Elementary Number Theory in Nine ChaptersCambridge University Press, 14.10.1999 - 407 Seiten This book is intended to serve as a one-semester introductory course in number theory. Throughout the book a historical perspective has been adopted and emphasis is given to some of the subject's applied aspects; in particular the field of cryptography is highlighted. At the heart of the book are the major number theoretic accomplishments of Euclid, Fermat, Gauss, Legendre, and Euler, and to fully illustrate the properties of numbers and concepts developed in the text, a wealth of exercises have been included. It is assumed that the reader will have 'pencil in hand' and ready access to a calculator or computer. For students new to number theory, whatever their background, this is a stimulating and entertaining introduction to the subject. |
Inhalt
Figure 17 | 6 |
10 | 24 |
E | 29 |
圖力椉七法古 | 31 |
13 The principle of mathematical induction | 39 |
6 | 44 |
21 The division algorithm | 49 |
31 Euclid on primes | 79 |
7 | 210 |
8 | 239 |
9 | 284 |
9+3 | 293 |
Figure 95 | 296 |
Tables | 305 |
Answers to selected exercises | 315 |
Table A1 | 343 |
41 Perfect numbers | 127 |
5 | 150 |
61 Polynomial congruences | 182 |
Table A13 | 389 |
| 390 | |
Andere Ausgaben - Alle anzeigen
Häufige Begriffe und Wortgruppen
a₁ arithmetic Arithmetica called canonical representation cipher ciphertext composite congruences conjecture consecutive continued fraction convergents coprime cubes Decipher denote the number Determine digital root divides divisible element enciphered equal equation established Euclidean algorithm Euler example Exercises exist integers Fermat Fermat's Little Theorem Ferrers diagram finite form 4k formula Gauss gcd(a gcd(m given greatest common divisor Hence implies induction infinite number integral squares letters Mathematical mathematical induction mathematician Mersenne modulo multiplicative natural numbers number of distinct number of partitions number theoretic function number theory obtain odd number odd prime p³n perfect number plaintext polynomial positive integer Poulet prime factors prime numbers primitive root problem Proof Prove Pythagorean triple quadratic residue rational number residue system modulo result follows sequence Show solve square number superincreasing sequence Suppose Table term Theorem triangle triangular numbers
Beliebte Passagen
Seite 3 - The time has come,' the Walrus said, ' To talk of many things: Of shoes - and ships - and sealing wax Of cabbages - and kings And why the sea is boiling hot And whether pigs have wings.
Verweise auf dieses Buch
104 Number Theory Problems: From the Training of the USA IMO Team Titu Andreescu,Dorin Andrica,Zuming Feng Eingeschränkte Leseprobe - 2007 |
Aspects of Combinatorics and Combinatorial Number Theory Sukumar Das Adhikari Eingeschränkte Leseprobe - 2002 |