论文标题
三个第五大国的完美力量
Perfect powers in sum of three fifth powers
论文作者
论文摘要
在本文中，我们确定了算术进展中三个第五大能的总和。更准确地说，我们完全解决了二聚体方程$$（x-d）^5 + x^5 +（x + d）^5 = z^n，〜n \ geq 2，$ d，其中$ d，x，x，z \ in \ mathbb {z} $和$ d = 2 = 2^a5^a5^b $ with $ a，b $ a，b \ geq 0 $。
In this paper we determine the perfect powers that are sums of three fifth powers in an arithmetic progression. More precisely, we completely solve the Diophantine equation $$ (x-d)^5 + x^5 + (x + d)^5 = z^n,~n\geq 2, $$ where $d,x,z \in \mathbb{Z}$ and $d = 2^a5^b$ with $a,b\geq 0$.
