奇合数n不是完全数的一些命题

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.

Several results on the positive odd numbers n is not perfect number

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 .