Existence of nontrivial solutions of a rational difference equation

We prove that the Putnam difference equation xn+1=xn+xn−1+xn−2xn−3xnxn−1+xn−2+xn−3,n=0,1,… has a positive solution which is not eventually equal to 1. This provides positive confirmation of a conjecture due to G. Ladas [Open problems and conjectures, J. Difference Equ. Appl. 4 (1998) 497–499].