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Old 2009-12-11, 06:11   #6
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Dec 2008

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Originally Posted by CRGreathouse View Post
I think not.

1. It's not obvious how Matiyasevich's theorem (Hilbert X, Robinson-Davis-Putnum-Matiyasevich, etc.) applies; it doesn't show that there are no solutions, only that proving that you've found all solutions is hard in the general case.
2. This isn't like the general case. Diophantine equations with 9 variables are known to be universal, but only with ridiculously high degrees (~10^45 as I recall). You have a degree-10 equation with only four variables.
3. Wiles' theorem doesn't seem well-equipped for the additive explosion on the LHS. Three terms is vastly different from two terms.
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Originally Posted by CRGreathouse View Post
Also, there aren't many mathematicians in the world capable of extending his proof, and (to my knowledge) none here/
Would it be worth asking Wiles or one of his former Ph.D. students (i.e. Brian Conrad)?
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