{"kind":"task","effective_mode":"full","benchmark":{"kind":"benchmark","effective_mode":"full","slug":"omni-math","formal_name":"Omni-MATH","introduction":"Omni-MATH evaluates mathematical reasoning on Olympiad-level problems. Its official dataset contains 4,428 problems accompanied by domain and difficulty information.","introduction_ja":"","introduction_en":"","category":"Category not supplied","task_count":null,"acquisition_status":"Acquisition status not supplied","official_url":"https://huggingface.co/datasets/KbsdJames/Omni-MATH","indexing_mode":"index","profile":{"resources":[],"task_format":"","scoring":"","metric":"","size":"","answer_access":"","license":"","citation":"","maintainer":"","released":"","why_hard":"","related":[],"history":"","construction":"","limitations":"","saturation":"","scores":[]}},"task_id":"69d4b421-ce06-5997-9415-3d46a5338802","task_key":"test--69d4b421-ce06-5997-9415-3d46a5338802","task_revision_id":"1","upstream_id":"","short_description":"(a) Does $\\sum_{i=1}^{p-1} \\frac{1}{i} \\equiv 0\\left(\\bmod p^{2}\\right)$ for all…","config":"","split":"test","body":"{\"problem\":\"(a) Does $\\\\sum_{i=1}^{p-1} \\\\frac{1}{i} \\\\equiv 0\\\\left(\\\\bmod p^{2}\\\\right)$ for all odd prime numbers $p$? (Note that $\\\\frac{1}{i}$ denotes the number such that $\\\\left.i \\\\cdot \\\\frac{1}{i} \\\\equiv 1\\\\left(\\\\bmod p^{2}\\\\right)\\\\right)$ (b) Do there exist 2017 positive perfect cubes that sum to a perfect cube? (c) Does there exist a right triangle with rational side lengths and area 5? (d) A magic square is a $3 \\\\times 3$ grid of numbers, all of whose rows, columns, and major diagonals sum to the same value. Does there exist a magic square whose entries are all prime numbers? (e) Is $\\\\prod_{p} \\\\frac{p^{2}+1}{p^{2}-1}=\\\\frac{2^{2}+1}{2^{2}-1} \\\\cdot \\\\frac{3^{2}+1}{3^{2}-1} \\\\cdot \\\\frac{5^{2}+1}{5^{2}-1} \\\\cdot \\\\frac{7^{2}+1}{7^{2}-1} \\\\cdot \\\\ldots$ a rational number? (f) Do there exist an infinite number of pairs of distinct integers $(a, b)$ such that $a$ and $b$ have the same set of prime divisors, and $a+1$ and $b+1$ also have the same set of prime divisors?\"}","display_format":"math","language":"","answer_status":"published","assets":[],"source_url":"https://huggingface.co/datasets/KbsdJames/Omni-MATH","history":"initial import","indexing_mode":"index","subproblems":[],"grids":[]}