Question

Kết quả của số tự nhiên n để số 2n + 3 chia hết cho 3n + 1 là

Answer 1

\(\Rightarrow3\left(2n+3\right)⋮3n+1\\ \Rightarrow6n+9⋮3n+1\\ \Rightarrow2\left(3n+1\right)+7⋮3n+1\\ \Rightarrow2n+1\inƯ\left(7\right)=\left\{1;7\right\}\\ \Rightarrow n\in\left\{0;3\right\}\)

Answer 2

Ta có: \(\left(2n+3\right)⋮\left(3n+1\right)\)

\(\Rightarrow3\left(2n+3\right)⋮\left(3n+1\right)\)

\(\Rightarrow6n+9⋮3n+1\)

\(\Rightarrow3n+1+3n+1+7⋮3n+1\)

Do \(3n+1⋮3n+1\)

\(\Rightarrow7⋮3n+1\Rightarrow3n+1\leftarrowƯ\left(7\right)=\left\{1;7\right\}\)

Với \(3n+1=1\Rightarrow n=0\)

       \(3n+1=7\Rightarrow n=2\)

Vậy \(n\in\left\{0;2\right\}\)