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arXiv · 2005.08833

Functions with integer-valued divided differences

Andrew O'Desky
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Abstract

Let $s_0,s_1,s_2,\ldots$ be a sequence of rational numbers whose $m$th divided difference is integer-valued. We prove that $s_n$ is a polynomial function in $n$ if $s_n \ll θ^n$ for some positive number $θ$ satisfying $θ< e^{1 + \tfrac{1}{2} + \cdots+ \tfrac{1}{m}} -1$.

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Andrew O'Desky. 2021-09-11. Functions with integer-valued divided differences. https://doi.org/10.1016/j.jnt.2021.06.020

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