Question

Determinați valorile întregi ale lui x pentru care:
a) 8/x €Z
b) 6/x apartine N​

Answer 1

$a) \frac{8}{x} \: \in \: \mathbb{Z} = > x \: \in \: D_{8}$

$D_{8}=\left\{\pm1,\pm2,\pm4,\pm8\right\}</p><p>$

$1)x = - 1 = > \frac{8}{ - 1} = - 8 \: \in \: \mathbb{Z}$

$2)x = 1 = > \frac{8}{1} = 8 \: \in \: \mathbb{Z}$

$3)x = - 2 = > \frac{8}{ - 2} = - 4 \: \in \: \mathbb{Z}$

$4)x = 2 = > \frac{8}{2} = 4 \: \in \: \mathbb{Z}$

$5)x = - 4 = > \frac{8}{ - 4} = - 2 \: \in \: \mathbb{Z}$

$6)x = 4 = > \frac{8}{4} = 2 \: \in \: \mathbb{Z}$

$7)x = - 8 = > \frac{8}{ - 8} = - 1 \: \in \: \mathbb{Z}$

$8)x = 8 = > \frac{8}{8} = 1 \: \in \: \mathbb{Z}$

$b) \frac{6}{x} \: \in \: \mathbb{N} = > x \: \in \: D_{6_{+}}$

$D_{6_{+}}=\left\{1,2,3,6\right\}$

$1)x = 1 = > \frac{6}{1} = 6 \: \in \: \mathbb{N}$

$2)x = 2 = > \frac{6}{2} = 3 \: \in \: \mathbb{N}$

$3) x = 3 = > \frac{6}{3} = 2 \: \in \: \mathbb{N}$

$4)x = 6 = > \frac{6}{6} = 1 \: \in \: \mathbb{N}$