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-

Tinku Tara June 3, 2023 Geometry 0 Comments

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

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.

$${Let}\:{A}\:{be}\:{a}\:{subset}\:{of}\:\left\{\mathrm{0};\mathrm{1};\centerdot\centerdot\centerdot;\mathrm{1997}\right\}\: \\ $$$${containing}\:{more}\:{than}\:\mathrm{1000}\:{elements}. \\ $$$${Prove}\:{that}\:{A}\:{contains}\:{either}\:{a}\:{power} \\ $$$${of}\:\mathrm{2}\:{or}\:{two}\:{distinct}\:{integers}\:{whose}\: \\ $$$${sum}\:{is}\:{a}\:{power}\:{of}\:\mathrm{2}. \\ $$

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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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