Ta có \(\overline{2x16}⋮9\Leftrightarrow x+9⋮9\Leftrightarrow x\in\left\{0;9\right\}\)
Với \(x=0\Leftrightarrow9n^2=2016\Leftrightarrow n^2=224\Leftrightarrow n=4\sqrt{14}\left(ktm\right)\)
Với \(x=9\Leftrightarrow9n^2=2916\Leftrightarrow n^2=324\Leftrightarrow n=18\left(tm\right)\)
Vậy \(n=24\)