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Romania Team Selection Test
2010 Romania Team Selection Test
5
5
Part of
2010 Romania Team Selection Test
Problems
(1)
Divisibility by $n!$
Source: Romania TST 1 2010, Problem 5
8/25/2012
Let
a
a
a
and
n
n
n
be two positive integer numbers such that the (positive) prime factors of
a
a
a
be all greater than
n
n
n
. Prove that
n
!
n!
n
!
divides
(
a
−
1
)
(
a
2
−
1
)
⋯
(
a
n
−
1
−
1
)
(a - 1)(a^2 - 1)\cdots (a^{n-1} - 1)
(
a
−
1
)
(
a
2
−
1
)
⋯
(
a
n
−
1
−
1
)
. AMM Magazine
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