[tex]\it ab=16-a-b \Rightarrow ab+a+b+16|_{+1} \Rightarrow ab+a+b+1=17 \Rightarrow \\ \\ \Rightarrow (ab+b)+(a+1)=17 \Rightarrow b(a+1)+(a+1)=17 \Rightarrow \\ \\ \Rightarrow (a+1)(b+1)=17 =1\cdot17=17\cdot1\ \ \ \ \ \ (*)\\ \\ (*) \Rightarrow \begin{cases} \it a+1\in\{1,\ 17\}|_{-1} \Rightarrow a\in\{0,\ \ 16\}\\ \\ \it b+1\in\{17,\ 1\}|_{-1} \Rightarrow b\in\{16,\ 0\}\end{cases}[/tex]
[tex]\it (a,\ b)\in\{(0,\ 16),\ \ (16,0)\} \Rightarrow a\cdot b= 0[/tex]
