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12
2016-2017 Fall OMO Problem 12
2016-2017 Fall OMO Problem 12
Source:
November 16, 2016
Online Math Open
Problem Statement
For each positive integer
n
≥
2
n\ge 2
n
≥
2
, define
k
(
n
)
k\left(n\right)
k
(
n
)
to be the largest integer
m
m
m
such that
(
n
!
)
m
\left(n!\right)^m
(
n
!
)
m
divides
2016
!
2016!
2016
!
. What is the minimum possible value of
n
+
k
(
n
)
n+k\left(n\right)
n
+
k
(
n
)
?Proposed by Tristan Shin
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