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.