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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
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  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

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