The On power integral bases of certain pure number fields defined by x¹²⁰-m

Let K be a pure number field with α a complex root of a monic irreducible polynomial F(x) = x¹²⁰-m ∈ Z[x] with m ≠ ± 1. In this paper, we study the monogenity of K. More precisely, we prove that if m is square-free, m ≡ 14, m ≡ ± 1 9, and m ∈ \ ∓ 1, 7, 18 \ 25, then K is monogenic. On the other hand, if m ≡ 14, m ≡ 1 9, or m ≡ 1 25, then K is not monogenic. Our results are illustrated by some computational examples.