On a family of biquadratic fields that do not admit a unit power integral basis

Abstract

In this paper, we consider the following family of biquadratic fields: K = \mathbb{Q}(\sqrt{18n^2 + 17n + 4},\sqrt{2n^2 + n}), and show that provided that 18n^2 + 17n + 4 and 2n^2 +n are both square-free, K does not admit a power integral basis consisting of units.