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Argentina National Olympiad
2003 Argentina National Olympiad
1
1/ [x] - 1/[2x]= 1/6{x}
1/ [x] - 1/[2x]= 1/6{x}
Source: Argentina 2003 OMA L3 p1
May 12, 2024
floor function
algebra
fractional part
Problem Statement
Find all positive numbers
x
x
x
such that:
1
[
x
]
−
1
[
2
x
]
=
1
6
{
x
}
\frac{1}{[x]}-\frac{1}{[2x]}=\frac{1}{6\{x\}}
[
x
]
1
−
[
2
x
]
1
=
6
{
x
}
1
where
[
x
]
[x]
[
x
]
represents the integer part of
x
x
x
and
{
x
}
=
x
−
[
x
]
\{x\}=x-[x]
{
x
}
=
x
−
[
x
]
.
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