{"title":"Legendre–Teege Quadratic Reciprocity","authors":"Mark B. Villarino","doi":"10.1080/00029890.2023.2184164","DOIUrl":null,"url":null,"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.","PeriodicalId":7761,"journal":{"name":"American Mathematical Monthly","volume":null,"pages":null},"PeriodicalIF":0.4000,"publicationDate":"2023-03-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"American Mathematical Monthly","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1080/00029890.2023.2184164","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"MATHEMATICS","Score":null,"Total":0}
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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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