Adler A., Cloury J.E. — Theory of Numbers: A Text and Source Book of Problems :: Электронная библиотека попечительского совета мехмата МГУ

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Adler A., Cloury J.E. — Theory of Numbers: A Text and Source Book of Problems

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Название: Theory of Numbers: A Text and Source Book of Problems

Авторы: Adler A., Cloury J.E.

Аннотация:

This text presents the principal ideas of classical number theory emphasizing the historical development of these results and the important figures who worked on them. It is intended to introduce third or fourth-year undergraduates to mathematical proofs by presenting them in a clear and simple way and by providing complete, step-by-step solutions to the problems with as much detail as students would be expected to provide themselves. This is the only book in number theory that provides detailed solutions to 800 problems, with complete references to the results used so that the student can follow each step of the argument.

Язык:

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1995

Количество страниц: 402

Добавлена в каталог: 28.03.2010

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Предметный указатель

Jacobi symbol      151
Legendre symbol      129
greatest common divisor      8
$a \equiv b (mod m)$ a congruent to b modulo m      40
$a \nmid b$ a does not divide b      7
$a \not\equiv b$ (mod m) a not congruent to b modulo m      40
a divides b      7
$F_{n}$ nth Fermat number      198
$M_{n}$ nth Mersenne number      197
number of representations of n as a sum of two squares      228
least common multiple      9
greatest integer not exceeding x      13
$\phi(n)$ Euler $\phi$ -function      75
$\pi(x)$ number of primes not exceeding x      200
$\sigma(n)$ sum of positive divisors of n      12
$\tau(n)$ number of positive divisors of n      12
Al-Karaji      221
al-Khwarizmi      7
Algebra (Euler)      356
Approximations to $\pi$       284 301
Approximations, best rational      284
Approximations, rational      282
Arithmetica (Diophantus)      267
Aryabhata      37
Associate      358 367
Bachet, Claude      6
Bertrand's postulate      201
Bhaskara      355
Binary gcd algorithm      36
Binary quadratic form      388
Brahmagupta's identity      320
Brouncker, William      314
Calendars      47 285
Carmichael function      187
Carmichael number      86
Ch'in Chiu-Shao      68
Chebyshev, Pavnuty      218
Chinese remainder theorem      46
Disquisitiones Arithmeticae (Gauss)      69
Divisibility tests      42
Division algorithm      7 359
Division algorithm for polynomials      103
divisors      7
Divisors, number of positive      12
Divisors, proper      10
Divisors, sum of positive      12
Eisenstein, Ferdinand      156
Elements (Euclid)      37
Euclid      37
Euclidean algorithm      14
Euclidean Algorithm, еxtended Euclidean Algorithm      15

Euclidean quadratic field      368
Euler $\phi$ -function      75
Euler's criterion      73 129
Euler's theorem      76
Euler, Leonhard      99
Extended Euclidean algorithm      15
Factoring large numbers      347
Factoring Method, Legendre's      327
Factorization, prime      11
Fermat number      198
Fermat prime      198
Fermat's last theorem      224
Fermat, Pierre de      98
ind a index of a      164
Modulus      40
Multiple      7
Multiplicative function      13
Nonresidue, quadratic      128
Norm Gaussian      358
Norm in $Q(\sqrt(d))$       367
Number of positive divisors      12
Number of representations      228 235
ord a order of a      159
Order of an integer      159
Partial quotient      271
Pell's equation      314
Pell's Equation, $x^{2} - dy^{2} = -1$       322
Pell's Equation, $x^{2} - dy^{2} = 1$       315
Pell's Equation, $x^{2} - dy^{2} = N$       324
Pell's Equation, least positive solution      317
Perfect number      196
Period of a continued fraction      278
Periodic continued fraction      278
Polynomial congruence, root      101
Polynomial congruence, solution      101 102 106
Power residue      165
Prime      10
Prime, $x^{k} = a (mod m)$       165
Prime, Gaussian      358
Sum of positive divisors      12
Sum of squares, four squares      233
Sum of squares, four squares, number of representations      235
Sum of squares, three squares      235
Sum of squares, two relatively prime squares      229
Sum of squares, two squares      228
Sum of squares, two squares, number of representations      229
Unique factorization theorem      11 361 369
Unit Gaussian      358
Unit of $Q(\sqrt{d})$       367
Waring's problem      236
Wilson's theorem      73

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