[tex]a) \frac{8}{x} \: \in \: \mathbb{Z} = > x \: \in \: D_{8}[/tex]
[tex]D_{8}=\left\{\pm1,\pm2,\pm4,\pm8\right\}
[/tex]
[tex]1)x = - 1 = > \frac{8}{ - 1} = - 8 \: \in \: \mathbb{Z}[/tex]
[tex]2)x = 1 = > \frac{8}{1} = 8 \: \in \: \mathbb{Z}[/tex]
[tex]3)x = - 2 = > \frac{8}{ - 2} = - 4 \: \in \: \mathbb{Z}[/tex]
[tex]4)x = 2 = > \frac{8}{2} = 4 \: \in \: \mathbb{Z}[/tex]
[tex]5)x = - 4 = > \frac{8}{ - 4} = - 2 \: \in \: \mathbb{Z}[/tex]
[tex]6)x = 4 = > \frac{8}{4} = 2 \: \in \: \mathbb{Z}[/tex]
[tex]7)x = - 8 = > \frac{8}{ - 8} = - 1 \: \in \: \mathbb{Z}[/tex]
[tex]8)x = 8 = > \frac{8}{8} = 1 \: \in \: \mathbb{Z}[/tex]
[tex]b) \frac{6}{x} \: \in \: \mathbb{N} = > x \: \in \: D_{6_{+}}[/tex]
[tex]D_{6_{+}}=\left\{1,2,3,6\right\}[/tex]
[tex]1)x = 1 = > \frac{6}{1} = 6 \: \in \: \mathbb{N}[/tex]
[tex]2)x = 2 = > \frac{6}{2} = 3 \: \in \: \mathbb{N}[/tex]
[tex]3) x = 3 = > \frac{6}{3} = 2 \: \in \: \mathbb{N}[/tex]
[tex]4)x = 6 = > \frac{6}{6} = 1 \: \in \: \mathbb{N}[/tex]
