{"about":{"site":"https://codewithpapers.app","non_affiliation":"Code with Papers and Syntology are not affiliated with, endorsed by, or sponsored by Papers with Code, Meta, or the pwc-archive mirror.","licence":"CC BY-SA 4.0","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","attribution":"https://codewithpapers.app/attribution","modified":"archive material modified by Syntology; see the attribution page"},"url":"/paper/bounds-on-the-number-of-squares-in-recurrence-1","title":"Bounds on the number of squares in recurrence sequences: arbitrary $b$, III","arxiv_id":"2504.07040","date":"2025-04-09","proceeding":null,"authors":["Paul M Voutier"],"abstract":"We generalise our earlier work on the number of squares in binary recurrence sequences, $\\left\\{ y_{k} \\right\\}_{k \\geq -\\infty}$. In the notation of our previous papers, here we consider the case when $N_{\\alpha}$ is any negative integer and $y_{0}=b^{2}$ for any positive integer, $b$. We show that there are at most $4$ distinct squares with $y_{k}$ sufficiently large. This allows us to also show that there are at most $9$ distinct squares in such sequences when $b=1,2$ or $3$, or once $d$ is sufficiently large.","url_abs":"https://arxiv.org/abs/2504.07040v1","url_pdf":"https://arxiv.org/pdf/2504.07040v1.pdf","source":{"archive":"pwc-archive (Hugging Face), CC BY-SA 4.0","snapshot":"2025-07-28","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","row_kind":"links_only","authors_date_abstract":"arXiv metadata, CC0 1.0 (https://info.arxiv.org/help/license), from the Kaggle arXiv metadata snapshot of 2026-09-12"},"code_links":[{"paper_slug":"bounds-on-the-number-of-squares-in-recurrence-1","repo_url":"https://github.com/PV-314/hypgeom","is_official":1,"mentioned_in_paper":0,"mentioned_in_github":0,"framework":"none","reach":null}],"tasks":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"syntology_url":null,"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}