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Prime ideal factorization and \(p\)-integral basis of quintic number fields defined by \(X^5+aX+b\). (English) Zbl 1407.11145

Summary: Based on Newton polygon techniques, for every prime integer \(p\), a \(p\)-integral basis of \(\mathbb{Z}_K\), and the factorization of the principal ideal \(p\mathbb{Z}_K\) into prime ideals of \(\mathbb{Z}_K\) are given, where \(K\) is a quintic number field defined by an irreducible trinomial \(X^5+aX+b\in\mathbb{Z}[X]\).

MSC:

11Y40 Algebraic number theory computations
11R16 Cubic and quartic extensions
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