# A Double Summation

Algebra Level 4

Let $$\alpha_1 , \alpha_2 , \alpha_3 ,\ldots , \alpha_{100}$$ be the hundredth roots of unity. Then evaluate the summation

$\large \mathop{\sum\sum}_{1\leq i <j\leq 100} (\alpha_i\alpha_j)^5.$

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