About perfect numbers

Prove the following about perfect numbers:

1. Any odd perfect number can't be a square number.
2. The sum of reciprocals of factors of a perfect number is equal to that perfect number.
3. Prove that odd perfect numbers are of the form:

N=p^(4x+1)* Q^2, where p is of the form (4y+1).

4. Also prove that no odd perfect number is a multiple of 105.
5. The smallest factor of an odd perfect number <= (2k + 6)/3, where k is the number of it's prime factors.
6. Prove that, if p is of the form (12k + 1), corresponding odd perfect number will always be of the form (12k + 1).