A polynomial that represents integers for all integer values of the variables. An integer polynomial is a special case of such a polynomial. In general, every integer representing polynomial f(x) of degree n in the variable x can be written in the form f(x) = A_0 + A_1(x 1) + A_2(x 2) + ... + A_n(x n), where (n k) is a binomial coefficient and A_0, A_1, ..., A_n are integers.