This is problem 1.49 Of Rotman´s Introduction to theory of groups
Describe all the homomorphisms from $\Bbb{Z}_{12}$ to itself. Which of them are isomorphisms?
Knowing that there are $12!$ bijections between $\Bbb{Z}_{12}$ and itself, I tried by defining $f:\Bbb{Z}_{12} \to \Bbb{Z}_{12}$ trying to find some restriction by imposing that $f$ should be a homomorphism but arrived to nothing. Any hint?