Ba chữ số tận cùng của 2004^ 200 là

Giải chi tiết:

\(\begin{array}{l}{10002004^{200}} = {\left( {{{({{2004}^2})}^{10}}} \right)^{10}}{10002004^1} \equiv 4\quad \\\left( {\bmod 1000} \right){2004^2} \equiv 16\quad \left( {\bmod 1000} \right) \Rightarrow {({2004^2})^{10}} \equiv {16^{10}}\quad \\\left( {\bmod 1000} \right){16^{10}}\quad \left( {\bmod 1000} \right){16^3} = 4096 \equiv 96\quad \left( {\bmod 1000} \right){({16^3})^3} = {16^9} \equiv {96^3}\quad \\\left( {\bmod 1000} \right){96^2} = 9216 \equiv 216\quad \left( {\bmod 1000} \right){96^3} = 216 \cdot 96 = 20736 \equiv 736\quad \\\left( {\bmod 1000} \right) \Rightarrow {16^{10}} = {16^9} \cdot {16^1} \equiv 736 \cdot 16 = 11776 \equiv 776\quad \\\left( {\bmod 1000} \right){({2004^2})^{10}} \equiv 776\quad \left( {\bmod 1000} \right){2004^{200}} = {({16^{10}})^{10}} \equiv {776^{10}}\quad \\\left( {\bmod 1000} \right)376,625,{776776^2} = 602176 \equiv 776\quad \\\left( {\bmod 1000} \right){776^{10}} \equiv {776^5} \equiv \ldots \equiv 376\quad \\\left( {\bmod 1000} \right){2004^{200}} \equiv 376\quad \left( {\bmod 1000} \right).\end{array}\)

Đáp án cần điền là: 376