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Iran MO (3rd Round)
2023 Iran MO (3rd Round)
2
Permutation x divisibility
Permutation x divisibility
Source: Iran MO 2023 3rd round , Combinatorics exam P2
August 19, 2023
combinatorics
Problem Statement
Find the number of permutations of
{
1
,
2
,
.
.
.
,
n
}
\{1,2,...,n\}
{
1
,
2
,
...
,
n
}
like
{
a
1
,
.
.
.
,
a
n
}
\{a_1,...,a_n\}
{
a
1
,
...
,
a
n
}
st for each
1
≤
i
≤
n
1 \leq i \leq n
1
≤
i
≤
n
:
a
i
∣
2
i
a_i | 2i
a
i
∣2
i
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