Integer-valued Polynomial

In mathematics, an integer-valued polynomial (also known as a numerical polynomial) P(t) is a polynomial whose value P(n) is an integer for every integer n. Every polynomial with integer coefficients is integer-valued, but the converse is not true. For example, the polynomial

takes on integer values whenever t is an integer. That is because one of n and n + 1 must be an even number. (The values this polynomial takes are the triangular numbers.)

Integer-valued polynomials are objects of study in their own right in algebra, and frequently appear in algebraic topology.