## Elementary introduction to number theoryThis accessible Third Edition incorporates especially complete & detailed arguments, illustrating definitions, theorems, & subtleties of proof with explicit numerical examples whenever possible. |

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### Contents

PRELIMINARY CONSIDERATIONS | 1 |

DIVISIBILITY PROPERTIES OF INTEGERS | 39 |

PRIME NUMBERS | 70 |

Copyright | |

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### Common terms and phrases

algorithm Caesar cipher canonical representation Chinese remainder theorem cipher common divisor common multiple complete residue system Computer Exercise convergents Corollary deciphering DEFINITION digits divisible enciphering equation Euler's criterion example exist integers factor Fermat's theorem following theorem follows from Theorem form 4k formula function guess hence Hint implies incongruent solutions modulo integers modulo integral squares least element least positive integer least residue modulo mathematical induction Mersenne primes Miller test modp nonzero notation Note number of positive Number Theory obtain odd prime plaintext polynomial positive divisors primitive root modulo prove pseudoprime to base Pythagorean triple quadratic nonresidue quadratic residue modulo quadratic surd real number reduced residue system relatively prime residue system modulo result is true result of Exercise Section simple continued fraction solvable solve Suppose theory of numbers values well-ordering principle Wilson's theorem Write a computer Write a program zero