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a + b is a power of 2 for subset of {1,2,..., 1998} with 1000 elements

Source: Rioplatense 1998 L3 P4

September 19, 2022

number theorypower of 2

Problem Statement

Let

M

be a subset of

\{1,2,..., 1998\}

with

1000

elements. Prove that it is always possible to find two elements

a

and

b

M

, not necessarily distinct, such that

a + b

is a power of

2