From: Karl Lui Barrus <klbarrus@owlnet.rice.edu>
Date: Tue, 26 Apr 94 20:55:56 PDT
To: johnsonc@chem.udallas.edu (Carrie A. Johnson)
Subject: Re: prime numbers
In-Reply-To: <9404262331.AA13940@chem.udallas.edu>
Message-ID: <9404270355.AA17650@flammulated.owlnet.rice.edu>
MIME-Version: 1.0
Content-Type: text/plain


Carrie A. Johnson wrote:
> I'm just wondering if anyone knows whether or not (1+4k) can be 
>written as the sum of squares or not, and if so, what the proof 
>of that is? 

Hm... interesting.  There is a related problem about every integer
being represented as the sum of four squares, but you ask if
(1+4k) can be written as a sum of squares, without mentioning a limit
on the number of squares.

If this is the case, then each number of the form (1+4k) is easily
represented as the sum of squares: 4 is represented as 2^2 up to k
times, and 1 is just 1^2.

So for example 21 is 1^2 + 2^2 + 2^2 + 2^2 + 2^2 + 2^2.

Pretty cheesy, eh? ;)

-- 
Karl L. Barrus: klbarrus@owlnet.rice.edu         
keyID: 5AD633 hash: D1 59 9D 48 72 E9 19 D5  3D F3 93 7E 81 B5 CC 32 

"One man's mnemonic is another man's cryptography" 
  - my compilers prof discussing file naming in public directories