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The purpose of this volume is to give a simple account of classical number theory and to impart some of the historical background in which the subject evolved. Although primarily intended for use as a textbook in a one-semester course at the undergraduate level, it is designed to be used in teachers’ institutes or as supplementary reading in mathematics survey courses. The work is well suited for prospective secondary school teachers for whom a little familiarity with number theory may be particularly helpful.

The theory of numbers has always occupied a unique position in the world of mathematics. This is due to the unquestioned historical importance of the subject: it is one of the few disciplines having demonstrable results that predate the very idea of a university or an academy. Nearly every century since classical antiquity has witnessed new and fascinating discoveries relating to the properties of numbers; and, at some point in their careers, most of the great masters of the mathematical sciences have contributed to this body of knowledge. Why has number theory held such an irresistible appeal for the leading mathematicians and for thousands of amateurs? One answer lies in the basic nature of its problems. Although many questions in the field are extremely hard to decide, they can be formulated in terms simple enough to arouse the interest and curiosity of those with little mathematical training. Some of the simplest sounding questions have withstood intellectual assaults for ages and remain among the most elusive unsolved problems in the whole of mathematics.