## From number theory to secret codesThis text/software package shows how a knowledge of number theory can be used to write messages in a secret form. For those with secrets but no interest in number theory, the cryptographic section can easily be used to encipher & decipher messages without any knowledge of number theory. The rest of the text & programs explain all the mathematics required to understand why the cryptographic system works. A knowledge of arithmetic is required but no calculus is needed. Exercises & examples are provided throughout the text. Suitable for advanced secondary school & undergraduate students of mathematics & teachers of mathematics, particularly of number theory. Software: available on 3.5" disks for IBM compatible machines. |

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### Contents

Introduction | 1 |

Continued Fractions and Rational Approximations | 21 |

Modular Arithmetic | 52 |

Copyright | |

3 other sections not shown

### Common terms and phrases

absolute value ak+i alb and eld approximations blocks of numbers choose common divisor complete quotients composite number computer displays congruent modulo continued fraction expansion coprime deciphering divide divisible divisors in common enciphered form enciphering power enter equation Euclid's algorithm example Exercise factor h factorisation Farey pair Farey sequence following numbers form a Farey forming mediants fractions nld fractions with denominator gives highest common factor inequalities infinite sequence instance integers irrational number least residue linear combination lowest terms modular arithmetic modulo 11 multiple natural numbers non-zero number x original numbers p2k+ilq2k+i pilqi pk-ilqk-i polynomial congruences positive number positive primes press RETURN prime divisors prime factors prime numbers prime or composite product of primes qk-i quadratic irrational rational numbers real number relatively prime remainder roots satisfy set of residues Similarly smaller numbers successive convergents suppose whole number write zero