On a family of biquadratic fields that do not admit a unit power integral basis
Copyright policy )On a family of biquadratic fields that do not admit a unit power integral basis
Summary: In this paper, we consider the following family of biquadratic fields: \par \(\mathbb{K} = \mathbb Q(\sqrt{18n^2 + 17n + 4},\sqrt{2n^2+n})\), and show that provided that \(18n^2 + 17n + 4\) and \(2^n+n\) are both square-free, \(\mathbb{K}\) does not admit a power integral basis consisting of units.
Multiplicative and norm form equations, Cubic and quartic extensions, Integral representations related to algebraic numbers; Galois module structure of rings of integers, power integral basis, unit sum number problem, system of Pell equations
Multiplicative and norm form equations, Cubic and quartic extensions, Integral representations related to algebraic numbers; Galois module structure of rings of integers, power integral basis, unit sum number problem, system of Pell equations
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