[tex]\it \dfrac{7}{2a-1} \in\mathbb{Z} \Rightarrow 2a-1|7 \Rightarrow 2a-1\in D_7 \Rightarrow 2a-1\in\{\pm1,\ \ \pm7\} \Rightarrow\\ \\ \Rightarrow 2a-1\in\{-7,\ \ -1,\ \ 1,\ \ 7\}|_{+1} \Rightarrow 2a\in\{-6,\ \ 0,\ \ 2,\ \ 8\}|_{:2} \Rightarrow \\ \\ \Rightarrow a\in\{-3,\ \ 0,\ \ 1,\ \ 4\}=A[/tex]
