{"title":"Four terms equations","authors":"Lianxiang Wang","doi":"10.1016/S1385-7258(89)80010-1","DOIUrl":null,"url":null,"abstract":"<div><p>We give the complete solutions to the diophantine equation <em>X+Y+Z=W</em> in coprime positive integers <em>X, Y, Z, W</em> such that each of the numbers <em>X, Y, Z, W</em> has prime factors 2 and 3 only. The solution with the largest value of <em>W</em> is 2<sup>3</sup>3<sup>3</sup> + 2<sup>9</sup> + 1= 3<sup>6</sup>. The method works for any pair of primes (<em>p, q</em>) in place of (2, 3).</p></div>","PeriodicalId":100664,"journal":{"name":"Indagationes Mathematicae (Proceedings)","volume":"92 3","pages":"Pages 355-361"},"PeriodicalIF":0.0000,"publicationDate":"1989-09-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1016/S1385-7258(89)80010-1","citationCount":"7","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Indagationes Mathematicae (Proceedings)","FirstCategoryId":"1085","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S1385725889800101","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 7
Abstract
We give the complete solutions to the diophantine equation X+Y+Z=W in coprime positive integers X, Y, Z, W such that each of the numbers X, Y, Z, W has prime factors 2 and 3 only. The solution with the largest value of W is 2333 + 29 + 1= 36. The method works for any pair of primes (p, q) in place of (2, 3).
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