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PEN L Problems
11
L 11
L 11
Source:
May 25, 2007
Linear Recurrences
Problem Statement
Let the sequence
{
K
n
}
n
≥
1
\{K_{n}\}_{n \ge 1}
{
K
n
}
n
≥
1
be defined by
K
1
=
2
,
K
2
=
8
,
K
n
+
2
=
3
K
n
+
1
−
K
n
+
5
(
−
1
)
n
.
K_{1}=2, K_{2}=8, K_{n+2}=3K_{n+1}-K_{n}+5(-1)^{n}.
K
1
=
2
,
K
2
=
8
,
K
n
+
2
=
3
K
n
+
1
−
K
n
+
5
(
−
1
)
n
.
Prove that if
K
n
K_{n}
K
n
is prime, then
n
n
n
must be a power of
3
3
3
.
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