They're Not All The Same Degree!
Number Theory
Level
5
\[\large \dfrac {x^3+y^3}{3}+xy = 2007\]
Let there be \(n\) unordered positive integral solutions to the above equation. Call these solutions \((x_1, y_1), (x_2, y_2) , \ldots, (x_n, y_n)\). Find the value of
\[\displaystyle \sum_{i=1}^n x_i y_i. \]
by
Sharky Kesa