Numbers have fascinated the human race for millennia. The Pythagoreans studied many properties of the natural numbers 1, 2, 3, . . . , and the famous theorem of Pythagoras, though geometrical, has a pronounced numbertheoretic content. Earlier Babylonian civilizations had noted empirically many so-called Pythagorean triples, such as 3, 4, 5 and 5, 12, 13. These are natural numbers a, b, c such that
a2 + b2 = c2. (1)
A clay tablet from about 1500 BC includes the triple 4961, 6480, 8161, demonstrating the sophisticated techniques of the Babylonians.