[tex]\it Fie\ d\ \in\ \mathbb{N}^*\\ \\ d|8n+5 \Rightarrow d|(8n+5)\cdot5 \Rightarrow d|40n+25 \ \ \ \ \ (1)\\ \\ d|5n+3 \Rightarrow d|(5n+3)\cdot8 \Rightarrow d|40n+24 \ \ \ \ \ (2)\\ \\ (1),\ (2) \Rightarrow d|40n+25-40n-24 \Rightarrow d|1 \Rightarrow d=1\ \ \ \ (3)\\ \\ (1),\ (2),\ (3) \Rightarrow frac\c{\it t}ia\ \ \dfrac{8n+5}{5n+3}\ este\ ireductibil\breve a\ .[/tex]
