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!
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!
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$)