The irrational numbers $\alpha ,\beta ,\gamma ,\delta$ are such that $\forall$ $n\in \mathbb{N}$ : $[n\alpha ].[n\beta ]=[n\gamma ].[n\delta ]$. Is it true that the sets $\{ \alpha ,\beta \}$ and $\{ \gamma ,\delta \}$ are equal?
Problem
Source: IV International Festival of Young Mathematicians Sozopol 2013, Theme for 10-12 grade
Tags: number theory, Sets, equation