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Elementary number theory / David M. Burton.

By: Burton, David M.
Material type: materialTypeLabelBookPublisher: Dubuque, Iowa : Wm. C. Brown, c1989Edition: 2nd ed.Description: xvii, 450 p. : ill. ; 24 cm.ISBN: 0697059197.Subject(s): Number theoryDDC classification: 512.72
Contents:
Some preliminary considerations -- Divisibility theory in the integers -- Primes and their distribution -- The theory of congruences -- Fermat's theorem -- Number-theoretic functions -- Euler's generalization of Fermat's theorem -- Primitive roots and indices -- The quadratic reciprocity law -- Perfect numbers -- The Fermat conjecture -- Representation of integers as sums of squares -- Fibonacci numbers and continued fractions.
Holdings
Item type Current library Call number Copy number Status Date due Barcode Item holds
General Lending MTU Bishopstown Library Lending 512.72 (Browse shelf(Opens below)) 1 Available 00025710
Total holds: 0

Includes bibliographical references (pages 405-411) and index.

Some preliminary considerations -- Divisibility theory in the integers -- Primes and their distribution -- The theory of congruences -- Fermat's theorem -- Number-theoretic functions -- Euler's generalization of Fermat's theorem -- Primitive roots and indices -- The quadratic reciprocity law -- Perfect numbers -- The Fermat conjecture -- Representation of integers as sums of squares -- Fibonacci numbers and continued fractions.

CIT Module MATH 8006 - Recommended reading

Table of contents provided by Syndetics

  • 1 Some Preliminary Considerations
  • 1.1 Mathematical Induction
  • 1.2 The Binomial Theorem
  • 1.3 Early Number Theory
  • 2 Divisibility Theory in the Integers
  • 2.1 The Division Algorithm
  • 2.2 The Greatest Common Divisor
  • 2.3 The Euclidean Algorithm
  • 2.4 The Diophantine Equation ax+by=c
  • 3 Primes and Their Distribution
  • 3.1 The Fundamental Theorem of Arithmetic
  • 3.2 The Sieve of Eratosthenes
  • 3.3 The Goldbach Conjecture
  • 4 The Theory of Congruences
  • 4.1 Carl Friedrich Gauss
  • 4.2 Basic Properties of Congruence
  • 4.3 Special Divisibility Tests
  • 4.4 Linear Congruences
  • 5 Fermat's Theorem
  • 5.1 Pierre de Fermat
  • 5.2 Fermat's Factorization Method
  • 5.3 The Little Theorem
  • 5.4 Wilson's Theorem
  • 6 Number-Theoretic Functions
  • 6.1 The Functions ¿¿nd ¿&#227
  • 6.2 The Mobius Inversion Formula
  • 6.3 The Greatest Integer Function
  • 6.4 An Application to the Calendar
  • 7 Euler's Generalization of Fermat's Theorem
  • 7.1 Leonhard Euler
  • 7.2 Euler's Phi-Function
  • 7.3 Euler's Theorem
  • 7.4 Some Properties of the Phi-Function
  • 7.5 An Application to Cryptography
  • 8 Primitive Roots and Indices
  • 8.1 The Order of an Integer Modulo n
  • 8.2 Primitive Roots for Primes
  • 8.3 Composite Numbers Having Prime Roots
  • 8.4 The Theory of Indices
  • 9 The Quadratic Reciprocity Law
  • 9.1 Euler's Criterion
  • 9.2 The Legendre Symbol and Its Properties
  • 9.3 Quadratic Reciprocity
  • 9.4 Quadratic Congruences with Composite Moduli
  • 10 Perfect Numbers
  • 10.1 The Search for Perfect Numbers
  • 10.2 Mersenne Primes
  • 10.3 Fermat Numbers
  • 11 The Fermat Conjecture
  • 11.1 Pythagorean Triples
  • 11.2 The Famous ¡§Last Theorem¡¨
  • 12 Representation of Integers as Sums of Squares
  • 12.1 Joseph Louis Lagrange
  • 12.2 Sums of Two Squares
  • 12.3 Sums of More than Two Squares
  • 13 Fibonacci Numbers
  • 13.1 The Fibonacci Sequence
  • 13.2 Certain Identities Involving Fibonacci Numbers
  • 14 Continued Fractions
  • 14.1 Srinivasa Ramanujan
  • 14.2 Finite Continued Fractions
  • 14.3 Infinite Continued Fractions
  • 14.4 Pell's Equation
  • 15 Some Twentieth-Century Developments
  • 15.1 Hardy, Dickson, and Erdos
  • 15.2 Primality Testing and Factorization
  • 15.3 An Application to Factoring: Remote Coin-Flipping
  • 15.4 The Prime Number Theorem

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