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2019 Switzerland - Final Round
3
2019 Switzerland MO P3
2019 Switzerland MO P3
Source: 2019 Switzerland MO
March 10, 2019
algebra
Problem Statement
Find all periodic sequences
x
1
,
x
2
,
…
x_1,x_2,\dots
x
1
,
x
2
,
…
of strictly positive real numbers such that
∀
n
≥
1
\forall n \geq 1
∀
n
≥
1
we have
x
n
+
2
=
1
2
(
1
x
n
+
1
+
x
n
)
x_{n+2}=\frac{1}{2} \left( \frac{1}{x_{n+1}}+x_n \right)
x
n
+
2
=
2
1
(
x
n
+
1
1
+
x
n
)
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