Does the equation x^10+y^10+z^10=t^2 have positive integer solutions? What's the best approach to determine this? What's possible method to prove if 95% that there are no solutions?
10
-
3$\begingroup$ I don't understand your last question. Also, why have you picked those particular exponents? $\endgroup$– Yemon ChoiCommented Nov 20, 2009 at 23:18
-
6$\begingroup$ Diophantine equations are hard. It might be the case that there are no solutions but that this is very hard to prove. I'd be more motivated to think about it if you explained why you were interested. If you've just written down a random equation---well, we can all do that... $\endgroup$– Kevin BuzzardCommented Nov 20, 2009 at 23:42
-
1$\begingroup$ This question looks totally random. If you provide some motivation for your question, and clarify the meaning of your last question, I'll reopen the question. $\endgroup$– Anton GeraschenkoCommented Nov 21, 2009 at 1:08
-
1$\begingroup$ Also, I think that a more detailed version of this question is indeed appropriate for mathoverflow. $\endgroup$– David Zureick-BrownCommented Nov 21, 2009 at 1:53
-
1$\begingroup$ This seemed like a perfectly good question to me. By the way, the equation presumably DOES have positive integer solutions, just not one where (x,y,z,t) are coprime. $\endgroup$– JSECommented Nov 21, 2009 at 3:40
|
Show 5 more comments