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arXiv · 1309.4030

Perfect powers expressible as sums of two fifth or seventh powers

Sander R. Dahmen·Samir Siksek
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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 nonexistence 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.

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Sander R. Dahmen, Samir Siksek. 2014-01-26. Perfect powers expressible as sums of two fifth or seventh powers. https://arxiv.org/abs/1309.4030

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