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## Homework Statement

Show that the number of group homomorphisms from Zn to Zn is equal to n. How many of these are isomorphisms?

## The Attempt at a Solution

It has been shown by other proofs that the number of homomorphisms from Zm to Zn is the gcd(m,n), but here m=n, so the gcd(n,n)=n so that is the number of homomorphisms. (Correct?) and I have no idea how to determine how many would be isomorphisms.