Solving Fermat-type equations $x^5+y^5=dz^p$
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- by Nicolas Billerey and Luis V. Dieulefait PDF
- Math. Comp. 79 (2010), 535-544 Request permission
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 earlier results for this equation. We finally discuss the present limits of the method by looking at the case $d=3$.References
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Additional Information
- Nicolas Billerey
- Affiliation: Université Pierre et Marie Curie – Paris 6, UMR 7586, Case 247, 4, place Jussieu, Institut de Mathématiques, 75252 Paris, France
- MR Author ID: 823614
- Email: billerey@math.jussieu.fr
- Luis V. Dieulefait
- Affiliation: Departament d’Algebra i Geometria, Universitat de Barcelona, Gran Via de les Corts Catalanes 585, (08007) Barcelona, Spain
- MR Author ID: 671876
- Email: ldieulefait@ub.edu
- Received by editor(s): July 10, 2008
- Received by editor(s) in revised form: January 28, 2009
- Published electronically: July 22, 2009
- © Copyright 2009
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Math. Comp. 79 (2010), 535-544
- MSC (2000): Primary 11F11, 11D41, 14H52; Secondary 11D59
- DOI: https://doi.org/10.1090/S0025-5718-09-02294-7
- MathSciNet review: 2552239