Introduction to the theory of numbers: Leonard E Dickson

Description

The aim of this book is not technique, but the central ideas of the subject. Topics are not abandoned just at the point when they become most interesting, but are carried to fruition with attention to both classic and recent literature. Topics are excluded if their full treatment requires results capable of proof only by intricate analytic methods. In spite of this limitation, the material presented is fairly representative of the vast literature.

The first three chapters treat divisibility, congruences, quadratic residues, and the reciprocity law. Binary quadratic orms are treated fully in four chaptesr without the usual restrict to integral coefficients. These chapters are interspersed with four chapters on Diophantine equations, the first of which is quite elementary, the second involves the notion of reduced binary quadratic forms, while the last two are elementary (and may be read early) but involve long chains of arguments.

The book is intended for beginners and develops the subject from first principles. College algebra is the only prerequisite except in chapter X. But there is a gradual accumuation of definitions, concepts, and notations which the reader must become thoroughly familiar before he can profit by the second part of the book. For this reason, he should solve many of the numerous problems, which were carefully selected and are not beyond beginners.

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