Trolling IMO Problems: 1

$\begin{aligned} &~&2^3&\equiv &1\pmod7 \\ &\Longrightarrow ~~~&2^{3n}~~~&\equiv ~~~&1\pmod7 \\ &\Longrightarrow ~~~&2^{3n}+1~~~&\equiv ~~~&2\pmod7\\ &\Longrightarrow ~~~&2^{3n+1}+1~~~&\equiv ~~~&3\pmod7\\ &\Longrightarrow ~~~&2^{3n+2}+1~~~&\equiv ~~~& 5\pmod7\\ \end{aligned}$ $\therefore~~~ \text{Answer:}~~~\fbox{0}$

2^3=1