Inspired by Mr. \(\pi\) (The force awakens)

Algebra Level 5

Let \(a_1, a_2, \ldots , a_n\) be the roots of the polynomial \(\displaystyle \sum_{k=1}^n kx^k = 0 \). If \( \displaystyle \sum_{k=1}^n \dfrac1{(1-a_k)^2} = -13 \), find \(n\).


Inspiration.

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