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Omni-MATH / Determine the greatest real number C, such that for every positive integer n≥2, there exists x₁,x₂,...,x_(n)∈[−1,1], so that ∏_(1≤i<j≤n)(x_(i)−x_(j))≥C^((n(n−1))/(2)).

Problem

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problem

Determine the greatest real number C C , such that for every positive integer n2 n\ge 2 , there exists x1,x2,...,xn[1,1] x_1, x_2,..., x_n \in [-1,1], so that 1i<jn(xixj)Cn(n1)2\prod_{1\le i<j\le n}(x_i-x_j) \ge C^{\frac{n(n-1)}{2}}.
Plain-text mathematical notation (without MathML)
Determine the greatest real number C, such that for every positive integer n≥2, there exists x₁,x₂,...,x_(n)∈[−1,1], so that
∏_(1≤i<j≤n)(x_(i)−x_(j))≥C^((n(n−1))/(2)).
Original LaTeX notation
Determine the greatest real number $ C $, such that for every positive integer $ n\ge 2 $, there exists $ x_1, x_2,..., x_n  \in [-1,1]$, so that
$$\prod_{1\le i<j\le n}(x_i-x_j) \ge C^{\frac{n(n-1)}{2}}$$.

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