如何快速计算 $2^{2019}$?
如何快速计算 $2^{2019}$?
Hint:
令 $m1=2\times 2$, 则
\[
\begin{aligned}
m2:=2^4=m1\times m1\\
m3:=2^8=2^4\times 2^4=m2\times m2\\
m4:=2^{16}=2^8\times 2^8=m3\times m3\\
m5:=2^{32}=2^{16}\times 2^{16}=m4\times m4\\
\end{aligned}
\]
如何快速计算 $2^{2019}$?
Hint:
令 $m1=2\times 2$, 则
\[
\begin{aligned}
m2:=2^4=m1\times m1\\
m3:=2^8=2^4\times 2^4=m2\times m2\\
m4:=2^{16}=2^8\times 2^8=m3\times m3\\
m5:=2^{32}=2^{16}\times 2^{16}=m4\times m4\\
\end{aligned}
\]