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2018 PUMaC Algebra A
7
7
Part of
2018 PUMaC Algebra A
Problems
(1)
2018 PUMaC Algebra A7
Source:
11/25/2018
Let the sequence
{
a
n
}
n
=
−
2
∞
\left \{ a_n \right \}_{n = -2}^\infty
{
a
n
}
n
=
−
2
∞
satisfy
a
−
1
=
a
−
2
=
0
,
a
0
=
1
a_{-1} = a_{-2} = 0, a_0 = 1
a
−
1
=
a
−
2
=
0
,
a
0
=
1
, and for all non-negative integers
n
n
n
,
n
2
=
∑
k
=
0
n
a
n
−
k
a
k
−
1
+
∑
k
=
0
n
a
n
−
k
a
k
−
2
n^2 = \sum_{k = 0}^n a_{n - k}a_{k - 1} + \sum_{k = 0}^n a_{n - k}a_{k - 2}
n
2
=
k
=
0
∑
n
a
n
−
k
a
k
−
1
+
k
=
0
∑
n
a
n
−
k
a
k
−
2
Given
a
2018
a_{2018}
a
2018
is rational, find the maximum integer
m
m
m
such that
2
m
2^m
2
m
divides the denominator of the reduced form of
a
2018
a_{2018}
a
2018
.
PuMAC
algebra