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arXiv · 1108.3212

On the interpolation of integer-valued polynomials

Fedor Petrov·Vladislav Volkov
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Abstract

It is well known, that if polynomial with rational coefficients of degree $n$ takes integer values in points $0,1,...,n$ then it takes integer values in all integer points. Are there sets of $n+1$ points with the same property in other integral domains? We show that answer is negative for the ring of Gaussian integers $\mathbb{Z}[i]$ when $n$ is large enough. Also we discuss the question about minimal possible size of set, such that if polynomial takes integer values in all points of this set then it is integer-valued.

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Fedor Petrov, Vladislav Volkov. 2011-08-16. On the interpolation of integer-valued polynomials. https://arxiv.org/abs/1108.3212

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