Integer Polynomial

A polynomial of the form

having coefficients  that are all integers. An integer polynomial gives integer values for all integer arguments of (Nagell 1951, p. 73). The set of integer polynomials is denoted . Integer polynomials are sometimes also called "integral polynomials," although this usage should be deprecated due to its confusing use of the term "integral" as an adjective.

An integer polynomial is called primitive if the greatest common divisor .

REFERENCES:

Nagell, T. "Prime Divisors of Integral Polynomials" and "Divisibility of Integral Polynomials with Regard to a Prime Modulus." §25 and 29 in Introduction to Number Theory. New York: Wiley, pp. 73, 81-83, and 93-98, 1951.