{"paper":{"title":"Decomposable polynomials in second order linear recurrence sequences","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Christina Karolus, Clemens Fuchs, Dijana Kreso","submitted_at":"2017-03-09T13:32:33Z","abstract_excerpt":"We study elements of second order linear recurrence sequences $(G_n)_{n= 0}^{\\infty}$ of polynomials in $\\mathbb{C}[x]$ which are decomposable, i.e. representable as $G_n=g\\circ h$ for some $g, h\\in \\mathbb{C}[x]$ satisfying $\\operatorname{deg}g,\\operatorname{deg}h>1$. Under certain assumptions, and provided that $h$ is not of particular type, we show that $\\operatorname{deg}g$ may be bounded by a constant independent of $n$, depending only on the sequence."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1703.03258","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"}