\(\left(n+5\right)⋮\left(n+1\right)\)
\(\left(n+1\right)+4⋮\left(n+1\right)\)
Vì n+1\(⋮\)n+1
Buộc 4\(⋮\)n+1=>n+1ϵƯ(4)={1;2;4}
Với n+1=1=>n=0
n+1=2=>n=1
n+1=4=>n=3
Vậy nϵ{0;1;3}
(n + 5) \(\vdots\) (n + 1)
(n + 1 + 4) \(\vdots\) (n + 1)
\(\implies\) (n + 1) \(\vdots\) (n + 1)
4 \(\vdots\) (n + 1)
\(\implies\) n + 1 \(\in\) Ư(4) = {1 ; 2 ; 4}
\(\implies\) n \(\in\) {0 ; 1 ; 3}
Ta có:\(n+5⋮n+1\)
\(\Leftrightarrow n+1+4⋮n+1\)
\(\Leftrightarrow4⋮n+1\)
\(\Leftrightarrow n+1\inƯ\left(4\right)\)
Mà \(n\in N\Rightarrow n+1\ge1\)
\(\Leftrightarrow n+1\in\left\{1;2;4\right\}\)
\(\Leftrightarrow n\in\left\{0;1;3\right\}\)
