Fie n, numărul cerut.
[tex]\it \left.\begin{aligned} \it n:8=x\ \ rest\ 7 \Rightarrow n=8x+7|_{+1} \Rightarrow n+1=8x+8 \Rightarrow n+1\in M_8\\ \\ \it n:7=y\ \ rest\ 6 \Rightarrow n=7y+6|_{+1} \Rightarrow n+1=7y+7 \Rightarrow n+1\in M_7 \end{aligned} \right\} \Rightarrow \\ \\ \\ \Rightarrow n+1\in M_7\cap M_8 \Rightarrow n+1\in\{56,\ \ 112,\ \ 168,\ ...\}|_{-1} \Rightarrow n\in\{55,\ \ 111,\ \ 167,\ ...\} \Rightarrow \\ \\ \Rightarrow \bf{num\breve arul\ \ cerut\ \ este\ \ n=111.}[/tex]
