Recall that an integer n is called perfect if it equals the sum of all its divisors d with 1 d For example, 28 is perfect because 1+2+4+7+14 = 28. Let a be a positive integer. Prove that 2a - 1 is...

Recall that an integer n is called perfect if it equals the sum of all its divisors d with 1

d <>

For example, 28 is perfect because 1+2+4+7+14 = 28. Let a be a positive integer. Prove that 2^a
- 1 is prime, then n = 2^a-1
(2^a
-1) is perfect