$$\eqalign{ & a)\,\,\overline {ab} .a - c = 1\,\,\left( {a,\,\,b,\,\,c \in N,\,0 \le a,b,c \le 9,a \ne 0} \right) \cr & \overline {ab} .a = 1 + c \cr & 0 \le c \le 9 \Rightarrow 1 \le 1 + c \le 10 \cr & \Rightarrow 1 \le \overline {ab} .a \le 10 \cr & \Rightarrow \overline {ab} = 10 \Rightarrow a = 1;\,\,b = 0 \cr & \Rightarrow 10.1 - c = 1 \cr & \Rightarrow c = 9 \cr} $$

\[\begin{array}{l} b)\,\,\overline {a5} .3\overline {bc} = 7850\,\,\,\\ a \in \left\{ {1;\,\,2;\,\,3;\,\,.....;\,\,9} \right\}\\ b,\,\,c \in \left\{ {0;\,\,1;\,\,2;.....;\,\,9} \right\}\\ Ta\,\,\,co:\,\,\,15 \le \overline {a5} \le 95;\,\,\,300 \le \overline {3bc} \le 399.\\ + )\,\,\,\overline {a5} = 15\\ \Rightarrow \overline {3bc} = 7850:15 \approx 523,33\,\,\,\\ \Rightarrow \overline {a5} = 15\,\,khong\,\,thoa\,\,man.\\ + )\,\,\overline {a5} = 25 \Rightarrow a = 2\\ \Rightarrow \overline {3bc} = 7850:25 = 314\\ \Rightarrow b = 1;\,\,c = 4.\\ + )\,\,\overline {a5} = 35\\ \Rightarrow \overline {3bc} = 7850:35 \approx 224,285\\ \Rightarrow \overline {a5} = 35\,\,khong\,\,thoa\,\,man.\\ Vay\,\,\,a = 2,\,\,b = 1,\,\,c = 4. \end{array}\]