Ta có: \(2n+1⋮6-n\)
\(\Leftrightarrow2n+1⋮-\left(n-6\right)\)
\(\Leftrightarrow2n-12+13⋮n-6\)
\(\Leftrightarrow2\left(n-6\right)+13⋮n-6\)
\(\Leftrightarrow13⋮n-6\)
\(\Rightarrow n-6\inƯ\left(13\right)=\left\{-13;-1;1;13\right\}\)
\(n=\left\{-7;5;7;19\right\}\)