Sum of roots\(^{200}\)

Algebra Level 4

Let \(f(x) = 1+x+x^2+ \cdots + x^{199}\) and \(a_1, a_2, a_3, \cdots a_{199}\) be the roots of \(f(x)\). Find \(\displaystyle \sum_{k=1}^{199} a_k^{200}\).

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