Proving Perfect Number Proof: 2p-1(2p-1)

[srfriggen]

Homework Statement

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

Homework Equations

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

Why does \sigma(2^p-1)=2^p-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

The Attempt at a Solution

 

[Dick]

Homework Statement

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

Homework Equations

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

Why does \sigma(2^p-1)=2^p-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

The Attempt at a Solution

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?

 

[srfriggen]

aha, thanks!

 

[Dick]

aha, thanks!

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

 

[srfriggen]

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

oh man I can't believe I missed that