The generalized Fermat equation Ax2 + Byr = Czp and applications
Abstract
In this paper, we develop the modular method for the generalized Fermat equation appearing in the title, within the framework of Darmon's program and using Frey hyperelliptic curves. As an application, we study a conjecture of Laradji, Mignotte, and Tzanakis concerning the equation 5x2+q2n=y5.
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