{"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":"28aa594b-f216-59fa-98de-c07c8624e0be","task_key":"test--28aa594b-f216-59fa-98de-c07c8624e0be","task_revision_id":"1","upstream_id":"","short_description":"Let $\\mathbb{N}_{\\geqslant 1}$ be the set of positive integers.","config":"","split":"test","body":"{\"problem\":\"Let $\\\\mathbb{N}_{\\\\geqslant 1}$ be the set of positive integers. \\nFind all functions $f \\\\colon \\\\mathbb{N}_{\\\\geqslant 1} \\\\to \\\\mathbb{N}_{\\\\geqslant 1}$ such that, for all positive integers $m$ and $n$:\\n\\\\[\\\\mathrm{GCD}\\\\left(f(m),n\\\\right) + \\\\mathrm{LCM}\\\\left(m,f(n)\\\\right) =\\n\\\\mathrm{GCD}\\\\left(m,f(n)\\\\right) + \\\\mathrm{LCM}\\\\left(f(m),n\\\\right).\\\\]\\n\\nNote: if $a$ and $b$ are positive integers, $\\\\mathrm{GCD}(a,b)$ is the largest positive integer that divides both $a$ and $b$, and $\\\\mathrm{LCM}(a,b)$ is the smallest positive integer that is a multiple of both $a$ and $b$.\"}","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":[]}