{"title":"关于\\(D(-3)\\) -四倍倍数的存在性 \\(\\mathbb{Z}\\)","authors":"A. Filipin, Ana Jurasic","doi":"10.3336/gm.57.2.03","DOIUrl":null,"url":null,"abstract":"In this paper we prove that there does not exist a set of four non-zero polynomials from \\(\\mathbb{Z}[X]\\), not all constant, such that the product of any two of its distinct elements decreased by \\(3\\) is a square of a polynomial from \\(\\mathbb{Z}[X]\\).","PeriodicalId":0,"journal":{"name":"","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2022-12-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"On the existence of \\\\(D(-3)\\\\)-quadruples over \\\\(\\\\mathbb{Z}\\\\)\",\"authors\":\"A. Filipin, Ana Jurasic\",\"doi\":\"10.3336/gm.57.2.03\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"In this paper we prove that there does not exist a set of four non-zero polynomials from \\\\(\\\\mathbb{Z}[X]\\\\), not all constant, such that the product of any two of its distinct elements decreased by \\\\(3\\\\) is a square of a polynomial from \\\\(\\\\mathbb{Z}[X]\\\\).\",\"PeriodicalId\":0,\"journal\":{\"name\":\"\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.0,\"publicationDate\":\"2022-12-30\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.3336/gm.57.2.03\",\"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/10.3336/gm.57.2.03","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
On the existence of \(D(-3)\)-quadruples over \(\mathbb{Z}\)
In this paper we prove that there does not exist a set of four non-zero polynomials from \(\mathbb{Z}[X]\), not all constant, such that the product of any two of its distinct elements decreased by \(3\) is a square of a polynomial from \(\mathbb{Z}[X]\).
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