MathDB

Let

n \geq 3

be an integer and

a_1,a_2,...,a_n

be positive real numbers such that

m

is the smallest and

M

is the largest of these numbers. It is known that for any distinct integers

1 \leq i,j,k \leq n

, if

a_i \leq a_j \leq a_k

then

a_ia_k \leq a_j^2

. Show that

a_1a_2 \cdots a_n \geq m^2M^{n-2}

and determine when equality holds

Problem Statement