On the generalized Fermat equation over totally real fields

2015/05/22 by Deconinck, Heline · 4 citations
#FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.1505.06117

Abstract

In a recent paper, Freitas and Siksek proved an asypmtotic version of Fermat's Last Theorem for many totally real fields. We prove an extension of their result to generalized Fermat equations of the form A x^p+B y^p+ C z^p=0, where A, B, C are odd integers belonging to a totally real field.

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• A survey on the generalized Fermat equation of various signatures over totally real fields
• Non-trivial Solutions of Aa^p+Bb^p=Cc³ over Number Fields
• Effective Generalized Fermat equation of signature (2p, 2q, r) with odd narrow class number
• Solving Fermat-type equations over quadratic fields

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