Fermat's Last Theorem

For any positive integer $n\geq 3$, there are no positive integers x, y, z such that

xⁿ+yⁿ=zⁿ.

This statement appeared in the marginal notes of one of the most famous and successful number theorists in the 1600's, Pierre de Fermat. Fermat's notes were scribbled in his copy of Diophantus' book, with his added comment that he had found a marvelous proof of the theorem but the margin was too small to contain it. This statement was only discovered after his death. No other notes of his on this problem have ever been discovered. To this date (1992), it has defied the best efforts of the greatest mathematicians to prove or disprove the above statement. A prize, called the Wolfskehl Prize, worth about $ 10,000 and administered at the University of Göttingen in Germany is available for a correct proof that there are no positive integral solutions to the above equation.

Spectacular Update: In the year 2000, Fermat's Last Theorem is a known theorem, having been laid to rest in 1994 by Andrew Wiles.