Solving Fermat-type equations x^5+y^5=dz^p
Number Theory
2008-06-11 v2
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 . 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.
Cite
@article{arxiv.0802.1217,
title = {Solving Fermat-type equations x^5+y^5=dz^p},
author = {Nicolas Billerey and Luis Dieulefait},
journal= {arXiv preprint arXiv:0802.1217},
year = {2008}
}
Comments
major revision: mistakes corrected, several new cases covered