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From: MJackson.Wbst@PARC-MAXC.ARPA
Newsgroups: net.ai
Subject: Re: Fermat's Last Theorem & Undecidable Propositions
Message-ID: <17227@sri-arpa.UUCP>
Date: Thu, 1-Mar-84 08:34:00 EST
Article-I.D.: sri-arpa.17227
Posted: Thu Mar  1 08:34:00 1984
Date-Received: Fri, 9-Mar-84 01:20:10 EST
Lines: 30

Fermat's Last Theorem:

is the assertion that

                A^N + B^N = C^N

has no solution in integers for N > 2.  (For N = 2, of course, all the
well-known right triangles like [3,4,5] are solutions.)

The Four-Color Theorem:

states that any planar map can be colored so that no two adjacent
regions are the same color using no more than four different colors.
(Regions must be connected; "adjacent" means having a common boundary of
finite length, i.e. not just touching at a point.

The latter was shown to be true by two mathematicians at the University
of Illinois, using a combination of traditional mathematical reasoning
and computer-assisted analysis of a large set of graphs.  An article
describing the proof can be found in a back issue of /Scientific
American/.

The former appears in a manuscript by Fermat, with a marginal notation
to the effect that he had found a slick proof, but didn't have enough
space to write it down.  This was discovered after his death, of course.
Most mathematicians believe the theorem to be true, and most do not
think Fermat is likely to have found a valid proof, but neither
proposition has been proved beyond question.

Mark