Home > IMO, Problem Solving > Irreductible Polynomial TST 2003

Irreductible Polynomial TST 2003

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, Romanian TST 2003

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