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

From ProofWiki
Jump to navigation Jump to search

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


$\text{I}$. 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


Source work progress