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**minivan15** 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 [1]n, [2]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?