# Number crunching

Number Theory Level pending

$\large x^2 +y^2=1997(x-y)$

Let all the pairs of positive integers $$(x,y)$$ satisfying the equation above be denoted by $$(x_1, y_1) , (x_2, y_2) , \ldots , (x_n, y_n)$$. Find $$\displaystyle \dfrac1{2287} \sum_{j=1}^n (x_j + y_j)$$.

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