On the Shorey-Tijdeman Diophantine equation involving terms of Lucas sequences

Mahadi Ddamulira, Florian Luca, Robert Tichy

Let $r\ge 1$ be an integer and $\mathbf{U}:=\{U_n{\}}_{n\ge 0}$ be the Lucas sequence given by $U_0=0,U_1=1$, and $U_{n+2}=r{U}_{n+1}+U_n$ for $n\ge 0$. In this paper, we explain how to…