[tex]\text{Fie $(3n+7;5n+12)=d$.}[/tex]
[tex]\Rightarrow \left \{ {{d\ |\ 3n+7} \atop {d\ |\ 5n+12}} \right. \text{(Inmultim $3n+7$ cu 5 si $5n+12$ cu 3 pentru a le reduce)}\\\\\Rightarrow\left \{ {{d\ | 15n+35} \atop {d\ |\ 15n+36}} \right. \text{(Reducem $15n+35$ cu $15n+36$)}\\\\\Rightarrow d\ |\ 1 \Rightarrow d = 1 \Rightarrow (3n+7;5n+12)=1 \Rightarrow (a;b)=1[/tex]
==Luke48==
