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Topic: for all integers x coprime to n, x^(n-1) = 1 mod n -> that n square
free

Replies: 2   Last Post: Oct 25, 2009 6:48 PM

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 Robert Israel Posts: 3,262 Registered: 2/1/07
Re: for all integers x coprime to n, x^(n-1) = 1 mod n -> that n square free
Posted: Oct 25, 2009 6:48 PM

> G Patel <gaya.patel@gmail.com> writes:
>

> > How can I show that if for all integers x coprime to n, x^(n-1) = 1
> > (mod n), then n is necessarily square free?

>
> Hint: Your hypothesis implies phi(n) divides n-1.
> But if p^2 divides n for some prime p, then p divides phi(n).

Oops, sorry, both of those phi's should be lambda's (lambda(n) =
Carmichael function).
--
Robert Israel israel@math.MyUniversitysInitials.ca
Department of Mathematics http://www.math.ubc.ca/~israel
University of British Columbia Vancouver, BC, Canada

Date Subject Author
10/25/09 gaya.patel@gmail.com
10/25/09 Robert Israel
10/25/09 Robert Israel