2011/08/16 by Petrov, Fedor, Volkov, Vladislav
#11C08 #11R11 #13F20 #Commutative Algebra (math.AC) #FOS: Mathematics #Number Theory (math.NT)
paper · doi:10.48550/arxiv.1108.3212
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 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.