Okay, I have a few questions pertaining to perfect numbers.
Q1:
The theorem in my book states that a prime power is never a perfect number. Therefore if p is a prime, then p^n cannot be a perfect number. Can anyone explain why this is?
Q2:
Suppose that p is a prime and that (2^p)-1 is also prime (in fact a Mersenne prime) . It can be prove that :
n = [2^(p-1)]*[(2^p)-1] is a perfect number. How can this be proven? I've tried like 5 times and can't get anywhere with this.