A multi-Frey approach to Fermat equations of signature $(r,r,p)$

Nicolas Billerey, Imin Chen, Luis Dieulefait +1

In this paper, we give a resolution of the generalized Fermat equations $$x^5+y^5=3z^n\text{ and }{x}^{13}+y^{13}=3z^n,$$ for all integers $n\ge 2$, and all integers $n…