\(n+3⋮n+1\)
\(\Leftrightarrow\)\(n+1+2⋮n+1\)
Mà \(n+1⋮n+1\)
\(\Rightarrow\)\(2⋮n+1\)
\(\Rightarrow n+1\inƯ\left(2\right)\)
\(\Rightarrow n+1\in\left\{-2;-1;1;2\right\}\)
\(\Rightarrow n\in\left\{-3;-2;0;1\right\}\)
Vậy \(n\in\left\{-3;-2;0;1\right\}\)