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\sum_{i=1}^{n} \prod_{j\ne i} (x_i-x_j)^p\ge 0

Source: IMAC Arhimede 2013 p6

May 6, 2019
inequalitiesalgebraSums and ProductsProductSum

Problem Statement

Let pp be an odd positive integer. Find all values of the natural numbers n≥2n\ge 2 for which holds ∑i=1n∏j≠i(xi−xj)p≥0\sum_{i=1}^{n} \prod_{j\ne i} (x_i-x_j)^p\ge 0 where x1,x2,..,xnx_1,x_2,..,x_n are any real numbers.
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