# Number Theory or Algebra? Part 9

Find the number of possible co-ordinate $$(x, y)$$, in which $$x$$ and $$y$$ are both positive integers, which satisfies the equation

$$\sum^{1999}_{i = 1}i^{2538} = 4x^{2} + 8y^{3} + 2$$

Details and Assumptions :

$$i$$ is a dummy variable, not $$\sqrt{-1}$$

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