\((2n+1)⋮(n-3)\)
\((n-3)⋮(n-3)\)\(\Rightarrow2\left(n-3\right)=(2n-6)⋮(n-3)\)
\(\Rightarrow\left(2n+1-2n+6\right)⋮\left(n-3\right)\)\(\Rightarrow7⋮\left(n-3\right)\)\(\Rightarrow n-3\inƯ\left(7\right)=\left\{\pm1;\pm7\right\}\)
\(\Rightarrow n\in\left\{-4;2;4;10\right\}\)
Vậy \(n\in\left\{-4;2;4;10\right\}\)