On repunit generalized Cullen numbers
Colloquium Mathematicum
MSC: Primary 11D45; Secondary 11D61
DOI: 10.4064/cm9437-10-2024
Published online: 18 November 2024
Abstract
Let $s$ be an integer with $s\ge 2$ and let $R_s$ be the number of solutions of the equation $ns^{ n}+1=(b^m-1)/(b-1)$ in integers $b\ge 2$, $m\ge 3$ and $n\ge 2$. In 2022, Alahmadi and Luca proved that $R_2=0$. In this paper, we prove that for any prime power $p^\ell $, $R_{p^\ell }=0$.
