[tex]\it \dfrac{17}{3x+2} \in\mathbb{Z} \Rightarrow 3x+2|17\Rightarrow 3x+2\in\{\pm1,\ \pm17\}\Rightarrow 3x+2\in\{-17,\ -1,\ 1,\ 17\}|_{-2}\Rightarrow \\ \\ \Rightarrow 3x\in\{-19,\ -3,\ -1,\ 15\}|_{:3}\ \stackrel{x\in\mathbb{Z}}{\Longrightarrow}\ S=\{-1,\ \ 5\}[/tex]
