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1000-element subset M of {0,1,...,2001}, has power of 2 or 2 nos with sum 2

Source: Switzerland - Swiss TST 2001 p10

February 18, 2020

Subsetsnumber theorySumpower of 2

Problem Statement

Prove that every

1000

-element subset

M

of the set

\{0,1,...,2001\}

contains either a power of two or two distinct numbers whose sum is a power of two.