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From: cmpbsdb@gitpyr.UUCP (Don Barry)
Newsgroups: net.math
Subject: Re: Can you prove/disprove this?
Message-ID: <1117@gitpyr.UUCP>
Date: Fri, 29-Nov-85 23:37:41 EST
Article-I.D.: gitpyr.1117
Posted: Fri Nov 29 23:37:41 1985
Date-Received: Sat, 30-Nov-85 07:09:06 EST
References: <34080@lanl.ARPA>
Distribution: net
Organization: Georgia Institute of Technology
Lines: 19

In article <34080@lanl.ARPA>, dxm@lanl.ARPA writes:
> .... numbers of the form 
> 
> 		x = 2^(n-1) * (2^n - 1)
> 
> are perfect if n is a prime number.....

Actually, the result you have hit upon only holds true for those values
of n that yield the Mersenne primes.  For every mersenne prime, there exists
a perfect number - a result established by Euler long ago.  Of course, your
"x" above goes up so rapidly with n that you can only test the first few
values, where the mersennes are happily populated.  
  
-- 

Don Barry (Chemistry Dept)          CSnet: cmpbsdb%gitpyr.GTNET@gatech.CSNET
Georgia Institute of Technology    BITNET: CMPBSDB @ GITVM1
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