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2 Let $eta=e^{frac{2pi i}n}$ , an $n$ -th root of unity. For pedagogical reasons and inspiration, I ask to see different proofs (be it elementary, sophisticated, theoretical, etc) for the following product evaluation. If $T(n)=frac{(3n-2)(n-1)}2$ and $i=sqrt{-1}$ then $$prod_{j<k}^{0,n-1}(eta^k-eta^j)=n^{frac{n}2}i^{T(n)}.$$ gr.group-theory cv.complex-variables soft-question teaching elementary-proofs share | cite | improve this question edited 6 hours ago asked 6 hours ago