To the question, "Is there any odd Perfect Number?" Nobody knows the answer to that question. The only sure thing we know is that if N is such odd perfect number then N is greater than 10^300 (Brent, Cohen & Te Riele, 1991).
There is a project underway athttp://www.oddperfect.org/ seeking to extend
the limit beyond 10^300
Suppose that a natural number n is odd and n is equal to the sum of all its positive divisors (including 1 and excluding n) Then n is not divisible by 105.
True or False?