100 Roots

Algebra Level 4

Let the 100 roots of the equation \(x^{100}-5x+2=0\) be \(r_{1}, r_{2}, r_{3},\ldots, r_{100}\). Find \[ r_{1}^{100}+r_{2}^{100}+r_{3}^{100}+\cdots+r_{100}^{100} . \]

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