Open Access

Periodic solutions of arbitrary length in a simple integer iteration

Advances in Difference Equations20062006:035847

DOI: 10.1155/ADE/2006/35847

Received: 28 May 2005

Accepted: 19 July 2005

Published: 27 February 2006

Abstract

We prove that all solutions to the nonlinear second-order difference equation in integers yn+1 = ay n -yn-1, {a :|a|<2, a≠0,±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.

[123]

Authors’ Affiliations

(1)
University of Rhode Island

References

  1. Clark D, Lewis JT: Symmetric solutions to a Collatz-like system of difference equations. Congr. Numer. 1998, 131: 101–114.MathSciNetMATHGoogle Scholar
  2. James G, James RC: Mathematics Dictionary. 4th edition. Van Nostrand Reinhold, New York; 1976.MATHGoogle Scholar
  3. Niven I: Irrational Numbers, The Carus Mathematical Monographs, no. 11. The Mathematical Association of America. Distributed by John Wiley & Sons, New York; 1956.Google Scholar

Copyright

© Dean Clark. 2006

This article is published under license to BioMed Central Ltd. 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.