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PEN L Problems
13
13
Part of
PEN L Problems
Problems
(1)
L 13
Source:
5/25/2007
The sequence
{
x
n
}
n
≥
1
\{x_{n}\}_{n \ge 1}
{
x
n
}
n
≥
1
is defined by
x
1
=
x
2
=
1
,
x
n
+
2
=
14
x
n
+
1
−
x
n
−
4.
x_{1}=x_{2}=1, \; x_{n+2}= 14x_{n+1}-x_{n}-4.
x
1
=
x
2
=
1
,
x
n
+
2
=
14
x
n
+
1
−
x
n
−
4.
Prove that
x
n
x_{n}
x
n
is always a perfect square.
induction
algebra
polynomial
quadratics
difference of squares
special factorizations
Linear Recurrences