تقرير
Asymptotic Fermat's Last Theorem for a family of equations of signature $(2, 2n, n)$
| العنوان: | Asymptotic Fermat's Last Theorem for a family of equations of signature $(2, 2n, n)$ |
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| المؤلفون: | García, Pedro-José Cazorla |
| سنة النشر: | 2024 |
| المجموعة: | Mathematics |
| مصطلحات موضوعية: | Mathematics - Number Theory, 11D61 (Primary), 11D41, 11F80, 11F11 (Secondary) |
| الوصف: | In this paper, we study the integer solutions of a family of Fermat-type equations of signature $(2, 2n, n)$, $Cx^2 + q^ky^{2n} = z^n$. We provide an algorithmically testable set of conditions which, if satisfied, imply the existence of a constant $B_{C, q}$ such that if $n > B_{C,q}$, there are no solutions $(x, y, z, n)$ of the equation. Our methods use the modular method for Diophantine equations, along with level lowering and Galois theory. Comment: 20 pages |
| نوع الوثيقة: | Working Paper |
| URL الوصول: | http://arxiv.org/abs/2404.14098 |
| رقم الأكسشن: | edsarx.2404.14098 |
| قاعدة البيانات: | arXiv |
| الوصف غير متاح. |