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1979 IMO Longlists
78
78
Part of
1979 IMO Longlists
Problems
(1)
omega(n) is the number of prime divisors of n
Source: ILL 1979 - Problem 78.
6/5/2011
Denote the number of different prime divisors of the number
n
n
n
by
ω
(
n
)
\omega (n)
ω
(
n
)
, where
n
n
n
is an integer greater than
1
1
1
. Prove that there exist infinitely many numbers
n
n
n
for which
ω
(
n
)
<
ω
(
n
+
1
)
<
ω
(
n
+
2
)
\omega (n)< \omega (n+1)<\omega (n+2)
ω
(
n
)
<
ω
(
n
+
1
)
<
ω
(
n
+
2
)
holds.
inequalities
number theory unsolved
number theory