A classical introduction to modern number theory / Kenneth Ireland, Michael Rosen

Includes bibliographical references (pages 375-384) and index

Preface to the second edition -- Preface -- Unique fractorization -- Applications of unique fractorization -- Congruence -- Structure uf U (Z/nZ) -- Quadratic reciprocity -- Quadratic Gauss sums -- Finite fields -- Gauss and Jacobi sums -- Cubic and biquadratic reciprocity -- Equations over finite fields -- Zeta function -- Algebraic number theory -- Quadratic and cyclotomic fields -- Stickelberger relation and the Eisenstein reciprocity law -- Bernoulli numbers -- Dirichlet L-functions -- Diophantine equations -- Eliptic curves -- Mordell-Weil theorem -- New progress in arithmetic geometry -- Selected hints for the exercises -- Bibliography -- Index