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arXiv · 0802.1217

Solving Fermat-type equations x^5+y^5=dz^p

Nicolas Billerey·Luis Dieulefait
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Abstract

In this paper we are interested in solving the Fermat-type equations x^5+y^5=dz^p where d is a positive integer and p a prime number $\ge 7$. 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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Nicolas Billerey, Luis Dieulefait. 2008-06-11. Solving Fermat-type equations x^5+y^5=dz^p. https://arxiv.org/abs/0802.1217

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