Solution
= Solution
By <Euclidean division>, write $a=qn+r$ and $b=sn+t$, with <integers> $q,s$ and $0\leq r,t<n$. The hypothesis is $a\equiv b\pmod n$. Apply the addition rule from part (b)(i) with $-qn\equiv-sn\equiv0\pmod n$ to obtain
$$
r=a-qn\equiv b-sn=t\pmod n.
$$
Therefore $n\mid r-t$. But $-n<r-t<n$, and the only multiple of $n$ in that interval is zero. Hence
$$
\boxed{r=t,}
$$
so the two <remainders> agree.