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inequality

Source: Mathematics Regional Olympiad of Mexico Southeast 2019 P5

October 23, 2021
Setsinequalities

Problem Statement

Let nn a natural number and A={1,2,3,⋯ ,2n+1−1}A=\{1, 2, 3, \cdots, 2^{n+1}-1\}. Prove that if we choose 2n+12n+1 elements differents of the set AA, then among them are three distinct number a,ba,b and cc such that
bc<2a2<4bcbc<2a^2<4bc
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