Vì : \(5n+9⋮5n+1\)
Mà : \(n+1⋮n+1\Rightarrow5\left(n+1\right)⋮n+1\Rightarrow5n+5⋮n+1\)
\(\Rightarrow\left(5n+9\right)-\left(5n+5\right)⋮n+1\)
\(\Rightarrow5n+9-5n-5⋮n+1\Rightarrow4⋮n+1\)
\(\Rightarrow n+1\in\left\{1;2;4\right\}\Rightarrow n\in\left\{0;1;3\right\}\)
Vậy \(n\in\left\{0;1;3\right\}\)