# 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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