# An algebra problem by Rahil Sehgal

Algebra Level 4

If $$n \ge 3$$ and $$1,\alpha_{1}, \alpha_2, \alpha_3, \cdots \alpha_{n-1}$$ are the $$n^\text{th}$$ roots of unity, then find the value of

$\large \underbrace{\sum \sum}_{1\le i<j\le (n-1)} \alpha_i \alpha_j.$

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