Simple Search

Query:

Enter a query and click »Search«...

Format:

Display: entries per page entries

Zbl 0945.11001
Bressoud, David; Wagon, Stan
A course in computational number theory. With CD-ROM. (English)
[B] Emeryville, CA: Key College Publishing in cooperation with Springer. xii, 367 p. DM 129.00; öS 942.00; sFr. 117.00; \sterling 44.50; \$ 64.95 (2000). ISBN 1-930190-10-7/hbk

This book is an introduction to elementary computational number theory. It is structured in nine chapters, and two appendices. Moreover, it is provided with a CD-ROM, which however requires Mathematica. \par Chapter one is a recall of fundamentals, like the Euclidean algorithm, modular arithmetic or fast powers. Chapter two is devoted to solving linear congruences, and treats pseudoprimes as well. Chapter three concerns mainly Euler's $\varphi$ function and primitive roots for primes. Chapter four treats prime numbers, in particular prime testing and certification. Some applications, like the RSA cryptosystem, are described in Chapter five. Chapter six speaks about quadratic residues and provides a proof of the quadratic reciprocity law. Continued fractions are the heart of Chapter seven. The applications to prime testing of Lucas sequences is presented in Chapter eight. Chapter nine concerns Gaussian numbers and the problem of the decomposition of primes in sums of two squares. \par Appendix A is an introduction to Mathematica, and finally appendix B provides a proof that Lucas certificates exist.
[Franck Leprévost (Berlin)]

MSC 2000:: *11-01 Textbooks (number theory)
11Yxx Computational number theory

Keywords: modular arithmetic; Euclid's algorithm; Chinese remainder theorem; prime numbers; RSA cryptosystem; factoring algorithms; quadratic residues; continued fractions; primality tests

Comment on this Item PDF MathML XML ASCII DVI PS BibTeX Online Ordering

	Scientific prize winners of the ICM 2010
	Overhang
	Lie groups, physics and geometry. An introduction for physicists, engineers and chemists.

Simple Search

Zentralblatt MATH Berlin [Germany]