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2022 Greece Junior Math Olympiad
4
4
Part of
2022 Greece Junior Math Olympiad
Problems
(1)
When is it a common divisor?
Source: Greece Junior National Olympiad 2022, Problem 4
2/26/2022
Find all couples of non-zero integers
(
x
,
y
)
(x,y)
(
x
,
y
)
such that,
x
2
+
y
2
x^2+y^2
x
2
+
y
2
is a common divisor of
x
5
+
y
x^5+y
x
5
+
y
and
y
5
+
x
y^5+x
y
5
+
x
.
number theory