{"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/on-a-question-of-mordell","title":"On a question of Mordell","arxiv_id":"2007.01209","date":"2020-07-02","proceeding":null,"authors":["Andrew R. Booker","Andrew V. Sutherland"],"abstract":"We make several improvements to methods for finding integer solutions to $x^3+y^3+z^3=k$ for small values of $k$. We implemented these improvements on Charity Engine's global compute grid of 500,000 volunteer PCs and found new representations for several values of $k$, including $k=3$ and $k=42$. This completes the search begun by Miller and Woollett in 1954 and resolves a challenge posed by Mordell in 1953.","url_abs":"https://arxiv.org/abs/2007.01209v3","url_pdf":"https://arxiv.org/pdf/2007.01209v3.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":"on-a-question-of-mordell","repo_url":"https://github.com/AndrewVSutherland/SumsOfThreeCubes","is_official":1,"mentioned_in_paper":0,"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}