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Nicolae Coculescu
2007 Nicolae Coculescu
1
Fractional part property
Fractional part property
Source:
December 13, 2019
algebra
equations
Floor
fractional part
Problem Statement
Let be two real numbers
x
,
y
,
x,y,
x
,
y
,
and a natural number
n
0
n_0
n
0
such that
{
n
0
x
}
=
{
n
0
y
}
\{ n_0x \} = \{ n_0y \}
{
n
0
x
}
=
{
n
0
y
}
and
{
(
n
0
+
1
)
x
}
=
{
(
n
0
+
1
)
y
}
,
\{ (n_0+1)x \} = \{ (n_0+1)y \} ,
{(
n
0
+
1
)
x
}
=
{(
n
0
+
1
)
y
}
,
where
{
}
\{\}
{
}
denotes the fractional part. Show that
{
n
x
}
=
{
n
y
}
,
\{ nx \} =\{ ny \} ,
{
n
x
}
=
{
n
y
}
,
for any natural number
n
.
n.
n
.
Ovidiu Pop
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