## Elementary introduction to number theory |

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### Contents

Preliminary Considerations | 1 |

Divisibility Properties of Integers | 21 |

Prime Numbers | 40 |

Copyright | |

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belongs canonical representation Chinese remainder theorem complete residue system completely multiplicative computation congruent modulo Definition divided equation equivalent Euler's criterion example exist integers exponent Fermat's theorem Find following theorem follows from Theorem form 4fc Gauss given congruence greatest common divisor Hint implies incongruent solutions modulo infinitely many primes integers not exceeding integers q integral coefficients least common multiple least element least positive Lemma mathematical induction modulo 29 mth power residues notation number of positive number-theoretic function obtain odd prime positive divisors positive integers power residues modulo preceding theorem prime number primitive Pythagorean triplet primitive root modulo proof is complete properties quadratic character quadratic residue modulo real number reduced residue system relatively prime residue system modulo result of Exercise Section set of positive Similarly solution of f(x solvable solving Suppose Theorem 2.1 theory of numbers tion well-ordering principle Wilson's theorem zero