## Theory of Numbers

×Close# Theory of Numbers

## 1st ed.

## by Amin Witno

####
Published
**2008**
by
BookSurge
in
North Charleston, SC
.

Written in English

###### Subjects

### About the Edition

Theory of Numbers is a carefully written textbook for an elementary number theory course with minimal prerequisites. It begins with the classical theory of divisibility, primes, and modular arithmetic; and ends with computational topics of factorization, pseudoprimes, and primality testing. Ideal for self-study or for a one-semester course, the relatively small, measured contents include numerous exercises strategically dispersed throughout the text in order to retain theoretical context and reinforce understanding. As an extended workout, every chapter concludes with a partially guided project touching on a wide range of problems, from the old sums-of-squares theorems to the more recent cryptographical protocols.

### Table of Contents

1 | Divisibility | 1 |

2 | Prime Numbers | 12 |

3 | Modular Arithmetic | 21 |

4 | Exponentiation | 31 |

5 | Primitive Roots | 43 |

6 | Quadratic Residues | 52 |

7 | Factorization | 63 |

8 | Pseudoprime Composites | 74 |

9 | Primality Proving | 84 |

A | Mathematical Induction | 96 |

B | Binomial Coefficients | 98 |

C | Primitive Root Theorem | 101 |

D | Modular Square Roots | 103 |

E | Rabin's Probabilistic Test | 108 |

F | Testing Primes with Lucas Sequences | 110 |

Answers & Hints | 115 | |

Primes < 10^4 | 124 | |

Pseudoprimes < 10^7 | 127 | |

Bibliography | 130 | |

Notation | 133 | |

Index | 134 |

### Edition Notes

Includes bibliographical references (p. 130-132) and index.

### Classifications

## History

- Created September 27, 2008
- 7 revisions

April 29, 2011 | Edited by OCLC Bot | Added OCLC numbers. |

April 13, 2010 | Edited by Open Library Bot | Linked existing covers to the edition. |

December 15, 2009 | Edited by WorkBot | link works |

May 12, 2009 | Edited by ImportBot | Found a matching record from Library of Congress . |

September 27, 2008 | Created by ImportBot | Imported from Library of Congress MARC record. |