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arXiv · 2605.02632

The generalized Fermat equation $Ax^2 + By^r = Cz^p$ and applications

Pedro-José Cazorla García·Angelos Koutsianas·Lucas Villagra-Torcomian
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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 $5x^2+q^{2n}=y^5$.

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Pedro-José Cazorla García, Angelos Koutsianas, Lucas Villagra-Torcomian. 2026-05-04. The generalized Fermat equation $Ax^2 + By^r = Cz^p$ and applications. https://arxiv.org/abs/2605.02632

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