{"paper":{"title":"On a divisibility relation for Lucas sequences","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Amalia Pizarro-Madariaga, Florian Luca, Pantelimon Stanica, Takao Komatsu, Yuri Bilu","submitted_at":"2015-11-06T02:04:05Z","abstract_excerpt":"In this note, we study the divisibility relation $U_m\\mid U_{n+k}^s-U_n^s$, where ${\\bf U}:=\\{U_n\\}_{n\\ge 0}$ is the Lucas sequence of characteristic polynomial $x^2-ax\\pm 1$ and $k,m,n,s$ are positive integers."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1511.01970","kind":"arxiv","version":2},"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"}