This book introduces number theory, developing examples before giving a formal definition and a theorem, to reveal how the concept arises naturally, to conjecture a theorem that describes an evident pattern, and to show how a proof of the theorem emerges from understanding non-trivial examples. Chapters address induction, congruences, the basic algebra of number theory, multiplicative functions, the distribution of prime numbers, Diophantine problems, power residues, quadratic residues and equations, square roots and factoring, rational approximations to real numbers, and binary quadratic forms. Each chapter includes an appendix that can be used as supplementary material to expand on topics. The book incorporates problems of varying difficulty, as well as examples, and emphasizes the themes of special numbers, subjects in their own right, formulas, interesting issues, and fun and famous problems. Readers should be familiar with the commonly used sets of numbers N,Z, and Q, as well as polynomials with integer coefficients, denoted by Z[ x]. An expanded edition that provides a more comprehensive, “masterclass” approach and additional material is also available. Annotation ©2020 Ringgold, Inc., Portland, OR (protoview.com)
