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Niven I., Zuckerman H.S. — An Introduction to the Theory of Numbers
Niven I., Zuckerman H.S. — An Introduction to the Theory of Numbers

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Название: An Introduction to the Theory of Numbers

Авторы: Niven I., Zuckerman H.S.

Аннотация:

Our purpose is to present a reasonably complete introduction to the theory of numbers within the compass of a single volume. The basic concepts are presented in the first part of the book, followed by more specialized material in the final three chapters. Paralleling this progress from general topics to more particular discussions, we have attempted to begin the book at a more leisurely pace than we have followed later. Thus the later parts of the book are set forth in a more compact and sophisticated presentation than are the earlier parts.
The book is intended for seniors and beginning graduate students in American and Canadian universities.


Язык: en

Рубрика: Математика/

Серия: Сделано в холле

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1960

Количество страниц: 259

Добавлена в каталог: 15.05.2011

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
$\alpha\beta$ theorem      232 235
Abelian groups      53
Additive groups      55
Algebraic integer      178 186
Algebraic numbers      177
Algebraic numbers, closure properties      179 180
Algebraic numbers, degree of      178
Algebraic numbers, field of      181
Algebraic numbers, minimal equation      178
Algorithm      4
Algorithm, Euclidean      7
Approximation by rationals      131 143 148
Artin, E.      238
Associate      186
Asymptotic density      222
Belonging to exponent      48 60
Bertrand's postulate      171
Binary operation      52
Binary quadratic form      116
Canonical form, factorization      14
Cassels, J.W.S.      237
Chinese remainder theorem      31
Common divisor      4
Common divisor of polynomials      174
Common multiple      8
Commutative group      53
Complete residue system      22 55
Composite number      10
Congruence      20
Congruence, degree of      29
Congruence, degree two, prime modulus      47
Congruence, identical      29
Congruence, number of solutions      28 46
Congruence, number of solutions, $ax \equiv b (mod \ m)$      24 29
Congruence, number of solutions, $a_{0}x^{n}+a_{1}x^{n-1}+\cdots+a_{n} \equiv 0 (mod\ m)$      28 38
Congruence, number of solutions, $x^{2}\equiv -1(mod \ p)$      25
Congruence, number of solutions, $x^{2}\equiv a (mod\ p)$      50
Congruence, number of solutions, $x^{n}\equiv a (mod\ p)$      48
Congruence, number of solutions, prime modulus      44
Congruence, number of solutions, prime power modulus      40
Conjugate numbers      184
Continued fraction      134
Continued fraction, convergents of      140
Continued fraction, finite      137
Continued fraction, infinite      140
Continued fraction, periodic      152
Continued fraction, simple      135
Convergent      140
Convergent, secondary      148
Coprime      6
Cubic residue      51
Cyclic group      59
Davenport, H.      237
Definite form      116
Degree of a congruence      29
Degree of a polynomial      173
Degree of an algebraic number      178
density      222
Density of square-free integers      226
Density, $\alpha\beta$ theorem      232 235
Density, asymptotic      222
Density, natural      222
Density, Schnirelmann      231
Density, sets of density zero      228
Descent, proof by      101
Dickson, L. E.      237
Diophantine equations      94
Diophantine equations, $4x^{2}+y^{2}=n$      110
Diophantine equations, $ax^{2}+by^{2}+cz^{2}=0$      113
Diophantine equations, $a_{1}x_{1}+\cdots+a_{k}x_{k}=c$      95
Diophantine equations, $x-dy^{2}=\pm 1$      159
Diophantine equations, $x^{2}+y^{2}=n$      106
Diophantine equations, $x^{2}+y^{2}=z^{2}$      97
Diophantine equations, $x^{2}_{1}+x^{2}_{2}+x^{2}_{3}+x^{2}_{4}=n$      102
Diophantine equations, $x^{4}+y^{4}=z^{2}$      99
Diophantine equations, $\sum x^{4}_{i}=n$      105
Diophantine equations, ax + by = c      95
Dirichlet's theorem      19
Discriminant      117
Divisibility      3
Divisibility of algebraic integers      186
Divisibility of polynomials      173
Division algorithm      3
divisors      3
Divisors, sum of      83
Dyson, F.J.      238
Empty sums and products      35
Equivalent quadratic forms      120 121
Eratosthenes, sieve of      17
Euclid's theorem      15
Euclidean algorithm      7
Euclidean quadratic fields      192
Euler's $\phi$-function      23 34 88 230
Euler's formula      208
Euler's Generalization of Fermat's Theorem      23
Factorial      79
Factorial, power of prime in      79
Factorization, unique      11 13 192
Farey sequence      128
Fermat's last theorem      102
Fermat's method of infinite descent      101
Fermat's theorem      23 26 60
Fibonacci numbers      92
Field      60 181
FORM      116
Function, recurrence      90
Functions, $\mu(n)$      87 225
Functions, $\phi(n)$      23 34 88
Functions, $\Pi(x)$      15 164
Functions, $\sigma(n)$      83 85 212
Functions, $\tau(n)$      83 85 224
Functions, p(n)      200 211
Functions, [x]      65 78
Fundamental Theorem of Arithmetic      13
Gauss's lemma      65
Gauss's polynomial lemma      176
Gaussian integers      189
Gaussian primes      198
Generating functions      204
Generator      59
Graph      202
Greatest common divisor      4
Greatest common divisor of polynomials      175
Greatest common divisor, Euclidean algorithm      7
Greatest integer function      65 78
Group      53
Group generator      59
Group isomorphism      55
Group, abelian      53
Group, commutative      53
Group, cyclic      59
Group, finite      53
Group, infinite      53
Group, order of      53
Group, order of an element      59
Hardy, G.H.      237
Heaslet, M.H.      237
Hurwitz' theorem      149
Idempotent      63
Identical congruence      29
Identity element      53
Indefinite form      116
INDEX      49
Infinite continued fraction      140 143
Infinite descent      101
Infinitude of primes      15
INTEGER      1
Integer, algebraic      178 186
Integer, Gaussian      189
Integer, quadratic      187
Inverse element      53
Inversion formula      87
Irrational number, expansion of      141
Irrationality of e      83
Irreducible polynomial      175
Isomorphism      55 183
Jacobi symbol      71
Jacobi's formula      214
Jones, B.W.      237
Le Veque, W.L.      237
Least common multiple      8
Legendre symbol      64
Legendre's Theorem      113
Lehmer, D.H.      237
Lehmer, D.N.      238
Lemma of Gauss      65
Lemma of Gauss on polynomials      176
Magic square      34
Mann's theorem      232 238
Mann, H.B.      232 238
Mathematical induction      2
Minimal equation      178
Modulus      20
Moebius function      87
Moebius inversion formula      87
Monic polynomial      173
Mordell, L.J.      238
Multiple      3
Multiplicative function      84
Multiplicative group      57
Nagell, T.      237
Natural density      222
Natural number      1
Negative form      116
Niven, I.      237
Nonresidue      64
Norm      12 188
Notation      see "Symbols"
nth power residues      48
Number, algebraic      177
Number, perfect      86
Number, prime      1
Numerical function      83
Order of an element      59
Ore, O.      237
Parity      9
Partial quotient      135
Partitions      200
Partitions, divisibility properties      220
Pell's equation      158
Perfect number      86
Periodic continued fraction      152
Pollard, H.      238
Polynomial congruence      182
Polynomials over the rationals      173
Polynomials, irreducible      175
Polynomials, monic      173
Polynomials, primitive      176
Positive form      116
Power residue      48
Prime number theorem      15
Prime, relatively      6
PRIMES      1 10 111 164
Primes in arithmetic progression      19
Primes in quadratic fields      191 195
Primes, contained in factorial      79
Primes, distribution of      15 164
Primes, Gaussian      198
Primes, infinite number of      15
Primitive polynomial      176
Primitive root      49 60
Primitive solution      99
Pythagorean triple      100
Quadratic field      187
Quadratic forms      116
Quadratic forms, equivalent      120 121
Quadratic forms, reduced      122
Quadratic irrationals      152
Quadratic irrationals, expansion of      141
Quadratic nonresidue      64
Quadratic reciprocity      68 73
Quadratic residue      64
Ramanujan, S.      238
Rational approximation      131
Rational integer      179
Reciprocity, quadratic      68 73
Recurrence function      90
Reduced quadratic form      122
Reduced residue system      22 57
Relatively prime      6
Relatively prime in pairs      6
Remainder theorem      31
Representation by quadratic forms      116
Residue      22
Residue, quadratic      64
Residue, system, complete      22 55
Residue, system, complete, reduced      22 57
Ring      60
Scherk, P.      238
Schnirelmann density      231
Secondary convergent      148
Sieve of Eratosthenes      17
Simple continued fraction      134 135
Skolem, Th.      238
Square-free      15
Square-free, integers, density      226
Subgroup      61
Sum of four squares      102
Sum of fourth powers      105
Sum of two squares      106
Symbols, $<a_{0}, a_{1}, \cdots>$      140
Symbols, $<x_{0}, x_{1}, \cdots, x_{j}>$      135
Symbols, $a \equiv b (mod\ m)$, $a\not\equiv b (mod\ m)$      20
Symbols, $R(\xi)$      181
Symbols, $[a_{1}, a_{2}, \cdots, a_{n}]$      8
Symbols, $\in$, $\cup$, $\cap$      221
Symbols, $\mu(n)$      87
Symbols, $\phi(m)$      23
Symbols, $\pi(x)$      15 164
Symbols, $\prod\limits_{p|n}$, $\sum\limits_{d|n}$      35
Symbols, $\sigma(n)$      83
Symbols, $\sim$      121
Symbols, $\tau(n)$      83
Symbols, ${a\choose p}$      64
Symbols, ${P\choose Q}$      71
Symbols, (b, c), $(b_{1}, b_{2}, \cdots, b_{n})$      4
Symbols, a|b, $a\dagger b$, $a^{K}||b$      3
Symbols, p(n), $p_{m}(n)$, $p^{0}(n)$, $p^{d}(n)$, $q^{e}(n)$, $q^{0}(n)$      200
Symbols, [x]      65 78
Totally multiplicative function      84
Totient      23 34
Unique factorization      11 13
Unique factorization in quadratic fields      192
UNIT      186 190
Universal form      117
Uspensky, J.V.      237
Vandiver, H.S.      238
Vinogradov, I.M.      237
Waring's problem      104
Wilson's theorem      24
Wright, E.M.      237
Zero element      60
Zero form      116
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