## Elementary number theory: an algebraic approach |

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### Contents

Preface Chapter 1 Linear Diophantine Equations | 1 |

Divisibility and Unique Factorization | 3 |

The Diophantine Equation ax + b c | 6 |

Copyright | |

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algebraic integers algorithm analogue Appendix argument arithmetic associates chapter Chinese remainder theorem coefficients computing congruence modulo conjugate converse Corollary 26.2 coset cyclic groups decimal expansion defined Definition Diophantine equation x2 division enjoys unique factorization equivalent solutions Euclidean domain Euclidean norm Euler example exponent fact Fermat conjecture finite form 4k function fundamental unit Gaussian integers greatest common divisor hence homomorphism ideal implies improper unit inertial infinitely many primes integers less integral domain isomorphism JV(a lattice points Lemma Let g n e B(m number theory odd prime Pell's equation positive integers prime in A(m primitive Pythagorean triple primitive root product of primes proof of Theorem Prove Pythagorean triple Quadratic Reciprocity ramifies rational integers rational numbers rational primes congruent representable integers residue ring Section sequence solutions to Eq Solve the Diophantine solves Eq square free subgroup subring subset Suppose true unique factorization domain write