Perfect powers expressible as sums of two fifth or seventh powers

• Autorzy: Sander R. Dahmen , Samir Siksek
• Języki publikacji: EN

Abstrakty

EN

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.

Kategorie tematyczne

• 11F80: Galois representations
• 11D41: Higher degree equations; Fermat's equation
• 11G30: Curves of arbitrary genus or genus ≠ 1 over global fields

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Acta Arithmetica
• Rocznik: 2014
• Tom: 164
• Numer: 1
• Strony: 65-100

Daty

wydano

2014

Twórcy

autor

Sander R. Dahmen

• Department of Mathematics, VU University Amsterdam, De Boelelaan 1081a, 1081 HV Amsterdam, The Netherlands

autor

Samir Siksek

• Mathematics Institute, University of Warwick, Coventry, CV4 7AL, United Kingdom

Identyfikatory

DOI

10.4064/aa164-1-5