X^3 + y^3 + z^3 = 6xyz

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Theorem

The equation:

$x^3 + y^3 + z^3 = 6 x y z$

has exactly one solution:

$x = 1$
$y = 2$
$z = 3$


Proof


Sources

  • 1995: Erik DofsSolutions of $x^3 + y^3 + z^3 = n x y z$ (Acta Arith. Vol. 73: pp. 201 – 213)