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2012 APMO
3
APMO 2012 #3
APMO 2012 #3
Source: APMO 2012 #3
April 2, 2012
modular arithmetic
number theory
prime
Divisibility
Problem Statement
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.
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