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Re: odd-perfect numbers don't exist

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  • leavemsg1
    Message 1 of 6 , Dec 5, 2011
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      > ... this's more readable, I hope.
      >............................2*t...........t - 2
      >........................._________......_________
      >.........................\..............\
      >..........................\..............\
      > N=(2^t)*(2^(t +1) -1) =...}..2^r...-.....}..2^s....; (t +1)= p
      > from a Mersenne prime..../............../
      >........................./________....../________
      >............................r= 1...........s= 1
      > ...

      --- In primenumbers@yahoogroups.com, "leavemsg1" <leavemsg1@...> wrote:
      >
      > Hi, Dr. Smith,
      >
      > I got it!!!!!!!!!!!!!!!... here it is...
      > you can visit my website... www.oddperfectnumbers.com.
      > or read below.
      > ...
      > for those of you that have visited my website, I've spent
      > the last 10 years (almost 100 drafts) searching for a rea-
      > sonable explanation for why odd-perfect numbers don't exist,
      > and here it is...
      > ...
      > a puzzle of antiquity, fittingly solved, if you will...
      > using simple algebra.
      > ...
      > the first few 'perfect' numbers are 6, 28, 496, and 8128.
      > Euler proved that they were all of the form... N= (2^(n-1))
      > *(2^n -1), he knew that the (2^n -1) portion had to always
      > be prime, and he also noted that sigma(N) = 2N when N is a
      > 'perfect' number. Notice how I'm putting the quotations
      > around the word 'perfect'.
      > ...
      > the situation was more perfect than you might imagine, and
      > I'm sure that you will be convinced that Euler's famous form-
      > ula cannot be altered as he mentioned in order to produce an
      > odd-perfect number! Here's what was missing...
      >............................2*t...........t - 2
      >........................._________......_________
      >.........................\..............\
      >..........................\..............\
      > N=(2^t)*(2^(t +1) -1) =...}..2^r...-.....}..2^s....; (t +1)= p
      > from a Mersenne prime..../............../
      >........................./________....../________
      >............................r= 1...........s= 1
      > ...
      > (OR) 6 = 2^1 +2^2 -(0),
      > 28 = 2^1 +2^2 +2^3 +2^4 -(2^1),
      > 496 = 2^1 +2^2 +2^3 +2^4 +2^5 +2^6 +2^7 +2^8 - (2^3 +2^2 +2^1),
      > 8128 = etc.
      > ...
      > when 'N' is 'perfect', 'N' is equal to the sum (or rather the
      > difference) of two summations that are purely binary. It was
      > more delicate that previously thought. Changing the base from
      > '2' to something else would be the only meaningful change to
      > such a demanding, connective equation, and that leads us to the
      > conclusion that an 'odd-perfect-number notion' is out of the
      > question, and can't be 'perfect'.
      > ...
      > thus, odd-perfect numbers don't exist!
      > ...
      > obviously, when someone as prolific as Euler stated that this
      > problem was too complicated to be easily solved, every mathema-
      > tician was easily pursuaded to believe it; but if you (OR) I
      > decided to retain Euler's already-proven formula for an odd-
      > perfect number, it's surprising to me that we could have been
      > mislead by his prior conclusion!
      > ...
      > *QED
      > Bill Bouris
      > 12/5/2011
      > ...
      >
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