## Topics in Number TheoryClassic two-part work now available in a single volume assumes no prior theoretical knowledge on reader's part and develops the subject fully. Volume I is a suitable first course text for advanced undergraduate and beginning graduate students. Volume II requires a much higher level of mathematical maturity, including a working knowledge of the theory of analytic functions. Contents range from chapters on binary quadratic forms to the Thue-Siegel-Roth Theorem and the Prime Number Theorem. Includes numerous problems and hints for their solutions. 1956 edition. Supplementary Reading. List of Symbols. Index. |

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### Contents

INTRODUCTION | 1 |

THE EUCLIDEAN ALGORITHM AND ITS CONSEQUENCES | 14 |

CONGRUENCES | 24 |

PRIMITIVE ROOTS AND INDICES | 48 |

QUADRATIC RESIDUES | 63 |

NUMBERTHEORETIC FUNCTIONS AND THE DISTRIBUTION OF PRIMES | 81 |

SUMS OF SQUARES | 125 |

PELLS EQUATION AND SOME APPLICATIONS | 137 |

BINARY QUADRATIC FORMS | 1 |

ALGEBRAIC NUMBERS | 34 |

APPLICATIONS TO RATIONAL NUMBER THEORY | 82 |

THE THUESIEGELROTH THEOREM | 121 |

IRRATIONALITY AND TRANSCENDENCE | 161 |

DIRICHLETS THEOREM | 201 |

THE PRIME NUMBER THEOREM | 229 |

RATIONAL APPROXIMATIONS TO REAL NUMBERS | 159 |

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### Common terms and phrases

algebraic integer algebraic number field basis chapter complex numbers congruence consider constant continued fraction converges deduce defined degree Diophantine equation divides divisible divisor elementary elements equivalent Euclidean Euclidean algorithm example exponent factor field conjugates finitely following theorem function fundamental region generali2ed Hence implies induction inequality infinitely many solutions integral coefficients irreducible Legendre symbol linear log log mathematics matrix modulo multiplicative non2ero nonresidue number theory obtain odd prime pair Pell's equation polynomial positive integers primitive root PROBLEMS proof is complete proof of Theorem properties proved quadratic residue rational integers rational numbers real number reduced form reduced residue system region relatively prime representation result root of unity Section sequence Show solvable square Suppose tion transcendental transformation Unique Factori2ation unit values Wronskian