\(\dfrac{x}{8}-\dfrac{1}{4}=\dfrac{1}{y}\)
\(\Leftrightarrow\dfrac{x-2}{8}=\dfrac{1}{y}\)
\(\Leftrightarrow x-2=\dfrac{8}{y}\)
Do \(x-2\in Z\Rightarrow\dfrac{8}{y}\in Z\)
\(\Rightarrow y=Ư\left(8\right)\)
\(\Rightarrow y=\left\{-8;-4;-2;-1;1;2;4;8\right\}\)
\(\Rightarrow x=\left\{1;0;-2;-6;10;6;4;3\right\}\)