Counting primitive integral solutions to spherical generalized Fermat equations

Santiago Arango-Piñeros

A solution $(x,y,z)\in {\mathbb{Z}}^3-\{(0,0,0)\}$ to a generalized Fermat equation \[ Ax^a + By^b + Cz^c = 0, \] is called \emph{primitive} if $\gcd (x,y,z)=1$. By work of Beukers…