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.