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PEN L Problems
10
L 10
L 10
Source:
May 25, 2007
Linear Recurrences
Problem Statement
The sequence
{
y
n
}
n
≥
1
\{y_{n}\}_{n \ge 1}
{
y
n
}
n
≥
1
is defined by
y
1
=
y
2
=
1
,
y
n
+
2
=
(
4
k
−
5
)
y
n
+
1
−
y
n
+
4
−
2
k
.
y_{1}=y_{2}=1,\;\; y_{n+2}= (4k-5)y_{n+1}-y_{n}+4-2k.
y
1
=
y
2
=
1
,
y
n
+
2
=
(
4
k
−
5
)
y
n
+
1
−
y
n
+
4
−
2
k
.
Determine all integers
k
k
k
such that each term of this sequence is a perfect square.
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