rational arithmetic→313f
fractions→313f
Multiplication of fractions→313
Division→313
Addition→313
subtraction→313
fixed slash→314
floating slash→314
floating point→314
slash arithmetic→314f
round→314
mediant rounding→314
Henrici,→315
Matula,→315f
Zaremba→315
Kornerup→315f
comparing two fractions→315
representations for $∞$→315
overflow→315
greatest common divisor→316f
gcd: Greatest common divisor→316
least common multiple→316f
lcm: Least common multiple→316
Euclid's algorithm→317f
Eudoxus→318
von Fritz→318
Egyptian→318
Babylonian→318
algorithms→318
Knuth,→318
Euclid→318f
Greek math→318f
proof→319
induction→319f
Stein→321
halving→321
binary gcd algorithm→321f
MIX, binary version→322f
SLB→322
SRB→322
JAE→322
JAO→322
JXE→322
JXO→322
Halve→322
Euclid's algorithm→323f
Harris→323
Extended Euclid's algorithm→325f
Bradley→325
linear equations→326
Diophantine equations→326f
multiple-precision gcd→327f
Lehmer→328
binary gcd algorithm→330f
lattice-point model→330f
recurrence equations→332f
Brent→335
Traub→335
least common multiple→336
balanced ternary→336
binary gcd algorithm→336f
inclusion and exclusion→337
M\"obius function→337
Ces\`aro→337
divide $u$ by $v$ modulo $m$→337
reciprocal modulo $m$→337
lattice-point model→338f
Brent→338f
determinant→338
Harris→339
Gosper→339
Pratt→339
continued fractions→339f
Perron,→339
Khinchin,→339
Wynn→339
Wall,→339
Tropfke,→339
Euler→340
continuants→340f
regular continued fraction→341f
infinite continued fraction→341
partial quotients→342
Greek math→342
Eudoxus→342
Becker,→342
Fibonacci numbers→343
Lam\'e→343
Floyd→344
lattice-point model→344
Gauss,→346
Laplace→346
Kuz'min→346
L\'evy→346
Wirsing→346
linear operators→346f
Knopp,→347
Wirsing→350
Babenko→350f
MIX (actually 1009!)→350
\t Iur'ev→350
measure theory→350f
partial quotients→351f
regular continued fraction→352
von Mangoldt's function→355
Dixon→356
Heilbronn→356f
Porter→356
Knuth→357
Collins,→357
determinant→358
regular continued fraction→358f
continuant→358f
Lagrange→359f
decimal system→359
quadratic irrationality→359
Davenport,→359
LeVeque,→359
periodic→359
Hurwitz,→360
doubling a continued fraction→360
halving a continued fraction→360
Gosper→360
coroutine→360
Euler,→360
tangent→360
Euler's constant→360
Sweeney→360
Wrench,→360
Shanks,→360
Wirsing→361
Babenko→361
von Mangoldt function→361
M\"obius function→361
Euler totient function→361
least remainder algorithm→361
Morse code→361
Euler,→361
Heilbronn→362
Yao→362
Knuth→362
Bradley→362
Motzkin→363
Straus→363
Mikusinski→363
Gosper→363
Stern--Peirce tree→363
Shallit→363
Liouville→363
transcendental→363
Kempner,→363
Lagrange→363
Matula→363
slash arithmetic→363f
rounding→363
Factorization: Discovering factors. Of integers,→364f
prime→364
Legendre→366
de la Vall\'ee Poussin→366
Vall\'ee Poussin→366
prime number theorem→366f
primes, distribution of→366f
Walfisz,→366
Weyl→366
exponential sums→366
Riemann→366f
Littlewood→366
Hardy→366
zeta function→366
Riemann hypothesis→366
Brent→367
Lehmer→367
Dickman→367
Ramaswami→367
Norton,→367
normal distribution→368
Hardy→369
Wright,→369
Erd\H os→369
Kac,→369
permutations→369
Knuth→369
Trabb Pardo→369
Monte Carlo, method for factoring→369f
Rho method, see Monte Carlo method for factoring→369f
Pollard→369
random mapping→369
Fermat→371f
Dickson→371
Lehman→371
perfect square→372
sieve procedure→373f
Boolean operations→373
logical operations→373
{\:tMIX}→373
AND→373
Wunderlich→374
Lehmer→374
Lehmer, Emma→374
prime numbers, verifying primality→374f
Lucas→375
Lehmer→375
Fermat's theorem→375
Fermat→375
Mersenne→375
order of $x$ modulo $n$→375
Aurifeuille→376
Dickson→376
quadradic reciprocity→377
Brillhart→378
Selfridge→378
Brillhart→378
Lehmer,→378
Selfridge→378
Wunderlich,→378
Williams→378
Judd,→378
probabilistic algorithms→379f
random numbers, using, see also probabilistic algorithms→379f
Miller→379f
Generalized Riemann Hypothesis→380
Riemann hypothesis, generalized→380
GRH→380
ERH, see GRH→380
Weinberger,→380
Solovay→380
Strassen,→380
Rabin,→380
Traub→380
Adleman→380
algebraic integers→380
Rumely→380
continued fractions→380f
Legendre→380
Kraitchik,→380
Lehmer→380
Powers→380
Brillhart→380
Morrison→380
IBM 360/91 computer→380
Schroeppel→383f
Wunderlich→383f
Morrison,→384
Brillhart,→384
Hickerson,→385
Shanks,→385f
quadratic forms→385
Pollard→385
fast Fourier transform→385
Guy,→385
Conway→385
Dixon→385
probabilistic algorithm→385f
binomial distribution→386
cryptanalysis→386f
secure communications→386f
Rivest→386
Shamir→386
Adleman→386
RSA box→386f
Random numbers, machines for generating→387
cube roots→387f
logarithmic law of leading digits→387
Lehman→388
Diffie→388
public key cryptography→388
Hellman→388
signatures, digital→388f
Rabin→389
square root modulo m→389
Mersenne→389f
primes, useful→390
perfect numbers→391
Fermat,→391
Descartes,→391
Euler→391
Lucas→391f
Pervushin→391
Powers→391
Kraitchik→391
Mersenne primes→391f
CRAY-I→391
Lehmer→391
linear recurrences→392f
rank of apparition→393
quadratic reciprocity→394
Fermat→394
sieve→395
Eratosthenes→395
Selfridge→395
Dixon→395
Lucas→395
Lehmer→395
Mersenne primes→395
Pratt→395
ART ON REPRO REQUIRED→395
MIX (actually 1009)→395
Pollard→396
Guy→396
Rabin→396
Jacobi symbol→396
Solovay→396
Strassen→396
L. Monier→396
Adleman→396
Riemann→396
zeta function→396
Robinson→397
Lucas→397
Lehmer→397
Dixon→397
Schnorr→397
Dixon→397
Weinberger→397
Shamir→398
automata→398
GAUSS→398