Legendre–Teege Quadratic Reciprocity

IF 0.4 4区数学 Q4 MATHEMATICS

American Mathematical Monthly Pub Date : 2023-03-13 DOI:10.1080/00029890.2023.2184164

Mark B. Villarino

引用次数: 0

Abstract

Abstract Legendre published the first attempted proof of the law of Quadratic Reciprocity. In its final form (1797), however, it had a gap in the form of an unproven hypothesis. Some 125 years later, Herman Teege published the first rigorous proof of that hypothesis. Then, 48 years later, Kenneth Rogers published a second (but implicit) proof. These proofs elevated Legendre’s attempt to the list of complete proofs. No detailed exposition of these proofs appears in the literature. Our paper fills that gap.

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legende - teege二次互易性

勒让德发表了第一个关于二次互易律的尝试证明。然而，在它的最终形式(1797年)中，它有一个未被证实的假设形式的缺陷。大约125年后，赫尔曼·蒂格(Herman Teege)发表了对这一假设的第一个严格证明。48年后，肯尼斯·罗杰斯(Kenneth Rogers)发表了第二个(但隐含的)证明。这些证明将勒让德的尝试提升到了完整证明的行列。没有这些证明的详细说明出现在文献中。我们的论文填补了这一空白。

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

American Mathematical Monthly Mathematics-General Mathematics

CiteScore

0.80

自引率

20.00%

发文量

127

审稿时长

6-12 weeks

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