G7.2 Find $b$, if $b$ is the remainder when $1998^{10}$ is divided by $10^{4}$.
$\begin{aligned} 1998^{10} & =(2000-2)^{10} \\ & =\sum_{k=0}^{10} C_{k}^{10} \cdot 2000^{10-k} \cdot 2^{k} \\ & =\sum_{k=0}^{9} C_{k}^{10} \cdot 2000^{10-k} \cdot 2^{k}+2^{10} \\ & \equiv 2^{10} \bmod 10^{4}\left(\because C_{9}^{10} \cdot 2000^{10-9} \cdot 2^{1}=10000 \mathrm{~m}, \text { where } m \text { is an integer }\right) \\ & \equiv 1024 \bmod 10^{4} \\ \Rightarrow b= & 1024\end{aligned}$