[tex]\displaystyle \\
10^n + 314 = \\ \\ =1\underbrace{0000\hdots 0000}_{\text{n zerouri}} + 314 = \\ \\
=1\underbrace{0000\hdots 0}_{\text{n-3 zerouri}}314 \\ \\
\text{Suma cifrelor numarului este: } \\ \\
1 + 0(n-3) + 3+1+4 = 1+0+3+1+4 = \boxed{9} \\ \\
\Longrightarrow ~~~ (10^n + 314)~\vdots~9[/tex]
