{"title":"关于 D(n)-四元组的不存在性","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":18282,"journal":{"name":"Mathematica Slovaca","volume":"7 1","pages":""},"PeriodicalIF":0.9000,"publicationDate":"2024-08-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"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\":18282,\"journal\":{\"name\":\"Mathematica Slovaca\",\"volume\":\"7 1\",\"pages\":\"\"},\"PeriodicalIF\":0.9000,\"publicationDate\":\"2024-08-14\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Mathematica Slovaca\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.1515/ms-2024-0063\",\"RegionNum\":3,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Mathematica Slovaca","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1515/ms-2024-0063","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS","Score":null,"Total":0}
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].
期刊介绍：
Mathematica Slovaca, the oldest and best mathematical journal in Slovakia, was founded in 1951 at the Mathematical Institute of the Slovak Academy of Science, Bratislava. It covers practically all mathematical areas. As a respectful international mathematical journal, it publishes only highly nontrivial original articles with complete proofs by assuring a high quality reviewing process. Its reputation was approved by many outstanding mathematicians who already contributed to Math. Slovaca. It makes bridges among mathematics, physics, soft computing, cryptography, biology, economy, measuring, etc. The Journal publishes original articles with complete proofs. Besides short notes the journal publishes also surveys as well as some issues are focusing on a theme of current interest.
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