Question 114
Let $a, b, c$ be non-negative real numbers such that $(a+b)(b+c)(c+a) \neq 0$. Find the minimum of
$$
(a + b + c)^{2016} \left( \frac{1}{a^{2016} + b^{2016}} + \frac{1}{b^{2016} + c^{2016}} + \frac{1}{c^{2016} + a^{2016}} \right).
$$
$$
(a + b + c)^{2016} \left( \frac{1}{a^{2016} + b^{2016}} + \frac{1}{b^{2016} + c^{2016}} + \frac{1}{c^{2016} + a^{2016}} \right).
$$