Number Theory or Algebra? Part 9

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

i=11999i2538=4x2+8y3+2\sum^{1999}_{i = 1}i^{2538} = 4x^{2} + 8y^{3} + 2

Details and Assumptions :

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

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