丢番图方程的解

IF 0.2 Q4 MATHEMATICS

JP Journal of Algebra Number Theory and Applications Pub Date : 2022-05-12 DOI:10.17654/0972555522016

P. Tiebekabe, Serge Adonsou, I. Diouf

{"title":"丢番图方程的解","authors":"P. Tiebekabe, Serge Adonsou, I. Diouf","doi":"10.17654/0972555522016","DOIUrl":null,"url":null,"abstract":"\\noindent In this article, we determine all the integers $c$ having at least two representations as difference between two linear recurrent sequences. This is a variant of the Pillai's equation. This equation is an exponential Diophantine equation. The proof of our main theorem uses lower bounds for linear forms of logarithms, properties of continued fractions, and a version of the Baker-Davenport reduction method in Diophantine approximation.","PeriodicalId":43248,"journal":{"name":"JP Journal of Algebra Number Theory and Applications","volume":"1 1","pages":""},"PeriodicalIF":0.2000,"publicationDate":"2022-05-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"ON SOLUTIONS OF THE DIOPHANTINE EQUATION\",\"authors\":\"P. Tiebekabe, Serge Adonsou, I. Diouf\",\"doi\":\"10.17654/0972555522016\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"\\\\noindent In this article, we determine all the integers $c$ having at least two representations as difference between two linear recurrent sequences. This is a variant of the Pillai's equation. This equation is an exponential Diophantine equation. The proof of our main theorem uses lower bounds for linear forms of logarithms, properties of continued fractions, and a version of the Baker-Davenport reduction method in Diophantine approximation.\",\"PeriodicalId\":43248,\"journal\":{\"name\":\"JP Journal of Algebra Number Theory and Applications\",\"volume\":\"1 1\",\"pages\":\"\"},\"PeriodicalIF\":0.2000,\"publicationDate\":\"2022-05-12\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"JP Journal of Algebra Number Theory and Applications\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.17654/0972555522016\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q4\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"JP Journal of Algebra Number Theory and Applications","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.17654/0972555522016","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"MATHEMATICS","Score":null,"Total":0}

引用次数: 0

摘要

在本文中，我们确定所有具有至少两种表示形式的整数$c$作为两个线性循环序列之间的差。这是皮莱方程的一个变体。这个方程是指数丢番图方程。我们主要定理的证明使用了对数线性形式的下界，连分式的性质，以及丢芬图近似中贝克-达文波特约简方法的一个版本。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

查看原文本刊更多论文

ON SOLUTIONS OF THE DIOPHANTINE EQUATION

\noindent In this article, we determine all the integers $c$ having at least two representations as difference between two linear recurrent sequences. This is a variant of the Pillai's equation. This equation is an exponential Diophantine equation. The proof of our main theorem uses lower bounds for linear forms of logarithms, properties of continued fractions, and a version of the Baker-Davenport reduction method in Diophantine approximation.

求助全文

通过发布文献求助，成功后即可免费获取论文全文。去求助

来源期刊

JP Journal of Algebra Number Theory and Applications MATHEMATICS-

自引率

0.00%

发文量

期刊介绍： The JP Journal of Algebra, Number Theory and Applications is a peer-reviewed international journal. Original research papers theoretical, computational or applied, in nature, in any branch of Algebra and Number Theory are considered by the JPANTA. Together with the core topics in these fields along with their interplay, the journal promotes contributions in Diophantine equations, Representation theory, and Cryptography. Realising the need of wide range of information for any emerging area of potential research, the journal encourages the submission of related survey articles as well.