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5
m_1m_2...m_n divisible by 2^n (Chile NMO 2000 P5)
m_1m_2...m_n divisible by 2^n (Chile NMO 2000 P5)
Source:
December 4, 2021
power of 2
divides
divisible
number theory
Problem Statement
Let
n
n
n
be a positive number. Prove that there exists an integer
N
=
m
1
m
2
.
.
.
m
n
‾
N =\overline{m_1m_2...m_n}
N
=
m
1
m
2
...
m
n
with
m
i
∈
{
1
,
2
}
m_i \in \{1, 2\}
m
i
∈
{
1
,
2
}
which is divisible by
2
n
2^n
2
n
.
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