## Elementary introduction to number theory |

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### Contents

PRELIMINARY CONSIDERATIONS | 1 |

DIVISIBILITY PROPERTIES OF INTEGERS | 31 |

PRIME NUMBERS | 59 |

Copyright | |

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assertion canonical representation Chinese remainder theorem common multiple complete residue system completely multiplicative congruent modulo contradiction convergent Corollary decimal expansion Definition denote the number divided equation example exist integers factor Fermat's theorem Fibonacci following theorem follows from Theorem form 4k given congruence greatest common divisor guess hence Hint i=l i=l implies incongruent solutions modulo infinitely many primes integers q integral coefficients integral squares irrational least element least positive integer least residue modulo mathematical induction modp nonnegative integer notation number of positive obtain odd prime perfect number positive divisors preceding theorem primitive Pythagorean triplet primitive root modulo problem proof is complete proof of Theorem quadratic nonresidue quadratic residue modulo real number reduced residue system relatively prime residue system modulo result is true result of Exercise sequence simple continued fraction solvable solving Suppose theory of numbers unique values well-ordering principle Wilson's theorem zero