Book:Leonard Eugene Dickson/History of the Theory of Numbers/Volume I

Leonard Eugene Dickson: History of the Theory of Numbers, Volume $\text { I: Divisibility and Primality }$

Published $\text {1919}$, AMS Chelsea

ISBN 0-8218-1934-8

Subject Matter

• Number Theory

Contents

PREFACE

Chapter.

$\text{I}$. Perfect, multiply perfect and amicable numbers

$\text{II}$. Formulas for the number and sum of divisors, problems of Fermat and Wallis

$\text{III}$. Fermat's and Wilson's theorems, generalizations and converses; symmetric functions of $1, 2, \ldots, p - 1$, modulo $p$

$\text{IV}$. Residue of $\paren {u^{p - 1} - 1} / p$ modulo $p$

$\text{V}$. Euler's $\phi$-function, generalizations; Farey series

$\text{VI}$. Periodic decimal fractions; periodic fractions; factors of $10^n \pm 1$

$\text{VII}$. Primitive roots, exponents, indices, binomial congruences

$\text{VIII}$. Higher congruences

$\text{IX}$. Divisibility of factorials and multinomial coefficients

$\text{X}$. Sum and number of divisors

$\text{XI}$. Miscellaneous theorems on divisibility, greatest common divisor, least common multiple

$\text{XII}$. Criteria for divisibility by a given number

$\text{XIII}$. Factor tables, lists of primes

$\text{XIV}$. Methods of factoring

$\text{XV}$. Fermat numbers $F_n = 2^{2^n} + 1$

$\text{XVI}$. Factors of $a^n \pm b^n$

$\text{XVII}$. Recurring series; Lucas' $u_n, v_n$

$\text{XVIII}$. Theory of prime numbers

$\text{XIX}$. Inversion of functions; Möbius function $\map \mu n$, numerical integrals and derivatives

$\text{XX}$. Properties of the digits of numbers

Author index

Subject index

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