Index for An Introduction to THE THEORY OF NUMBERS by G.H. Hardy and E.M. Wright Published by Oxford University Press, London Compiled by Robert E. Kennedy and Curtis Cooper Central Missouri State UniversityA | B | C | D | E | F | G | H | I | J | K | L | M | N | O | P | Q | R | S | T | U | V | W | Z

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Hardy and Wright'sThe Theory of Numberswas 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 should apply equally well to the fourth edition and the fifth edition. The page numbers are the same in both the softcover and hardcover editions.

INDEX 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 Big-Oh 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 Euler-Maclaurin 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 Fermat-Euler Theorem 63 Ferrier's Prime 22 Fibonacci Series 148, 153 Four-Square Problem 302, 315 Frequency (of a digit) 124 Fundamental Theorem of Arithmetic 3, 21, 179, 180, 185, 188, 211 Fundamental Point-Lattice 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 Right-Hand Divisor 307 Ideal 227 Index 71 Integer 1 Integers of k(rho) 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 Little-Oh 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 Merten's 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 Non-homogenous Forms 402 Non-Negative 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 Point-Lattice 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 Right-Ideal 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 Non-Residue 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 Right-Ideal 307 Rogers-Ramanujan Identities 290, 296 Root of f(x) (mod m) 82 Round Number 358 Scale (Base) 111 Selberg's Theorem 360 Self-Conjugate 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 Fermat-Euler 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 Three-Square 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

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