Ta có : \(n+3⋮n-2\)
\(\Leftrightarrow\left(n-2\right)+5⋮n-2\)
\(\Leftrightarrow5⋮n-2\)
\(\Leftrightarrow n-2\inƯ\left(5\right)=\left\{-1,1,-5,5\right\}\)
\(\Leftrightarrow n\in\left\{1,3,-2,7\right\}\)
n+3\(⋮\)n-2
(n-2)+5\(⋮\)n-2
vì n-2\(⋮\)n-2
\(\Rightarrow\)5\(⋮\)n-2hay n-2\(\in\)Ư(5)
Ư(5)\(=\){1,5,-1,-5}
\(\Rightarrow\)n-2{1,5,-1,-5}
\(\Rightarrow\)n\(\in\){3,1,-3,-7}
Vậy........