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Nigeria Contests
Nigerian Senior Mathematics Olympiad Round 3
2021 Nigerian MO Round 3
Problem 3
Problem 3
Part of
2021 Nigerian MO Round 3
Problems
(1)
Fifth and sitxh power of prime
Source: 2021 Nigerian MO Round 3/P3
12/19/2022
Find all pairs of natural numbers
(
p
,
n
)
(p, n)
(
p
,
n
)
with
p
p
p
prime such that
p
6
+
p
5
+
n
3
+
n
=
n
5
+
n
2
p^6+p^5+n^3+n=n^5+n^2
p
6
+
p
5
+
n
3
+
n
=
n
5
+
n
2
.
Diophantine equation
number theory
prime