\(\left(n+13\right)⋮n-5\)
\(n+13=n+13+5-5\)
\(=\left(n-5\right)+\left(13+5\right)\)
\(=\left(n-5\right)+18\)
Ta có: \(n-5⋮n-5\) để \(\left(n+13\right)⋮n-5\) thì \(18⋮n-5\)
\(\Rightarrow n-5\inƯ\left(18\right)\)
hay \(n-5\in\left\{1;2;3;6;9;18\right\}\)
Vậy \(n\in\left\{6;7;8;11;14;23\right\}\)