Revised and updated by John J. Watkins and Robin Wilson
Revised and updated by John J. Watkins and Robin Wilson

Book DetailsAnneli Lax New Mathematical LibraryVolume: 49; 2017; 134 pp
Number theory is the branch of mathematics concerned with the counting numbers, 1, 2, 3, ... and their multiples and factors. Of particular importance are odd and even numbers, squares and cubes, and prime numbers. But in spite of their simplicity, you will meet a multitude of topics in this book: magic squares, cryptarithms, finding the day of the week for a given date, constructing regular polygons, pythagorean triples, and many more.
In this revised edition, John Watkins and Robin Wilson have updated the text to bring it in line with contemporary developments. They have added new material on Fermat's Last Theorem, the role of computers in number theory, and the use of number theory in cryptography, and have made numerous minor changes in the presentation and layout of the text and the exercises.

Table of Contents

Cover

Preface to the Revised Edition

Introduction

History

Numerology

The Pythagorean Problem

Figurate Numbers

Magic Squares

Primes

Primes and Composite Numbers

The Sieve of Eratosthenes

Mersenne Primes

Fermat Primes

Divisors of Numbers

The Fundamental Factorization Theorem

Divisors

Problems Concerning Divisors

Perfect Numbers

Amicable Numbers

Divisors and Multiples

Greatest Common Divisor

Relatively Prime Numbers

Euclid's Algorithm

Least Common Multiple

The Pythagorean Theorem

Preliminaries

Solving the Pythagorean Equation

Pythagorean Triangles

Related Problems

Fermat's Last Theorem

Number Systems

Numbers for the Millions

Other Systems

Comparing Number Systems

Early Calculating Devices

Computers and their Number Systems

Cryptarithms

Congruences

What is a Congruence?

Properties of Congruences

The Algebra of Congruences

Powers of Congruences

Fermat's Little Theorem

Euler's Phi Function

Applying Congruences

Checking Computations

The Days of the Week

Tournament Schedules

Prime or Composite?

Cryptography

Secret Codes

Caesar Ciphers

Vigenère Ciphers

Public Key Ciphers

Solutions to Selected Problems

References

Index

Back Cover


Additional Material

Reviews

[I]t is full of interesting things and is worth showing to bright students.
Allen Stenger, MAA Reviews


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Number theory is the branch of mathematics concerned with the counting numbers, 1, 2, 3, ... and their multiples and factors. Of particular importance are odd and even numbers, squares and cubes, and prime numbers. But in spite of their simplicity, you will meet a multitude of topics in this book: magic squares, cryptarithms, finding the day of the week for a given date, constructing regular polygons, pythagorean triples, and many more.
In this revised edition, John Watkins and Robin Wilson have updated the text to bring it in line with contemporary developments. They have added new material on Fermat's Last Theorem, the role of computers in number theory, and the use of number theory in cryptography, and have made numerous minor changes in the presentation and layout of the text and the exercises.

Cover

Preface to the Revised Edition

Introduction

History

Numerology

The Pythagorean Problem

Figurate Numbers

Magic Squares

Primes

Primes and Composite Numbers

The Sieve of Eratosthenes

Mersenne Primes

Fermat Primes

Divisors of Numbers

The Fundamental Factorization Theorem

Divisors

Problems Concerning Divisors

Perfect Numbers

Amicable Numbers

Divisors and Multiples

Greatest Common Divisor

Relatively Prime Numbers

Euclid's Algorithm

Least Common Multiple

The Pythagorean Theorem

Preliminaries

Solving the Pythagorean Equation

Pythagorean Triangles

Related Problems

Fermat's Last Theorem

Number Systems

Numbers for the Millions

Other Systems

Comparing Number Systems

Early Calculating Devices

Computers and their Number Systems

Cryptarithms

Congruences

What is a Congruence?

Properties of Congruences

The Algebra of Congruences

Powers of Congruences

Fermat's Little Theorem

Euler's Phi Function

Applying Congruences

Checking Computations

The Days of the Week

Tournament Schedules

Prime or Composite?

Cryptography

Secret Codes

Caesar Ciphers

Vigenère Ciphers

Public Key Ciphers

Solutions to Selected Problems

References

Index

Back Cover

[I]t is full of interesting things and is worth showing to bright students.
Allen Stenger, MAA Reviews