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National and Regional Contests
PEN Problems
PEN E Problems
25
25
Part of
PEN E Problems
Problems
(1)
E 25
Source:
1/20/2013
Prove that
ln
n
≥
k
ln
2
\ln n \geq k\ln 2
ln
n
≥
k
ln
2
, where
n
n
n
is a natural number and
k
k
k
is the number of distinct primes that divide
n
n
n
.
logarithms
function