Thread: Diophantine Equation View Single Post
2009-12-11, 06:11   #6
flouran

Dec 2008

72×17 Posts

Quote:
 Originally Posted by CRGreathouse 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.
Thank you for the verification! I appreciate it!
Quote:
 Originally Posted by CRGreathouse 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)?