{"title":"On nonexistence of D(n)-quadruples","authors":"Zrinka Franušić, Ana Jurasić","doi":"10.1515/ms-2024-0063","DOIUrl":null,"url":null,"abstract":"In this paper, we show that there is no polynomial <jats:italic>D</jats:italic>(<jats:italic>n</jats:italic>)-quadruple in ℤ[<jats:italic>X</jats:italic>] for some polynomials <jats:italic>n</jats:italic> ∈ ℤ[<jats:italic>X</jats:italic>] that are not representable as a difference of squares of two polynomials in ℤ[<jats:italic>X</jats:italic>].","PeriodicalId":0,"journal":{"name":"","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-08-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1515/ms-2024-0063","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 0
Abstract
In this paper, we show that there is no polynomial D(n)-quadruple in ℤ[X] for some polynomials n ∈ ℤ[X] that are not representable as a difference of squares of two polynomials in ℤ[X].
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