Diophantus, an early explorer into the wonders of quadratic equations, had written a similar expression: x4 + y4 + z4 = u2. “Why,” asks Fermat, “did not Diophantus seek two [rather than three] fourth powers such that their sum is square? The problem is, in fact impossible, as by my method I am able to prove with all rigor.”11 Fermat observes that Pythagoras was correct that a2 + b2 = c2, but a3 + b3 would not be equal to c3, nor would any integer higher than 2 fit the bill: the Pythagorean theorem works only for squaring.
