Document Type : Research Paper

Author

• W.A.J. Kosmala

Department of Math. Sci., Appalachian State University, Boone, NC 28608, USA

Abstract

The main goal of this note is to introduce another second-order difference equation where every nontrivial solution is of minimal period 5, namely the difference equation:
$$x_{n+1}=\frac{1+x_{n-1}}{x_n{x}_{n-1}-1},n=1,2,3,...$$
with initial conditions $x_0$ and $x_1$ any real numbers such that $x_0{x}_1\ne 1$.

Keywords

• difference equation
• periodicity
• equilibrium points
• convergence