Tìm x,y nguyên sao cho: xy+2x+y+7= 0

 Ta có: xy+2x+y+7= 0

           xy+2x+y+2+5=0

           (xy+2x)+(y+2) = 0-5

           x.(y+2) + (y+2) = -5

             (y+2).(x+1) = -5

        => y+2; x+1 ∈ Ư(-5)

           Ư(-5) = {1;5;-1;-5}

   Ta có bảng sau:

\begin{array}{|c|c|c|}\hline \text{y+2}&\text{-5}&\text{-1}&\text{1}&\text{5}\\\hline \text{y}&\text{-7}&\text{-3}&\text{-1}&\text{3}\\\hline \text{x+1}&\text{1}&\text{5}&\text{-5}&\text{-1}\\\hline \text{x}&\text{0}&\text{4}&\text{-6}&\text{-2}\\\hline\end{array}

 Vậy (x,y) nhận các cặp giá trị tương ứng là : (0;-7), (4;-3), (-6;-1), (3;-2)