Burton David. Elementary number theory. International edition

Boston: Allyn and Bacon, Inc., 1976, — 390 p.Elementary number theory revised edition is written for undergraduate students, students who are preparing for math Olympiads, teachers. This book gives simple account of classical number theory, as well as to impart some of historical background in which the subject involved. This book will introduce you with many parts of modern number theory as: induction, divisibility, primes, congruences, functions etc. It will provide simple proofs for many problems.New To This Edition
Some Preliminary Considerations
Mathematical Induction
The Binomial Theorem
Early Number Theory
Divisibility Theory in the Integers
The Division Algorithm
The Greatest Common Divisor
The Euclidean Algorithm
The Diophantine Equation ax + by = c
Primes and Their Distribution
The Fundamental Theorem of Arithmetic
The Sieve of Eratosthenes
The Goldbach Conjecture
The Theory of Congruences
Karl Friedrich Gauss
Basic Properties of Congruence
Special Divisibility Tests
Linear Congruences
Fermat's Theorem
Pierre de Fermat
Fermat's Factorization Method
The Little Theorem
Wilson's Theorem
Number-Theoretic Functions
The Functions τ and σ
The Mobius Inversion Formula
The Greatest Integer Function
Euler's Generalization of Fermat's Theorem
Leonhard Euler
Euler's Phi-Function
Euler's Theorem
Some Properties of the Phi-Function
Primitive Roots and Indices
The Order of an Integer Modulo n
Primitive Roots for Primes
Composite Numbers Having Primitive Roots
The Theory of Indices
The Quadratic Reciprocity Law
Euler's Criterion
The Legendre Symbol and Its Properties
Quadratic Reciprocity
Quadratic Congruences with Composite Moduli
Perfect Numbers
The Search for Perfect Numbers
Mersenne Primes
Fermat Numbers
The Fermat Conjecture
Pythagorean Triples
The Famous "Last Theorem"
Representation of Integers as Sums of Squares
Joseph Louis Lagrange
Sums of Two Squares
Sums of More than Two Squares
Fibonacci Numbers and Contined Fractions
The Fibonacci Sequence
Certain Identities Involving Fibonacci Numbers
Finite Continued Fractions
Infinite Continued Fractions
Pell's Equation
Some Twentieth-Century Developments
/Miscellaneous Problems
Appendixes
The Prime Number Theorem
General References
Suggested Further Reading
Tables
Answers to Selected Problems