b"), Var("c"), Var("d")]), condition=And(Geq(Var("a"), Const(1)), Leq(Var("a"), Const(4)), Geq(Var("b"), Const(1)), Leq(Var("b"), Const(4)), Geq(Var("c"), C...
ALG
null
COMPUTE
sympy
B3
[ "B3" ]
0cd20d
alg_qf_psd_min_v1
null
5
0
[ "B3" ]
1
0.023
2026-03-10T09:21:34.008524Z
{ "verified": true, "answer": 93050, "timestamp": "2026-03-10T09:21:34.031583Z" }
91a2d8
CC BY 4.0
[ { "id": 2, "model": "openai/gpt-oss-120b", "score": 3, "correct": { "strict": true, "boxed": true, "relaxed": true }, "usage": { "prompt_tokens": 254, "completion_tokens": 20595 }, "timestamp": "2026-04-19T10:13:16.714Z", "answer": 93050 }, { ...
1
[ { "lemma": "B3", "status": "ok" }, { "lemma": "POLY_PADIC_VAL_CONST", "status": "no" } ]
{ "lo": -5.34, "mid": 1.1, "hi": 7.53 }
2340ab
geo_count_lattice_rect_v1_397696148_2820
Let $a = 128$ and $b = 471$. The number of lattice points in the rectangle $[0, a] \times [0, b]$, including the boundary, is denoted by $R$. Compute the remainder when $673 \cdot R$ is divided by $61208$.
29,472
graphs = [ Graph( let={ "a": Const(128), "b": Const(471), "result": LatticePointsRect(a=Ref(name='a'), b=Ref(name='b')), "Q": Mod(value=Mul(Const(673), Ref("result")), modulus=Const(61208)), }, goal=Ref("Q"), ) ]
GEOM
null
COUNT
sympy
[]
geo_count_lattice_rect_v1
null
3
0
null
null
0.001
2026-02-08T14:06:07.483318Z
{ "verified": true, "answer": 29472, "timestamp": "2026-02-08T14:06:07.484116Z" }
de68fc
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": 1318 }, "timestamp": "2026-02-24T19:50:37.648Z", "answer": 29472 }, { "...
1
[]
{ "lo": -2.43, "mid": 1.2, "hi": 4.84 }
767bf7
sequence_fibonacci_compute_v1_1470522791_415
Let $n$ be the number of prime numbers $p$ such that $2 \leq p \leq 73$. Compute the $n$th Fibonacci number.
10,946
graphs = [ Graph( let={ "_n": Const(2), "n": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Ref("_n")), Leq(Var("n"), Const(73)), IsPrime(Var("n"))))), "result": Fibonacci(arg=Ref(name='n')), }, goal=Ref("result"), ) ]
NT
null
COMPUTE
sympy
COUNT_PRIMES
[ "COUNT_PRIMES" ]
07c874
sequence_fibonacci_compute_v1
null
3
0
[ "COUNT_PRIMES" ]
1
0.001
2026-02-08T13:00:42.057436Z
{ "verified": true, "answer": 10946, "timestamp": "2026-02-08T13:00:42.058805Z" }
4e44f7
CC BY 4.0
[ { "id": 5, "model": "deepseek-ai/DeepSeek-V3.2", "score": 3, "correct": { "strict": true, "boxed": true, "relaxed": true }, "usage": { "prompt_tokens": 81, "completion_tokens": 561 }, "timestamp": "2026-02-15T08:26:25.271Z", "answer": 10946 }, { ...
1
[ { "lemma": "COUNT_DIVISOR_COUNT", "status": "no" }, { "lemma": "COUNT_PRIMES", "status": "ok" }, { "lemma": "DS2", "status": "no" }, { "lemma": "LTE_SUM", "status": "no" }, { "lemma": "V5", "status": "no" }, { "lemma": "V7", "status": "no" } ]
{ "lo": -6.96, "mid": -4.56, "hi": -1.46 }
f64cca
nt_min_crt_v1_2051736721_4631
Let $m = 7$ and $k = 11$. Find the smallest positive integer $n$ such that $1 \leq n \leq 77$, $n \equiv 4 \pmod{7}$, and $n \equiv 1 \pmod{11}$.
67
graphs = [ Graph( let={ "m": Const(7), "k": Const(11), "a": Const(4), "b": Const(1), "upper": Const(77), "result": MinOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Ref("upper")), Eq(Mod(valu...
NT
null
EXTREMUM
sympy
MOBIUS_COPRIME
[ "V8" ]
86348e
nt_min_crt_v1
null
4
0
[ "MOBIUS_COPRIME", "V8" ]
2
0.118
2026-02-08T18:03:29.460807Z
{ "verified": true, "answer": 67, "timestamp": "2026-02-08T18:03:29.578352Z" }
921cee
CC BY 4.0
[ { "id": 5, "model": "deepseek-ai/DeepSeek-V3.2", "score": 3, "correct": { "strict": true, "boxed": true, "relaxed": true }, "usage": { "prompt_tokens": 106, "completion_tokens": 850 }, "timestamp": "2026-02-18T13:20:20.354Z", "answer": 67 }, { ...
1
[ { "lemma": "COUNT_INTEGER_RANGE", "status": "no" }, { "lemma": "COUNT_PRIMES", "status": "no" }, { "lemma": "K13", "status": "no" }, { "lemma": "K16", "status": "no" }, { "lemma": "L3b", "status": "no" }, { "lemma": "V8", "status": "ok" } ]
{ "lo": -7.08, "mid": -0.29, "hi": 6.49 }
1a3e80
antilemma_cartesian_v1_655260480_1741
Let $m = 43$. Define $n$ to be the number of ordered pairs $(i, j)$ of integers with $1 \leq i \leq 42$, $1 \leq j \leq 43$, and $i + j = m$. Let $x$ be the number of ordered pairs $(a, b)$ such that $1 \leq a \leq 14$ and $1 \leq b \leq 17$. Define $c$ to be the number of ordered pairs $(i_1, j_1)$ with $1 \leq i_1 \l...
57,161
graphs = [ Graph( let={ "_m": Const(43), "_n": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("i"), Var("j")]), condition=Eq(Sum(Var("i"), Var("j")), Ref("_m")), domain=CartesianProduct(left=IntegerRange(start=Const(1), end=Const(42)), right=IntegerRange(start=Const(1), end=Co...
COMB
GEOM
COMPUTE
sympy
COUNT_SUM_EQUALS
[ "COUNT_SUM_EQUALS/COUNT_SUM_EQUALS", "COUNT_CARTESIAN" ]
961465
antilemma_cartesian_v1
quadratic_mod
3
0
[ "COUNT_CARTESIAN", "COUNT_SUM_EQUALS" ]
2
0.018
2026-02-08T16:19:09.336647Z
{ "verified": true, "answer": 57161, "timestamp": "2026-02-08T16:19:09.354612Z" }
271658
CC BY 4.0
[ { "id": 2, "model": "openai/gpt-oss-120b", "score": 3, "correct": { "strict": true, "boxed": true, "relaxed": true }, "usage": { "prompt_tokens": 283, "completion_tokens": 1033 }, "timestamp": "2026-02-24T20:37:25.339Z", "answer": 57161 }, { ...
1
[ { "lemma": "C2", "status": "no" }, { "lemma": "COUNT_CARTESIAN", "status": "ok" }, { "lemma": "COUNT_INTEGER_RANGE", "status": "no" }, { "lemma": "COUNT_SUM_EQUALS", "status": "ok" }, { "lemma": "V7", "status": "no" }, { "lemma": "V8", "status": "n...
{ "lo": -5.65, "mid": -3.17, "hi": -0.81 }
2ccf43
nt_min_coprime_above_v1_2051736721_4313
Let $m = 180$ and $n = 2$. Define $t_{\text{mod}}$ to be the number of integers $t$ such that $13 \leq t \leq 259$ and $t = 3a + 4b + 6$ for some positive integers $a \leq 59$ and $b \leq 19$. Let $r$ be the smallest integer $k$ such that $66667 \leq k \leq 66917$ and $\gcd(k, t_{\text{mod}}) = 1$. Let $f$ be the numbe...
66,795
graphs = [ Graph( let={ "_m": Const(180), "_n": Const(2), "start": Const(66666), "upper": Const(66917), "modulus": CountOverSet(set=SolutionsSet(var=Var("t"), condition=Exists(var=Var(name='a'), condition=Exists(var=Var(name='b'), condition=And(Geq...
NT
null
EXTREMUM
sympy
COUNT_FIB_DIVISIBLE
[ "COUNT_FIB_DIVISIBLE", "LIN_FORM" ]
d91a57
nt_min_coprime_above_v1
mod_exp
6
0
[ "COUNT_FIB_DIVISIBLE", "LIN_FORM" ]
2
0.027
2026-02-08T17:54:40.926327Z
{ "verified": true, "answer": 66795, "timestamp": "2026-02-08T17:54:40.952837Z" }
169c1a
CC BY 4.0
[ { "id": 5, "model": "deepseek-ai/DeepSeek-V3.2", "score": 3, "correct": { "strict": true, "boxed": true, "relaxed": true }, "usage": { "prompt_tokens": 236, "completion_tokens": 5039 }, "timestamp": "2026-02-18T10:05:01.820Z", "answer": 66795 }, ...
1
[ { "lemma": "COUNT_DIVISOR_COUNT", "status": "no" }, { "lemma": "COUNT_FIB_DIVISIBLE", "status": "ok" }, { "lemma": "K16", "status": "no" }, { "lemma": "LIN_FORM", "status": "ok" }, { "lemma": "LTE_SUM", "status": "no" }, { "lemma": "MOD_ADD", "stat...
{ "lo": -7.08, "mid": -0.29, "hi": 6.49 }
fb1dbc
comb_count_derangements_v1_124444284_6977
Let $n$ be the smallest divisor of $77$ that is at least $2$. Define $Q$ to be the remainder when $44121$ multiplied by the subfactorial of $n$ is divided by $50521$. Compute $Q$.
6,835
graphs = [ Graph( let={ "_n": Const(50521), "n": MinOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Const(2)), Divides(divisor=Var("d"), dividend=Const(77))))), "result": Subfactorial(arg=Ref(name='n')), "Q": Mod(value=Mul(Const(44121), Ref(...
NT
COMB
COUNT
sympy
MIN_PRIME_FACTOR
[ "MIN_PRIME_FACTOR" ]
bc3776
comb_count_derangements_v1
null
3
0
[ "MIN_PRIME_FACTOR" ]
1
0.001
2026-02-08T08:44:45.072421Z
{ "verified": true, "answer": 6835, "timestamp": "2026-02-08T08:44:45.073623Z" }
ee3412
CC BY 4.0
[ { "id": 5, "model": "deepseek-ai/DeepSeek-V3.2", "score": 3, "correct": { "strict": true, "boxed": true, "relaxed": true }, "usage": { "prompt_tokens": 100, "completion_tokens": 1214 }, "timestamp": "2026-02-13T21:22:59.720Z", "answer": 6835 }, {...
1
[ { "lemma": "COUNT_DIVISOR_COUNT", "status": "no" }, { "lemma": "LTE_DIFF_P2", "status": "no" }, { "lemma": "LTE_SUM", "status": "no" }, { "lemma": "MIN_PRIME_FACTOR", "status": "ok" }, { "lemma": "V3", "status": "no" }, { "lemma": "V8", "status": "...
{ "lo": -3.51, "mid": 1.33, "hi": 6.56 }