Congruences - proof problems 1) State what is meant by $a\equiv b \pmod n$.
2) Suppose that $a\equiv b \pmod n$ and $c\equiv d \pmod n$. Prove that

i) $a+c\equiv b+d \pmod n$
ii) $ac\equiv bd \pmod n$

For question 1, I would state that $n|(a-b)$
For part ii, I would simply use algebraic manipulation to get the desired result but i don't think I'm proving it.

Let $a = k_1n + b$ and $c = k_2n + d$, $k_1, k_2 \in \Bbb Z$. Then
$$
a+c = k_1n + b + k_2n + d = (k_1+k_2)n + (b+d)\\
ac = (k_1n+b)(k_2n+d) = (k_1k_2n+k_1d+k_2b)n+bd$$
