Problem

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Tags: inequalities unsolved, inequalities



Let $n$ be a positive integer. The real numbers $a_1,a_2,\cdots,a_n$ and $r_1,r_2,\cdots,r_n$ are such that $a_1\leq a_2\leq \cdots \leq a_n$ and $0\leq r_1\leq r_2\leq \cdots \leq r_n$. Prove that $\sum_{i=1}^n\sum_{j=1}^n a_i a_j \min (r_i,r_j)\geq 0$