{"title":"Asymptotic Fermat's last theorem for a family of equations of signature","authors":"Pedro-José Cazorla García","doi":"10.1112/mtk.12279","DOIUrl":null,"url":null,"abstract":"<p>In this paper, we study the integer solutions of a family of Fermat-type equations of signature <span></span><math></math>, <span></span><math></math>. We provide an algorithmically testable set of conditions which, if satisfied, imply the existence of a constant <span></span><math></math> such that if <span></span><math></math>, there are no solutions <span></span><math></math> of the equation. Our methods use the modular method for Diophantine equations, along with level lowering and Galois theory.</p>","PeriodicalId":18463,"journal":{"name":"Mathematika","volume":null,"pages":null},"PeriodicalIF":0.8000,"publicationDate":"2024-08-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1112/mtk.12279","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Mathematika","FirstCategoryId":"100","ListUrlMain":"https://onlinelibrary.wiley.com/doi/10.1112/mtk.12279","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 0
Abstract
In this paper, we study the integer solutions of a family of Fermat-type equations of signature , . We provide an algorithmically testable set of conditions which, if satisfied, imply the existence of a constant such that if , there are no solutions of the equation. Our methods use the modular method for Diophantine equations, along with level lowering and Galois theory.
期刊介绍：
Mathematika publishes both pure and applied mathematical articles and has done so continuously since its founding by Harold Davenport in the 1950s. The traditional emphasis has been towards the purer side of mathematics but applied mathematics and articles addressing both aspects are equally welcome. The journal is published by the London Mathematical Society, on behalf of its owner University College London, and will continue to publish research papers of the highest mathematical quality.
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
