Elementary Number Theory

Excellent text on number theory. Topic coverage is extensive: quadratic reciprocity, linear diophantine equations, Lagranges's 4-square theorem, Pell's equation and more. Proofs are very good and plenty of exercises.

This is a great book for the mathematically-interested layman, non-math-major undergraduate, and people in other fields (such as computer science) who want a fairly quick read on the basics of this fascinating field. It would also serve well as a a precursor/warmup for more advanced treatments of the subject.

Published in 1978, this book suffers very little from the illness of being dated. Of course, Fermat's last theorem has been proven and computers have grown much more powerful. However, those advances have little affect on the value of the book. Done well, basic number theory is timeless, and Dudley does it very well. The explanations of the fundamentals are sound and solved exercises are scattered throughout. Solutions to most of the odd numbered problems at the end of the chapters are also included. The coverage is fairly typical, so the book can still be used as the text for a course in beginning number theory. Chapter 23 contains a set of 267 additional problems, a set for each of the other chapters in the book. Solutions to most of the odd problems in this set are also included. I commend Dudley for including so many solutions; I have little time for authors of books who do not provide solutions to at least some of the exercises. If I ever teach a course in basic number theory, this is the book that I would use.

Some of the problems in this book are unlike any I've seen before, like Dudley gives a bunch of equations, you're supposed to see the pattern & he writes "guess & prove a theorem". Dudley's writing style is very informal & I thought it was a nice change from other books. Like the other person said, the book is clearly written and there are lots of examples. I had this book for a 3rd-year course, but I think a 1st or 2nd-year student could handle this book.

This is the excellent book if you want to study thenumber theory but don't know where to start. The explanations are sound and CLEAR. A lot of problemsare actually solved by an author and many answers tothe exercises are given at the end of book.