Conceptual Equation

Find all pairs of integer solutions satisfying \(x^2(y-1)+y^2(x-1)=1\)

If the solutions can be represented in the form \((x_i,y_i)\) where \(i=1,2,\ldots,n\) i.e \(n\) solutions are there then find : \(\displaystyle \sum_{i=1}^{n} (x_i+y_i)\)

Explicit example: If the solutions are \((0,2)\) & \((2,3)\) then you need to compute \(0+2+2+3=7\) and enter 7 as answer.

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