\(3n+1⋮n+4\\ 3\left(n+4\right)-11⋮n+4\)
\(\Leftrightarrow n+4\inƯ\left(11\right)\)
\(U\left(11\right)=\left\{1;-1;11;-11\right\}\\ \Leftrightarrow\left\{{}\begin{matrix}n+4=1\\n+4=-1\\n+4=11\\n+4=-11\end{matrix}\right.\Rightarrow\left\{{}\begin{matrix}n=-3\\n=-5\\n=7\\n=-15\end{matrix}\right.\)
Vậy \(n=\left\{-3;-5;7;-15\right\}\)