### Abstract

We derive an nth order difference equation as a dual of a very simple periodic equation, and construct (n + 1)/2 explicit integrals and integrating factors of this equation in terms of multi-sums of products. We also present a generating function for the degrees of its iterates, exhibiting polynomial growth. In conclusion we demonstrate how the equation in question arises as a reduction of a system of lattice equations related to an integrable equation of Levi and Yamilov. These three facts combine to suggest the integrability of the nth order difference equation.

Original language | English |
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Pages (from-to) | 1-12 |

Number of pages | 12 |

Journal | Journal of Physics A: Mathematical and Theoretical |

Volume | 45 |

Issue number | 13 |

DOIs | |

Publication status | Published - Apr 2012 |

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## Cite this

Demskoy, D., Tran, D. T., van der Kamp, P. H., & Quispel, G. R. W. (2012). A novel nth order difference equation that may be integrable.

*Journal of Physics A: Mathematical and Theoretical*,*45*(13), 1-12. https://doi.org/10.1088/1751-8113/45/13/135202