Let A be a subset of {0;1;∙∙∙;1997} containing more than 1000 elements. Prove that A contains either a power of 2 or two distinct integers whose sum is a power of 2.


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Question Number 10181 by 0942679167 last updated on 29/Jan/17

$L e t A b e a s u b s e t o f {0; 1; \cdot \cdot \cdot; 1997}$ $c o n t a i n i n g m o r e t h a n 1000 e l e m e n t s .$ $P r o v e t h a t A c o n t a i n s e i t h e r a p o w e r$ $o f 2 o r t w o d i s t i n c t i n t e g e r s w h o s e$ $s u m i s a p o w e r o f 2 .$
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