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Moldova Team Selection Test
1996 Moldova Team Selection Test
1
Prove that $2^{n-k}$ divides $n!$
Prove that $2^{n-k}$ divides $n!$
Source: Moldova TST 1996
August 8, 2023
number theory
Problem Statement
The number
n
n{}
n
cointains
k
k{}
k
units in binary system. Prove that
2
n
ā
k
2^{n-k}{}
2
n
ā
k
divides
n
!
n!
n
!
.
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