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PAMO 2023 Problem 2
Source: 2023 Pan African Mathematics Olympiad Problem 2
5/17/2023
Find all positive integers
m
m
m
and
n
n
n
with no common divisor greater than 1 such that
m
3
+
n
3
m^3 + n^3
m
3
+
n
3
divides
m
2
+
20
m
n
+
n
2
m^2 + 20mn + n^2
m
2
+
20
mn
+
n
2
. (Professor Yongjin Song)
PAMO
number theory