RO-TST 2003 Problem 5

Let $f\in\mathbb{Z}[X]$ be an irreducible polynomial over the ring of integer polynomials, such that $|f(0)|$ is not a perfect square. Prove that if the leading coefficient of $f$ is 1 (the coefficient of the term having the highest degree in $f$ ) then $f(X^2)$ is also irreducible in the ring of integer polynomials.

Mihai Piticari