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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2506.10667 |
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| _version_ | 1866918154993664000 |
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| author | Freitas, Nuno Stoll, Michael |
| author_facet | Freitas, Nuno Stoll, Michael |
| contents | 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 $w \in K$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_10667 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | The Generalized Fermat Equation $x^2 + y^3 = z^{25}$ Freitas, Nuno Stoll, Michael Number Theory 11G30, 11G35, 14K20 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 $w \in K$. |
| title | The Generalized Fermat Equation $x^2 + y^3 = z^{25}$ |
| topic | Number Theory 11G30, 11G35, 14K20 |
| url | https://arxiv.org/abs/2506.10667 |