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PEN M Problems
6
M 6
M 6
Source:
May 25, 2007
Recursive Sequences
Problem Statement
The sequence
{
a
n
}
n
≥
1
\{a_{n}\}_{n \ge 1}
{
a
n
}
n
≥
1
is defined by
a
1
=
1
,
a
n
+
1
=
2
a
n
+
3
a
n
2
+
1
.
a_{1}=1, \; a_{n+1}=2a_{n}+\sqrt{3a_{n}^{2}+1}.
a
1
=
1
,
a
n
+
1
=
2
a
n
+
3
a
n
2
+
1
.
Show that
a
n
a_{n}
a
n
is an integer for every
n
n
n
.
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