[tex]\it Fie\ d\in\mathbb{N}\\ \\ d\Big| a \Rightarrow d|5n+2 \Rightarrow d|(5n+2)\cdot3 \Rightarrow d|15n+6\ \ \ \ \ (1)\\ \\ d\Big| b \Rightarrow d|3n+1 \Rightarrow d|(3n+1)\cdot5 \Rightarrow d|15n+5\ \ \ \ \ (2)\\ \\ (1),\ (2) \Rightarrow d|15n+6-15n-5 \Rightarrow d|1 \Rightarrow d=1 \Rightarrow (a,\ b)=1\\ \\ Prin\ \ urmare,\ \ numerele\ a\ \d s i\ b\ sunt\ prime\ \hat\imath ntre\ ele[/tex]
