Title: On the interpolation of integer-valued polynomials
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.
Publication Year: 2011
Publication Date: 2011-08-16
Language: en
Type: preprint
Access and Citation
AI Researcher Chatbot
Get quick answers to your questions about the article from our AI researcher chatbot