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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