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Ore O. — Number theory and its history

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Название: Number theory and its history

Автор: Ore O.

Аннотация:

Unusually clear, accessible introduction covers counting, properties of numbers, prime numbers, Aliquot parts, Diophantine problems, congruences, much more. Bibliography.

Язык:

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1948

Количество страниц: 379

Добавлена в каталог: 17.11.2013

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID

Предметный указатель

Abacists      21 185
abacus      14 15 225 227
Abel, N. H.      343
Absolute value      28 348
Absorption law      103
Abu Kamil      139 140
Abu-l-Hasan Thabit ben Korrah      98 99
Abundant numbers      94 95
Ahmes      116—118
Al-Fakhri      185 187 193 208
Al-Jabr wAl-Muqabalah      19 20 187
Al-Kafi fil hisab      185
al-Karkhi      185—187 225
al-Khowarizmi, Mohammed ibn Musa      19 20 187 225
Albert, A. A.      39 164
Alcuin      94 121
Algebra      20 123
Algebra (Euler)      60 126 128 132 138 141 206
Algebra, syncopated      181
Algebraic congruences      234 235 249—258
Algebraic numbers      206 207
Algorism      20 21
Algorismus      21
aliquot parts      86 91 98
Amicable numbers      27 96—100
Amplitude      348 350
Apices      20
Arabic numerals      19 24 117
Archibald, R. C.      141
Archimedes      5 140 209 358
Aristotle      26
Arithmetic      180
Arithmetic (Sun — Tse)      245
Arithmetic mean      90 91
Arithmetic series      79
Arithmetics (Diophantos)      180—185 194 199 270
Aryabhata      122
Associative law      48 103
Astrology      28
Athelard of Bath      20
Attic numerals      11 15
Average      90
Babylonian numerals and system      2 16—18 36 37 172—179 188 312 324
Bachet, Claude, Sieur de M $\acute{e}$ ziriac      125 126 132 133 141 196 198
Barlow      93 131
Base (of number systems)      3
Bede, Venerable      6
Bell, E. T.      39
Bertelsen      69 77
Bhaskara      26 122 123 129 136 138 193 208
billion      5
Binary number systems      2 37
Birkhoff, G.      39 164
Bonconpagni, B.      207
Book of Precious Things in the Art of Reckoning, The      139
Brahma — Sphuta — Siddhanta      122 193
Brahmagupta      26 122 193 208 247 249
Brahmi numerals      19
Brancker      53
Briggs      317
Brun, V.      84
Buddha      4
Bull, L. S.      141
Burckhardt      54
Bureau      15
Cajori, F.      24
calculations      14 15
Calculus      15 55
Canon arithmeticus      285 301
Cardanus      98 195
Carmichael, R. D.      96 207 332 333 339 359
Casting, on the lines      15 225 227
Casting, Out Nines      15 225 227 229—231
Cataldi      73
Cattle problem      140
Chace, A. B.      141
Charlemagne      94 121
Chaucer      20
Checks      15
Checks, numerical      225—233
Chemac      54
Chemick, J.      334 339
Chinese remainder theorem      240 246—248 251 264 265 294 304
Chinese — Japanese numerals      11 12 16 17
Chuquet, Nicolas      98
Cipher      11 20
Ciphered numerals      12—13 19
Closed systems of numbers      158—163
Cogita Physico-mathematica      71
Colebrook, H. T.      141 208
Columna Rostrata      4
Commutative law      103
Complete Introduction to Algebra      see Algebra Euler
complex numbers      158—163 347 348
Composite numbers      50 51 331
Comptoir      15
Congruences      210ff.
Congruences, algebraic      234 235 249—258
Congruences, linear      236—240 275 276 298 299
Congruences, root of      234ff.
Congruences, simultaneous      240—250
Congruent      211ff.
Congruum      191 202
Construction by compass and ruler      341—345 349 351 352
Copernicus, Nikolaus      21
Cossica, or Cossick Art      195
Counters      1 15 21 227
Counting process      1 8
Coxeter, H. S. M.      358
Creak, T. G.      310 325
Crelle      54
Cross-cut      105
Cunningham, A. J. C.      85 96 285 310 324 325
Cuttaca      122
Cycle, solar, lunar, planetary      247
Cyclotomic equation      349
Dase      54
De Moivre      348—350
De Revolutionibus Orbium Coelestium      21
De temponmi ratione      6
De Thiende      see Disme La
Decadic number systems      1 3 12 33 34 226 233 279
Decimal expansion      311—325
Decimal expansion, finite      315—317
Decimal expansion, periodic      318—325
Decimal expansion, purely periodic      320 321
Decimal fractions      21 36 311—326
Decimal number systems      1 3 10 34 36
Decimal, circulating      315
Deficient numbers      94 95
Delian problem      see Doubling of cube) De Moivre theorem
Demotic numerals      13
Descartes, Ren $\acute{e}$       55 95 96 99
Determination      212
Dickson, L. E.      199 358 359
DIGITS      1 16
Diophantine equations or problems      165 184 193 204 207 208 268
Diophantos      168 179—185 187 193—196 198 199 203—205 208 211 268 270 313
Dirichlet, box principle of      268
Dirichlet, Lejeune      79 80 206 207 268
Dirichlet, theorem of      79 80 338
Disme, La      24 313 314 325
Disquisitiones Arithmeticae      74 209—211 225 233 243 256 263 297 301 315 323 341 358
Distributive laws      106 108
Divisibility      25 226—228
Divisible      29 213
Division      25 30
Division lemma      44
Divisor, common      41 47
Divisor, greatest common (g c.d.)      25 41 47 48 100—107 154

Divisors of a number      28 29 86
Divisors of a number, arithmetic mean of      90 91
Divisors of a number, average of      90
Divisors of a number, geometric mean of      87 88 91
Divisors of a number, harmonic mean of      90 91
Divisors of a number, maximal      328
Divisors of a number, number of      86
Divisors of a number, product of      87
Divisors of a number, proper      30
Divisors of a number, sum of      88 89 95
Divisors of a number, sum of, trivial      29
Doubling of cube (Delian problem)      340 341
Dual      103 105 106
Duplication      38
Dyadic number systems      2 37—39
Elements (Euclid)      41 52 65 92 166
Eleven      3
Equivalence relation      213
Eratosthenes      64 66 67 75 84 340
Eratosthenes, sieve of      64 66 67 84
Escott, E. B.      100 115
Etienne de la Roche      98
Euclid      41ff. 52 65 79 92 94 174 211 358
Euclid’s algorism      41—45 100 122 142 146 193
Euler, Leonhard      59—64 73 74 78 81 84 93 100 110 126—128 131 132 138 141 198 199 206 208 211 245 249 272 273 277 297
Euler’s congruence or theorem      272—280 290 292 303
Euler’s congruence or theorem, $\varphi$ -function      109—115 273 283 350
Euripides      340
Exchequer      8 9 15
Exponent, to which a number belongs      280—284
Exponent, to which a number belongs, $\pm one$       302 303 309
Exponent, to which a number belongs, universal      290 292 293 302 332
F$ numbers      see Numbers with
Factor      29
Factor tables      53 54 82 83 85
Factorization method, Euler’s      59—64
Factorization method, Fermat’s      54—58 62
Felkel      54
Ferdinand, Carl Wilhelm, Duke of Brunswick      209 210
Fermat numbers      74 75
Fermat numbers, primes      69 75 205 351—354 358 with
Fermat's theorem      272 273 277—280 326 339
Fermat's theorem, converse of      326 328 331 339
Fermat, Pierre de      54ff. 59 62 63 69 73—75 80 95 96 98 99 166 194 196 198 199 203—209 211 268 270—273 277 280
Fermat, Samuel      196
Fermat’s Last Theorem      203 208
fibonacci      see Leonardo
Field      163 164
Field, quadratic      163
Finger numbers      5—7
Finite decimal expansion      315—317
Foil      8
Forms, quadratic      63
Frederic II, Emperor      187 193
Frederic II, King of Prussia      60
Frenicle de Bessy      59 60 74 96 272
Galois, E.      343 344
Ganita — Sara — Sangraha      123 141
Gauss, C. F.      74 75 209—212 225 233 245 247 256 263 266 267 291 297 301 315 317 323 341 346—348 351 352 355 358
Gauss’s generalization of Wilson’s congruence      263 266 267 291 292
Gelon, King      5
Gematry (Gematria)      28
Geometric mean      87 88 91
Geometric progression      89 272
Gerbert, Pope Sylvester II      20
Glaisher, J. W. L.      54 95 113 115
Gobar numerals      20
Goldbach, Christian      60 81 84 85
Goldbach’s conjecture      81 84 85
Goodwin, H.      323 325
Greatest common divisor (g.c.d.)      25 41 47 48 100—107 154
Greatest common divisor (g.c.d.), associative law for      48 103
Greek numerals      11 13 15 28
Ground of Aries, The      21
Hadamard, J.      78
Hardy, G. H.      39 40 199 359
Harmonic mean      90 91
Heaslet, M. A.      39 40 43 359
Heath, T. L.      208
Hebrew numerals      28
Henry, Charles      208
Heraclitus      195
Hermite, C.      345
Herodianic numerals      11 15
Hieratic numerals      13
Hieroglyphic numerals      10 13
Hilbert, D.      199
Hill, G. E.      24
Hindu — Arabic numerals      15 19 21 24 312
Hindu — Brahmi numerals      13
Historical Prolegomenon      97
Holzman      194—196
Hopper, V. F.      40
Horoscope      97
Hundred      3
Iamblichus of Phalcis      97
Ibn Khaldun      97
Ideals      207
Idempotent law      103
Incongruent      211
Indeterminate problems      120 182
Indeterminate problems, linear      120 142 160 184 193 237 276
Indicator      110 294 302 333
indices      294—301 310 322 325
Infinite descent, method of      198 200
Ingham, A. E.      359
Integers      28
Integers, greatest, contained in a number      31
Integers, group of      1 2 10—13
Integral logarithm      77
Intersection      105 108
Jacobi, K. G. J.      285 301 310
Jenkinson      9n.
Jetons      15 20 227
John of Halifax      21
John of Palermo      188 193
Join      104
Jumeau, Andr $\acute{e}$       96
Karpinski, L. C.      24
Kraitchik, M.      76 85 285 310
kronecker      43
Kulik, J. P.      54
Kummer, E.      206 207
Lagrange, J. L.      199 211 256 259 282
Lam $\acute{e}$       43 206
Lambert, J. H.      53
Lattice points      151 152
Lattices      105 106
Lawther, H. P., Jr      305 309 310
Least common multiple (l.c.m.)      25 45— 9 100—107
Least common multiple (l.c.m.), associative law for      48 103
legendre      206 211
Lehmer, D. H.      54 75n. 331 339 359
Lehmer, D. N.      54 66 85 96
Leibniz      55 259
Leonardo Fibonacci (Pisano)      20 117 118 122 185 187 188 191—193 196 202 207 228 247 312
Liber Abaci      20 117 122 187 228 247
Liber quadratorum      188 203
Lilavati      26 122 123
Lindemann, F.      345
Linear congruences      236—240 275 276 298 299
Littlewood, J. E.      199
Local value, principle of      16
Logarithms      77 294 297 299 301 314 345
Logistics      181
Lucas, E.      73 96 326—328
Lucas, theorem of      326—328
MacDuffee, C. C.      40 164 358
MacLane, S.      39 164
Mahaviracarya      122 131 141

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