Let S={1,2,3,…,2046,2047,2048}. Two subsets A and B of 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.
combinatoricsSetsarithmetic