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Theorem eight

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  • FILIPPO GIORDANO
    If 2^p -1 is a prime, then the sum of powers (consisting of p elements) existing between 2^p-1 and 2^2(p-1), extremes included, is a perfect. Example: p=3;
    Message 1 of 2 , Jan 4, 2002
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      If 2^p -1 is a prime, then the sum of powers (consisting of p elements) existing between 2^p-1 and 2^2(p-1), extremes included, is a perfect.

      Example: p=3; 2^p -1 = 7;
      then the sum of 2^2 + 2^3 + 2^4 =
      = 4 + 8 + 16 (elements = 3 = p) = 28;

      Example:p=5; 2^p -1 = 31;
      then the sum of 2^4 + 2^5 + 2^6 + 2^7 + 2^8 =
      = 16 + 32 + 64 + 128+ 256 (elements = 5 =p) = 496;

      Example: p=7; 2^p -1= 127;
      then the sum of 2^6 + 2^7 + ...+ 2^12
      = 64 + 128 + ... + 4096 (element = 7 = p) = 8128.

      Filippo Giordano


      [Non-text portions of this message have been removed]
    • djbroadhurst
      FILIPPO GIORDANO has merely restated http://aleph0.clarku.edu/~djoyce/java/elements/bookIX/propIX36.html It s a good job that copyright on the Elements has
      Message 2 of 2 , Jan 4, 2002
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        FILIPPO GIORDANO has merely restated
        http://aleph0.clarku.edu/~djoyce/java/elements/bookIX/propIX36.html
        It's a good job that copyright on the Elements has expired :-)
        David
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