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

Subject Matter

 * Number Theory

Contents

 * PREFACE


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


 * Author index
 * Subject index