$2n+7\vdots n+2$
$\leftrightarrow 2n+4+3\vdots n+2$
$\leftrightarrow 2(n+2)+3\vdots n+2$
Ta nhận thấy: $2(n+2)\vdots n+2$
Mà $2(n+2)+3\vdots n+2$
$\to 3\vdots n+2$
$\to n+2\in Ư(3)=\{\pm 1;\pm 3\}$
$\to$ Bảng giá trị:
$\begin{array}{|c|c|c|}\hline n+2&1&3&-1&-3\\\hline n &-1&1&-3&-5\\\hline\end{array}$
Vậy $n=\{-1;1;-3;-5\}$