{"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-integers-whose-sum-is-the-reverse-of-their","title":"On Integers Whose Sum is the Reverse of their Product","arxiv_id":"2108.13441","date":"2021-08-30","proceeding":null,"authors":["Xander Faber","Jon Grantham"],"abstract":"We determine all pairs of positive integers $(a,b)$ such that $a+b$ and $a \\times b$ have the same decimal digits in reverse order: \\[ (2,2), (9,9), (3,24), (2,47), (2,497), (2,4997), (2,49997), \\ldots \\] We use deterministic finite automata to describe our approach, which naturally extends to all other numerical bases. Our automata are a variation on the notion of Young graphs, which were introduced by Sloane to study ``reverse multiples''.","url_abs":"https://arxiv.org/abs/2108.13441v2","url_pdf":"https://arxiv.org/pdf/2108.13441v2.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-integers-whose-sum-is-the-reverse-of-their","repo_url":"https://github.com/rationalpoint/reverse","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}