Choose a value of n and count the number of elements in Gn (Gn is the set of invertible congurence classes of Zn). Can you discover any rules between n and the number of elements in Gn?
I have so far that if n is prime then n, n, ... , [n-1]n are all in Gn
also if n = 2^m for some integer m, Gn contains all odd elements of Zn
and finally, I know the product of any two elements of Gn is in Gn, for
n >= 2
what conclusions can I draw knowing only this information? What have I missed?