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An Index for
An Introduction to THE THEORY OF NUMBERS
by G.H. Hardy and E.M. Wright
(published by the Oxford University Press, London)
This index compiled by Robert E. Kennedy and Curtis Cooper,
Central Missouri State University
Hardy and Wright's The Theory of Numbers was published in 1938
and is now in its fifth edition (1979). The authors admitted that there
were large gaps in their book and that the topics were presented with
very little depth. But why did this book become such a classic? In our
opinion, the preface to the first edition indicates the reason. There,
the authors write that their own personal interests dictated the material
to be included and chose topics that they considered "congenial". Thus,as
they stated in the preface, they could hardly have failed because "...the
subject matter being so attractive that only extravagant incompetence
could make it dull."
So, what is the purpose of compiling an index for a classic volume that
is probably one of the most respected number theory books of this century?
Because it doesn't have one!! It has always seemed, to us, that this had
to be an oversight on the part of Hardy and Wright or their publishers.
We believe that a good index for a mathematics book enhances the viability
of it as a reference for research and study. Hopefully, neither of the
authors would mind us constructing an index for their book.
This index is valid for both the 4th and 5th editions.
[ A B C
D E F G H
I J K L
M N O P Q
R S T U
V W X Y Z
]
 Abnormal Number, 21
 Additive Theory of Numbers, 273
 Algebraic Number, 159, 178
 Algebraic Irrational, 39
 Algebraic Equation, 159
 Algebraic Integer, 178
 Algebraic Field, 204
 Algebraic Number, 204
 Almost All, 8, 122
 Arithmetic of Quadratic Fields, 225
 Arithmetical Progression, 113
 Arithmetical Functions, 232
 Associate, 67, 181, 183, 305
 Associate (mod m), 89
 Asymptotically Equivalent, 8
 Average Order, 263, 272
 Bachet's Weights Problem, 115
 Bauer's Identical Congruence, 98, 100, 102
 Belongs to, 71
 Bernoulli's Numbers, 90
 Bertrand's Postulate, 343
 BigOh Notation, 7
 Binary Decimal, 111
 Binomial Coefficient, 63
 Biquadrate, 317, 327
 Bohr's Proof, 388
 Boundary, 31
 Bounded Quotients, 165
 Cantor's Ternary Set, 124
 Chinese Remainder Theorem (Theorem 121), 95
 Circular Representation, 390
 Class of Residues, 49
 Closed Region, 31
 Closed Set, 121
 Combinatorial Proof, 278
 Complete System of Residues, 49, 220
 Complete Set of Residues Prime to m, 52
 Composite Integer, 2
 Congruence, 49
 Conjugate Partitions, 274
 Conjugate, 305
 Continued Fraction, 127
 Continued Fraction Algorithm, 134
 Convergent, 128, 151, 164
 Convex Region, 31
 Coprime, 48
 Decimal, 107
 Dedekind Section, 377
 Degree, 204
 Dense in Itself, 121
 Dense, 377
 Derived Set, 121, 377
 Determinant, 397
 Digits (missing), 120, 122
 Diophantine Equation, 190, 191
 Dirichlet Series, 244, 248, 259
 Dirichlet's Theorem, 13, 18, 93, 373
 Dirichlet's Argument, 156, 176
 Dirichlet's Divisor Problem, 272
 Divisibility of Polynomials (mod m), 83
 Divisibility Tests, 114
 Divisibility in k(i), 182
 Divisibility (in an extension field), 208
 Divisible, 1
 Divisible (with respect to Ideals), 228
 Divisor (in an extension field), 208
 Durfee Square, 281
 Enumerable Set, 121
 Equivalent Points, 35
 Equivalent Numbers, 141
 Estemann's Proof, 386
 Euclid Number, 240
 Euclid's First Theorem, 3
 Euclid's Second Theorem, 4, 13
 Euclid's Theorem, 14, 16, 18
 Euclid's Algorithm, 136, 179, 212
 Euclidean Construction, 58, 159
 Euclidean Number, 159
 Euclidean Field, 212
 Euclidean Quadratic Field, 213
 Euler's Constant, 39, 264, 351
 Euler's Function, 52
 Euler's Identity, 284, 285
 Euler's Conjecture, 332
 EulerMaclaurin Sum Formula, 90
 Even Convergent, 132
 Excluded Interval, 377
 Farey Series, 23, 30, 36, 268
 Farey Arc, 30
 Farey Dissection, 30
 Farey Point, 30
 Fermat Number, 14
 Fermat Prime, 19, 58
 Fermat's Conjecture, 6, 14, 18
 Fermat's Theorem, 63, 71, 85, 86, 87
 Fermat's Last Theorem, 73, 190, 202, 231
 Fermat's Theorem in k(i), 219
 Fermat's Problem, 332
 FermatEuler Theorem, 63
 Ferrier's Prime, 22
 Fibonacci Series, 148, 153
 FourSquare Problem, 302, 315
 Frequency (of a digit), 124
 Fundamental Theorem of Arithmetic, 3, 21,179, 180, 185, 188, 211
 Fundamental PointLattice, 26
 Fundamental Lattice, 26
 Fundamental Parallelogram, 34
 Fundamental Theorem of Arithmetic, 246
 Gauss's Sum, 54
 Gauss's Lemma, 74
 Gaussian Integer, 178, 182, 189
 Generating Function, 244
 Goldbach's Theorem(conjecture), 19, 22
 Highest Common Divisor, 20, 48, 186
 Highest Common RightHand Divisor, 307
 Ideal, 227
 Index, 71
 Integer, 1
 Integers of k(), 187
 Integral Lattice, 26
 Integral Polynomial, 82
 Integral Quaternion, 304, 306
 Interior Point, 31
 Irrational Number, 38, 112
 Jacobi's Theorem, 282
 Kloosterman's Sum, 56
 Kronecker's Theorem, 375, 382, 384, 393
 Lagrange's Proof, 87
 Lagrange's Theorem, 302
 Lambert Series, 257
 Lattice, 26
 Lattice Point, 264
 Least Common Multiple, 48
 Least Residue, 49
 Legendre's Symbol, 68, 80
 Legendre's Theorem, 320
 Lettenmeyer's Proof, 384
 Leudesdorf's Theorem, 100
 Limit Point, 121
 Linear Conguences, 51, 94
 Linearly Independent, 379, 381
 Liouville's Theorem, 161
 LittleOh Notation, 7
 Logarithmic Function, 8
 Lucas Series, 148
 Lucas's Test, 16, 223, 231
 Maximum Period, 114
 Measure Zero, 121
 Mediant, 23
 Mersenne Prime, 18, 240
 Mersenne Number, 14, 80, 148, 224
 Mertens' Theorem, 351
 Mesh, 376
 Method of Descent, 194, 300
 Minimal Residue, 73
 Minkowski's Theorem, 32
 Minkowski's Theorem (Converse), 407
 Mobius Inversion Formula, 236, 251
 Mobius Function, 234, 243, 360
 Moduli, 19
 Multiplicative Function, 53, 235
 Neighbourhood, 121
 Nim, 117
 Nonhomogenous Forms, 402
 NonNegative Integer, 1
 Norm of an Integer, 182
 Norm, 309
 Normal Numbers, 124
 Normal Order, 356
 Null Modulus, 20
 Null Set, 122, 168
 Number,
 Abnormal, 21
 Algebraic, 159, 178
 Algebraic, 204
 Bernoulli's, 90
 Equivalent, 141
 Euclid, 240
 Euclidean, 159
 Fermat, 14
 Irrational, 38, 112
 Mersenne, 14, 80, 148, 224
 Normal, 124
 Perfect, 239
 Quadratfrei, 269
 Round, 358
 Transcendental, 159, 160, 170, 173, 177
 Triangular, 284
 Odd Convergent, 132
 Open Region, 31
 Order of Magnitude, 7, 260
 Order of a mod m, 71
 Order of Approximation, 158
 Partition, 273
 Pell's Equation, 217
 Perfect Set, 121
 Perfect Number, 239
 Periodic Continued Fractions, 143
 PointLattice, 26
 Positive Integer, 1
 Positive Definite, 397
 Primality Tests, 78
 Prime Integer, 2
 Prime Number Theorem (Theorem 6), 9, 374
 Prime in k(1), 181
 Prime in k(i), 183, 219
 Prime (in an extension field), 208
 Prime (with respect to Ideals), 228
 Prime Quaternions, 309
 Prime Pairs, 371
 Primitive Root of Unity, 55
 Primitive Root, 71, 115
 Primitive Polynomial, 205
 Principal Ideal, 229
 Principle RightIdeal, 307
 Prouhet and Tarry's Problem, 328
 Pure Recurring Decimal, 110
 Pythagoras' Theorem, 39, 42
 Quadratfrei, 16
 Quadratfrei Scale, 112
 Quadratfrei Number, 269
 Quadratic Residue, 67
 Quadratic NonResidue, 68
 Quadratic Surd, 144, 146
 Quadratic Field, 204, 206
 Quadratic Form, 396
 Quaternion, 303, 316
 Ramanujan's Sum, 55, 237
 Ramanujan's Continued Fraction, 295
 Rational Integer, 1, 178
 Rational Approximation, 163, 166
 Real Euclidean Field, 213
 Reciprocity Law, 76
 Recurring Decimal, 109
 Reflected Ray Problem, 378
 Regular Polygon, 57
 Residue, 49, 87
 Riemann Zeta Function, 245
 RightIdeal, 307
 RogersRamanujan Identities, 290, 296
 Root of f(x) (mod m), 82
 Round Number, 358
 Scale (Base), 111
 Selberg's Theorem, 360
 SelfConjugate Partition, 278
 Set of Points, 121
 Sieve of Eratosthenes, 3
 Simple Continued Fraction, 131, 132, 138
 Simple Field, 212
 Simply Normal, 124
 Simultaneous Approximation, 169
 Square Lattice, 229
 Standard Form, 2
 Star Region, 410
 Tchebotaref's Theorem, 405, 413
 Tchebychef's Theorem, 9, 345, 373
 Terminating Decimal, 109
 Theorem,
 Euclid's First, 3
 Euclid's Second, 4, 13
 Euclid's Second, 4, 13
 Euclid's, 14, 16, 18
 Fermat's, 63, 71, 85, 86, 87
 Fermat's Last, 73, 190, 202, 231
 Fermat's in k(i), 219
 FermatEuler, 63
 Goldbach's (Conjecture), 19, 22
 Jacobi's, 282
 Kronecker's, 375, 382, 384, 393
 Lagendre's, 320
 Lagrange's, 302
 Leudesdorf's, 100
 Liouville's, 161
 Mertin's, 351
 Minkowski's, 32, 407
 Prime Number (Theorem 6), 9, 374
 Pythagoras', 39, 42
 Selberg's, 360
 Tchebotaref's, 405, 413
 Tchebychef's, 9, 345, 373
 Von Staudt's, 90
 Wilson's, 68,81,86,87
 Wolstenhome's, 88, 93,100
 ThreeSquare Problem, 316
 Transcendental Number, 159, 160, 170, 173, 177
 Triangular Number, 284
 Uniform Distribution, 390
 Unimodular Transformation, 28
 Unities of k(1), 181
 Unity in k(i), 182
 Unity (in an extension field), 208
 Unity, 305
 Vector, 376
 Visible Point, 29, 409
 Von Staudt's Theorem, 90
 Vulgar Fraction, 23
 Waring's Problem, 297, 317, 325, 335
 Wilson's Theorem, 68, 81, 86, 87
 Wolstenholme's Theorem, 88, 93, 100
 Zeta Function, 245
(Placed on the web with the permission of the
authors.)
