{"title":"丢番图三元{2,b, c}的可拓性","authors":"Nikola Adžaga, A. Filipin, Ana Jurasic","doi":"10.2478/auom-2021-0016","DOIUrl":null,"url":null,"abstract":"Abstract The aim of this paper is to consider the extensibility of the Diophantine triple {2, b, c}, where 2 < b < c, and to prove that such a set cannot be extended to an irregular Diophantine quadruple. We succeed in that for some families of c’s (depending on b). As corollary, for example, we prove that for b/2 − 1 prime, all Diophantine quadruples {2, b, c, d} with 2 < b < c < d are regular.","PeriodicalId":0,"journal":{"name":"","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2021-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"The extensibility of the Diophantine triple {2, b, c}\",\"authors\":\"Nikola Adžaga, A. Filipin, Ana Jurasic\",\"doi\":\"10.2478/auom-2021-0016\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Abstract The aim of this paper is to consider the extensibility of the Diophantine triple {2, b, c}, where 2 < b < c, and to prove that such a set cannot be extended to an irregular Diophantine quadruple. We succeed in that for some families of c’s (depending on b). As corollary, for example, we prove that for b/2 − 1 prime, all Diophantine quadruples {2, b, c, d} with 2 < b < c < d are regular.\",\"PeriodicalId\":0,\"journal\":{\"name\":\"\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.0,\"publicationDate\":\"2021-06-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.2478/auom-2021-0016\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.2478/auom-2021-0016","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 0
摘要
摘要考虑了2 < b < c的Diophantine三元组{2,b, c}的可拓性,并证明了该集合不能被扩展到不规则的Diophantine四重组。我们成功地证明了c的一些族(取决于b)。作为推论,例如,我们证明了对于b/2−1素数,所有2 < b < c < d的Diophantine四元组{2,b, c, d}都是正则的。
The extensibility of the Diophantine triple {2, b, c}
Abstract The aim of this paper is to consider the extensibility of the Diophantine triple {2, b, c}, where 2 < b < c, and to prove that such a set cannot be extended to an irregular Diophantine quadruple. We succeed in that for some families of c’s (depending on b). As corollary, for example, we prove that for b/2 − 1 prime, all Diophantine quadruples {2, b, c, d} with 2 < b < c < d are regular.