{"title":"legende - teege二次互易性","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":"{\"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}","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}
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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