Question 71
Prove that there are no positive integers $x, y, z$ such that
$$
x^2 y^4 - x^4 y^2 + 4x^2 y^2 z^2 + x^2 z^4 - y^2 z^4 = 0.
$$
$$
x^2 y^4 - x^4 y^2 + 4x^2 y^2 z^2 + x^2 z^4 - y^2 z^4 = 0.
$$
MathNet 2011 Question 71
Math Olympiad Vault · MathNet 2011