Introduction

At Columbia University there is a Babylonian clay tablet called Plimpton 322 that is more than 3800 years old and not much larger than a cell phone. Written in cuneiform script with 4 columns and 15 rows, it contains numbers written in base 60 (just as base 10 is standard today, base 60 was standard in Babylon). Each row gives a Pythagorean triple, that is, three whole numbers x, y, z satisfying

x2 + y2 = z2

(for example, 32 + 42 = 52 and 127092 + 135002 = 185412 are triples from the tablet). This is one of the earliest examples where integers are studied for their interesting properties, not just for counting objects.