Mathematical puzzle

If I'm not wrong in what I've read, since I'm not a matematician, I can tell you that Fermat first supposed (and perhaps demonstrated, but just to himself...) that there was such a theorem on integers (the so called third Fermat's t.) that you can't have solutions of the diophantine equation: x^n+y^n=z^n for n2. Of course n=2 has as solutions the so called pitagorean triplets or thriads. Euler demonstrated the t. for n=3 and for other cases. In 1995 (I'm not sure of the date and of the name of the scientist) a certain English professor Vailey, who had spent nearly all his life in attempting to solve the problem reached finally a solution universally accepted. Later on, many other Authors have given many different demonstrations... on the acceptability of which nothing I can tell you. But, what about 3^3+4^3+5^3=6^3 and, what could be its geometrical interpretation (apart from the fact that U can build a complete cube using the brics deriving from other three different cubes... I wanna know if exists such a figure where you can apply this result, since for n=2 there are special rectangle triangula). best regards

^3 means 3 times z, as in z x z x z = ? I need to know before I can think of a possibe solution.

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I think you want 3 different integers, otherwise it will be x=y=z=0 easily. So, after many minutes of desperate thinking and calculating, at one moment, I realized that integers can also be negative! So the answer would be x=-1, y=1 and z=0. Am I right?