Fermat's Last Theorem over $\mathbb{Q}(\sqrt{2},\sqrt{3})$

Abstract

In this paper, we begin the study of the Fermat equation $x^n+y^n=z^n$ over real biquadratic fields. In particular, we prove that there are no non-trivial solutions to the Fermat equation over $\mathbb{Q}(\sqrt{2},\sqrt{3})$ for $n\ge 4$.

Accepted in Algebra & Number Theory. Changes: minor corrections; included link to GitHub repository; Section 7 improved

References in corpus (2)

• Two-cover descent on hyperelliptic curves
• Fermat's Last Theorem and modular curves over real quadratic fields