{"paper":{"title":"A Class of Permutation Binomials over Finite Fields","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"math.NT","authors_text":"Xiang-dong Hou","submitted_at":"2012-10-02T19:04:22Z","abstract_excerpt":"Let $q>2$ be a prime power and $f={\\tt x}^{q-2}+t{\\tt x}^{q^2-q-1}$, where $t\\in\\Bbb F_q^*$. It was recently conjectured that $f$ is a permutation polynomial of $\\Bbb F_{q^2}$ if and only if one of the following holds: (i) $t=1$, $q\\equiv 1\\pmod 4$; (ii) $t=-3$, $q\\equiv \\pm1\\pmod{12}$; (iii) $t=3$, $q\\equiv -1\\pmod 6$. We confirm this conjecture in the present paper."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1210.0881","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"}