[tex]\it \dfrac{9n+14}{3n+1}= \dfrac{9n+3+11}{3n+1}= \dfrac{9n+3}{3n+1}+ \dfrac{11}{3n+1}= \dfrac{3(3n+1)}{3n+1}+ \dfrac{11}{3n+1}\in\mathbb{Z}\Rightarrow\\ \\ \\ \Rightarrow \dfrac{11}{3n+1}\in\mathbb{Z}} \Rightarrow 3n+1|11 \Rightarrow 3n+1\in D_{11} \Rightarrow 3n+1\in\{\pm1,\ \pm11\} \Rightarrow \\ \\ \\ \Rightarrow 3n+1\in\{-11,\ -1,\ 1,\ 11\}|_{-1} \Rightarrow 3n\in\{-12,\ -2,\ 0,\ 10\} \\ \\ \\ Dar, 3n\in\mathbb{Z} \Rightarrow 3n\in\{-12,\ 0\}|_{:3} \Rightarrow n\in\{-4,\ 0\}[/tex]
