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Re: no square-free odd number can be perfect.

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  • djbroadhurst
    ... Descartes remarked on this in 1638. Moroever, he knew that only one prime divisor may be raised to an odd power, which follows from merely considering
    Message 1 of 2 , Jul 15, 2011
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      --- In primenumbers@yahoogroups.com,
      Kermit Rose <kermit@...> wrote:

      > we today can make an elementary and simple proof that
      > no square-free odd number can be perfect

      Descartes remarked on this in 1638. Moroever, he knew that
      only one prime divisor may be raised to an odd power,
      which follows from merely considering sigma(N) modulo 4.

      http://www-history.mcs.st-and.ac.uk/HistTopics/Perfect_numbers.html
      gives a translation of part of his letter to Mersenne, which
      I gave in French in an earlier posting.

      David
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