I have a question about how I have to do this exercise for my math study:
Let d, n $\in$ $\mathbb{Z}$>0 with d|n.
a) Prove that there is a homomorphism f: $\mathbb{Z}$/n$\mathbb{Z}$ $\rightarrow$ $\mathbb{Z}$/d$\mathbb{Z}$ and that f(a mod n) = (a mod d) for every a $\in$ $\mathbb{Z}$.
b) Is f surjective?
To prove homomorphism, I have to prove that the general rule: f(r + s) = f(r) + f(s) holds, and that the function f is well-defined, but I haven't worked a lot with residue classes, so I don't actually know how to do this exercise. I have a lot more of this exercises to do, so I thought that maybe you could show me this one, and then I can do the rest on myself. Your help would be very much appreciated, because I'm stucked here for a few days now.
Thanks in advance!!!