104 Number Theory Problems: From the Training of the USA IMO Team

This is a very good book for high-school students interested in mathematical competitions and for their coaches. It is also a good resource for the college students interested in number theory.

The first chapter, Foundations of Number Theory, can be used for an introductory short course in number theory and has very good examples/problems throughout. It can also complement a college course in number theory.

The 104 Number Theory Problems mentioned in the title of the book are divided into two groups of 52 problems and included in chapters 2 (Introductory Problems) and 3 (Advanced Problems). What is most important is that each of the included problems has at least one detailed solution included in the two chapters that follow. In the Preface the authors advise the readers to look at the solutions, even if they have solved a particular problem by themselves. Very good advice indeed, given that the solutions contain lots of interesting and valuable information that can be used in solving many other problems.

In short, this book is a very valuable tool for any student/coach interested in preparing for mathematics competitions, especially for the International Mathematical Olympiad. College students participating in the Putnam competition might also find quite a few interesting problems. Moreover, any course in number theory could be supplemented with this book and could use some of the references included. Even research mathematicians working in number theory will find this book of value in their pursuits.

Mihaela Poplicher is an associate professor of mathematics at the University of Cincinnati. Her research interests include functional analysis, harmonic analysis, and complex analysis. She is also interested in the teaching of mathematics. Her email address is [email protected].