{"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/a-new-method-in-the-problem-of-three-cubes","title":"A New Method in the Problem of Three Cubes","arxiv_id":"1802.06776","date":"2018-02-18","proceeding":null,"authors":["Armen Avagyan","Gurgen Dallakyan"],"abstract":"In the current paper we are seeking P1(y),P2(y),P3(y) with the highest possible degree polynomials with integer coefficients, and Q(y) via the lowest possible degree polynomial, such that P1(y)^3+P2(y)^3+P3(y)^3=Q(y). Actually, the solution of this problem has close relation with the problem of the sum of three cubes a^3+b^3+c^3=d, since deg Q(y)=0 case coincides with above mentioned problem. It has been considered estimation of possibility of minimization of deg Q(y). As a conclusion, for specific values of d we survey a new algorithm for finding integer solutions of a^3+b^3+c^3=d.","url_abs":"http://arxiv.org/abs/1802.06776v1","url_pdf":"http://arxiv.org/pdf/1802.06776v1.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":"a-new-method-in-the-problem-of-three-cubes","repo_url":"https://github.com/saltstack/pytest-salt-factories","is_official":0,"mentioned_in_paper":0,"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}