Diophantine Equation with Balancing-like Sequences Associated to the Pillai-Tijdeman-type Problem

Bijan Kumar Patel, Prashant Tiwari

Let $\{x_n{\}}_{n\ge 0}$ be the balancing-like sequence defined by $x_{n+1}=A{x}_n-x_{n-1}$, for $A>2$, where $x_0=0$ and $x_1=1$. In this paper, we demonstrate how to f…