The three-volume series History of the Theory of Numbers is the work of the distinguished mathematician Leonard Eugene Dickson, who taught at the University of Chicago for four decades and is celebrated for his many contributions to number theory and group theory. This first volume in the series, which is suitable for upper-level undergraduates and graduate students, is devoted to the subjects of divisibility and primality. It can be read independently of the succeeding volumes, which explore diophantine analysis and quadratic and higher forms.
Within the twenty-chapter treatment are considerations of perfect, multiply perfect, and amicable numbers; formulas for the number and sum of divisors and problems of Fermat and Wallis; Farey series; periodic decimal fractions; primitive roots, exponents, indices, and binomial congruences; higher congruences; divisibility of factorials and multinomial coefficients; sum and number of divisors; theorems on divisibility, greatest common divisor, and least common multiple; criteria for divisibility by a given number; factor tables and lists of primes; methods of factoring; Fermat numbers; recurring series; the theory of prime numbers; inversion of functions; properties of the digits of numbers; and many other related topics. Indexes of authors cited and subjects appear at the end of the book.
By:
Leonard Eugene Dickson
Imprint: Dover
Country of Publication: United States
Volume: 01
Dimensions:
Height: 217mm,
Width: 141mm,
Spine: 26mm
Weight: 526g
ISBN: 9780486442327
ISBN 10: 0486442322
Series: Dover Books on Mathematics
Pages: 486
Publication Date: 03 June 2005
Audience:
General/trade
,
ELT Advanced
Format: Paperback
Publisher's Status: Unspecified
I. Perfect, multiply perfect, and amicable numbers II. Formulas for the number and sum of divisors, problems of Fermat and Wallis III. Fermat's and Wilson's theorems, generalizations and converses; symmetric functions of 1, 2, ..., p-1, modulo p IV Residue of (up-1-1)/p modulo p V. Euler's function, generalizations; Farey series VI. Periodic decimal fractions; periodic fractions; factors of 10n VII. Primitive roots, exponents, indices, binomial congruences VIII. Higher congruences IX. Divisibility of factorials and multinomial coefficients X. Sum and number of divisors XI. Miscellaneous theorems on divisibility, greatest common divisor, least common multiple XII. Criteria for divisibility by a given number XIII. Factor tables, lists of primes XIV. Methods of factoring XV. Fermat numbers XVI. Factors of an+bn XVII. Recurring series; Lucas' un, vn XVIII. Theory of prime numbers XIX. Inversion of functions; Mobius' function; numerical integrals and derivatives XX. Properties of the digits of numbers Indexes
