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Problem 8 of Third round

Source: IV International Festival of Young Mathematicians Sozopol 2013, Theme for 10-12 grade

January 24, 2020
number theorySetsequation

Problem Statement

The irrational numbers α,β,γ,δ\alpha ,\beta ,\gamma ,\delta are such that ∀\forall n∈Nn\in \mathbb{N} : [nα].[nβ]=[nγ].[nδ][n\alpha ].[n\beta ]=[n\gamma ].[n\delta ]. Is it true that the sets {α,β}\{ \alpha ,\beta \} and {γ,δ}\{ \gamma ,\delta \} are equal?
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