Asymptotic Fermat's last theorem for a family of equations of signature

IF 0.8 3区数学 Q2 MATHEMATICS

Mathematika Pub Date : 2024-08-29 DOI:10.1112/mtk.12279

Pedro-José Cazorla García

引用次数: 0

Abstract

In this paper, we study the integer solutions of a family of Fermat-type equations of signature , . We provide an algorithmically testable set of conditions which, if satisfied, imply the existence of a constant such that if , there are no solutions of the equation. Our methods use the modular method for Diophantine equations, along with level lowering and Galois theory.

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符号方程组的渐近费马最后定理

本文研究了符号为 , 的费马方程组的整数解。我们提供了一组可通过算法检验的条件，如果满足这些条件，就意味着存在一个常数，即如果，则方程没有解。我们的方法使用了 Diophantine 方程的模块法，以及水平降低和伽罗瓦理论。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Mathematika MATHEMATICS, APPLIED-MATHEMATICS

CiteScore

1.40

自引率

0.00%

发文量

审稿时长

>12 weeks

期刊介绍： Mathematika publishes both pure and applied mathematical articles and has done so continuously since its founding by Harold Davenport in the 1950s. The traditional emphasis has been towards the purer side of mathematics but applied mathematics and articles addressing both aspects are equally welcome. The journal is published by the London Mathematical Society, on behalf of its owner University College London, and will continue to publish research papers of the highest mathematical quality.