{"paper":{"title":"On the Lucas Property of Linear Recurrent Sequences","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Hao Zhong, Tianxin Cai","submitted_at":"2016-03-25T09:59:57Z","abstract_excerpt":"We say that an arithmetical function $S:\\mathbb{N}\\rightarrow\\mathbb{Z}$ has Lucas property if for any prime $p$, \\begin{equation*}\n  S(n)\\equiv S(n_{0})S(n_{1})\\ldots S(n_{r})\\pmod p, \\end{equation*} where $n=\\sum_{i=0}^{r}n_{i}p^{i}$, with $0 \\leq n_{i} \\leq p-1,n,n_{i}\\in\\mathbb{N}$.\n  In this note, we discuss the Lucas property of Fibonacci sequences and Lucas numbers. Meanwhile, we find some other interesting results."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1603.07863","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"}