On the generalized Fermat equation $x^{13}+y^{13}=z^n$

Alex J. Best, Sander R. Dahmen, Nuno Freitas

Let $n\in {\mathbb{Z}}_{\ge 2}$. We study the generalized Fermat equation \[x^{13}+y^{13}=z^n, \quad x,y,z \in \mathbb{Z}, \quad \gcd(x,y,z)=1.\] Using a combination of techniques,…