Papers › The Generalized Fermat Equation x² + y³ = z²⁵
The Generalized Fermat Equation x² + y³ = z²⁵
Nuno Freitas, Michael Stoll
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We consider the generalized Fermat equation (*) x² + y³ = z²⁵. Using the known parameterization of the primitive integral solutions to x² + y³ = z⁵ (due to Edwards), we reduce the solution of (*) to the solution of five specific equations of the form H(u,v) = w⁵, where H is homogeneous of degree $10$ with coefficients in a sextic number field K, u and v are coprime (rational) integers, and w ∈K.
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