## Number theoryNumber theory |

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### Contents

1 | |

Chapter 2 Representation of Numbers by Decomposable Forms | 75 |

Chapter 3 The Theory of Divisibility | 155 |

Chapter 4 Local Methods | 251 |

Chapter 5 Analytic Methods | 309 |

Algebraic Supplement | 390 |

Tables | 422 |

433 | |

### Common terms and phrases

algebraic number field assume basis called Chapter character modulo coefficient ring coincides complete complex numbers congruence congruent modulo consider contains converges Corollary corresponding cyclotomic field decomposition Dedekind ring definition degree denote determined discriminant divide divisible divisor classes equals equation equivalent extension K/k field of rational finite extension finite number form f formula full module function fundamental units Gaussian sum group G Hence integral closure integral divisors irreducible isomorphism lattice Lemma linear matrix maximal order metric minimum polynomial multiplication natural number nonsingular norm number of divisor number of solutions obtain p-adic integers p-adic numbers power series prime divisors prime element prime number primitive principal divisor Problem proof of Theorem proved quadratic form rational integers rational numbers real numbers relatively prime representation represents zero residue class residue class field root satisfies Section semigroup sequence Show solvable subgroup theory of divisors valuation variables vectors