The theory of remainders 余数理论

An imaginative introduction to number theory, this unique approach employs a pair of fictional characters, Ant and Gnam.Ant leads Gnam through a variety of theories, and together,they put the theories into action--applying linear diophantine equations to football scoring, using a black-magic device to simplify problems in modular structures, and developing intriguing modifications to the rules of chess.
Appropriate for anyone familiar with algebra at the high-school level, The Theory of Remainders offers a captivating introduction to both number theory and abstract algebra. Both elementary and challenging, it provides a view of mathematics as a conceptual net and illustrates the differences between conceptual and paraconceptual claims--an excellent start to expanding students' perspectives on mathematics.

Preface
Acknowledgments
Sections
1 The Black Magic Device
2 The Modular Systems
3 Basic Concepts of Factorization and Divisibility
4 The Algebraic Structure of the Modular Systems
5 Remainder Tests
6 The Football Problem:Linear Diophantine Equations
7 Forward-Looking and Right-Thinking Male Chauvinist Chess
8 Miscellaneous Problems
9 Solutions to Problems
Commentary
Intex