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PEN M Problems
5
M 5
M 5
Source:
May 25, 2007
Recursive Sequences
Problem Statement
Show that there is a unique sequence of integers
{
a
n
}
n
≥
1
\{a_{n}\}_{n \ge 1}
{
a
n
}
n
≥
1
with
a
1
=
1
,
a
2
=
2
,
a
4
=
12
,
a
n
+
1
a
n
−
1
=
a
n
2
±
1
(
n
≥
2
)
.
a_{1}=1, \; a_{2}=2, \; a_{4}=12, \; a_{n+1}a_{n-1}=a_{n}^{2}\pm1 \;\; (n \ge 2).
a
1
=
1
,
a
2
=
2
,
a
4
=
12
,
a
n
+
1
a
n
−
1
=
a
n
2
±
1
(
n
≥
2
)
.
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