  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.
