Textbook in PDF format

International edition.
This book presents the principal ideas of classical elementary number theory, emphasizing the historical development of these results and the important figures who worked on them. This book is also intended to introduce students to mathematical prooves by presenting them in a clear and simple way and by providing complete, step-by-step solutions to the problems with as much detail as students would be expected to provide themselves. Throughout, we have tried to indicate the important ideas in a proof or numerical technique and to show the students computational shortcuts whenever possible.
The book is intended as a text for either a one-term or two-term course in elementary number theory, usually given at American and Canadian colleges and universities in the third year. Typically, such courses are taken by juniors and seniors, but increasingly, second-year students (including those at two-year colleges) take such a course, and the material is very accessible to them.
There are few formal prerequisites for the material in this book; in particular, no previous course in abstract algebra is necessary. Students should be familiar with proofs by mathematical induction, and frequent use will be made of the fact that any nonempty set of positive integers contains a smallest element. A few of the proofs use basic properties of limits of sequences of real numbers; for example, students should know that an increasing sequence of real numbers which is bounded above is convergent.
This book is intended to be a self-contained text for a course in elementary number theory, as well as a source book of solved problems