parmenides51 wrote: Let $x_1,x_2,...,x_n$ be positive real numbers for which $$\frac{1}{1+x_1}+\frac{1}{1+x_2}+...+\frac{1}{1+x_n}=1$$Prove that $x_1x_2...x_n \ge (n -1)^n$. 2001 Kazakhstan https://artofproblemsolving.com/community/c6h299899p1683764 https://math.stackexchange.com/questions/1895638/am-gm-inequality-problem-solution-explanation?noredirect=1 https://artofproblemsolving.com/community/c6h399294p2447481