Crandall & Pomerance - Page 2

ewmayer · 2005-10-15, 00:16

Well, my first edition of C&P has a whole section in Chapter 1 titled "smooth numbers" which precisely defines what that is taken to mean. Also, I don't think the book was ever intended as a self-contained primer on the elementary aspects of number theory - the speed at which various sections get into hard research problems should make that eminently clear.

ET_ · 2005-10-15, 00:43

Quote:

Originally Posted by ewmayer

Well, my first edition of C&P has a whole section in Chapter 1 titled "smooth numbers" which precisely defines what that is taken to mean. Also, I don't think the book was ever intended as a self-contained primer on the elementary aspects of number theory - the speed at which various sections get into hard research problems should make that eminently clear.

Chapter 1.4.5, page 44 on my edition...

R.D. Silverman · 2005-10-15, 13:07

Quote:

Originally Posted by Peter Nelson

I'm just saying to present a definition wouldn't do any harm.

They bother to define "smooth".

This edition has extended and revised exercises.

The exercises and "research problems" are well worth reading through (even if one cannot attempt or fully complete them) because they hint at or describe further factual and informative results not found in the main text.

The term "smooth" is specific to the topic of factoring.

"coprime", on the other hand, is a term that comes from elementary number
theory. It is quite proper for the authers to assume that a reader knows
elementary number theory, but *not* terminology that is specific to their
book.

alpertron · 2005-10-15, 15:34

The idea of Mersennewiki is to find definitions of words used in the context of factorization and primality proving in a level understandable for the majority of the participants of this forum.

So after defining those terms in the wiki, you just can write "read the wiki", giving just a link to the proper definition.

I think that at least one hundred definitions are missing there, including "smooth".

Peter Nelson · 2005-10-16, 00:50

Quote:

Originally Posted by R.D. Silverman

The term "smooth" is specific to the topic of factoring.

"coprime", on the other hand, is a term that comes from elementary number
theory. It is quite proper for the authers to assume that a reader knows
elementary number theory, but *not* terminology that is specific to their
book.

You are right, of course Bob.

This was not apparent to me earlier because my (weak) knowledge of number theory has gaps in it.

In view of the level of the rest of the text I suppose they are right to assume knowledge of basic maths.

Peter Nelson · 2005-10-16, 00:53

BTW, for the wiki......

Same chapter in second edition 1.4.5 Smooth numbers (page 48)

Definition 1.4.8:

A positive integer is said to be y-smooth if it does not have any prime factor exceeding y.

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2005-10-15, 00:16	#12
ewmayer ∂²ω=0 Sep 2002 República de California 11647₁₀ Posts	Well, my first edition of C&P has a whole section in Chapter 1 titled "smooth numbers" which precisely defines what that is taken to mean. Also, I don't think the book was ever intended as a self-contained primer on the elementary aspects of number theory - the speed at which various sections get into hard research problems should make that eminently clear.

2005-10-15, 15:34	#15
alpertron Aug 2002 Buenos Aires, Argentina 2·683 Posts	The idea of Mersennewiki is to find definitions of words used in the context of factorization and primality proving in a level understandable for the majority of the participants of this forum. So after defining those terms in the wiki, you just can write "read the wiki", giving just a link to the proper definition. I think that at least one hundred definitions are missing there, including "smooth".

2005-10-16, 00:53	#17
Peter Nelson Oct 2004 1021₈ Posts	BTW, for the wiki...... Same chapter in second edition 1.4.5 Smooth numbers (page 48) Definition 1.4.8: A positive integer is said to be y-smooth if it does not have any prime factor exceeding y.