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China mathematical olympiad 1995 problem5

Source: China mathematical olympiad 1995 problem5

September 15, 2013
inequalities unsolvedinequalities

Problem Statement

Let a1,a2,⋯ ,a10a_1,a_2,\cdots ,a_{10} be pairwise distinct natural numbers with their sum equal to 1995. Find the minimal value of a1a2+a2a3+⋯+a9a10+a10a1a_1a_2+a_2a_3+\cdots +a_9a_{10}+a_{10}a_1.
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