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Contests
National and Regional Contests
India Contests
India National Olympiad
1989 India National Olympiad
5
5
Part of
1989 India National Olympiad
Problems
(1)
problem 5 of Indian Mathematical Olympiad 1989
Source: Number theory (divisibility)
9/1/2009
For positive integers
n
n
n
, define
A
(
n
)
A(n)
A
(
n
)
to be
(
2
n
)
!
(
n
!
)
2
\frac {(2n)!}{(n!)^{2}}
(
n
!
)
2
(
2
n
)!
. Determine the sets of positive integers
n
n
n
for which (a)
A
(
n
)
A(n)
A
(
n
)
is an even number, (b)
A
(
n
)
A(n)
A
(
n
)
is a multiple of
4
4
4
.
number theory unsolved
number theory