What is the number of positive solutions to
$$ (x^{1000} + 1)(1 + x^2 + x^4 + \cdots + x^{998}) = 1000x^{999}? $$
I tried to solve it. First I used by using sum of Geometric Progression. Then the equation becomes too complicated and is in the power of 1998. How can I get the number of positive solutions with that equation?
Thanks in advance.