Monogenity of iterates of irreducible binomials

One of the oldest problems of algebraic number theory is to find a method to determine if the ring of integers of a number field K is Zθ for some θ∈K; a field for which the answer to this question is affirmative is referred to as a monogenic field. Suppose f(x)=xm−a∈Zx is a monic irreducible polynomial and αn∈C is a root of fn(x), the n-fold composition of f. In this article, we prove a necessary and sufficient condition for Kn=Q(αn) to be monogenic for every n∈N and m≥2.