Solving Fermat-type equations x⁵+y⁵=dz^p

2008/02/08 by Billerey, Nicolas, Dieulefait, Luis · 1 citation
#FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.0802.1217

Abstract

In this paper we are interested in solving the Fermat-type equations x⁵+y⁵=dz^p where d is a positive integer and p a prime number ≥ 7. We describe a new method based on modularity theorems which allows us to improve all the results in a previous paper of the first author. We finally discuss the present limitations of the method by looking at the case d=3.

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• A survey on the generalized Fermat equation of various signatures over totally real fields

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