{"paper":{"title":"Composite polynomials in 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","submitted_at":"2018-10-29T14:23:25Z","abstract_excerpt":"Let $(G_n(x))_{n=0}^\\infty$ be a $d$-th order linear recurrence sequence having polynomial characteristic roots, one of which has degree strictly greater than the others. Moreover, let $m\\geq 2$ be a given integer. We ask for $n\\in\\mathbb{N}$ such that the equation $G_n(x)=g\\circ h$ is satisfied for a polynomial $g\\in\\mathbb{C}[x]$ with deg$g=m$ and some polynomial $h\\in\\mathbb{C}[x]$ with deg$h>1$. We prove that for all but finitely many $n$ these decompositions can be described in \"finite terms\" coming from a generic decomposition parameterized by an algebraic variety. All data in this descr"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1810.12141","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"}