Elementary Number Theory with Applications
Elsevier, 8 мая 2007 г. - Всего страниц: 800
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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Chapter 2 Divisibility
Chapter 3 Greatest Common Divisors
Chapter 4 Congruences
Chapter 5 Congruence Applications
Chapter 6 Systems of Linear Congruences
Chapter 7 Three Classical Milestones
Chapter 8 Multiplicative Functions
Chapter 11 Quadratic Congruences
Chapter 12 Continued Fractions
Chapter 13 Miscellaneous Nonlinear Diophantine Equations
Solutions to OddNumbered Exercises
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affine cipher arbitrary integer Assume canonical decomposition check digit ciphertext composite number compute conjecture contradiction Corollary denote the number digital root diophantine equation division algorithm divisor E X E R C I S E S enciphering encryption euclidean algorithm Euler Exercise Fermat number Fermat’s Last Theorem Figure Find the number following example illustrates following theorem Gauss incongruent solutions induction infinitely least positive least residues modulo Lemma linear congruence linear system mathematician Mersenne number Mersenne primes mod 9 modp multiplicative number theory odd integer odd prime perfect number plaintext positive integer prime factor prime numbers primitive Pythagorean triple primitive root modulo PROOF Let Prove Pythagorean triangle Pythagorean triple quadratic nonresidue quadratic reciprocity quadratic residue recursively relatively prime remainder sequence simple continued fraction solution of x2 solvable Solve square Suppose Table triangular numbers true twin primes Verify yields