Modular congruences, Q-curves, and the diophantine equation x⁴ + y⁴ = z^p

2003/04/27 by Luis Dieulefait, Dieulefait, Luis
Mathematics · #11D41 #11F11 #Algebraic Geometry (math.AG) #FOS: Mathematics #Number Theory (math.NT) #math.AG #math.NT #msc:11D41 #msc:11F11

paper · pdf · doi:10.48550/arxiv.math/0304425

arxiv created 2003/04/27 · arxiv updated 2009/11/30

Abstract

We prove two results concerning the generalized Fermat equation x⁴+y⁴=z^p. In particular we prove that the First Case is true if p ≠ 7.

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