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2023 China Team Selection Test
P13
P13
Part of
2023 China Team Selection Test
Problems
(1)
2023 China TST Problem 13
Source: 2023 China TST Problem 13
3/27/2023
Does there exists a positive irrational number
x
,
{x},
x
,
such that there are at most finite positive integers
n
,
{n},
n
,
satisfy that for any integer
1
≤
k
≤
n
,
1\leq k\leq n,
1
≤
k
≤
n
,
{
k
x
}
≥
1
n
+
1
?
\{kx\}\geq\frac 1{n+1}?
{
k
x
}
≥
n
+
1
1
?
number theory