On Pillai’s Problem involving Lucas sequences of the second kind

期刊论文
出版模式：

开放获取
发表日期：

2024年5月13日

查看全文

Sebastian Heintze,
Volker Ziegler

摘要

In this paper, we consider the Diophantine equation $ V_n - b^m = c $ $V_{n} - b^{m} = c$ for given integers b, c with $ b \ge 2 $ $b \geq 2$ , whereas $ V_n $ $V_{n}$ varies among Lucas-Lehmer sequences of the second kind. We prove under some technical conditions that if the considered equation has at least three solutions (n, m) , then there is an upper bound on the size of the solutions as well as on the size of the coefficients in the characteristic polynomial of $ V_n $ $V_{n}$ .