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Serbia JBMO TST
2012 Serbia JBMO TST
2
$x^2+y^2+z^2-xy-yz-zx=3$
$x^2+y^2+z^2-xy-yz-zx=3$
Source: Serbia JBMO TST 2012
October 6, 2023
Problem Statement
Show that the equation
x
2
+
y
2
+
z
2
−
x
y
−
y
z
−
z
x
=
3
x^2+y^2+z^2-xy-yz-zx=3
x
2
+
y
2
+
z
2
−
x
y
−
yz
−
z
x
=
3
has an infinity solutions over nonnegative integers.
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