andrew@inmet.UUCP (02/29/84)
#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.