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arXiv · 2506.10667

The Generalized Fermat Equation $x^2 + y^3 = z^{25}$

Nuno Freitas·Michael Stoll
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Abstract

We consider the generalized Fermat equation (*) $x^2 + y^3 = z^{25}$. Using the known parameterization of the primitive integral solutions to $x^2 + y^3 = z^5$ (due to Edwards), we reduce the solution of (*) to the solution of five specific equations of the form $H(u,v) = w^5$, where $H$ is homogeneous of degree $10$ with coefficients in a sextic number field $K$, $u$ and $v$ are coprime (rational) integers, and $w \in K$.

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Nuno Freitas, Michael Stoll. 2025-06-12. The Generalized Fermat Equation $x^2 + y^3 = z^{25}$. https://arxiv.org/abs/2506.10667

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