TABLE OF CONTENTS.

CHAPTER. PAGE.

I. Perfect, multiply perfect, and amicable numbers................. 3

II. Formulas for the number and sum of divisors, problems of Fermat

and Wallis................................................ 51

III. Fermat's and Wilson's theorems, generalizations and converses;

symmetric functions of 1, 2,..., p—1, modulo p.............. 59

IV. Residue of (up~"1 — l)/p modulo p.............................. 105

V. Euler's <£-function, generalizations; Farey series.................. 113

VI. Periodic decimal fractions; periodic fractions; factors of 10n=*=l.... 159

VII. Primitive roots, exponents, indices, binomial congruences......... 181

VIII. Higher congruences.......................................... 223

IX. Divisibility of factorials and multinomial coefficients............. 263

X. Sum and number of divisors................................... 279

XI. Miscellaneous theorems on divisibility, greatest common divisor,

least common multiple..................................... 327

XII. Criteria for divisibility by a given number...................... 337

XIII. Factor tables, lists of primes.................................. 347

XIV. Methods of factoring......................................... 357

XV. Fermat numbers Fn^2^+l.................................. 375

XVI. Factors of an=*=6n............................................ 381

XVII. Recurring series; Lucas' un, vn................................ 393

XVIII. Theory of prime numbers..................................... 413

XIX. Inversion of functions; Mobius' function /*(n); numerical integrals

and derivatives............................................ 441

XX. Properties of the digits of numbers............................. 453

Author index................................................ 467

Subject index............................................... 484

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