The Diophantine Equation x4 ± y4 = iz2 in Gaussian Integers

被引：6

作者：

Najman, Filip ^{[1
]}

机构：

[1] Univ Zagreb, Dept Math, Zagreb 10000, Croatia

来源：

AMERICAN MATHEMATICAL MONTHLY | 2010年 / 117卷 / 07期

关键词：

D O I：

10.4169/000298910X496769

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this note we find all the solutions of the Diophantine equation x(4) +/- y(4) = iz(2) using elliptic curves over Q(i). Also, using the same method we give a new proof of Hilbert's result that the equation x(4) +/- y(4) = z(2) has only trivial solutions in Gaussian integers.

引用

页码：637 / 641

页数：5

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