The author proves that the following difference equation
where , has a positive solution which converges to zero. This result solves Open Problem 11.4.10 (a) of M. R. S. Kulenović and G. Ladas [Dynamics of second order rational difference equations. With open problems and conjectures. (Boca Raton, FL: Chapman and Hall/CRC) (2002; Zbl 0981.39011)].