Question

Tìm số nguyên n sao cho:

3n + 8 ⋮ 2n + 7

Answer 1

\(\Leftrightarrow2n+7\in\left\{1;-1;5;-5\right\}\)

\(\Leftrightarrow2n\in\left\{-6;-8;-2;-12\right\}\)

hay \(n\in\left\{-3;-4;-1;-6\right\}\)

Answer 2

\(\Leftrightarrow6n+14⋮2n+7\\ \Leftrightarrow3\left(2n+7\right)-7⋮2n+7\\ \Leftrightarrow2n+7\inƯ\left(7\right)=\left\{-7;-1;1;7\right\}\\ \Leftrightarrow2n\in\left\{-14;-8;-6;0\right\}\\ \Leftrightarrow n\in\left\{-7;-4;-3;0\right\}\)