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2014 Cuba MO
5
x^2 - y = z^2, y^2 - z = x^2, z^2 - x = y^2
x^2 - y = z^2, y^2 - z = x^2, z^2 - x = y^2
Source: 2014 Cuba 2.5
September 20, 2024
algebra
system of equations
System
Problem Statement
Determine all real solutions to the system of equations:
x
2
−
y
=
z
2
x^2 - y = z^2
x
2
−
y
=
z
2
y
2
−
z
=
x
2
y^2 - z = x^2
y
2
−
z
=
x
2
z
2
−
x
=
y
2
z^2 - x = y^2
z
2
−
x
=
y
2
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