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2023 IMO Problems/Problem 4

Revision as of 22:36, 13 July 2023 by Gwang2008 (talk | contribs) (Created page with "==Problem 4== Let <math>x_1, x_2, \cdots , x_{2023}</math> be pairwise different positive real numbers such that <cmath>a_n = \sqrt{(x_1+x_2+···+x_n)(\frac1{x_1} + \frac1{x...")
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Problem 4

Let $x_1, x_2, \cdots , x_{2023}$ be pairwise different positive real numbers such that \[a_n = \sqrt{(x_1+x_2+···+x_n)(\frac1{x_1} + \frac1{x_2} +···+\frac1{x_n})}\] is an integer for every $n = 1,2,\cdots,2023$. Prove that $a_{2023} \ge 3034$.

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