Preface
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.
R. D. CARMICHAEL.