{"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/fermat-s-last-theorem-and-modular-curves-over","title":"Fermat's Last Theorem and modular curves over real quadratic fields","arxiv_id":"2102.11699","date":"2021-02-23","proceeding":null,"authors":["Philippe Michaud-Jacobs"],"abstract":"In this paper we study the Fermat equation $x^n+y^n=z^n$ over quadratic fields $\\mathbb{Q}(\\sqrt{d})$ for squarefree $d$ with $26 \\leq d \\leq 97$. By studying quadratic points on the modular curves $X_0(N)$, $d$-regular primes, and working with Hecke operators on spaces of Hilbert newforms, we extend work of Freitas and Siksek to show that for most squarefree $d$ in this range there are no non-trivial solutions to this equation for $n \\geq 4$.","url_abs":"https://arxiv.org/abs/2102.11699v7","url_pdf":"https://arxiv.org/pdf/2102.11699v7.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":"fermat-s-last-theorem-and-modular-curves-over","repo_url":"https://github.com/michaud-jacobs/flt-quad","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":1,"framework":"none","reach":null}],"tasks":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}