2021
DOI: 10.48550/arxiv.2111.05899
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On power integral bases of certain pure number fields defined by $X^{60}-m$

Abstract: Let K be a pure number field generated by a complex root of a monic irreducible polynomial±1 a square free integer. In this paper, we study the monogeneity of K. We prove that if m 1 (mod 4), m ∓1 (mod 9) and m {∓1, ∓7} (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.

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