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Is it legal to designate a specific X, Y and Z in the process of forming a counterexample? Or is it that for the set of X and Y with the stated relationships there is a Z, a, b and c which satisfies?

Happy 410$^{th}$ Birthday Fermat!

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    It's simple. Are X, Y and Z independent? If so then Xa+Yb!=Zc for X=C0, Y=C1, Z=C2 can be a counterexample. Or is some combination of X, Y and Z interdependent due to the conditions of the conjecture?2011-08-18
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    Actually... I'm having a hard time figuring out what in the world this conjecture says too. It seems to be saying that given naturals $X,Y,Z$ with given shared factors there exist (or doesn't exist, depending on the factors) naturals $a,b,c>2$ such that $X^a+Y^b+Y^c$. I think.2011-08-18
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    Um, that's not an equation. Is there a typo somewhere?2011-08-18
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    Sigh. Yes it's a typo.2011-08-18
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    A user who has voted to close this question wishes to undo it; however, I don't believe even moderators have the power to do that. What I'd request is that the next person who wants to vote to close this question instead makes a comment to that effect here, but not vote to close themselves, letting this user's close vote act as their own.2011-08-18

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