A period 5 difference equation

Author

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:
xn+1 =
1 + xn−1
xnxn−1 − 1, n = 1, 2, 3, . . .
with initial conditions x0 and x1 any real numbers such that x0x1 6= 1.

Keywords