\(n^2+5⋮n+1\)
Mà \(n+1⋮n+1\)
\(\Leftrightarrow\left\{{}\begin{matrix}n^2+5⋮n+1\^2+n⋮n+1\end{matrix}\right.\)
\(\Leftrightarrow n-5⋮n+1\)
Mà \(n+1⋮n+5\)
\(\Leftrightarrow6⋮n+1\)
\(\Leftrightarrow n+1\inƯ\left(6\right)\)
\(\Leftrightarrow\left[{}\begin{matrix}n+1=1\+1=2\+1=3\+1=6\end{matrix}\right.\) \(\Leftrightarrow\left[{}\begin{matrix}n=0\=1\=2\=5\end{matrix}\right.\)