{"paper":{"title":"A Class of Permutation Trinomials over Finite Fields","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Xiang-dong Hou","submitted_at":"2013-03-03T21:02:17Z","abstract_excerpt":"Let $q>2$ be a prime power and $f=-{\\tt x}+t{\\tt x}^q+{\\tt x}^{2q-1}$, where $t\\in\\Bbb F_q^*$. We prove that $f$ is a permutation polynomial of $\\Bbb F_{q^2}$ if and only if one of the following occurs: (i) $q$ is even and $\\text{Tr}_{q/2}(\\frac 1t)=0$; (ii) $q\\equiv 1\\pmod 8$ and $t^2=-2$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1303.0568","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"}