{"paper":{"title":"The number of distinct and repeated squares and cubes in the Fibonacci sequence","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Yuke Huang, Zhiying Wen","submitted_at":"2016-03-14T11:23:59Z","abstract_excerpt":"The Fibonacci sequence $\\mathbb{F}$ is the fixed point beginning with $a$ of morphism $\\sigma(a,b)=(ab,a)$. In this paper, we get the explicit expressions of all squares and cubes, then we determine the number of distinct squares and cubes in $\\mathbb{F}[1,n]$ for all $n$, where $\\mathbb{F}[1,n]$ is the prefix of $\\mathbb{F}$ of length $n$. By establishing and discussing the recursive structure of squares and cubes, we give algorithms for counting the number of repeated squares and cubes in $\\mathbb{F}[1,n]$ for all $n$, and get explicit expressions for some special $n$ such as $n=f_m$ (the Fi"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1603.04211","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"}