MathDB
Problems
Contests
National and Regional Contests
China Contests
South East Mathematical Olympiad
2013 South East Mathematical Olympiad
5
China South East Mathematical Olympiad 2013 problem 5
China South East Mathematical Olympiad 2013 problem 5
Source:
August 10, 2013
floor function
calculus
algebra unsolved
algebra
Problem Statement
f
(
x
)
=
∑
i
=
1
2013
[
x
i
!
]
f(x)=\sum\limits_{i=1}^{2013}\left[\dfrac{x}{i!}\right]
f
(
x
)
=
i
=
1
∑
2013
[
i
!
x
]
. A integer
n
n
n
is called good if
f
(
x
)
=
n
f(x)=n
f
(
x
)
=
n
has real root. How many good numbers are in
{
1
,
3
,
5
,
…
,
2013
}
\{1,3,5,\dotsc,2013\}
{
1
,
3
,
5
,
…
,
2013
}
?
Back to Problems
View on AoPS