# On power integral bases for certain pure number fields defined by x24 – m

@article{Fadil2020OnPI,
title={On power integral bases for certain pure number fields defined by x24 – m},
journal={arXiv: Number Theory},
year={2020}
}
• Published 19 June 2020
• Mathematics
• arXiv: Number Theory
Let $K=\mathbb{Q}(\alpha)$ be a number field generated by a complex root $\alpha$ of a monic irreducible polynomial $f(x)=x^{12}-m$, with $m\neq 1$ is a square free rational integer. In this paper, we prove that if $m \equiv 2$ or $3$ (mod 4) and $m\not\equiv \mp 1$ (mod 9), then the number field $K$ is monogenic. If $m \equiv 1$ (mod 8) or $m\equiv \mp 1$ (mod 9), then the number field $K$ is not monogenic.
12 Citations
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. Let K = Q ( θ ) be a number ﬁeld generated by a complex root θ of a monic irreducible trinomial F ( x ) = x n + ax + b ∈ Z [ x ] . There is an extensive literature of monogenity of number ﬁelds
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