What constitutes a proof of congruence in modular arithmetic? 
In this problem, don’t use a calculator. The answers can be derived without doing much computation, try to find these simple solutions.
(a) $4 + 5 + 6 ≡ 0 \pmod {5}$

My professor gave me some congruences to prove in my latest discrete HW. They seem pretty easy, but I'm not sure what constitutes a proof. I know that a congruence of numbers $a, b$ and $n$ would have the following characteristics:
1) $a-b$ would be a multiple of $n$
2) $a$ is $b$ more than a multiple of $n$
3) $a / n$ has remainder $b$
...would showing any of these three things to be true (or all three to be true) constitute a proof? 

Better: $5\equiv 0\pmod 5$, $6\equiv 1\pmod 5$, and $4\equiv -1\pmod 5$, so $4+5+6\equiv -1+0+1 \equiv 0\pmod 5$.
