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Putnam
1999 Putnam
6
Putnam 1999 A6
Putnam 1999 A6
Source:
December 22, 2012
Putnam
college contests
Problem Statement
The sequence
(
a
n
)
n
≥
1
(a_n)_{n\geq 1}
(
a
n
)
n
≥
1
is defined by
a
1
=
1
,
a
2
=
2
,
a
3
=
24
,
a_1=1,a_2=2,a_3=24,
a
1
=
1
,
a
2
=
2
,
a
3
=
24
,
and, for
n
≥
4
,
n\geq 4,
n
≥
4
,
a
n
=
6
a
n
−
1
2
a
n
−
3
−
8
a
n
−
1
a
n
−
2
2
a
n
−
2
a
n
−
3
.
a_n=\dfrac{6a_{n-1}^2a_{n-3}-8a_{n-1}a_{n-2}^2}{a_{n-2}a_{n-3}}.
a
n
=
a
n
−
2
a
n
−
3
6
a
n
−
1
2
a
n
−
3
−
8
a
n
−
1
a
n
−
2
2
.
Show that, for all
n
n
n
,
a
n
a_n
a
n
is an integer multiple of
n
n
n
.
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