MathDB
IMC 2006, problem 4, day 1

Source:

July 22, 2006
functionalgebrapolynomialrational functionIMCcollege contests

Problem Statement

Let f be a rational function (i.e. the quotient of two real polynomials) and suppose that f(n)f(n) is an integer for infinitely many integers n. Prove that f is a polynomial.