History of the Theory of Numbers

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; Möbius' function; numerical integrals and derivatives XX. Properties of the digits of numbers Indexes