Question

Bài 3. Cho . Tìm n € N để A nguyên.

Answer 1

\(A=\dfrac{5n+1}{n+1}\left(n\ne-1\right)\)

\(\Rightarrow A=\dfrac{5n-4+5}{n+1}\)

\(\Rightarrow A=5-\dfrac{4}{n+1}\)

\(\Rightarrow4⋮\left(n+1\right)\)

\(\Rightarrow n+1\inƯ\left(4\right)=\left\{1;2;4;-1;-2;-4\right\}\)

\(\Rightarrow n\in\left\{0;1;3;-2;-3;-5\right\}\)

Mà \(n\in N\)

\(\Rightarrow n\in\left\{0;1;3\right\}\)