{"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":"noindex","profile":{"resources":[],"task_format":"","scoring":"","metric":"","size":"","answer_access":"","license":"","citation":"","maintainer":"","released":"","why_hard":"","related":[]}},"task_id":"8a544dab-82bd-5a45-bb09-b844a680907c","task_key":"test--8a544dab-82bd-5a45-bb09-b844a680907c","task_revision_id":"4","upstream_id":"","short_description":"Let $n=p_1^{a_1}p_2^{a_2}\\cdots p_t^{a_t}$ be the prime factorisation of $n$.…","config":"","split":"test","body":"{\"problem\":\"Let $n=p_1^{a_1}p_2^{a_2}\\\\cdots p_t^{a_t}$ be the prime factorisation of $n$. Define $\\\\omega(n)=t$ and $\\\\Omega(n)=a_1+a_2+\\\\ldots+a_t$. Prove or disprove:\\nFor any fixed positive integer $k$ and positive reals $\\\\alpha,\\\\beta$, there exists a positive integer $n>1$ such that\\ni) $\\\\frac{\\\\omega(n+k)}{\\\\omega(n)}>\\\\alpha$\\nii) $\\\\frac{\\\\Omega(n+k)}{\\\\Omega(n)}<\\\\beta$.\"}","display_format":"text","language":"","answer_status":"published","assets":[],"source_url":"https://huggingface.co/datasets/KbsdJames/Omni-MATH","history":"initial import","indexing_mode":"noindex","subproblems":[],"grids":[]}