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National and Regional Contests
Kyrgyzstan Contests
Kyrgyzstan National Olympiad
2009 Kyrgyzstan National Olympiad
5
Divisibility(KgNM2009)
Divisibility(KgNM2009)
Source:
April 27, 2011
induction
floor function
number theory unsolved
number theory
Problem Statement
Prove for all natural
n
n
n
that
40
n
⋅
n
!
∣
(
5
n
)
!
\left. {{{40}^n} \cdot n!} \right|(5n)!
40
n
⋅
n
!
∣
(
5
n
)!
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