{"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/formalizing-mason-stothers-theorem-and-its","title":"Formalizing Mason-Stothers Theorem and its Corollaries in Lean 4","arxiv_id":"2408.15180","date":"2024-08-27","proceeding":null,"authors":["Jineon Baek","Seewoo Lee"],"abstract":"The ABC conjecture implies many conjectures and theorems in number theory, including the celebrated Fermat's Last Theorem. Mason-Stothers Theorem is a function field analogue of the ABC conjecture that admits a much more elementary proof with many interesting consequences, including a polynomial version of Fermat's Last Theorem. While years of dedicated effort are expected for a full formalization of Fermat's Last Theorem, the simple proof of Mason-Stothers Theorem and its corollaries calls for an immediate formalization. We formalize an elementary proof by Snyder in Lean 4, and also formalize many consequences of Mason-Stothers, including nonsolvability of Fermat-Cartan equations in polynomials, nonparametrizability of a certain elliptic curve, and Davenport's Theorem. We compare our work to existing formalizations of the Mason-Stothers by Eberl in Isabelle and Wagemaker in Lean 3 respectively. Our formalization has been integrated into the mathlib library of Lean 4.","url_abs":"https://arxiv.org/abs/2408.15180v1","url_pdf":"https://arxiv.org/pdf/2408.15180v1.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":"formalizing-mason-stothers-theorem-and-its","repo_url":"https://github.com/seewoo5/lean-poly-abc","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":1,"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}