# Diophantine Equation 2

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. $$\displaystyle\sum_{i=1}^n (x_i+y_i)= a+b+b+a+\cdots$$.

Another Diophantine Equation.

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