MathNet 2016-part-03 — 184 problems (EN–VI) Question 11

Let $n \ge 3$ and $a_1, a_2, \ldots, a_n$ be positive real numbers for which $\frac{1}{1+a_1^4} + \frac{1}{1+a_2^4} + \ldots + \frac{1}{1+a_n^4} = 1$ holds. Prove the inequality $a_1 a_2 \ldots a_n \ge (n-1)^{n/4}$.