Customer Reviews

Power Play (Spectrum)

5 star:		(1)
4 star:		(0)
3 star:		(0)
2 star:		(0)
1 star:		(0)

 

 

Integers are the most adorable of all mathematical objects. Simple in concept, yet boundless in mystery. In this volume, the author explores some of the territory marked out by integers taken to integral powers. While most of this territory has been thoroughly explored, like trips to your favorite places, each time yields new joy and insight.
The specific topics of the chapters are:

1) Odd integers and squares.
2) Pythagorean triples and their relations.
3) Sequences.
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.