RO-NMO 2004 Problem 111

Let $n \geq 3$ be an integer and $F$ be the focus of the parabola $y^2=2px$ . A regular polygon $A_1 A_2 \ldots A_n$ has the center in $F$ and none of its vertices lie on $Ox$ . $\left( FA_1 \right., \left( FA_2 \right., \ldots, \left( FA_n \right.$ intersect the parabola at $B_1,B_2,\ldots,B_n$ .

Prove that $$FB_1 + FB_2 + \ldots + FB_n > np .$$

Calin Popescu