POLYNOMIAL D(4)-QUADRUPLES OVER GAUSSIAN INTEGERS

被引：0

作者：

Trebjesanin, Marija bliznac ^{[1
]}

Bujacic, Sanda ^{[2
]}

机构：

[1] Univ Split, Fac Sci, Rudera Boskov 33, Split 21000, Croatia

[2] Univ Rijeka, Fac Math, Radmile Matejc 2, Rijeka 51000, Croatia

来源：

GLASNIK MATEMATICKI | 2024年 / 59卷 / 01期

关键词：

Diophantine m-tuples; polynomials; regular quadruples; DIOPHANTUS; VARIANT;

D O I：

暂无

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

A set {a, b, c, d} of four non-zero distinct polynomials in Z[i][X] is said to be a Diophantine D(4)-quadruple if the product of any two of its distinct elements increased by 4 is a square of some polynomial in Z[i][X]. In this paper we prove that every D(4)-quadruple in Z[i][X] is regular, or equivalently that the equation (a + b - c - d)(2) = (ab + 4)(cd + 4) holds for every D(4)-quadruple in Z[i][X].

引用

页码：1 / 31

页数：31

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