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Baltic Way
2012 Baltic Way
17
17
Part of
2012 Baltic Way
Problems
(1)
Number of Divisors in the Exponent
Source: 2012 Baltic Way, Problem 17
11/22/2012
Let
d
(
n
)
d(n)
d
(
n
)
denote the number of positive divisors of
n
n
n
. Find all triples
(
n
,
k
,
p
)
(n,k,p)
(
n
,
k
,
p
)
, where
n
n
n
and
k
k
k
are positive integers and
p
p
p
is a prime number, such that
n
d
(
n
)
ā
1
=
p
k
.
n^{d(n)} - 1 = p^k.
n
d
(
n
)
ā
1
=
p
k
.
number theory unsolved
number theory