Perfection

A Perfect Number is a positive integer that is equal to the sum of its proper positive divisors.
For example: 6 = 1 + 2 + 3.

Euclid proved that [2^(p−1)]*(2^p−1) is an even perfect number whenever 2^p−1 is prime.
('^' here represents exponentiation: 2^2 = 2*2 = 4; 2^3 = 2*2*2 = 8; 3^2 = 3*3 = 9.)

Euler proved that every even perfect number has the form given above.

Does an odd perfect number exist?
No one knows.