MathDB

Suppse that

X=\{1,2, \ldots, 2^{1996}-1\}

, prove that there exist a subset

A

that satisfies these conditions: a)

1\in A

and

2^{1996}-1\in A

; b) Every element of

A

except

1

is equal to the sum of two (possibly equal) elements from

A

; c) The maximum number of elements of

A

2012

. Romania

Problem Statement