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2017 JBMO Shortlist
NT5
NT5
Part of
2017 JBMO Shortlist
Problems
(1)
find positive n so that exists prime p with p^n-(p-1)^n$ a power of 3
Source: JBMO Shortlist 2017 NT5
7/25/2018
Find all positive integers
n
n
n
such that there exists a prime number
p
p
p
, such that
p
n
−
(
p
−
1
)
n
p^n-(p-1)^n
p
n
−
(
p
−
1
)
n
is a power of
3
3
3
.Note. A power of
3
3
3
is a number of the form
3
a
3^a
3
a
where
a
a
a
is a positive integer.
number theory
Power
positive integer
prime