This paper studies the properties of solutions of the rational difference equation
where and the initial conditions are not both zero.
The main result answers positively the open problem posed by M. R. S. Kulenović and G. Ladas [Dynamics of second-order rational difference equations. With open problems and conjectures, Boca Raton, FL: Chapman & Hall/CRC (2002; Zbl 0981.39011), Conjecture 9.5.5], i.e., the positive equilibrium point of equation () is globally asymptotically stable. Furthermore, the authors prove the boundedness of every nonnegative solution and provide a detailed analysis of the invariant intervals and semicycles.