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.

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.