Is 2(2^(p) − 1) a divisor of n? How about 2^2(2^(p − 1))? Finish the proof.

A positive integer is called whole if it equals the sum of its positive divisors.

Example: 6 is whole because the divisors of 6are 1,2 and 3 and 6=1+2+3.

Show that 28 is whole.

We want to show that the number n = 2^(p−1)(2^(p) − 1) is a whole number when 2^(p) − 1 is prime.

What are the divisors of 2^(p−1)? (it might help to try various values: what are the divisors of 2^3 or 2^4…?)

What is their sum? Hint: 1+2+2^2 +…2^k =2^(k+1) −1(geometric series)

Is 2(2p − 1) a divisor of n? How about 22(2p − 1)? Finish the proof.