Đáp án:
$\begin{array}{l}
P = {4^{10}} + {4^{11}} + {4^{12}} + {4^{13}} + ... + {4^{199}}\\
= \left( {{4^{10}} + {4^{11}}} \right) + \left( {{4^{12}} + {4^{13}}} \right) + ... + \left( {{4^{198}} + {4^{199}}} \right)\\
= {4^{10}}\left( {1 + 4} \right) + {4^{12}}\left( {1 + 4} \right) + ... + {4^{198}}\left( {1 + 4} \right)\\
= {4^{10}}.5 + {4^{12}}.5 + ... + {4^{198}}.5\\
= \left( {{4^{10}} + {4^{12}} + ... + {4^{198}}} \right).5 \vdots 5
\end{array}$
Vậy P chia hết cho 5