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Soros Olympiad in Mathematics
VI Soros Olympiad 1999 - 2000 (Russia)
9.2
[x] {x} = 1999x (VI Soros Olympiad 1990-00 R1 9.2)
[x] {x} = 1999x (VI Soros Olympiad 1990-00 R1 9.2)
Source:
May 27, 2024
algebra
number theory
fractional part
floor function
Problem Statement
Solve the equation
[
x
]
{
x
}
=
1999
x
[x]\{x\} = 1999x
[
x
]
{
x
}
=
1999
x
, where
[
x
]
[x]
[
x
]
denotes the largest integer less than or equal to
x
x
x
, and
{
x
}
=
x
ā
[
x
]
\{x\} = x -[x]
{
x
}
=
x
ā
[
x
]
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