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

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

2008-02-08

arxiv.org/abs/0802.1217v2

Mathematics

Number Theory

major revision: mistakes corrected, several new cases covered

Scientific paper

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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