奇合数 n 不是完全数的一些命题

摘要

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 ofσ(πα) ≡ 2(mod8) ,some results on the composite number n = παq2β11 …q2βss be the form of 4m + 1 was not perfect were given . Similarly ,the conditions of n = παq2β11 …q2βss was not odd perfect number in the condition ofσ(πα) ≡ 6(mod8) can be discussed .Therefore ,a series of conditions of the form of 4m+1 was not perfect number could be given .%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4m＋1型合数不是完全数的一系列条件。