# [RC5] Beal's Problem A DN challenge?

Robert L. Barry umbarryr at cc.UManitoba.CA
Sun Jul 4 16:39:12 EDT 1999

```Fermat's Last Theorem claimed that there were no whole number solutions to the equation:

x^n + y^n = z^n  for n greater than 2.

This 300 year old problem was finally solved by Andrew Wiles, whose two papers (consisting of 130 pages in total) were published in Annals of Mathematics (May, 1995).

Fermat's Theorem is a special case of "Beal's Problem" in which the exponents m = n = r in the equation:

x^m+ y^n = z^r

Another famous problem (for one's general knowledge) is that of Euler's conjecture, which states that there are no solutions to the equation:

x^4 + y^4 + z^4 = w^4

After two hundred years, Euler's conjecture was finally proved to be false by the solution found by Naom Elkies of Harvard University in 1988:

2,682,440^4 + 15,365,639^4 + 18,796,760^4 = 20,615,673^4

Even though Fermat's Last Theorem is probably one of the most widely known and talked about mathematical riddles, it is also admitted by those mathematicians who understand it to have no known practical applications.  It did wonders for the advancement of pure mathematics, but that's about it.

My point here is that even though "Beal's Problem" is interesting, I personally can't see reason enough for d.net to pursue it beyond the cash prize alone.  I believe that we are working together on the RC5-64 project to prove a point regarding the reliability of data encryption and cryptography in general.  As well, many of our fellow key-crackers (myself included) are looking forward to the OGR project, which, unlike "Beal's Problem", has several useful applications in the real world.

Just my \$0.02.  ;-)

-----
Robert L. Barry II
Computer Engineering IV
University of Manitoba
umbarryr at cc.umanitoba.ca
http://home.cc.umanitoba.ca/~umbarryr/
ICQ # : 3973441

----- Original Message -----
From: Keith McLaurin <skmac at ix.netcom.com>
To: <rc5 at lists.distributed.net>
Sent: Sunday, July 04, 1999 2:29 AM
Subject: Re: [RC5] Beal's Problem A DN challenge?

I believe this is Fermat's Last Theorm...
I thought it had recently been solved.

David Cantrell wrote:
>
> Mike Burgess said:
>
> > I don't know if this would be suitable for Distributed.Net, but it looks
> > interesting: http://www.maa.org/devlin/devlin_12_97.html Beal's Problem xm
> > + yn = zr   (The 2nd letter should be in SuperScript, as an exponent.)

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