Seemingly Innocent Inequality

Algebra Level 5

\[\sum_{k=1}^{n} x_k^2 \le \sum_{k=1}^n \dfrac{1}{x_k^2}\]

Given that \(x_1,x_2, \ldots,x_n\) are positive reals whose sum is \(n\), find the largest integer \(n\) such that the inequality above always holds true.

If you think all positive integers \(n\) make the inequality hold true, enter 0 as your answer.

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