Question

Tìm \(n\in N\)sao cho :

a) \(15-2n⋮n+1\)

b) \(\left(6n+9\right)⋮\left(4n-1\right)\)

Answer 1

Ta có\(15-2n⋮n+1\)

\(\Rightarrow17-2\left(n+1\right)⋮n+1\)

\(\Rightarrow17⋮n+1\)

\(\Rightarrow n+1\inƯ\left(17\right)=\left\{1;17\right\}\)

\(\Rightarrow n=\left\{0;16\right\}\)

Answer 2

Ta có \(6n+9⋮4n-1\)

\(\Rightarrow4\left(6n+9\right)⋮4n-1\)

\(\Rightarrow24n+36⋮4n-1\)

\(\Rightarrow6\left(4n-1\right)+42⋮4n-1\)

\(\Rightarrow42⋮4n-1\)

\(\Rightarrow4n-1\inƯ\left(42\right)=\left\{1;2;3;6;7;14;21;42\right\}\)

mà \(n\in N\Rightarrow n=\left\{1;2\right\}\)