On Monogenity of Certain Pure Number Fields Defined by x60 − m

Abstract

Let K be a pure number field generated by a complex root of a monic irreducible polynomial \(F(x)=x^{60}-m\in \mathbb {Z}[x]\), with m≠ ± 1 a square free integer. In this paper, we study the monogenity of K. We prove that if m≢1 (mod 4), m≢ ± 1 (mod 9) and \(\overline {m}\not \in \{\pm 1,\pm 7\} ~(\textup {mod}~{25})\), then K is monogenic. But if m ≡ 1 (mod 4), m ≡± 1 (mod 9), or m ≡± 1 (mod 25), then K is not monogenic. Our results are illustrated by examples.