Abstract
We study the difference equation x(n+1) = alpha - x(n)/x(n-1), n is an element of N-0, where alpha is an element of R and where x(-1) and x(0) are so chosen that the corresponding solution (x(n)) of the equation is defined for every n is an element of N. We prove that when alpha = 3 the equilibrium (x) over bar = 2 of the equation is not stable, which corrects a result due to X. X. Yan, W. T. Li, and Z. Zhao. For the case a = 1, we show that there is a strictly monotone solution of the equation, and we also find its asymptotics. An explicit formula for the solutions of the equation are given for the case alpha = 0.