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MathLinks Contest 2nd
5.3
0253 permutation 2nd edition Round 5 p2
0253 permutation 2nd edition Round 5 p2
Source:
May 10, 2021
combinatorics
2nd edition
Problem Statement
Let
n
≥
3
n \ge 3
n
≥
3
and
σ
∈
S
n
\sigma \in S_n
σ
∈
S
n
a permutation of the first
n
n
n
positive integers. Prove that the numbers
σ
(
1
)
,
2
σ
(
2
)
,
3
σ
(
3
)
,
.
.
.
,
n
σ
(
n
)
\sigma (1), 2\sigma (2), 3\sigma(3), ... , n\sigma (n)
σ
(
1
)
,
2
σ
(
2
)
,
3
σ
(
3
)
,
...
,
nσ
(
n
)
cannot form an arithmetic, nor a geometric progression.
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