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an inequality with distinct positive integers by Panaitopol

Source: Romanian IMO Team Selection Test TST 1999, problem 5

September 24, 2005
inequalitiesinequalities proposed

Problem Statement

Let x1,x2,…,xnx_1,x_2,\ldots,x_n be distinct positive integers. Prove that x12+x22+⋯+xn2≥2n+13(x1+x2+⋯+xn). x_1^2+x_2^2 + \cdots + x_n^2 \geq \frac {2n+1}3 ( x_1+x_2+\cdots + x_n). Laurentiu Panaitopol
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