{"paper":{"title":"On a conjecture about a class of permutation trinomials","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Daniele Bartoli","submitted_at":"2017-12-28T14:23:43Z","abstract_excerpt":"We prove a conjecture by Tu, Zeng, Li, and Helleseth concerning trinomials $f_{\\alpha,\\beta}(x)= x + \\alpha x^{q(q-1)+1} + \\beta x^{2(q-1)+1} \\in \\mathbb{F}_{q^2}[x]$, $\\alpha\\beta \\neq 0$, $q$ even, characterizing all the pairs $(\\alpha,\\beta)\\in \\mathbb{F}_{q^2}^2$ for which $f_{\\alpha,\\beta}(x)$ is a permutation of $\\mathbb{F}_{q^2}$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1712.10017","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"}