{"title":"Finding all <i>S</i>-Diophantine quadruples for a fixed set of primes <i>S</i>.","authors":"Volker Ziegler","doi":"10.1007/s00605-021-01605-w","DOIUrl":null,"url":null,"abstract":"<p><p>Given a finite set of primes <i>S</i> and an <i>m</i>-tuple <math><mrow><mo>(</mo> <msub><mi>a</mi> <mn>1</mn></msub> <mo>,</mo> <mo>…</mo> <mo>,</mo> <msub><mi>a</mi> <mi>m</mi></msub> <mo>)</mo></mrow> </math> of positive, distinct integers we call the <i>m</i>-tuple <i>S</i>-Diophantine, if for each <math><mrow><mn>1</mn> <mo>≤</mo> <mi>i</mi> <mo><</mo> <mi>j</mi> <mo>≤</mo> <mi>m</mi></mrow> </math> the quantity <math> <mrow><msub><mi>a</mi> <mi>i</mi></msub> <msub><mi>a</mi> <mi>j</mi></msub> <mo>+</mo> <mn>1</mn></mrow> </math> has prime divisors coming only from the set <i>S</i>. For a given set <i>S</i> we give a practical algorithm to find all <i>S</i>-Diophantine quadruples, provided that <math><mrow><mo>|</mo> <mi>S</mi> <mo>|</mo> <mo>=</mo> <mn>3</mn></mrow> </math> .</p>","PeriodicalId":0,"journal":{"name":"","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1007/s00605-021-01605-w","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1007/s00605-021-01605-w","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"2021/7/19 0:00:00","PubModel":"Epub","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 0
Abstract
Given a finite set of primes S and an m-tuple of positive, distinct integers we call the m-tuple S-Diophantine, if for each the quantity has prime divisors coming only from the set S. For a given set S we give a practical algorithm to find all S-Diophantine quadruples, provided that .
求助内容：
应助结果提醒方式：
京公网安备 11010802042870号
