The integer solutions to \[\displaystyle x^2+xy+y^2=x^2y^2\] are ordered pairs \(\displaystyle (x_1,y_1), (x_2,y_2),\ldots,(x_n,y_n)\).

Find \(\displaystyle \sum_{i=1}^{n}(x_i+y_i)\).

If \(\displaystyle (a,b)\) is a solution, so is \(\displaystyle (b,a)\), and the sum (the answer) involves both of them, i.e. \(\displaystyle\sum_{i=1}^n (x_i+y_i)= a+b+b+a+\cdots\).

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