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目录
英文摘要………………………………………………………………………………………………1中文摘要…………………………………………………………………………………………2梅森数的性质……………………………………………………………………………………………3引理1.1…………………………………………………………………………………………………3引理1.2…………………………………………………………………………………………………3引理1.3………………………………………………………………………………………………4引理1.4………………………………………………………………………………………………5完全数与Euler定理………………………………………………………………………………5定理2.1………………………………………………………………………………………………5奇完全数不是完全数的命题……………………………………………………………………………5命题3.1…………………………………………………………………………………………………6命题3.2………………………………………………………………………………………………7命题3.3………………………………………………………………………………………………8推论3.4…………………………………………………………………………………………………8命题3.5…………………………………………………………………………………………………9命题3.6………………………………………………………………………………………………9命题3.7…………………………………………………………………………………………………10奇完全数的两个充分必要条件………………………………………………………………………10定理4.1…………………………………………………………………………………………………10定理4.2………………………………………………………………………………………………12参考文献………………………………………………………………………………………………13
Abstract
Inthispaper.Wemainlydiscusstheexistenceoftheoddperfectnumbers.Asamatteroffact,Itisaverydifficultproblemtofindanoddperfectnumber.Itisaninternationalpuzzle.Nevertheless,Wefind5criterionsofanoddperfectnumberbeingnotaanperfectnumber.Meanwhilewealsofind2necessaryandsufficientconditionsoftheoddperfectnumbers.Atthesametime,WecitedtheconclusionsaboutthecorrespondencebetweentheoddperfectnumberandtheMersenne’sprime,andwealsoprovetheEulerTheoremofperfectnumberinourcontext.
Keywords:perfectnumberMensenne’sprimeoddperfectnumber
Numbertheory
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