What can be more basic in mathematics than integer numbers like 1, 2, 3, and so on? Thus, one should hardly be surprised that the study of such numbers goes back to the very beginnings of formal mathematics, to Greek mathematicians of the sixth century B.C. Today, this field of mathematics is known as number theory. Number theory involves the analysis of the properties of the natural numbers (1, 2, 3, etc.) and, more generally, of all integers, positive or negative, and zero (...-2,-1, 0, 1, 2...).

The Greek natural philosopher Pythagoras of Samos carried out some of the earliest and most primitive research on number theory. Indeed, Pythagoras became virtually obsessed by the natural numbers and taught that they formed the basis of the natural universe. Although many of Pythagoras' ideas were more mystical and rational, his interest in numbers led to a great deal of early study in the field. For...