On the difference equation xn+1=α+xn−1xn

In this paper we study the behavior of the solutions of the difference equation xn+1=α+xn−1xn,n=0,1,… where αα is a negative number. Included are results which considerably improve and correct those in the recently published paper: [A.E. Hamza, On the recursive sequence xn+1=α+xn−1xn, J. Math. Anal. Appl. 322 (2006), 668–674]. We also refute Conjecture 2 in [G. Ladas, Open problems and conjectures, J. Difference. Equ. Appl. 7 (2) (2001), 477–482].