MathDB

Call a positive integer challenging if it can be expressed as

2^a(2^b+1)

, where

a,b

are positive integers. Prove that if

X

is a set of challenging numbers smaller than

2^n (n

is a given positive integer) and

|X|\ge \frac{4}{3}(n-1)

, there exist two disjoint subsets

A,B\subset X

such that

|A|=|B|

and

\sum_{a\in A}a=\sum_{b \in B}b

Problem Statement