# Can the Sinha Conjecture have constants?

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!

-
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

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$) - It does link to the eilab page at least. Is the link on eilab.org/sinha.htm more acceptable to you? – user474632 Aug 18 '11 at 1:39 @user474632: Have you looked at that page? Its crazy. I added another paragraph after reading some more. Sorry I am so sceptical. – Eric Naslund Aug 18 '11 at 1:43 @user474632: Also what kind of a homepage is this for a corporation?: eilab.org There is the title, and a completely blank page!!?! There are no links going anywhere!!! I really have trouble believing they put up a 450 000$ 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