[tex]\it xy-(x+y) =2016 \Rightarrow xy - x - y =2016 \Rightarrow
\\ \\
\Rightarrow xy - x - y +1 = 2016 + 1 \Rightarrow y(x-1) -(x-1) = 2017 \Rightarrow
\\ \\
\Rightarrow (x-1)(y-1)=2017 = 2017\cdot1=1\cdot2017[/tex]
[tex]\it I)\ \ \begin{cases} \it x-1=2017 \Rightarrow x = 2018
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\it y-1=1 \Rightarrow y = 2 \end{cases}
\\ \\ \\
II)\ \ \begin{cases} \it x-1=1 \Rightarrow x = 2
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\it y-1=2017 \Rightarrow y = 2018 \end{cases}[/tex]
