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Regional Mathematical Olympiad
2024 India Regional Mathematical Olympiad
6
RMO KV 2024 Q6
RMO KV 2024 Q6
Source: RMO KV 2024 Q6
November 3, 2024
combinatorics
Problem Statement
Let
X
X
X
be a set of
11
11
11
integers. Prove that one can find a nonempty subset
{
a
1
,
a
2
,
⋯
,
a
k
}
\{a_1, a_2, \cdots , a_k \}
{
a
1
,
a
2
,
⋯
,
a
k
}
of
X
X
X
such that
3
3
3
divides
k
k
k
and
9
9
9
divides the sum
∑
i
=
1
k
4
i
a
i
\sum_{i=1}^{k} 4^i a_i
∑
i
=
1
k
4
i
a
i
.
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