Thread: Smooth?
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Old 2004-10-31, 08:07   #3
xilman's Avatar
May 2003
Down not across

10,639 Posts

Originally Posted by Xyzzy
In several threads I have come across a term that I do not understand:

"smooth group order"

What does this mean? Not only do I not know what "smooth" means, I have no idea what a "group order" is...

I assume you know what a group is, in mathematical jargon. If not, say so and I'll explain.

The order of a group is the number of elements in it. It's just an integer

The term "smooth" when applied to an integer means that the integer may be factored entirely into small primes. This, of course, begs the question of what is meant by "small". Frequently it can be deduced from context. Where greater precision is needed, the term "B-smooth" is generally used. A B-smooth integer has all its prime factors less than or equal to B. So, for example, 128 is 5-smooth (indeed, it's 2-smooth), as are 125 and 120, but 121 is not 5-smooth, though it is 11-smooth.

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