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A Proof on Quasiperfect Numbers

  1. Mar 4, 2012 #1
    A Quasiperfect number is any number for which the sum of it's divisors is equal to one minus twice the number, or a number where the following form is true,

    σ(n)=2n+1

    One of the well known and most difficult questions in mathematics is whether such numbers exist at all. I have created a rather interesting proof to show that quasiperfect numbers do not exist. I use a process of transformation to create a situation necessary for the existence of a quasiperfect number, and then show that such a situation is impossible, therefore disproving the possibility of a quasiperfect number.

    View attachment On the Nonexistence of Quasiperfect Numbers.pdf
     
    Last edited: Mar 4, 2012
  2. jcsd
  3. Mar 4, 2012 #2
    Why not use the same argument with n=2x+1 to prove that odd numbers do not exist?
     
  4. Mar 5, 2012 #3
    Hi, Joseph,
    there is a problem when going from eq.8 to eq.9: [itex]1 - (h(n) - 2)[/itex] is not [itex]-(h(n)+1)[/itex] (which is negative), but [itex]3 - h(n)[/itex] (which is positive).
     
  5. Mar 5, 2012 #4
    Which would mean that my proof is fallous.:redface: Oh, well back to the drawing board. Anyone have any ideas where to go from here. Any help would be appreciated.
     
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