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On the generalized Fermat equation over totally real fields

Volume 173 / 2016

Heline Deconinck Acta Arithmetica 173 (2016), 225-237 MSC: Primary 11D41; Secondary 11F80, 11F03. DOI: 10.4064/aa8171-1-2016 Published online: 2 May 2016


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.


  • Heline DeconinckMathematics Institute
    University of Warwick
    Coventry, CV4 7AL, United Kingdom

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