The generalized Fermat equation $Ax^2 + By^r = Cz^p$ and applications
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arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2026
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| _version_ | 1866909012544454656 |
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| author | García, Pedro-José Cazorla Koutsianas, Angelos Villagra-Torcomian, Lucas |
| author_facet | García, Pedro-José Cazorla Koutsianas, Angelos Villagra-Torcomian, Lucas |
| contents | 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 $5x^2+q^{2n}=y^5$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_02632 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | The generalized Fermat equation $Ax^2 + By^r = Cz^p$ and applications García, Pedro-José Cazorla Koutsianas, Angelos Villagra-Torcomian, Lucas Number Theory 11D41 (Primary), 11G10 (Secondary) 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 $5x^2+q^{2n}=y^5$. |
| title | The generalized Fermat equation $Ax^2 + By^r = Cz^p$ and applications |
| topic | Number Theory 11D41 (Primary), 11G10 (Secondary) |
| url | https://arxiv.org/abs/2605.02632 |