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12
$n!\cdot(n+1)!\cdot(n+2)!$ divides $(3n)!$
$n!\cdot(n+1)!\cdot(n+2)!$ divides $(3n)!$
Source: Moldova TST 2021
September 20, 2021
number theory
Problem Statement
Prove that
n
!
⋅
(
n
+
1
)
!
⋅
(
n
+
2
)
!
n!\cdot(n+1)!\cdot(n+2)!
n
!
⋅
(
n
+
1
)!
⋅
(
n
+
2
)!
divides
(
3
n
)
!
(3n)!
(
3
n
)!
for every integer
n
≥
3
n \geq 3
n
≥
3
.
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