Abstract
We deal with functions which fulfil the condition \({\Delta_h^{n+1} \varphi(x)\in\mathbb{Z}}\) for all x, h taken from some linear space V. We derive necessary and sufficient conditions for such a function to be decent in the following sense: there exist functions \({f\colon V\rightarrow \mathbb{R},\ g\colon V \rightarrow \mathbb{Z}}\) such that \({\varphi = f + g}\) and \({\Delta_h^{n+1}f(x)=0}\) for all \({x, h\in V}\).
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Lewicka, A. On polynomial congruences. Aequat. Math. 90, 1115–1127 (2016). https://doi.org/10.1007/s00010-016-0427-x
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DOI: https://doi.org/10.1007/s00010-016-0427-x