{"title":"An open problem on Jeśmanowicz' conjecture concerning primitive Pythagorean triples","authors":"Hai Yang, Ruiqin Fu","doi":"10.3336/gm.54.2.02","DOIUrl":null,"url":null,"abstract":"Let m > 31 be an even integer with gcd(m, 31) = 1. In this paper, using some elementary methods, we prove that the equation (m2 −312)x +(62m) = (m2 +312)z has only the positive integer solution (x, y, z) = (2, 2, 2). This result resolves an open problem raised by T. Miyazaki (Acta Arith. 186 (2018), 1–36) about Jeśmanowicz’ conjecture concerning primitive Pythagorean triples.","PeriodicalId":55601,"journal":{"name":"Glasnik Matematicki","volume":"75 1","pages":"271-277"},"PeriodicalIF":0.5000,"publicationDate":"2019-12-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"1","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Glasnik Matematicki","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.3336/gm.54.2.02","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 1
Abstract
Let m > 31 be an even integer with gcd(m, 31) = 1. In this paper, using some elementary methods, we prove that the equation (m2 −312)x +(62m) = (m2 +312)z has only the positive integer solution (x, y, z) = (2, 2, 2). This result resolves an open problem raised by T. Miyazaki (Acta Arith. 186 (2018), 1–36) about Jeśmanowicz’ conjecture concerning primitive Pythagorean triples.
期刊介绍：
Glasnik Matematicki publishes original research papers from all fields of pure and applied mathematics. The journal is published semiannually, in June and in December.
京公网安备 11010802042870号
京ICP备2023020795号-1
分享
求助内容：
应助结果提醒方式：
扫码关注我们
