{"title":"关于奇完全数的欧拉形式","authors":"Balchandar Reddy Sangam","doi":"10.22457/apam.v22n1a07685","DOIUrl":null,"url":null,"abstract":"Euler has proved that an odd perfect number, if exists, must be of the form ... , ≡ ≡ 1 (mod 4). In this article, we show: (i) An alternative proof to the Euler’s form of odd perfect numbers. (ii) An odd number of the form: , ≡ ≡ 1 (mod 4) cannot be perfect.","PeriodicalId":305863,"journal":{"name":"Annals of Pure and Applied Mathematics","volume":"164 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"On the Euler’s Form of an odd Perfect Number\",\"authors\":\"Balchandar Reddy Sangam\",\"doi\":\"10.22457/apam.v22n1a07685\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Euler has proved that an odd perfect number, if exists, must be of the form ... , ≡ ≡ 1 (mod 4). In this article, we show: (i) An alternative proof to the Euler’s form of odd perfect numbers. (ii) An odd number of the form: , ≡ ≡ 1 (mod 4) cannot be perfect.\",\"PeriodicalId\":305863,\"journal\":{\"name\":\"Annals of Pure and Applied Mathematics\",\"volume\":\"164 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"1900-01-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Annals of Pure and Applied Mathematics\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.22457/apam.v22n1a07685\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Annals of Pure and Applied Mathematics","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.22457/apam.v22n1a07685","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Euler has proved that an odd perfect number, if exists, must be of the form ... , ≡ ≡ 1 (mod 4). In this article, we show: (i) An alternative proof to the Euler’s form of odd perfect numbers. (ii) An odd number of the form: , ≡ ≡ 1 (mod 4) cannot be perfect.
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