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Greece Contests
Greece Team Selection Test
2017 Greece Team Selection Test
2
2
Part of
2017 Greece Team Selection Test
Problems
(1)
Integer and factors
Source: Greece team selection test problem 2
5/3/2017
Prove that the number
A
=
(
4
n
)
!
(
2
n
)
!
n
!
A=\frac{(4n)!}{(2n)!n!}
A
=
(
2
n
)!
n
!
(
4
n
)!
is an integer and divisible by
2
n
+
1
2^{n+1}
2
n
+
1
, where
n
n
n
is a positive integer.
number theory
Greece
combinatorics
TST
binomial coefficients