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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? – user474632 Aug 18 '11 at 1:36
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. – anon Aug 18 '11 at 1:43
Um, that's not an equation. Is there a typo somewhere? – user474632 Aug 18 '11 at 1:52
Sigh. Yes it's a typo. – anon Aug 18 '11 at 1:54
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. – Zev Chonoles Aug 18 '11 at 2:04

First of all, what exactly do you mean by the Sinha Conjecture?

The Wikipedia article on the Sinha conjecture is just terrible. It could quite possibly be the worst Wikipedia article I have ever read. There is a bunch of nonsense. I mean, just look at this paragraph:

"So, first of all, Sinha tried to solve the Beal Conjecture and found the proof of Beal Conjecture, which immediately succeeded to gain two additional conjectures, more precisely, the Sinha Conjecture. This conjecture is more complex and challenging than Beal's earlier proposal. Sinha is never going to claim the Beal Conjecture Prize awarding money ever. He believes, if his proof leads us into a complicated conjecture then the Beal Conjecture, then other attempts to proof the Beal Conjecture must lead us into more deep inside of FLT in future. Money is priceless before the research and future developments of our knowledge, he believes."

I am really sceptical in general of this so called Sinha. The official website talks about sinha, and from what I read he has worked on FLT, quantum gravity, a high efficiency combustion engine, AND the development of a low cost thermonuclear reactor... quite possibly the largest problems in a wide range of fields. Also note that he apparently has not studied any of these fields as his degrees are in bio... just sceptical thats all.

Beal Conjecture: The Beal conjecture however is still open, and is very real. If you can find $X$, $Y$, $Z$, $a$, $b$, $c$ with $a,b,c>2$ and $X,Y,Z$ all pairwise coprime then the conjecture does not hold, and you are finished. (You also win 100 000$)

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It does link to the eilab page at least. Is the link on more acceptable to you? – user474632 Aug 18 '11 at 1:39
@user474632: Have you looked at that page? Its crazy. I added another paragraph after reading some more. Sorry I am so sceptical. – Eric Naslund Aug 18 '11 at 1:43
@user474632: Also what kind of a homepage is this for a corporation?: There is the title, and a completely blank page!!?! There are no links going anywhere!!! I really have trouble believing they put up a 450 000$ prize for a conjecture which can be found in no reliable sources... and when the webpage has about a total of 10 pages... – Eric Naslund Aug 18 '11 at 1:46
I can appreciate skepticism when it leads to a point. I don't know very well how to verify the site. – user474632 Aug 18 '11 at 1:54
@User474632: A problem for me is you don't reference anything mathematical in your question, so what let me ask again: What do you mean by the Sinha Conjecture? My personal guess is that you meant the Beal conjecture, so I provided an answer in that case. – Eric Naslund Aug 18 '11 at 1:59

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