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2023 Thailand Online MO
3
n!|a^{n!}-1
n!|a^{n!}-1
Source: 2023 Thailand Online MO P3
February 12, 2023
number theory
Problem Statement
Let
a
a
a
and
n
n
n
be positive integers such that the greatest common divisor of
a
a
a
and
n
!
n!
n
!
is
1
1
1
. Prove that
n
!
n!
n
!
divides
a
n
!
ā
1
a^{n!}-1
a
n
!
ā
1
.
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