{"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":"8ed39eb6-d242-529c-a8f3-d694ad76fac9","task_key":"test--8ed39eb6-d242-529c-a8f3-d694ad76fac9","task_revision_id":"1","upstream_id":"","short_description":"The sequence $\\left(z_{n}\\right)$ of complex numbers satisfies the following…","config":"","split":"test","body":"{\"problem\":\"The sequence $\\\\left(z_{n}\\\\right)$ of complex numbers satisfies the following properties: $z_{1}$ and $z_{2}$ are not real. $z_{n+2}=z_{n+1}^{2} z_{n}$ for all integers $n \\\\geq 1$. $\\\\frac{z_{n+3}}{z_{n}^{2}}$ is real for all integers $n \\\\geq 1$. $\\\\left|\\\\frac{z_{3}}{z_{4}}\\\\right|=\\\\left|\\\\frac{z_{4}}{z_{5}}\\\\right|=2$ Find the product of all possible values of $z_{1}$.\"}","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":[]}