This book is a country walk through the magical world of numbers. Most people will have recognised some of the fascinating patterns exhibited by many numbers; some of these indicate a deep and complex structure which is revealed in this book in a way … see full wiki
1) Odd integers and squares.
2) Pythagorean triples and their relations.
4) Pell's equation.
5) Equal sums of equal powers.
6) Digits and sums of powers.
7) Interesting sets.
The level of the motivating text is deliberately kept low. Most talented high school math students will be able to follow it with a bit of guidance. Higher order material is reserved for the problems and each section terminates with a large problem set. There are two parts to each set and solutions to all are included, although some are simply a pointer to the proper reference. The level of difficulty is quite broad. Skill sets needed to solve the problems ranges from basic high school algebra up to that of experienced undergraduate math majors.
Since they can be used in so many different contexts, material about the integers tends to be scattered throughout the literature. The extensive bibliography included in this book is a welcome road map that can be used to track down the desired specifics.
If you are teaching mathematics at any level and looking for problem sets to motivate and challenge the better students, then this book is for you. It is also fun to read if you are an integer aficionado.
Published in Smarandache Notions Journal, reprinted with permission.
What did you think of this review?
A book by Edward B. Burger
A book by Edward Packel
A book by H. G. Eggleston