2007 Diophantine equation.....

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

Call S=x1+y1+x2+y2+.........+xn1+yn1+xn+ynS=x_1+y_1+x_2+y_2+.........+x_{n-1}+y_{n-1}+x_n+y_n which is the value of SS?

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