The diophantine equation $(2^{k}-1)(3^{k}-1)=x^{n}$

期刊论文
出版模式：

开放获取
发表日期：

2025年7月24日

查看全文

Bo He,
Chang Liu

摘要

In this paper, we investigate the Diophantine equation $\begin{aligned} (2^k - 1)(3^k - 1) = x^n \end{aligned}$ $\begin{matrix} (2^{k} - 1) (3^{k} - 1) = x^{n} \end{matrix}$ and prove that it has no solution in positive integers $k, x, n > 2$ $k, x, n > 2$ .

The diophantine equation \((2^{k}-1)(3^{k}-1)=x^{n}\)

摘要