Integer-Representing Polynomial

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  of degree  in the variable  can be written in the form

where  is a binomial coefficient and , , ...,  are integers (Nagell 1951, p. 121).

REFERENCES:

Nagell, T. "Polynomials Representing Integers." §35 in Introduction to Number Theory. New York: Wiley, pp. 115-120 and 121, 1951.