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Perfect powers expressible as sums of two fifth or seventh powers
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Dahmen, Sander R. and Siksek, Samir (2014) Perfect powers expressible as sums of two fifth or seventh powers. Acta Arithmetica, Volume 164 (Number 1). pp. 65-100. doi:10.4064/aa164-1-5 ISSN 0065-1036.
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Official URL: http://dx.doi.org/10.4064/aa164-1-5
Abstract
We show that the generalized Fermat equations with signatures (5,5,7), (5,5,19), and (7,7,5) (and unit coefficients) have no non-trivial primitive integer solutions. Assuming GRH, we also prove the non-existence of non-trivial primitive integer solutions for the signatures (5,5,11), (5,5,13), and (7,7,11). The main ingredients for obtaining our results are descent techniques, the method of Chabauty–Coleman, and the modular approach to Diophantine equations.
Item Type: | Journal Article | ||||||
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Divisions: | Faculty of Science, Engineering and Medicine > Science > Mathematics | ||||||
Journal or Publication Title: | Acta Arithmetica | ||||||
Publisher: | Polska Akademia Nauk: Instytut Matematyczny | ||||||
ISSN: | 0065-1036 | ||||||
Official Date: | 25 January 2014 | ||||||
Dates: |
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Volume: | Volume 164 | ||||||
Number: | Number 1 | ||||||
Page Range: | pp. 65-100 | ||||||
DOI: | 10.4064/aa164-1-5 | ||||||
Status: | Peer Reviewed | ||||||
Publication Status: | Published | ||||||
Access rights to Published version: | Restricted or Subscription Access | ||||||
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