# Elementary Number Theory with Applications

Elsevier, May 8, 2007 - Mathematics - 800 pages
This second edition updates the well-regarded 2001 publication with new short sections on topics like Catalan numbers and their relationship to Pascal's triangle and Mersenne numbers, Pollard rho factorization method, Hoggatt-Hensell identity. Koshy has added a new chapter on continued fractions. The unique features of the first edition like news of recent discoveries, biographical sketches of mathematicians, and applications--like the use of congruence in scheduling of a round-robin tournament--are being refreshed with current information. More challenging exercises are included both in the textbook and in the instructor's manual.

Elementary Number Theory with Applications 2e is ideally suited for undergraduate students and is especially appropriate for prospective and in-service math teachers at the high school and middle school levels.

* Loaded with pedagogical features including fully worked examples, graded exercises, chapter summaries, and computer exercises
* Covers crucial applications of theory like computer security, ISBNs, ZIP codes, and UPC bar codes
* Biographical sketches lay out the history of mathematics, emphasizing its roots in India and the Middle East

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For a textbook on number theory, this particular one is a breath of fresh air. Like many math texts aimed at even the undergraduate level, corollaries and proofs are key, and this book is filled with understandable ones. The book contains examples relevant to its respective problem sets.
The book and its problem sets contain many interesting topics, including several investigations on unsolved number theory conjectures (which makes it a lot worth learning). By the end of the book, the reader will be familiar with notable mathematicians present and past, and their contributions to number theory. This book lives up to its title and it is a great starting point for aspiring number theorists and numberphiles (like Fermat). I would recommend it as a second or third year undergraduate number theory textbook.

### Contents

 Chapter 1 Fundamentals 1 Chapter 2 Divisibility 69 Chapter 3 Greatest Common Divisors 155 Chapter 4 Congruences 211 Chapter 5 Congruence Applications 247 Chapter 6 Systems of Linear Congruences 295 Chapter 7 Three Classical Milestones 321 Chapter 8 Multiplicative Functions 355
 Chapter 11 Quadratic Congruences 495 Chapter 12 Continued Fractions 551 Chapter 13 Miscellaneous Nonlinear Diophantine Equations 579 Appendix 631 Tables 641 References 657 Solutions to OddNumbered Exercises 665 Credits 757

 Chapter 9 Cryptology 413 Chapter 10 Primitive Roots and Indices 455