Problem 1

Algebra Level 5

\[\big(x^{2010}+1)(1+x^{2}+x^{4}+...+x^{2008})=2010x^{2009}\]

Let \(S\) denote the set of all real values of \(x\) such that they satisfy the equation above, then the number of elements in \(S\) is?

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