MathDB
2010 SMO (7)

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November 2, 2010
inequalities unsolvedinequalities

Problem Statement

Let nn be a positive integer. The real numbers a1,a2,⋯ ,ana_1,a_2,\cdots,a_n and r1,r2,⋯ ,rnr_1,r_2,\cdots,r_n are such that a1≤a2≤⋯≤ana_1\leq a_2\leq \cdots \leq a_n and 0≤r1≤r2≤⋯≤rn0\leq r_1\leq r_2\leq \cdots \leq r_n. Prove that ∑i=1n∑j=1naiajmin⁡(ri,rj)≥0\sum_{i=1}^n\sum_{j=1}^n a_i a_j \min (r_i,r_j)\geq 0
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