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In mathematics, an integer-valued polynomial P {\displaystyle P} is a polynomial whose value P {\displaystyle P} 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 t and t + 1 {\displaystyle t+1} must be an even number.
Integer-valued polynomials are objects of study in their own right in algebra, and frequently appear in algebraic topology.
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