The Theory of Numbers

The purpose of this little book is to give the reader a convenient introduction to the theory of numbers, one of the most extensive and most elegant disciplines in the whole body of mathematics. The arrangement of the material is as follows: The first five chapters are devoted to the development of those elements which are essential to any study of the subject. The sixth and last chapter is intended to give the reader some indication of the direction of further study with a brief account of the nature of the material in each of the topics suggested. The treatment throughout is made as brief as is possible consistent with clearness and is confined entirely to fundamental matters. This is done because it is believed that in this way the book may best be made to serve its purpose as an introduction to the theory of numbers.Numerous problems are supplied throughout the text. These have been selected with great care so as to serve as excellent exercises for the student’s introductory training in the methods of number theory and to afford at the same time a further collection of useful results. The exercises marked with a star are more difficult than the others; they will doubtless appeal to the best students. Finally, I should add that this book is made up from the material used by me in lectures in Indiana University during the past two years; and the selection of matter, especially of exercises, has been based on the experience gained in this way.