Advances in Difference Equations
Volume 2006 (2006), Article ID 35847, 9 pages

Periodic solutions of arbitrary length in a simple integer iteration

Dean Clark

University of Rhode Island, Kingston 02881, RI, USA

Received 28 May 2005; Accepted 19 July 2005

Copyright © 2006 Dean Clark. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


We prove that all solutions to the nonlinear second-order difference equation in integers yn+1=aynyn1,{a:|a|<2,a0,±1},y0,y1, are periodic. The first-order system representation of this equation is shown to have self-similar and chaotic solutions in the integer plane.