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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 6:29 PM
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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).
--
Robert Israel israel@math.MyUniversitysInitials.ca
Department of Mathematics http://www.math.ubc.ca/~israel
University of British Columbia Vancouver, BC, Canada



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