On the generalized Fermat equation over totally real fields
Volume 173 / 2016
Acta Arithmetica 173 (2016), 225-237
MSC: Primary 11D41; Secondary 11F80, 11F03.
DOI: 10.4064/aa8171-1-2016
Published online: 2 May 2016
Abstract
In a recent paper, Freitas and Siksek proved an asymptotic 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.
