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odd-perfect numbers don't exist

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  • leavemsg1
    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
    Message 1 of 6 , Dec 5, 2011
      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
      ...
    • leavemsg1
      Message 2 of 6 , Dec 5, 2011
        > ... 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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