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From: stan@clyde.UUCP
Newsgroups: net.math
Subject: Re: Mersenne, Fermat, Perfection, and History
Message-ID: <221@clyde.UUCP>
Date: Sun, 23-Oct-83 19:51:44 EDT
Article-I.D.: clyde.221
Posted: Sun Oct 23 19:51:44 1983
Date-Received: Wed, 26-Oct-83 00:20:51 EDT
References: <1674@gatech.UUCP>
Organization: Bell Labs Whippany NJ
Lines: 18

Path: clyde!akgua!emory!gatech!spaf
From: spaf@gatech.UUCP

Euclid, in book 9 of "Elements," proved that if (2^p-1) is prime, then
the product of (2^p-1) and (2^(p-1)) is perfect.  Euclid showed (about
2000 years later) that every EVEN perfect number must be of this form.
^^^^ ^^^^^ ^^^^^
(The proofs are simple and can be provided on request.) The
relationship to Mersenne primes should be obvious.

=-=-=-=-=-=-=-=-=-=
I declare.  Some people really take a long time to get around
to publishing.  Do you s'pose it took him that long to get his
thesis done?

		Stan King			phone: 201-386-7433
		Bell Labs, Whippany, NJ		Cornet:  8+232-7433
		room 2A-111			uucp:	 clyde!stan