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? 

We have that $4 + 5 + 6 = 15$. Recall the definition of the congruence relation: $a \equiv b \pmod{n}$ if and only if $n \big | (a - b)$. So $5 \big | (15 - 0)$, which implies that $4 + 5 + 6 \equiv 0 \pmod{5}$. 
