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National and Regional Contests
Thailand Contests
Thailand National Olympiad
2015 Thailand Mathematical Olympiad
5
Number theory
Number theory
Source: Thailand MO 2015
May 28, 2016
number theory
Problem Statement
Let
n
n
n
be an integer greater than
6
6
6
.Show that if
n
+
1
n+1
n
+
1
is a prime number,than
⌈
(
n
−
1
)
!
n
(
n
+
1
)
⌉
\left\lceil \frac{(n-1)!}{n(n+1)}\right \rceil
⌈
n
(
n
+
1
)
(
n
−
1
)!
⌉
is
O
D
D
.
ODD.
O
DD
.
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