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arXiv · 1911.00606

The periodic integral orbits of polynomial recursions with integer coefficients

Hassan Sedaghat
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Abstract

We show that polynomial recursions $x_{n+1}=x_{n}^{m}-k$ where $k,m$ are integers and $m$ is positive have no nontrivial periodic integral orbits for $m\geq3$. If $m=2$ then the recursion has integral two-cycles for infinitely many values of $k$ but no higher period orbits. We also show that these statements are true for all quadratic recursions.

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Hassan Sedaghat. 2019-11-01. The periodic integral orbits of polynomial recursions with integer coefficients. https://doi.org/10.5644/sjm.18.01.08

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