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Author:   Hans Riesel (Royal Institute of Technology, Stockholm, Sweden)
Publisher:   Birkhauser Boston Inc
Imprint:   Birkhauser Boston Inc
Edition:   2nd Revised edition
Volume:   Vol 126
Dimensions:   Width: 15.60cm , Height: 2.80cm , Length: 23.40cm
Weight:   0.851kg
ISBN:  

9780817637439

ISBN 10:   0817637435
Pages:   480
Publication Date:   01 October 1994
Audience:   College/higher education ,  Professional and scholarly ,  General/trade ,  Undergraduate ,  Postgraduate, Research & Scholarly
Format:   Hardback
Publisher's Status:   Active
Availability:   Out of print, replaced by POD  
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Reviews

Here is an outstanding technical monograph on recursive number theory and its numerous automated techniques. It successfully passes a critical milestone not allowed to many books, viz., a second edition. Many good things have happened to computational number theory during the ten years since the first edition appeared and the author includes their highlights in great depth. Several major sections have been rewritten and totally new sections have been added. The new material includes advances on applications of the elliptic curve method, uses of the number field sieve, and two new appendices on the basics of higher algebraic number fields and elliptic curves. Further, the table of prime factors of Fermat numbers has been significantly up-dated. ...Several other tables have been added so as to provide data to look for large prime factors of certain 'generalized' Fermat numbers, while several other tables on special numbers were simply deleted in the second edition. Still one can make several perplexing assertions or challenges: (1) prove that F\sb 5, F\sb 6, F\sb 7, F\sb 8 are the only four consecutive Fermat numbers which are bi-composite; (2) Show that F\sb{14} is bi- composite. (This accounts for the difficulty in finding a prime factor for it.) (3) What is the smallest Fermat quadri-composite?; and (4) Does there exist a Fermat number with an arbitrarily prescribed number of prime factors? All in all, this handy volume continues to be an attractive combination of number-theoretic precision, practicality, and theory with a rich blend of computer science. <p>a Zentralblatt Math

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