Elementary Number Theory with ApplicationsThis 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 |
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 |
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Common terms and phrases
algorithm application arbitrary Assume base block check digit cipher ciphertext Clearly composite compute congruence conjecture consecutive contains continued fraction contradiction Corollary defined definition denote Determine developed digits discovered distinct divided divisible elements enciphering equation established Euler exactly Exercise exist expressed fact Fermat Figure Find following example illustrates formula four function given implies incongruent induction infinitely integer n known largest least residues Lemma letter linear system mathematician Mathematics Mersenne method modp multiplicative Notice number theory odd prime pair perfect number positive integer prime factor primitive root modulo problem proof properties Prove Pythagorean triple quadratic residue Read recursively relatively prime remainder result sequence solution solvable Solve square step Suppose symbol Table Theorem triangle true unique University Verify yields