How to indicate all the endomorphisms and automorphisms of $(\mathbb{Z}, +)$?
I know that endomorphism is a homomorphism from a certain group to itself and automorphism is an endomorphism which is also bijective. Therefore I can give some examples of endomorphisms such as $f(\mathbb{Z}) = n\mathbb{Z}$ or automorphisms like $f(x)=x$ or $f(x)=-x$. I assume the automorphisms are connected to the generator of $\mathbb{Z}$ but I don't have anything to back it up with except from my intuition.
My problem is that I can't tell, not even mentioning proving, if the examples I thought of are the only existing endomorphisms and automorphisms of $(\mathbb{Z}, +)$.