On the Difference of Two Fourth Powers

IF 0.7 3区数学 Q2 MATHEMATICS

Proceedings of the Edinburgh Mathematical Society Pub Date : 2023-11-10 DOI:10.1017/s0013091523000706

Nguyen Xuan Tho

引用次数: 0

Abstract

Abstract We investigate the equation $D=x^4-y^4$ in field extensions. As an application, for a prime number p , we find solutions to $p=x^4-y^4$ if $p\equiv 11$ (mod 16) and $p^3=x^4-y^4$ if $p\equiv 3$ (mod 16) in all cubic extensions of $\mathbb{Q}(i)$ .

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关于两次四次方之差

研究了域扩展中的方程$D=x^4-y^4$。作为一个应用，对于素数p，我们找到了$p=x^4-y^4$ if $p\equiv 11$ (mod 16)和$p^3=x^4-y^4$ if $p\equiv 3$ (mod 16)在$\mathbb{Q}(i)$的所有三次扩展中的解。

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

Proceedings of the Edinburgh Mathematical Society 数学-数学

CiteScore

1.10

自引率

0.00%

发文量

审稿时长

6 months

期刊介绍： The Edinburgh Mathematical Society was founded in 1883 and over the years, has evolved into the principal society for the promotion of mathematics research in Scotland. The Society has published its Proceedings since 1884. This journal contains research papers on topics in a broad range of pure and applied mathematics, together with a number of topical book reviews.