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  • Research Article
  • Open Access

Periodic solutions of arbitrary length in a simple integer iteration

Advances in Difference Equations20062006:035847

https://doi.org/10.1155/ADE/2006/35847

  • Received: 28 May 2005
  • Accepted: 19 July 2005
  • Published:

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.

Keywords

  • Differential Equation
  • Partial Differential Equation
  • Ordinary Differential Equation
  • Functional Analysis
  • Periodic Solution

[123]

Authors’ Affiliations

(1)
University of Rhode Island, Kingston, RI 02881, USA

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.

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