MathDB
Problems
Contests
International Contests
Silk Road
2022 Silk Road
3
Algebra Problem
Algebra Problem
Source: SRMC 2022 P3
May 23, 2022
algebra
Problem Statement
In an infinite sequence
{
α
}
,
{
α
2
}
,
{
α
3
}
,
⋯
\{\alpha\}, \{\alpha^2\}, \{\alpha^3\}, \cdots
{
α
}
,
{
α
2
}
,
{
α
3
}
,
⋯
there are finitely many distinct values
.
.
.
Show that
α
\alpha
α
is an integer
.
(
{
x
}
. (\{x\}
.
({
x
}
denotes the fractional part of
x
.
)
x.)
x
.
)
(Golovanov A.S.)
Back to Problems
View on AoPS