Which immediately answers in the affirmative another question I had: (If P(Z) = Z, does its derivative P'(X) also take Z —> Z ?) —Dan Victor Miller wrote: ----- ... The theorem is as follows: for a positive integer n define f_n(x) = x(x-1)...(x-n+1)/n!, and f_0(x) = 1. These are clearly is integer valued at all integers. Every polynomial with rational coefficients which is integer valued at all integers is an linear combination of the f_n(x) with integer coefficients. ... -----