## A Concise Introduction to the Theory of NumbersNumber theory has a long and distinguished history and the concepts and problems relating to the subject have been instrumental in the foundation of much of mathematics. In this book, Professor Baker describes the rudiments of number theory in a concise, simple and direct manner. Though most of the text is classical in content, he includes many guides to further study which will stimulate the reader to delve into the great wealth of literature devoted to the subject. The book is based on Professor Baker's lectures given at the University of Cambridge and is intended for undergraduate students of mathematics. |

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### Contents

III | 1 |

VI | 2 |

VII | 3 |

VIII | 4 |

IX | 6 |

X | 7 |

XI | 8 |

XII | 9 |

XXXIV | 41 |

XXXV | 43 |

XXXVI | 44 |

XXXVII | 46 |

XXXVIII | 48 |

XXXIX | 50 |

XL | 53 |

XLI | 56 |

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### Common terms and phrases

algebraic integers algebraic number field arithmetic asserts assume binary form Chapter congruence continued fraction defined denote divides Euclidean fields Euler exist integers expressed fact Fermat Fermat's conjecture Fermat's theorem finite forms with discriminant function Gauss Gaussian field Gaussian integer Gaussian prime given gives Hence implies inequality infinitely integer coefficients integer solutions irreducible elements Lagrange's theorem law of quadratic Legendre symbol linear forms Liouville's theorem Minkowski's Mordell multiplicative natural number number of solutions number theory obtain odd prime or(n pa/q partial quotients Pell equation plainly polynomial with integer positive integers prime power primitive root mod proof prove quadratic irrational quadratic non-residue mod quadratic reciprocity quadratic residue mod rational integers rational points readily verified real numbers reduced set relatively prime satisfies set of residues soluble solution in positive solutions mod suffices theory of numbers Thue equation Thue's theorem unique factorization whence zeros