History of the Theory of Numbers, Volume I Divisibility and Primality

by Dickson, Leonard Eugene

• ISBN13: 9780486442327
• ISBN10: 0486442322
• Format: Paperback
• Copyright: 2005-06-03
• Publisher: Dover Publications

Summary

This 1st volume in the seriesHistory of the Theory of Numberspresents the material related to the subjects of divisibility and primality. This series is the work of a distinguished mathematician who taught at the University of Chicago for 4 decades and is celebrated for his many contributions to number theory and group theory. 1919 edition.

Author Biography

Leonard Eugene Dickson taught at the University of Chicago.

Table of Contents

Perfect, multiply perfect, and amicable numbers	p. 3
Formulas for the number and sum of divisors, problems of Fermat and Wallis	p. 51
Fermat's and Wilson's theorems, generalizations and converses; symmetric functions of 1, 2,..., P-1, modulo p	p. 59
Residue of (u[superscript p-1]-1)/p modulo p	p. 105
Euler's o-function, generalizations; Farey series	p. 113
Periodic decimal fractions; periodic fractions; factors of 10[superscript n plus or minus]1	p. 159
Primitive roots, exponents, indices, binomial congruences	p. 181
Higher congruences	p. 223
Divisibility of factorials and multinomial coefficients	p. 263
Sum and number of divisors	p. 279
Miscellaneous theorems on divisibility, greatest common divisor, least common multiple	p. 327
Criteria for divisibility by a given number	p. 337
Factor tables, lists of primes	p. 347
Methods of factoring	p. 357
Fermat numbers F[subscript n] = 2[superscript 2n] + 1	p. 375
Factors of a[superscript n plus or minus]b[superscript n]	p. 381
Recurring series; Lucas' u[subscript n], v[subscript n]	p. 393
Theory of prime numbers	p. 413
Inversion of functions; Mobius' function [mu](n); numerical integrals and derivatives	p. 441
Properties of the digits of numbers	p. 453
Author index	p. 467
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