## Elementary number theory |

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### Contents

The Greatest Common Divisor of Two Numbers | 11 |

Prime Numbers and Factorization into Prime Factors | 18 |

The Greatest Common Divisor of Several Numbers | 26 |

Copyright | |

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### Common terms and phrases

BRUN'S THEOREM canonical decomposition character modulo class number coefficients complete set congruence consequently converges Definition denote diophantine equation divisible exactly Examples Exercises for Chapter fact Farey sequence finite follows from Theorem formula fundamental discriminant greatest common divisor hence hyperbola infinite number infinitely many primes integers interval Jacobi symbol Jacobi's Let w>0 log log modulo natural numbers number of positive number of solutions number theory number-theoretic function obviously odd number odd prime otherwise p=3 mod pair Pell's equation perfect number perfect square positive divisors positive multiples positive numbers prime factors prime numbers proof of Theorem proved quadratic non-residue quadratic residue reader Reciprocity Law reduced set relatively prime residue class mod residues mod right-hand side set of residues so-called solutions of 28 solvable square-free suffices Theorem 113 Theorem 121 Theorem 35 Theorem 84 Theorem 98 Vorlesungen iiber Zahlentheorie