MathDB
Problems
Contests
National and Regional Contests
India Contests
Regional Mathematical Olympiad
2010 India Regional Mathematical Olympiad
6
Number theory 2
Number theory 2
Source:
December 5, 2010
Problem Statement
For each integer
n
≥
1
n \ge 1
n
≥
1
define
a
n
=
[
n
[
n
]
]
a_n = \left[\frac{n}{\left[\sqrt{n}\right]}\right]
a
n
=
[
[
n
]
n
]
(where
[
x
]
[x]
[
x
]
denoted the largest integer not exceeding
x
x
x
, for any real number
x
x
x
). Find the number of all
n
n
n
in the set
{
1
,
2
,
3
,
⋯
,
2010
}
\{1, 2, 3, \cdots , 2010\}
{
1
,
2
,
3
,
⋯
,
2010
}
for which
a
n
>
a
n
+
1
a_n > a_{n+1}
a
n
>
a
n
+
1
Back to Problems
View on AoPS