History of the Theory of Numbers, Volume I: Divisibility and PrimalityCourier Corporation, 3 de juny 2005 - 512 pàgines The three-volume series History of the Theory of Numbers is the work of the distinguished mathematician Leonard Eugene Dickson, who taught at the University of Chicago for four decades and is celebrated for his many contributions to number theory and group theory. This first volume in the series, which is suitable for upper-level undergraduates and graduate students, is devoted to the subjects of divisibility and primality. It can be read independently of the succeeding volumes, which explore diophantine analysis and quadratic and higher forms. Within the twenty-chapter treatment are considerations of perfect, multiply perfect, and amicable numbers; formulas for the number and sum of divisors and problems of Fermat and Wallis; Farey series; periodic decimal fractions; primitive roots, exponents, indices, and binomial congruences; higher congruences; divisibility of factorials and multinomial coefficients; sum and number of divisors; theorems on divisibility, greatest common divisor, and least common multiple; criteria for divisibility by a given number; factor tables and lists of primes; methods of factoring; Fermat numbers; recurring series; the theory of prime numbers; inversion of functions; properties of the digits of numbers; and many other related topics. Indexes of authors cited and subjects appear at the end of the book. |
Continguts
Perfect multiply perfect and amicable numbers | 3 |
Formulas for the number and sum of divisors problems of Fermat and Wallis | 51 |
Fermats and Wilsons theorems generalizations and converses symmetric functions of 12 p1 modulo p | 59 |
Residue of uP1p modulo p | 105 |
Eulers qfunction generalizations Farey series | 113 |
Periodic decimal fractions periodic fractions factors of 10+ 1 | 159 |
Primitive roots exponents indices binomial congruences | 181 |
Higher congruences | 223 |
Criteria for divisibility by a given number | 337 |
YIII Factor tables lists of primes | 347 |
Methods of factoring | 357 |
Fermat numbers Fn2H1 XVI Factors of ab | 383 |
Recurring series Lucas un | 393 |
Theory of prime numbers | 413 |
Inversion of functions Möbius function pn numerical integrals and derivatives | 441 |
Properties of the digits of numbers | 453 |
Divisibility of factorials and multinomial coefficients | 263 |
Sum and number of divisors | 279 |
Miscellaneous theorems on divisibility greatest common divisor least common multiple | 327 |
Author index | 467 |
484 | |
Altres edicions - Mostra-ho tot
History of the Theory of Numbers: Divisibility and Primality, Volum 1 Leonard Eugene Dickson Previsualització limitada - 2012 |
Frases i termes més freqüents
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