History of the Theory of Numbers: Divisibility and Primality: 01 (Dover Books on Mathematics)

Book Details

• Publisher: Dover

• Author: Dickson, Leonard Eugene

• Language: English

• Edition: Illustrated

• ISBN: 9780486442327

• Pages: 512

• Cover: Paperback

• Dimensions: 8.4 x 5.5 x 1.1 inches

• Format: Illustrated

About the Book

History of the Theory of Numbers, Volume 1: Divisibility and Primality by Leonard Eugene Dickson is the first volume in a renowned three-part series that explores the foundational concepts of number theory. Written by a distinguished mathematician, this volume is a valuable resource for upper-level undergraduates and graduate students, providing an in-depth analysis of divisibility and primality. It can be read independently of the succeeding volumes, which cover Diophantine analysis and quadratic and higher forms.

The first volume features twenty chapters that delve into a range of number-theoretic topics, including perfect, multiply perfect, and amicable numbers, as well as formulas for divisors and problems posed by Fermat and Wallis. Dickson addresses complex ideas such as periodic decimal fractions, primitive roots, exponents, binomial congruences, and higher congruences. Other notable topics include the theory of prime numbers, methods for factoring, and the study of Fermat numbers.

The book also provides essential discussions on the greatest common divisor, least common multiple, divisibility criteria, and inversion of functions. Detailed factor tables, lists of primes, and criteria for divisibility by specific numbers are included, offering practical tools for number theory exploration. With its clear explanations and rich illustrations, this volume is a comprehensive guide for anyone interested in the subject.

Complete with indexes of authors and subjects, this volume serves as an indispensable reference for students and scholars of number theory, mathematics, and related fields.