{"paper":{"title":"Remarks on the distribution of the primitive roots of a prime","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Shane Chern","submitted_at":"2016-03-08T06:33:04Z","abstract_excerpt":"Let $\\mathbb{F}_p$ be a finite field of size $p$ where $p$ is an odd prime. Let $f(x)\\in\\mathbb{F}_p[x]$ be a polynomial of positive degree $k$ that is not a $d$-th power in $\\mathbb{F}_p[x]$ for all $d\\mid p-1$. Furthermore, we require that $f(x)$ and $x$ are coprime. The main purpose of this paper is to give an estimate of the number of pairs $(\\xi,\\xi^\\alpha f(\\xi))$ such that both $\\xi$ and $\\xi^\\alpha f(\\xi)$ are primitive roots of $p$ where $\\alpha$ is a given integer. This answers a question of Han and Zhang."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1603.02391","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}