Elementary number theory in nine chapters

Includes index

Includes bibliography (p. 411-420) and references

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

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 particular the field of cryptography is highlighted. At the heart of the book are the major number theoretic accomplishments of Euclid, Fermat, Gauss, Legendre, and Euler, and to fully illustrate the properties of numbers and concepts developed in the text, a wealth of exercises have been included. It is assumed that the reader will have 'pencil in hand' and ready access to a calculator or computer. For students new to number theory, whatever their background, this is a stimulating and entertaining introduction to the subject.