Orbits of Second Order Linear Recurrences over Finite Fields

Chatchawan Panraksa, Naveen Somasunderam

Let $Q$ be the matrix $\left(\begin{array}{cc}a& b\\ 1& 0\end{array}\right)$ in $G{L}_2({\mathbb{F}}_q)$ where ${\mathbb{F}}_q$ is a finite field, and let $G$ be the finite cyclic…