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2022 Silk Road
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Part of
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(1)
Algebra Problem
Source: SRMC 2022 P3
5/23/2022
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.)
algebra