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Korea National Olympiad
2023 Korea National Olympiad
1
easy sequence
easy sequence
Source: KMO 2023 P1
November 4, 2023
number theory
Problem Statement
A sequence of positive reals
{
a
n
}
\{ a_n \}
{
a
n
}
is defined below.
a
0
=
1
,
a
1
=
3
,
a
n
+
2
=
a
n
+
1
2
+
2
a
n
a_0 = 1, a_1 = 3, a_{n+2} = \frac{a_{n+1}^2+2}{a_n}
a
0
=
1
,
a
1
=
3
,
a
n
+
2
=
a
n
a
n
+
1
2
+
2
Show that for all nonnegative integer
n
n
n
,
a
n
a_n
a
n
is a positive integer.
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