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PAMO Problem 4: Two integers satisfying two divisbilities
Source: 2021 Pan-African Mathematics Olympiad, Problem 4
5/24/2021
Find all integers
m
m
m
and
n
n
n
such that
m
2
+
n
n
2
−
m
\frac{m^2+n}{n^2-m}
n
2
−
m
m
2
+
n
and
n
2
+
m
m
2
−
n
\frac{n^2+m}{m^2-n}
m
2
−
n
n
2
+
m
are both integers.
PAMO
number theory
Divisibility