{"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":"31c72276-398f-5033-b786-d80402eb5bd5","task_key":"test--31c72276-398f-5033-b786-d80402eb5bd5","task_revision_id":"1","upstream_id":"","short_description":"For every positive integer $n$ with prime factorization $n = \\prod_{i = 1}^{k}…","config":"","split":"test","body":"{\"problem\":\"For every positive integer $n$ with prime factorization $n = \\\\prod_{i = 1}^{k} p_i^{\\\\alpha_i}$, define\\n\\\\[\\\\mho(n) = \\\\sum_{i: \\\\; p_i > 10^{100}} \\\\alpha_i.\\\\]\\nThat is, $\\\\mho(n)$ is the number of prime factors of $n$ greater than $10^{100}$, counted with multiplicity.\\n\\nFind all strictly increasing functions $f: \\\\mathbb{Z} \\\\to \\\\mathbb{Z}$ such that\\n\\\\[\\\\mho(f(a) - f(b)) \\\\le \\\\mho(a - b) \\\\quad \\\\text{for all integers } a \\\\text{ and } b \\\\text{ with } a > b.\\\\]\\n\\n[i]\"}","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":[]}