3.https://diendan.hocmai.vn/threads/dai-so-9-phuong-trinh-nghiem-nguyen.621376/#post-3133729
8. Ta có: [tex](m^2+2)(n^2+2)\vdots mn\Leftrightarrow m^2n^2+2(m^2+n^2+2)\vdots mn\Leftrightarrow 2(m^2+n^2+2)\vdots mn[/tex]
Mà m,n lẻ nên (m,2)=(n,2)=1 hay [tex]m^2+n^2+2\vdots mn[/tex]
Lại có: m,n lẻ [tex]\Rightarrow m^2\equiv n^2\equiv 1(mod4)\Rightarrow m^2+n^2+2\vdots 4[/tex]
Vì (mn,4)=1 nên ta có đpcm.