{"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/complete-solving-the-quadratic-equation-mod-2","title":"Complete solving the quadratic equation mod $2^n$","arxiv_id":"1711.03621","date":"2017-11-09","proceeding":null,"authors":["S. M. Dehnavi","M. R. Mirzaee Shamsabad","A. Mahmoodi Rishakani"],"abstract":"Quadratic functions have applications in cryptography. In this paper, we investigate the modular quadratic equation $$ ax^2+bx+c=0 \\quad (mod \\,\\, 2^n), $$ and provide a complete analysis of it. More precisely, we determine when this equation has a solution and in the case that it has a solution, we not only determine the number of solutions, but also give the set of solutions in $O(n)$ time. One of the interesting results of our research is that, when this equation has a solution, then the number of solutions is a power of two.","url_abs":"https://arxiv.org/abs/1711.03621v1","url_pdf":"https://arxiv.org/pdf/1711.03621v1.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":"complete-solving-the-quadratic-equation-mod-2","repo_url":"https://github.com/remijullian1/sstic-2020","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}