Problem

Source: Chinese National Olympiad 2009 P4

Tags: inequalities, symmetry, function, algebra, polynomial, absolute value, inequalities proposed



Given an integer $ n > 3.$ Let $ a_{1},a_{2},\cdots,a_{n}$ be real numbers satisfying $ min |a_{i} - a_{j}| = 1, 1\le i\le j\le n.$ Find the minimum value of $ \sum_{k = 1}^n|a_{k}|^3.$