{"paper":{"title":"On the multiplicative order of the roots of $bX^{q^r+1}-aX^{q^r}+dX-c$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Eleni Tzanaki, Fabio E. Brochero Mart\\'inez, Lucas Reis, Theodoulos Garefalakis","submitted_at":"2016-11-30T15:32:18Z","abstract_excerpt":"In this paper, we find a lower bound for the order of the group $\\langle \\theta+\\alpha\\rangle \\subset \\overline{\\mathbb F_{q}}^*$, where $\\alpha\\in \\mathbb F_{q}$, $\\theta$ is a generic root of the polynomial $F_{A,r}(X)=bX^{q^r+1}-aX^{q^r}+dX-c\\in \\mathbb F_{q}[X]$ and $ad-bc\\ne0$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1611.10220","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"}