$\alpha,\beta$ are positive irrational numbers and $[\alpha[\beta x]]=[\beta[\alpha x]]$ for every positive $x$. Prove that $\alpha=\beta$
Source: St Petersburg Olympiad 2018, Grade 11, P6
Tags: irrational number, number theory
$\alpha,\beta$ are positive irrational numbers and $[\alpha[\beta x]]=[\beta[\alpha x]]$ for every positive $x$. Prove that $\alpha=\beta$