MathDB
Problems
Contests
International Contests
APMO
2012 APMO
3
3
Part of
2012 APMO
Problems
(1)
APMO 2012 #3
Source: APMO 2012 #3
4/2/2012
Determine all the pairs
(
p
,
n
)
(p , n )
(
p
,
n
)
of a prime number
p
p
p
and a positive integer
n
n
n
for which
n
p
+
1
p
n
+
1
\frac{ n^p + 1 }{p^n + 1}
p
n
+
1
n
p
+
1
is an integer.
modular arithmetic
number theory
prime
Divisibility