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Topic: Square free numbers
Replies: 25   Last Post: May 13, 2002 4:04 PM

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Scott Contini

Posts: 8
Registered: 12/13/04
Re: Square free numbers
Posted: May 8, 2002 6:05 PM
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Nicol So <nobody@no.spam.please> wrote in message news:<3CD94FC5.4826E3A2@no.spam.please>...
> Phil Carmody wrote:
> >
> > nospam wrote:

> > >
> > > How do I determine if a number is square free,
> > > without knowing its factors?

> >
> > The problem is as hard as factoring.

>
> How do you do factoring given the ability to decide square-freeness?


Good question! :o)

To rephrase Phil's statement, the fastest method *known* for testing
squarefreeness requires factoring (AFAIK). See page 8 of the
paper "The factorization of the 9th Fermat number" for more details.
You can download it from Mark Manesse's web page:

http://www.research.compaq.com/SRC/personal/msm/common/f9paper.ps

Scott







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