## Elementary Number Theory in Nine ChaptersThis book is intended to serve as a one-semester introductory course in number theory. Throughout the book a historical perspective has been adopted 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. |

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### Contents

Divisibility | 49 |

Prime numbers | 79 |

Perfect and amicable numbers | 127 |

Modular arithmetic | 150 |

Congruences of higher degree | 182 |

Cryptology | 210 |

Representations | 239 |

Partitions | 284 |

Tables | 305 |

The values of tn gn n un wan | 312 |

390 | |

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### Common terms and phrases

addition algorithm appears called century cipher ciphertext column common complete composite congruences conjecture Consider contains continued fraction contradiction convergents coprime cubes Decipher defined denote Determine difference digits discovered distinct divides divisible divisors element enciphered equal equation equivalent established Euler example Exercises exist expressed factors Fermat Figure follows formula four function gcd(a given greater greatest Hence implies included induction infinite integer n known least length less letters mathematical mathematician method modulo multiplicative namely natural numbers noted number theoretic obtain odd prime pairs partitions perfect number plaintext positive integer powers primitive root problem Proof Prove Pythagorean quadratic rational remainder representation represented residue respectively result sequence Show shown sides smallest solution solve square Suppose Table term Theorem theory triangle triangular numbers triple University values written