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If f is irreducible and |f(0)| not a square then f(x^2) irr.

Source: Romanian IMO Team Selection Test TST 2003, problem 5

September 24, 2005
algebrapolynomialcalculusintegrationfunctioncomplex numbersabsolute value

Problem Statement

Let f∈Z[X]f\in\mathbb{Z}[X] be an irreducible polynomial over the ring of integer polynomials, such that ∣f(0)∣|f(0)| is not a perfect square. Prove that if the leading coefficient of ff is 1 (the coefficient of the term having the highest degree in ff) then f(X2)f(X^2) is also irreducible in the ring of integer polynomials. Mihai Piticari
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