Let n be a positive integer and $x_1, x_2, ..., x_n > 0$ be real numbers so that $x_1 + x_2 +... + x_n =\frac{1}{x_1^2}+\frac{1}{x_2^2}+...+\frac{1}{x_n^2}$ Show that for each positive integer $k \le n$, there are $k$ numbers among $x_1, x_2, ..., x_n $ whose sum is at least $k$.