> G Patel <firstname.lastname@example.org> 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