Does anyone have any ideas on how to even start this problem? I am supposed to find a general solution in rational numbers for (aside from the trivial ones):(adsbygoogle = window.adsbygoogle || []).push({});

[itex]x^3+y^3=u^3+v^3[/itex]

Actually, I'm given the answer (which is really messy) and am supposed to show how to derive it. The book gives the hint to use a substitution x=X-Y, y=X+Y, u=U-V, and v=U+V and then factor the result in [itex]Q(\sqrt{-3})[/itex].

The hint was easy to enact, but led to another dead end. I figure you can start by trying to find integer solutions, but that doesn't help either. In fact, I can't even figure out how to make any progress at all. Not even a little bit.

Any clues out there at all?

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# Parametric representation

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