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Problems
Contests
National and Regional Contests
Netherlands Contests
Dutch IMO TST
2013 Dutch IMO TST
1
Perfect square regarding factorials
Perfect square regarding factorials
Source: Netherlands IMO team Selection Test 2013
October 21, 2014
factorial
number theory unsolved
number theory
Problem Statement
Show that
∑
n
=
0
2013
4026
!
(
n
!
(
2013
−
n
)
!
)
2
\sum_{n=0}^{2013}\frac{4026!}{(n!(2013-n)!)^2}
∑
n
=
0
2013
(
n
!
(
2013
−
n
)!
)
2
4026
!
is a perfect square.
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