{"paper":{"title":"On a conjecture on permutation polynomials over finite fields","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Wun-Seng Chou, Xiang-dong Hou","submitted_at":"2018-06-29T15:29:12Z","abstract_excerpt":"Let $\\Bbb F_q$ be the finite field with $q$ elements and let $p=\\text{char}\\,\\Bbb F_q$. It was conjectured that for integers $e\\ge 2$ and $1\\le a\\le pe-2$, the polynomial $X^{q-2}+X^{q^2-2}+\\cdots+X^{q^a-2}$ is a permutation polynomial of $\\Bbb F_{q^e}$ if and only if (i) $a=2$ and $q=2$, or (ii) $a=1$ and $\\text{gcd}(q-2,q^e-1)=1$. In the present paper we confirm this conjecture."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1806.11473","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"}