[tex]M=\left\{x\:\in\:M_{3}\: \: si \: \:x-1\:\in\:D_{14}\right\}[/tex]
[tex]D_{14}=\left\{\pm1,\pm2,\pm7,\pm14\right\}[/tex]
[tex]1)x - 1 = - 1[/tex]
[tex]x = - 1 + 1[/tex]
[tex]x = 0 \: \in \: M_{3}[/tex]
[tex]2)x - 1 = 1[/tex]
[tex]x = 1 + 1[/tex]
[tex]x = 2 \: \notin \: M_{3}[/tex]
[tex]3)x - 1 = - 2[/tex]
[tex]x = - 2 + 1[/tex]
[tex]x = - 1 \: \notin \: M_{3}[/tex]
[tex]4)x - 1 = 2[/tex]
[tex]x = 2 + 1[/tex]
[tex]x = 3 \: \in \: M_{3}[/tex]
[tex]5)x - 1 = - 7[/tex]
[tex]x = - 7 + 1[/tex]
[tex]x = - 6 \: \in \: M_{3}[/tex]
[tex]6)x - 1 = 7[/tex]
[tex]x = 7 + 1[/tex]
[tex]x = 8 \: \notin \: M_{3}[/tex]
[tex]7)x - 1 = - 14[/tex]
[tex]x = - 14 + 1[/tex]
[tex]x = - 13 \: \notin \: M_{3}[/tex]
[tex]8)x - 1 = 14[/tex]
[tex]x = 14 + 1[/tex]
[tex]x = 15 \: \in \: M_{3}[/tex]
[tex] = > x \: \in \: \left\{-6,0,3,15\right\}[/tex]
[tex] = > M=\left\{-6,0,3,15\right\}[/tex]
