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2003 AIME Problems
1
Multiple Factorials
Multiple Factorials
Source:
May 11, 2006
factorial
Problem Statement
Given that
(
(
3
!
)
!
)
!
3
!
=
k
⋅
n
!
,
\frac{((3!)!)!}{3!} = k \cdot n!,
3
!
((
3
!)!)!
=
k
⋅
n
!
,
where
k
k
k
and
n
n
n
are positive integers and
n
n
n
is as large as possible, find
k
+
n
k + n
k
+
n
.
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