5

Part of 2003 Romania Team Selection Test

Problems(1)

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

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

f(X^2)

is also irreducible in the ring of integer polynomials. Mihai Piticari

algebrapolynomialcalculusintegrationfunctioncomplex numbersabsolute value