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South East Mathematical Olympiad
2013 South East Mathematical Olympiad
3
China South East Mathematical Olympiad 2013 problem 3
China South East Mathematical Olympiad 2013 problem 3
Source:
August 10, 2013
algebra unsolved
algebra
Problem Statement
A sequence
{
a
n
}
\{a_n\}
{
a
n
}
,
a
1
=
1
,
a
2
=
2
,
a
n
+
1
=
a
n
2
+
(
−
1
)
n
a
n
−
1
a_1=1,a_2=2,a_{n+1}=\dfrac{a_n^2+(-1)^n}{a_{n-1}}
a
1
=
1
,
a
2
=
2
,
a
n
+
1
=
a
n
−
1
a
n
2
+
(
−
1
)
n
. Show that
a
m
2
+
a
m
+
1
2
∈
{
a
n
}
,
∀
m
∈
N
a_m^2+a_{m+1}^2\in\{a_n\},\forall m\in\Bbb N
a
m
2
+
a
m
+
1
2
∈
{
a
n
}
,
∀
m
∈
N
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