The authors extend the modular method to Ax² + By^r = Cz^p using Darmon's framework and Frey hyperelliptic curves, then apply it to study the conjecture 5x² + q^{2n} = y^5.
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The generalized Fermat equation $Ax^2 + By^r = Cz^p$ and applications
The authors extend the modular method to Ax² + By^r = Cz^p using Darmon's framework and Frey hyperelliptic curves, then apply it to study the conjecture 5x² + q^{2n} = y^5.