{"title":"Solutions to a Pillai-Type Equation Involving Tribonacci Numbers and S-Units","authors":"Herbert Batte, Florian Luca","doi":"10.1007/s00009-024-02702-4","DOIUrl":null,"url":null,"abstract":"<p>Let <span>\\( \\{T_n\\}_{n\\ge 0} \\)</span> be the sequence of Tribonacci numbers. In this paper, we study the exponential Diophantine equation <span>\\(T_n-2^x3^y=c\\)</span>, for <span>\\(n,x,y\\in \\mathbb {Z}_{\\ge 0}\\)</span>. In particular, we show that there is no integer <i>c</i> with at least six representations of the form <span>\\(T_n-2^x3^y\\)</span>.</p>","PeriodicalId":49829,"journal":{"name":"Mediterranean Journal of Mathematics","volume":"35 1","pages":""},"PeriodicalIF":1.1000,"publicationDate":"2024-07-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Mediterranean Journal of Mathematics","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1007/s00009-024-02702-4","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 0
Abstract
Let \( \{T_n\}_{n\ge 0} \) be the sequence of Tribonacci numbers. In this paper, we study the exponential Diophantine equation \(T_n-2^x3^y=c\), for \(n,x,y\in \mathbb {Z}_{\ge 0}\). In particular, we show that there is no integer c with at least six representations of the form \(T_n-2^x3^y\).
期刊介绍：
The Mediterranean Journal of Mathematics (MedJM) is a publication issued by the Department of Mathematics of the University of Bari. The new journal replaces the Conferenze del Seminario di Matematica dell’Università di Bari which has been in publication from 1954 until 2003.
The Mediterranean Journal of Mathematics aims to publish original and high-quality peer-reviewed papers containing significant results across all fields of mathematics. The submitted papers should be of medium length (not to exceed 20 printed pages), well-written and appealing to a broad mathematical audience.
In particular, the Mediterranean Journal of Mathematics intends to offer mathematicians from the Mediterranean countries a particular opportunity to circulate the results of their researches in a common journal. Through such a new cultural and scientific stimulus the journal aims to contribute to further integration amongst Mediterranean universities, though it is open to contribution from mathematicians across the world.
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
