Solving Fermat-type equations x^5+y^5=dz^p
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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.
major revision: mistakes corrected, several new cases covered
major revision: mistakes corrected, several new cases covered