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Problem 4.
Let  be pairwise different positive real numbers such that![\[a_n=\sqrt{(x_1+x_2+\dots+x_n)\left(\frac{1}{x_1}+\frac{1}{x_2}+\dots+\frac{1}{x_n}\right)}\]](https://latex.artofproblemsolving.com/8/a/e/8ae0bd1f55eb2fb0b7209b62739a9b98f462ee56.png) is an integer for every  Prove that  proposed by Merlijn Staps, Netherlands
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Problem 4.
Let be pairwise different positive real numbers such thatis an integer for every Prove that proposed by Merlijn Staps, Netherlands
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