Homework Help: Perfect Number Proof

1. Nov 30, 2013

srfriggen

1. The problem statement, all variables and given/known data

Prove: If 2p-1 is prime, then 2p-1(2p-1) is a perfect number.

2. Relevant equations

I am simply having trouble understanding one part of the end of the proof, namely:

Why does $\sigma$(2p-1)=2p-1 ?

The proof I'm working off of (trying to understand is on page 4 of this link: http://www.math.dartmouth.edu/~jvoight/notes/perfelem.pdf

3. The attempt at a solution
1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution

2. Nov 30, 2013

Dick

It's pretty easy. The divisors of 2^(p-1) are 1,2,2^2,2^3,...2^(p-1). The divisors form a geometric series. What's its sum?

3. Nov 30, 2013

srfriggen

aha, thanks!

4. Nov 30, 2013

Dick

Yeah, and actually this is already mentioned in the paper in Theorem 4.

5. Nov 30, 2013

srfriggen

oh man I can't believe I missed that :uhh: