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Cono Sur Olympiad
2013 Cono Sur Olympiad
5
5
Part of
2013 Cono Sur Olympiad
Problems
(1)
Cono Sur Olympiad 2013, Problem 5
Source:
8/22/2014
Let
d
(
k
)
d(k)
d
(
k
)
be the number of positive divisors of integer
k
k
k
. A number
n
n
n
is called balanced if
d
(
n
−
1
)
≤
d
(
n
)
≤
d
(
n
+
1
)
d(n-1) \leq d(n) \leq d(n+1)
d
(
n
−
1
)
≤
d
(
n
)
≤
d
(
n
+
1
)
or
d
(
n
−
1
)
≥
d
(
n
)
≥
d
(
n
+
1
)
d(n-1) \geq d(n) \geq d(n+1)
d
(
n
−
1
)
≥
d
(
n
)
≥
d
(
n
+
1
)
. Show that there are infinitely many balanced numbers.
number theory proposed
number theory