On the irreducibility of the iterates of 𝑥ⁿ-𝑏

Danielson, Lynda; Fein, Burton

doi:10.1090/S0002-9939-01-06258-X

On the irreducibility of the iterates of $x^{n}-b$
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Proc. Amer. Math. Soc. 130 (2002), 1589-1596 Request permission

Abstract:

Let $K$ be a field and suppose that $f(x)=x^{n}-b$ is irreducible in $K[x]$. We discuss the following question: under what conditions are all iterates of $f$ irreducible over $K$?

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