论文标题
在等式上$ x^2-2^m = y^n $
On the equation $x^2-2^m=y^n$
论文作者
论文摘要
在本文中，我们完成了方程解决方案的研究$ x^2-2^m = y^n $ for $ m \ in \ mathbb {z} $和$ n \ geq3 $。这是在未解决的情况下使用模块化方法实现的，即，我们证明$ x^2-2 = y^n $的唯一整数解决方案对于$ n \ geq2 $是$（\ pm1，-1）$时，当$ n $奇怪。
In this article we finish the study of solutions of the equation $x^2-2^m=y^n$ for $m\in\mathbb{Z}$ and $n\geq3$. This is achieved using the modularity method in unsolved cases, namely, we prove that the only integer solutions of $x^2-2=y^n$ for $n\geq2$ are $(\pm1,-1)$ when $n$ is odd.
