{"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/explicitly-bounding-perfect-powers-in","title":"Explicitly bounding perfect powers in elliptic divisibility sequences","arxiv_id":"2310.13244","date":"2023-10-20","proceeding":null,"authors":["Sander R. Dahmen","Joey M. van Langen"],"abstract":"In this paper we consider elliptic divisibility sequences generated by a point on an elliptic curve over $\\mathbb{Q}$ with $j$-invariant $1728$ given by an integral short Weierstrass equation. For several different such elliptic divisibility sequences, we determine explicitly a finite set of primes such that for all primes $l$ outside this set, the elliptic divisibility sequence contains no $l$-th powers. Our approach uses, amongst other ingredients, the modular method for $\\mathbb{Q}$-curves. The corresponding explicit computations fit into a general computational framework for $\\mathbb{Q}$-curves, for which they provide illustrative examples.","url_abs":"https://arxiv.org/abs/2310.13244v1","url_pdf":"https://arxiv.org/pdf/2310.13244v1.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":"explicitly-bounding-perfect-powers-in","repo_url":"https://github.com/sanderdahmen/bounding-perfect-powers-in-eds","is_official":1,"mentioned_in_paper":1,"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}