论文标题
等式$（x-d）^5 + x^5 +（x + d）^5 = y^n $
The equation $(x-d)^5 + x^5 + (x+d)^5 = y^n$
论文作者
论文摘要
在本文中，我们根据$ \ gcd（x，d）= 1 $和$ n \ geq 2 $求解标题方程。这概括了第一作者Patel和Siksek [BPS16]的早期工作。我们的主要工具包括Frey-hellegouarch曲线和相关的模块化形式，以及各种Chabauty型技术，用于确定小阳性属曲线上的合理点。
In this paper, we solve the equation of the title under the assumption that $\gcd(x,d)=1$ and $n\geq 2$. This generalizes earlier work of the first author, Patel and Siksek [BPS16]. Our main tools include Frey-Hellegouarch curves and associated modular forms, and an assortment of Chabauty-type techniques for determining rational points on curves of small positive genus.
