Vì \(n+3⋮n+1\)
Mà : \(n+1⋮n+1\)
\(\Rightarrow\left(n+3\right)-\left(n+1\right)⋮n+1\)
\(\Rightarrow n+3-n-1⋮n+1\Rightarrow2⋮n+1\)
\(\Rightarrow n+1\in\left\{1;2\right\}\Rightarrow n\in\left\{0;1\right\}\)
Vậy \(n\in\left\{0;1\right\}\) thỏa mãn đề bài