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International Contests
Pan African
2005 Pan African
1
Greatest Integer Equation
Greatest Integer Equation
Source: Pan African Maths Olympiad
August 11, 2005
Problem Statement
Let
[
x
]
[ {x} ]
[
x
]
be the greatest integer less than or equal to
x
x
x
, and let
{
x
}
=
x
−
[
x
]
\{x\}=x-[x]
{
x
}
=
x
−
[
x
]
. Solve the equation:
[
x
]
⋅
{
x
}
=
2005
x
[x] \cdot \{x\} = 2005x
[
x
]
⋅
{
x
}
=
2005
x
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