MathDB

Let

S = \{1, 2, 3, \ldots , 2046, 2047, 2048\}

. Two subsets

A

and

B

S

are said to be friends if the following conditions are true:
[*] They do not share any elements. [*] They both have the same number of elements. [*] The product of all elements from

A

equals the product of all elements from

B

.
Prove that there are two subsets of

S

that are friends such that each one of them contains at least

738

elements.

Problem Statement