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Perfect Number Proof

  1. Nov 30, 2013 #1
    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 [itex]\sigma[/itex](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. jcsd
  3. Nov 30, 2013 #2

    Dick

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    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?
     
  4. Nov 30, 2013 #3
    aha, thanks!
     
  5. Nov 30, 2013 #4

    Dick

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    Yeah, and actually this is already mentioned in the paper in Theorem 4.
     
  6. Nov 30, 2013 #5
    oh man I can't believe I missed that :uhh:
     
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