Elementary Number Theory with Applications

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Academic Press, 2002 - Всего страниц: 716
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The advent of modern technology has brought a new dimension to the power of number theory: constant practical use. Once considered the purest of pure mathematics, it is used increasingly now in the rapid development of technology in a number of areas, such as art, coding theory, cryptology, computer science, and other necessities of modern life.
Elementary Number Theory with Applications is the fruit of years of dreams and the author's fascination with the subject, encapsulating the beauty, elegance, historical development, and opportunities provided for experimentation and application. This is the only number theory book to show how modular systems can be employed to create beautiful designs, thus linking number theory with both geometry and art. It is also the only number theory book to deal with bar codes, Zip codes, International Standard Book Numbers (ISBN), and European Article Numbers (EAN). Emphasis is on problem-solving strategies (doing experiments, collecting and organizing data, recognizing patterns, and making conjectures). Each section provides a wealth of carefully prepared, well-graded examples and exercises to enhance the readers' understanding and problem-solving skills.

This is the only number theory book to:
Show how modular systems can be employed to create beautiful designs, thus linking number theory with both geometry and art
Deal with bar codes, Zip codes, International Standard Book Numbers (ISBN), and European Article Numbers (EAN)
Emphasize problem-solving strategies (doing experiments, collecting and organizing data, recognizing patterns, and making conjectures)
Provide a wealth of carefully prepared, well-graded examples and exercises to enhance the readers' understanding and problem-solving skills

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Содержание

27
68
Linear Diophantine Equations and Congruences
191
Congruence Applications
243
Systems of Linear Congruences
287
Multiplicative Functions
343
252
380
Computer Exercises
394
257
395
Canonical Decompositions
537
Appendix
583
Web Sites
591
271
597
483
599
10
603
Least Primitive Roots Modulo Primes
607
Solutions to OddNumbered Exercises
619

Chapter Summary
472
Quadratic Congruences
479
267
508
Nonlinear Diophantine Equations
533
161
632
Credits
705
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