# 2007 Diophantine equation.....

**Number Theory**Level 4

Find all the positive integer solutions \((x;y)\) of the equation: \(xy+x=2007y+2\).

Call \(S=x_1+y_1+x_2+y_2+.........+x_{n-1}+y_{n-1}+x_n+y_n\) which is the value of \(S\)?

Find all the positive integer solutions \((x;y)\) of the equation: \(xy+x=2007y+2\).

Call \(S=x_1+y_1+x_2+y_2+.........+x_{n-1}+y_{n-1}+x_n+y_n\) which is the value of \(S\)?

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