奇合数n不是完全数的一些命题  

Several results on the positive odd numbers nis not perfect number

作　　者：张四保 

机构地区：[1]喀什大学数学与统计学院,新疆喀什844008

出　　处：《安徽大学学报（自然科学版）》2016年第3期6-11,共6页Journal of Anhui University(Natural Science Edition)

基　　金：国家自然科学基金资助项目(11201411);喀什大学科研基金资助项目(142513)

摘　　要：奇完全数问题是数论中的一著名难题.探讨形如4 m+1的奇正整数n=παq2β11 q2β22…q2βss是否为完全数问题,给出其在σ(πα)≡2(mod8)条件下不是完全数的一些命题,由此可以类似地讨论其在σ(πα)≡6(mod8)条件下的情形,从而可以给出4 m+1型合数不是完全数的一系列条件.The problem of perfect number was a well-known difficult problem in number theory. In this paper, the problem that the positive odd numbers of the form 4m＋1 was not perfect number was studied. And in the condition of δ（πa^）≡2（mod8）, some results on the composite number n=πa^q12β1q2β3…q2^β5 be the form of 4m＋1 was not perfect were given. Similarly, the conditions of n=πa^q12β1q2β3…q2^β5was not odd perfect number in the condition of δ（πa^）≡6（mod8）（roodS） can be discussed. Therefore, a series of conditions of the form of 4m＋1 was not perfect number could be given.

关 键 词：完全数 奇完全数 条件 

分 类 号：O156[理学—数学]