Let n≥3n \geq 3n≥3 be an integer, and let a2,a3,…,ana_2, a_3, \ldots, a_na2,a3,…,an be positive real numbers such that a2a3⋯an=1a_2a_3 \cdots a_n = 1a2a3⋯an=1. Prove that (1+a2)2(1+a3)3⋯(1+an)n>nn.(1 + a_2)^2(1 + a_3)^3 \cdots (1 + a_n)^n > n^n.(1+a2)2(1+a3)3⋯(1+an)n>nn.