Elementary number theory in nine chapters /

This textbook is intended to serve as a one-semester introductory course in number theory and in this second edition it has been revised throughout and many new exercises have been added. Historical perspective is included and emphasis is given to some of the subject's applied aspects; in parti...

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Detalles Bibliográficos
Clasificación:Libro Electrónico
Autor principal: Tattersall, James J. (James Joseph), 1941-
Formato: Electrónico eBook
Idioma:Inglés
Publicado: Cambridge ; New York : Cambridge University Press, 2005.
Edición:2nd ed.
Temas:
Number theory.
Théorie des nombres.
MATHEMATICS > Number Theory.
Wiskunde.
Getaltheorie.
Acceso en línea:Texto completo
Tabla de Contenidos:
  • Cover
  • Half-title
  • Title
  • Copyright
  • Dedication
  • Contents
  • Preface
  • Preface to the Second Edition
  • 1 The intriguing natural numbers
  • 1.1 Polygonal numbers
  • 1.2 Sequences of natural numbers
  • 1.3 The principle of mathematical induction
  • 1.4 Miscellaneous exercises
  • 1.5 Supplementary exercises
  • 2 Divisibility
  • 2.1 The division algorithm
  • 2.2 The greatest common divisor
  • 2.3 The Euclidean algorithm
  • 2.4 Pythagorean triples
  • 2.5 Miscellaneous exercises
  • 2.6 Supplementary exercises
  • 3 Prime numbers
  • 3.1 Euclid on primes
  • 3.2 Number theoretic functions.
  • 3.3 Multiplicative functions
  • 3.4 Factoring
  • 3.5 The greatest integer function
  • 3.6 Primes revisited
  • 3.7 Miscellaneous exercises
  • 3.8 Supplementary exercises
  • 4 Perfect and amicable numbers
  • 4.1 Perfect numbers
  • 4.2 Fermat numbers
  • 4.3 Amicable numbers
  • 4.4 Perfect-type numbers
  • 4.5 Supplementary exercises
  • 5 Modular arithmetic
  • 5.1 Congruence
  • 5.2 Divisibility criteria
  • 5.3 Euler's phi-function
  • 5.4 Conditional linear congruences
  • 5.5 Miscellaneous exercises
  • 5.6 Supplementary exercises
  • 6 Congruences of higher degree
  • 6.1 Polynomial congruences.
  • 6.2 Quadratic congruences
  • 6.3 Primitive roots
  • 6.4 Miscellaneous exercises
  • 6.5 Supplementary exercises
  • 7 Cryptology
  • 7.1 Monoalphabetic ciphers
  • 7.2 Polyalphabetic ciphers
  • 7.3 Knapsack and block ciphers
  • 7.4 Exponential ciphers
  • 7.5 Supplementary exercises
  • 8 Representations
  • 8.1 Sums of squares
  • 8.2 Pell's equation
  • 8.3 Binary quadratic forms
  • 8.4 Finite continued fractions
  • 8.5 Infinite continued fractions
  • 8.6 p-Adic analysis
  • 8.7 Supplementary exercises
  • 9 Partitions
  • 9.1 Generating functions
  • 9.2 Partitions
  • 9.3 Pentagonal Number Theorem.
  • 9.4 Supplementary exercises
  • Tables
  • Answers to selected exercises
  • Exercises 1.1
  • Exercises 1.2
  • Exercises 1.3
  • Exercises 1.4
  • Exercise 2.1
  • Exercises 2.2
  • Exercises 2.3
  • Exercises 2.4
  • Exercises 2.5
  • Exercises 3.1
  • Exercises 3.2
  • Exercises 3.3
  • Exercises 3.4
  • Exercises 3.5
  • Exercises 3.6
  • Exercises 3.7
  • Exercises 4.1
  • Exercises 4.2
  • Exercises 4.3
  • Exercises 4.4
  • Exercises 5.1
  • Exercises 5.2
  • Exercises 5.3
  • Exercises 5.4
  • Exercises 5.5
  • Exercises 6.1
  • Exercises 6.2
  • Exercises 6.3
  • Exercises 6.4
  • Exercises 7.1
  • Exercises 7.2.

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