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National and Regional Contests
Austria Contests
Austrian MO National Competition
2009 Federal Competition For Advanced Students, P1
2
2
Part of
2009 Federal Competition For Advanced Students, P1
Problems
(1)
Old Austrian
Source:
5/2/2016
For a positive integers
n
,
k
n,k
n
,
k
we define k-multifactorial of n as
F
k
(
n
)
Fk(n)
F
k
(
n
)
=
(
n
)
(n)
(
n
)
.
(
n
−
k
)
(n-k)
(
n
−
k
)
(
n
−
2
k
)
(n-2k)
(
n
−
2
k
)
...
(
r
)
(r)
(
r
)
, where
r
r
r
is the reminder when
n
n
n
is divided by
k
k
k
that satisfy
1
<
=
r
<
=
k
1<=r<=k
1
<=
r
<=
k
Determine all non-negative integers
n
n
n
such that
F
20
(
n
)
+
2009
F20(n)+2009
F
20
(
n
)
+
2009
is a perfect square.
number theory