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2014 Turkey MO (2nd round)
5
5
Part of
2014 Turkey MO (2nd round)
Problems
(1)
Find all n such that two sets are identical
Source: Turkey National Olympiad 2014 P5
11/17/2014
Find all natural numbers
n
n
n
for which there exist non-zero and distinct real numbers
a
1
,
a
2
,
…
,
a
n
a_1, a_2, \ldots, a_n
a
1
,
a
2
,
…
,
a
n
satisfying
{
a
i
+
(
−
1
)
i
a
i
∣
1
≤
i
≤
n
}
=
{
a
i
∣
1
≤
i
≤
n
}
.
\left\{a_i+\dfrac{(-1)^i}{a_i} \, \Big | \, 1 \leq i \leq n\right\} = \{a_i \mid 1 \leq i \leq n\}.
{
a
i
+
a
i
(
−
1
)
i
1
≤
i
≤
n
}
=
{
a
i
∣
1
≤
i
≤
n
}
.
integration
algebra proposed
algebra