Show, which well-known ring is isomorphic to ring $End(\mathbf{Z})(+,ͦ,-,0,id)$ of homomorphisms $\mathbf{Z}$ -> $\mathbf{Z}$, where $\mathbf{Z}$ is commutative group $\mathbf{Z}(+)$ and 0 constant zero function.
I struggle with solving this, including the problem of what is considered a "known" ring.
$$\forall\;m\in\Bbb Z\;,\;\;f(m)=f(m\cdot 1)=mf(1)\implies f$$
is completely and uniquely determined by $\;f(1)\;$ , as written in the comments. Now, what image can you choose for $\;f(1)\;$ ? Can you see now what is $\;\text{End}\,(\Bbb Z)\;$ isomorphic to?