Introduction

At Columbia University there is a Babylonian clay tablet called Plimpton 322 that is over 3800 years old and not much larger than a cell phone. Written in cuneiform script with four 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.