论文标题
多项式$ d（4）$ - 高斯整数上的四倍体
Polynomial $D(4)$-quadruples over Gaussian Integers
论文作者
论文摘要
$ \ mathbb {z} [z} [z} [i] [x] $的四个非零不同多项式的$ $ \ {a，b，c，d \} $，据说是二磷$ d（4）$ - 四倍的二倍体，如果其两种不同的元素的产物增加了4个是$ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \; 在本文中，我们证明，每$ d（4）$ - Quadruple in $ \ Mathbb {z} [i] [X] $是常规的，或等于等于方程$$（a+b-c-d）^2 =（ab+4）（ab+4）（cd+4）$ 4 $ d（4）$ d（4）$ - quadruple in $ - quadruple in $ \ mathb}
A set $\{a, b, c, d\}$ of four non-zero distinct polynomials in $\mathbb{Z}[i][X]$ is said to be a Diophantine $D(4)$-quadruple if the product of any two of its distinct elements increased by 4 is a square of some polynomial in $\mathbb{Z}[i][X]$. In this paper we prove that every $D(4)$-quadruple in $\mathbb{Z}[i][X]$ is regular, or equivalently that the equation $$(a+b-c-d)^2=(ab+4)(cd+4)$$ holds for every $D(4)$-quadruple in $\mathbb{Z}[i][X]$.
