[tex]\it 1027:n=a\ rest\ 7\ \Rightarrow\ \begin{cases}\ \it 1027=n\cdot a+7|_{-7} \Rightarrow 1020=n\cdot a \Rightarrow n\in D_{1020}\ \ \ (1)\\ \\ \it n>7\ \ \ \ \ (1')\end{cases}\\ \\ \\ 601:n=b\ rest\ 6\ \Rightarrow\ \begin{cases}\ \it 601=n\cdot b+6|_{-6} \Rightarrow 595=n\cdot b \Rightarrow n\in D_{595}\ \ \ (2)\\ \\ \it n>6\ \ \ \ \ (2')\end{cases}[/tex]
[tex]\it 1113:n=c\ rest\ 8\ \Rightarrow\ \begin{cases}\ \it 1113=n\cdot c+8|_{-8} \Rightarrow 1105=n\cdot c \Rightarrow n\in D_{1105}\ \ \ (3)\\ \\ \it n>8\ \ \ \ \ (3')\end{cases}[/tex]
[tex]\it (1),\ (2),\ (3) \Rightarrow n\in D_{1020}\cap D_{595} \cap D_{1105}\\ \\ \\\left.\begin{aligned} \it 1020 = 2^2\cdot3\cdot5\cdot17\\ \\ \it 595=5\cdot7\cdot17\ \ \ \ \ \ \ \\ \\ \it 1105=5\cdot13\cdot17 \ \ \ \ \ \end{aligned}\right\} \ \stackrel{(3')}{\Longrightarrow} n\in \{17,\ 85\}[/tex]
