486 
Subject Index 
Primes 6n=fcl, 7 (see differ- 
ence, highest) 
, asymptotic distribu- 
tion of, 439, 449 
, density of, 329, 416 
in arith. progression. 
425 
-, infinity of, 413 
arith. progressions, 85, 395, 
415-20, 436 
-, large, 352^, 362, 
365, 386, 388 
-, law of apparition of. 
396, 398, 406 
repeti- 
tion of, 396-8 
-, miscellaneous results 
on, 436-9 
-, number of, 352-4, 
429-35, 450 
, product of, 126 
represented by quad- 
ratic forms, 417 
poly- 
nomials, 333, 414, 418, 
420-1 
-, simi of two, 421-4, 
435 
Primes, tables of, 347, 381 
, test for, 35, 276, 302, 
305, 360-65, 370, 374, 376- 
8, 380, 396-404, 426-8, 445 
-, to base 2, 22, 353-4 
Primitive diN-isor of a'^-b^, 388 
X-root, 202 
non-deficient number, 
31 
number, 327, 334 
root, 63, 65, 72, 103, 
117, 181-204, 222, 378-9 
-, imaginarj'. 
235-252 
136 
of unity, 133, 
ProbabUity, 138, 302, 308, 
328, 330, 333, 335, 407, 438 
Product of consecutive inte- 
gers, 79, 263-4, 269, 331 
differences, 269 
divisors, 58, 
332 
Pronic, 357 
Quadratic forms, 109, 130, 
158, 207, 210, 219, 276, 
318, 330, 361-5, 369-70, 
400, 415-8, 420-1 
residues, 23, 25, 29, 
65-8, 71, 76, 92, 109, 165, 
185, 189, 190, 196-8, 202, 
210, 213-4, 218, 221, 231, 
240, 245-6, 253-5, 275, 
277, 360, 363, 365, 373, 
382, 393, 395-6, 403 
Quasi-Mersenne number, 390 
Quotient (a«'")-l)/m, 102, 
10.5-112 
[{}^l)\ + l]/p, 109, 
112 
Rank (see matrix) 
Recurring series, 376-7, 393- 
411 
, algebraic the- 
or\- of, 407 
Reducible law of recurrence, 
409-10 
Redundantem, 3, 4 
Remainders on di\dding n by 
1, . . . , n, 290, 313, 327-31 
Roots of unity, 133, 136, 183- 
4, 245, 250, 256, 419 
Secondary nimaber, 327 
root, 191 
Series of composition, 332 
Lame, 411 
Leonardo Pis- 
ano, 393 
Sieve of Eratosthenes, 8, 
347-8, 353-6, 424, 439 
Similar modulo k, 260 
Simple sj'stem of numbers, 
455, 458 
Solution of alg. equations, 
407-8 
Sous-double, 33 
Squares, 52, 54, 284-6, 358, 
361, 366, 453-464 
Stencil, 349, 356, 359 
Substitutions, 75, 78-80, 82, 
85, 158, 232, 262 
Sum of divisors, 5, 18, 19, 
22, 42, 48, 52-8, 135, 139, 
279-325, 445, 450 
A-th powers of 
divisors, 38, 123, 151, 286- 
325, 450 
integers 
<n, 95, 106, 121, 123, 126, 
140, 332 
four squares, 283 
two squares. 
247, 286, 340, 360, 381-2, 
390, 402-3 
Superfluos, 3, 4 
SymboUc, 99, 119, 124, 141-2, 
144-5, 148, 248, 250, 278, 
296, 395, 399, 402, 449 
Symbols, Ein), 281; Er{n), 
296; F{a, N), M; Fr, 375; 
H{m), Hm, 264; Jkin), 147; 
Mg, 31; nin), 441; 0,305; 
Pm, 33; <^(n), 61, 113; 
(pkin), 140; qu, 105, 109; 
s^in), 48; s„, 95; 5„, „,, 96; 
a(n), 53, 279, 446; akin), 
rin),T{n),279; n(n),291; 
d(n),429; f/„,u„,393; ?(«), 
292; [x], 115, 276; /n, 42; 
*before author, not avail- 
able. 
Symmetric functions mod. 
p, 70, 95, 106, 143 
number, 112, 455, 
463-4 •. 
Tables, 10, 14, 16, 18, 21-2, 
25, 27, 30-2, 37-8, 45, 
48-9, 54-5, 110-2, 126, 135, 
137, 140, 156-7, 160-79, 
181, 183, 185, 187-203, 213, 
217, 219, 222, 244-5, 248- 
51, 254, 262, 296, 308, 318, 
331, 339-41, 347-58, 361^, 
366-7, 379, 381-4, 386, 388, 
390-1, 399, 417, 422, 432, 
446, 457 
Tahnud, 337 
Totient, 124-5, 148, 153, 246 
point, 154 
Totitives, 98, 124, 130-1, 246 
all primes, 132, 134 
Triangular number, 7, 9, 20, 
59, 284, 290, 295, 302, 310, 
373, 425, 427 
Trinomials, factors of, 391 
Uberflussig, 3 
Uberschiessende, 3 
tJbervollstandig, 3 
Unvollkommen, 3 
Unvollstiindig, 3 
Verwandte, 38, 47 
Vollkommen, 3 
Vollstandig, 3 
Wilson's theorem, 59-91, 99, 
103, 275 
, converse of, 
63, 427-8 
, generalization 
of, 65, 68-74, 77-84, 87, 
90-1 (see Galois) 
Zeta function, 121, 125-7, 
134, 139, 149, 292-3, 298-9, 
310,318,322,324,328,331, 
439, 448 
