Generalized Mordell curves, generalized Fermat curves, and the Hasse principle

Dong Quan Ngoc Nguyen

A generalized Mordell curve of degree $n\ge 3$ over $\bQ$ is the smooth projective model of the affine curve of the form $A{z}^2=B{x}^n+C$, where $A,B,C$ are nonzero integers. A…