k apartine Z pentru care 16/2k+1 apartine Z [latex]it dfrac{16}{2}k+1 in mathbb{Z} Longleftrightarrow 8k+1 in mathbb{Z} Longleftrightarrow k in mathbb{Z} [/latex] __________________________________________________________ n aparine Z pentru care 6/n+2 apartine Z [latex]it dfrac{6}{n} +2 in mathbb{Z} Longleftrightarrow dfrac{6}{n} in mathbb{Z} Longleftrightarrow n|6 Longleftrightarrow nin D_6 Longleftrightarrow \;\ \;\ Longleftrightarrow n in {pm1, pm2, pm3, pm6} } [/latex] _________________________________________________________ n apartine N pentru care apartine Z n∈ N,  8/3∉ N ⇒8/3-n ∉ Z

1) (2k+1)∈D16     2k+1 ∈ {-16; -8; -4; -2; -1; 1; 2; 4; 8;16 } 2k ∈ {-17; -9; -5; -3; -2; 0; 1; 3; 7; 15} ⇒   k ∈{-1,0} 2)  (n+2) ∈D6     n+2 ∈ {-6; -3; -2; -1; 1; 2; 3; 6}   n∈{-8; -5; -4; -3; -1; 0; 1; 4} 3) (3-n) ∈ D8   3-n ∈ (-8; -4; -2; -1; 1; 2; 4; 8}  n ∈ {11;7;5;4;2;1;-1;-5}