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From: andrew@inmet.UUCP
Newsgroups: net.ai
Subject: Re: Re: Fermat's Last Theorem & Undecida - (nf)
Message-ID: <945@inmet.UUCP>
Date: Tue, 28-Feb-84 23:42:40 EST
Article-I.D.: inmet.945
Posted: Tue Feb 28 23:42:40 1984
Date-Received: Fri, 2-Mar-84 00:13:28 EST
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#R:foxvax1:-31700:inmet:11000008:000:764
inmet!andrew    Feb 25 11:48:00 1984

Fermat's Last Theorem states that the equation

    n    n    n
   A  + B  = C

has solutions in positive integers a, b, c, n only when n = 2.

The "four-color map problem" states that any map (think of, say, a map of the
US) requires at most four colors to color all regions without using the same
color for any two adjacent ones.  (This is for 2-dimensional maps.  Maps
on a sphere or torus require more - 5 and 7, I think.)

The former has neither been proven nor disproven.  The latter was "proven"
with the aid of a computer program; many feel that this does not constitute
a true proof (see all the flames elsewhere in this group).  Incidentally,
the school where it was "proven" changed their postage meters to print
"FOUR COLORS SUFFICE" on outgoing mail.