Convenient way to write $x \bmod{n}$ I'm trying to figure out an easy way to write $x \bmod{n}$. 
For example, in this exercise, where I need to show that this is an homomorphism:
$$f:\Bbb{Z}/12\Bbb{Z}\to\Bbb{Z}/4\Bbb{Z}:x\bmod{12}\mapsto x\bmod{4}$$
Writing or typing down all those mod's, makes it quite a mess.
For example, I was thinking about something like this:
$$f(\overline{x+y}^{12})=f(x+y+12k)=\overline{x+y+12k}^4=\overline{x+y}^4+\overline{12k}^4=...$$
Just as an exmaple, my question is not about the math.
I'm quite sure that I'm not the first one with this problem, so how would you guys write this down ? Is there any "standard" for this ?
 A: Try $[x]_{12}$ and $[x]_4$ for the equivalences classes in the corresponding rings.
A: Well, I guess I might as well put my comment as an answer.
I would usually use $\equiv$ rather than $=$, and only write mod $n$ at the end. 
Though I agree with anon that there are situations in which it is unnecessary to write mod at all, if it's unlikely that there'd be any ambiguity.
I have also seen overlines used, as you suggest, but never with the superscript $n$, which I really don't recommend, as it looks too much like a power.
A: I would never write anything attached to an overline; I've seen students do it, but it is horribly confusing with powers (indeed what you typed was the power of overlined formulae, not an index attached to the overline). As has been said you can write $x\equiv y\equiv z\pmod5$ (be sure to type \pmod5, then the spacing and parentheses are done for you), as long as there is just one modulus as in your second example. You can also just say: compute in $\Bbb Z/5\Bbb Z$, and then you can write equals signs.
When there are different moduli as in the first example, there is no really easy solution. I would write the first example as
$$
  f: \Bbb Z/12\Bbb Z\to\Bbb Z/4\Bbb Z: x+12\Bbb Z\mapsto x+4\Bbb Z
$$
although in the end even writing $\overline x\mapsto\overline x$ would be unambiguous (though possibly confusing). You could also say $f$ is the canonical projection $\Bbb Z/12\Bbb Z\to\Bbb Z/4\Bbb Z$.
