Giải thích các bước giải:
\[\begin{array}{l}
+ )12 \equiv 2\left( {\bmod 10} \right)\\
\Rightarrow {12^{2012}} \equiv {2^{2012}}\left( {\bmod 10} \right)\\
\Rightarrow {12^{2012}} - {2^{2000}} \equiv {2^{2012}} - {2^{2000}}\left( {\bmod 10} \right)\\
+ ){2^{2012}} - {2^{2000}} = {2^{2000}}\left( {{2^{12}} - 1} \right)\\
{2^4} \equiv 1\left( {\bmod 5} \right) \Rightarrow {2^{12}} = {2^{4.3}} = {\left( {{2^4}} \right)^3} \equiv 1\left( {\bmod 5} \right)\\
\Rightarrow {2^{12}} - 1 \equiv 0\left( {\bmod 5} \right)\\
\Rightarrow {2^{2000}}\left( {{2^{12}} - 1} \right) \equiv 0\left( {\bmod 10} \right)\\
\Rightarrow {2^{2012}} - {2^{2000}} \equiv 0\left( {\bmod 10} \right)\\
\Rightarrow {12^{2012}} - {2^{2000}} \equiv 0\left( {\bmod 10} \right)\\
\Rightarrow {12^{2012}} - {2^{2000}} \vdots 10
\end{array}\]
