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
收藏
页码：637 / 641
页数：5
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