Đáp án:
$\begin{array}{l}
\left\{ \begin{array}{l}
{2^a} + {2^b} + {2^c} = 112\\
\left( {{2^b} - 1} \right).2n = 2394\\
\left( {{2^c} - 2} \right).2n = 1140\\
{2^c}.2n = 609
\end{array} \right. \Rightarrow \left\{ \begin{array}{l}
{2^a} + {2^b} + {2^c} = 112\\
\left( {{2^b} - 1} \right).2n = 2394\\
{2^c}.2n - 4n = 1140\\
{2^c}.2n = 609
\end{array} \right. \Rightarrow \left\{ \begin{array}{l}
{2^a} + {2^b} + {2^c} = 112\\
\left( {{2^b} - 1} \right).2n = 2394\\
{2^c}.2n = 609\\
- 4n = 1140 - 609
\end{array} \right.\\
\Rightarrow \left\{ \begin{array}{l}
{2^a} + {2^b} + {2^c} = 112\\
\left( {{2^b} - 1} \right).2n = 2394\\
{2^c}.2n = 609\\
- 4n = 1140 - 609
\end{array} \right.\left\{ \begin{array}{l}
{2^a} + {2^b} + {2^c} = 112\\
\left( {{2^b} - 1} \right).2n = 2394\\
{2^c} = \frac{{ - 406}}{{177}}\left( {vo\,li} \right)\\
n = - \frac{{531}}{4}
\end{array} \right.\\
\Rightarrow pt\,vô\,nghiệm
\end{array}$
