Abstract
In this article the periodic behaviour of solutions of the difference equation
x(n+1) = alpha\x(n)\ + beta x(n-1); alpha,beta,x(-1), x(0) is an element of (-infinity,infinity)
will be investigated. It will be shown that for all solutions x(n) to be periodic (with the same period) with alpha not equal 0, 1, it is necessary that \alpha\ is an element of (0,2)\ Q and beta = -1. Also, it will be shown that if \alpha\ = 2cos(theta), theta = pi/j, j = 2, 3,, then all solutions x(n) are periodic with period j(2).