{"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":"62496abf-de6f-5395-b174-5356aeb47dab","task_key":"test--62496abf-de6f-5395-b174-5356aeb47dab","task_revision_id":"1","upstream_id":"","short_description":"Let $p>2$ be a prime number. $\\mathbb{F}_{p}[x]$ is defined as the set of all…","config":"","split":"test","body":"{\"problem\":\"Let $p>2$ be a prime number. $\\\\mathbb{F}_{p}[x]$ is defined as the set of all polynomials in $x$ with coefficients in $\\\\mathbb{F}_{p}$ (the integers modulo $p$ with usual addition and subtraction), so that two polynomials are equal if and only if the coefficients of $x^{k}$ are equal in $\\\\mathbb{F}_{p}$ for each nonnegative integer $k$. For example, $(x+2)(2 x+3)=2 x^{2}+2 x+1$ in $\\\\mathbb{F}_{5}[x]$ because the corresponding coefficients are equal modulo 5 . Let $f, g \\\\in \\\\mathbb{F}_{p}[x]$. The pair $(f, g)$ is called compositional if $$f(g(x)) \\\\equiv x^{p^{2}}-x$$ in $\\\\mathbb{F}_{p}[x]$. Find, with proof, the number of compositional pairs (in terms of $p$ ).\"}","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":[]}