I2.3 When $1999^{\circ}$ is divided by 7, the remainder is $R$. Find the value of $R$.
$\begin{aligned} 1999^{81} & =(7 \times 285+4)^{81} \\ & =7 m+4^{81} \\ & =7 m+\left(4^{3}\right)^{27} \\ & =7 m+(7 \times 9+1)^{27} \\ & =7 m+7 n+1, \text { where } m \text { and } n \text { are integers }\end{aligned}$
$R=1$