{"title":"四项方程","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":"{\"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}","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
摘要
我们给出了丢色图方程X+Y+Z=W在素数正整数X, Y, Z, W中的完全解,使得每个数X, Y, Z, W只有素数因子2和3。W的最大值为2333 + 29 + 1= 36。该方法适用于任何一对素数(p, q)来代替(2,3)。
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).