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RE: [PrimeNumbers] Perfect Number / Mersenne Prime question

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  • Paul Leyland
    ... I ve been keeping out of this up to now, but it seems time to suggest that you have only proved that all EVEN perfect numbers lie in those two residue
    Message 1 of 12 , May 20, 2004
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      > It doesn't really need to be said, but your response to me
      > was of the same
      > value as your response to D├ęcio. They have nothing to do
      > with the question
      > that was posed, nor our responses. To repeat, the question
      > was "do all
      > perfect numbers larger than 28 end in 144 or 344 (in base 6)?"
      >
      > We both noted that yes, perfect numbers of the form
      > ((2^p)-1)(2^(p-1)) end
      > in 144 or 344 in base 6, but so do also for any odd values of
      > p, so the
      > proposed test can't be used to determine if a number is
      > perfect or not.

      I've been keeping out of this up to now, but it seems time to
      suggest that you have only proved that all EVEN perfect numbers
      lie in those two residue classes modulo 6^3.

      You have not proved, as far as I can tell, that ALL perfect numbers
      are even. To the best of my knowledge, nobody else has yet done so.

      Please note that I'm not criticising your proof of the restricted
      problem (which, in my opinion, is not quite as well posed as perhaps
      it ought to have been) but only pointing out that the full problem
      is rather harder.


      Paul
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