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2
Permutation times exponential zero
Permutation times exponential zero
Source: INMO 2022 Problem 2
March 6, 2022
INMO
INMO 2022
combinatorics
algebra
Problem Statement
Find all natural numbers
n
n
n
for which there is a permutation
σ
\sigma
σ
of
{
1
,
2
,
…
,
n
}
\{1,2,\ldots, n\}
{
1
,
2
,
…
,
n
}
that satisfies:
∑
i
=
1
n
σ
(
i
)
(
−
2
)
i
−
1
=
0
\sum_{i=1}^n \sigma(i)(-2)^{i-1}=0
i
=
1
∑
n
σ
(
i
)
(
−
2
)
i
−
1
=
0
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