Introduction to Number Theory

Introduction to Number Theory is dedicated to concrete questions about integers, to place an emphasis on problem solving by students. When undertaking a first course in number theory, students enjoy actively engaging with the properties and relationships of numbers.The book begins with introductory material, including uniqueness of factorization of integers and polynomials. Subsequent topics explore quadratic reciprocity, Hensel's Lemma, p-adic powers series such as exp(px) and...
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Introduction to Number Theory is dedicated to concrete questions about integers, to place an emphasis on problem solving by students. When undertaking a first course in number theory, students enjoy actively engaging with the properties and relationships of numbers.The book begins with introductory material, including uniqueness of factorization of integers and polynomials. Subsequent topics explore quadratic reciprocity, Hensel's Lemma, p-adic powers series such as exp(px) and log(1+px), the Euclidean property of some quadratic rings, representation of integers as norms from quadratic rings, and Pell's equation via continued fractions.Throughout the five chapters and more than 100 exercises and solutions, readers gain the advantage of a number theory book that focuses on doing calculations. This textbook is a valuable resource for undergraduates or those with a background in university level mathematics.