Originally Posted by
koko2009 For each odd composite numbern=>3, any number satisfying a^(n-1)≡1(modn )
is said to be a Fermat liar for n.
F-Liar={ a/1<= a<= n and a^(n-1)≡1(modn }
Show that F-Liar is a subgroup of Z^*n
i tried to solve this by finding the size or order of F and it must divide the order of Zn to be F a subgroup of Zn.
I think the size of Zn is n-1
and the size of F is n
but i could not get the whole prove
the order of Zn is less than or equal n/2 and the order of F must be less than or equal the order of Zn but how can I show that.