KöMaL 2009 A493

Prove that $\sum_{i=1}^n\ \sum_{j=1}^n \frac{a_ia_j}{{(p_i+p_j)}^c}\ge 0$ holds for arbitrary reals $a_1,a_2,\ldots,a_n$, and positive numbers $c,p_1,p_2,\ldots,p_n$.