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Saint Petersburg Mathematical Olympiad
2018 Saint Petersburg Mathematical Olympiad
6
Old and famous
Old and famous
Source: St Petersburg Olympiad 2018, Grade 11, P6
June 21, 2018
irrational number
number theory
Problem Statement
α
,
β
\alpha,\beta
α
,
β
are positive irrational numbers and
[
α
[
β
x
]
]
=
[
β
[
α
x
]
]
[\alpha[\beta x]]=[\beta[\alpha x]]
[
α
[
β
x
]]
=
[
β
[
αx
]]
for every positive
x
x
x
. Prove that
α
=
β
\alpha=\beta
α
=
β
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