^ TABLE OF CONTENTS. 
Chapter. page. 
I. Perfect, multiply perfect, and amicable numbers 3 
\ 11. Formulas for the number and simi 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 (wp~^ — l)/p modulo p 105 
V. Euler's (^function, generalizations; Farey series 113 
VI. Periodic decimal fractions; periodic fractions; factors of 10" =•=!... . 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 
v^IV. Methods of factoring 357 • 
XV. Fermat numbers F„ = 22"+l 375 
XVI. Factors of a"±6« 381 
XVII. Recurring series; Lucas' Un, Vn 393 
^VIII. Theory of prime numbers 413 
XIX. Inversion of functions; Mobius' function ix{n); numerical integrals 
and derivatives 441 
XX. Properties of the digits of numbers 453 
Author index 467 
Subject index 484 
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