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Balkan MO Shortlist
2016 Balkan MO Shortlist
N3
N3
Part of
2016 Balkan MO Shortlist
Problems
(1)
diophantine (x + y + z)^5 = 80xyz(x^2 + y^2 + z^2)
Source: Balkan BMO Shortlist 2016 N3
7/30/2019
Find all the integer solutions
(
x
,
y
,
z
)
(x,y,z)
(
x
,
y
,
z
)
of the equation
(
x
+
y
+
z
)
5
=
80
x
y
z
(
x
2
+
y
2
+
z
2
)
(x + y + z)^5 = 80xyz(x^2 + y^2 + z^2)
(
x
+
y
+
z
)
5
=
80
x
yz
(
x
2
+
y
2
+
z
2
)
,
number theory
Diophantine equation
diophantine
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