Ta có : \(n^2+4⋮n+1\)

\(\Rightarrow n.n+n-n+4⋮n +1\)

\(\Rightarrow n.\left(n+1\right)+4⋮n+1\)

\(\Rightarrow n.\left(n+1\right)-n+1+3⋮n+1\)

\(\Rightarrow n.\left(n+1\right)-1.\left(n+1\right)+3⋮n+1\)

Vì \(n.\left(n+1\right)⋮n+1\) ; \(1.\left(n+1\right)⋮n+1\)

\(\Rightarrow3⋮n+1\)

\(\Rightarrow n+1\inƯ\left(3\right)\)

\(\Rightarrow n+1\in\left\{-1;1;-3;3\right\}\)

\(\Rightarrow n\in\left\{-2;0;-4;2\right\}\)

Mà \(n\in N^{ }\)*

\(\Rightarrow n=2\)

Vậy n=2

đề bài vớ vẩn vậy bạn hẳn noi đi mình giải cho