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2024 Greece Junior Math Olympiad
4
4
Part of
2024 Greece Junior Math Olympiad
Problems
(1)
x^2+y^2+z^2+xy+yz+zx=6xyz diophantine
Source: Greece Junior Math Olympiad 2024 p4
3/2/2024
Prove that there are infinite triples of positive integers
(
x
,
y
,
z
)
(x,y,z)
(
x
,
y
,
z
)
such that
x
2
+
y
2
+
z
2
+
x
y
+
y
z
+
z
x
=
6
x
y
z
.
x^2+y^2+z^2+xy+yz+zx=6xyz.
x
2
+
y
2
+
z
2
+
x
y
+
yz
+
z
x
=
6
x
yz
.
number theory
Diophantine equation
diophantine