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On Monogenity of Certain Pure Number Fields Defined by $x^{60} − m$
Lhoussain El Fadil
,
Hanan Choulli
,
Omar Kchit
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 $m\neq \pm1$ a square free integer. In this paper, we study the {monogenity} of $K$. We prove that if $m\not\equiv 1~(\mathrm{mod}~{4})$, $m\not\equiv \pm 1 ~(\mathrm{mod}~{9}) $ and $\overline{m}\not\in\{\pm 1,\pm 7\} ~({\rm mod}~{25})$, then $K$ is monogenic. But if $m\equiv 1~({\rm mod}~{4})$, $m\equiv \pm1 ~({\rm mod}~{9})$, or $m\equiv \pm 1~({\rm mod}~{25})$, then $K$ is not monogenic. Our results are illustrated by examples.