奇完全数的欧拉因子

Euler Factor of Odd Perfect Number

证明了1)若pa+(a+1)k是奇完全数m的欧拉因子,a=2q-1若pmodq=1或q-1,则m的最小素因子不大于q.2)设pmod 5=4且pmod 7!=1则p5+6k不是奇完全数m的欧拉因子.3)设pmod 5=1且pmod 7=6,pmod 3=2则p9+10k不是奇完全数m的欧拉因子.

Let m = p^an. is odd. Perfect Number gcd（p, n） = 1 then p^a is Euler Factor of odd perfect number m The following results have been proved： 1 ） Suppose p mod 5 = 4 and p mod 7 ! = 1 , a = 5 ＋ 6k then p^a is not Euler factor 2） Suppose p mod 5 = 1 and p mod 7 = 6 , p mod 3 = 2,a= 9 ＋ 10k then p^a is not Euler factor.