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Problems
Contests
National and Regional Contests
Mexico Contests
Mexico National Olympiad
2014 Mexico National Olympiad
6
6
Part of
2014 Mexico National Olympiad
Problems
(1)
Relationship n and its number of divisors
Source: Mexico National Olympiad 2014
11/13/2014
Let
d
(
n
)
d(n)
d
(
n
)
be the number of positive divisors of a positive integer
n
n
n
(including
1
1
1
and
n
n
n
). Find all values of
n
n
n
such that
n
+
d
(
n
)
=
d
(
n
)
2
n + d(n) = d(n)^2
n
+
d
(
n
)
=
d
(
n
)
2
.
inequalities
induction
probability
number theory unsolved
number theory