Let $n$ a natural number and $A=\{1, 2, 3, \cdots, 2^{n+1}-1\}$. Prove that if we choose $2n+1$ elements differents of the set $A$, then among them are three distinct number $a,b$ and $c$ such that $$bc<2a^2<4bc$$
Source: Mathematics Regional Olympiad of Mexico Southeast 2019 P5
Tags: Sets, inequalities
Let $n$ a natural number and $A=\{1, 2, 3, \cdots, 2^{n+1}-1\}$. Prove that if we choose $2n+1$ elements differents of the set $A$, then among them are three distinct number $a,b$ and $c$ such that $$bc<2a^2<4bc$$