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nice FE, irreducibility map

Source: VJIMC 2011 2.4

May 28, 2021
fefunctional equationPolynomialsirreducibilityalgebra

Problem Statement

Find all Q\mathbb Q-linear maps Φ:Q[x]→Q[x]\Phi:\mathbb Q[x]\to\mathbb Q[x] such that for any irreducible polynomial p∈Q[x]p\in\mathbb Q[x] the polynomial Φ(p)\Phi(p) is also irreducible.
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