a)Do 5 ⋮ n+1 (n ϵ N)
\(\Rightarrow n+1\inƯ\left(5\right)\)\(=\left\{\pm1;\pm5\right\}\)
Ta có:
\(n+1=\left(-1\right)\Rightarrow n=\left(-2\right)\)
\(n+1=1\Rightarrow n=0\)
\(n+1=5\Rightarrow n=4\)
\(n+1=\left(-5\right)\Rightarrow n=\left(-6\right)\)
Mà \(n\in N\Rightarrow n=\left\{0;4\right\}\)
b) Từ (n+4) ⋮ (n+1) \(\left(n\in N\right)\)
\(\Rightarrow\left(n+1\right)+3⋮\left(n+1\right)\)
\(\Rightarrow3⋮\left(n+1\right)\)
\(\Rightarrow\left(n+1\right)\inƯ\left(3\right)=\left\{\pm1;\pm3\right\}\)
Ta có:
\(\left(n+1\right)=\left(-1\right)\Rightarrow n=\left(-2\right)\)
\(n+1=1\Rightarrow n=0\)
\(n+1=\left(-3\right)\Rightarrow n=\left(-4\right)\)
\(n+1=3\Rightarrow n=2\)
Mà \(n\in N\Rightarrow n=\left\{0,2\right\}\)
