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All-Russian Olympiad Regional Round
1998 All-Russian Olympiad Regional Round
10.5
{ (x + 1)^3 } = x^3 - All-Russian MO 1998 Regional (R4) 10.5
{ (x + 1)^3 } = x^3 - All-Russian MO 1998 Regional (R4) 10.5
Source:
September 17, 2024
fractional part
algebra
Problem Statement
Solve the equation
{
(
x
+
1
)
3
}
=
x
3
\{(x + 1)^3\} = x^3
{(
x
+
1
)
3
}
=
x
3
, where
{
z
}
\{z\}
{
z
}
is the fractional part of the number z, i.e.
{
z
}
=
z
ā
[
z
]
\{z\} = z - [z]
{
z
}
=
z
ā
[
z
]
.
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