## Theorem eight

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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;
Message 1 of 2 , Jan 4, 2002
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

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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
Message 2 of 2 , Jan 4, 2002
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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