"Larry Hammick" <larryhammick@telus.net> wrote in message news:<jKhEb.105881$bC.62790@clgrps13>...
"manro" <mantroh@yahoo.com> wrote in message
news:92d32e84.0312170350.5e46b1c8@posting.google.com...
The Barcelona conjecture:
Let c=(x+y+z)^p/(pxyz2^p)
for integer c,x,y,z and p prime greater than or equal to 5, the
Barcelona conjecture is that no solutions exist with gcd(c,xyz)=1 (no
c exist that shares no factor with x or y or z).
I haven't seen this conjecture before, but compare the Beal conjecture:
www.math.unt.edu/~mauldin/beal.html
Yes, I was aware of the Beal conjecture and briefly attempted to prove
it also :)
The reason you hadn't seen the Barcelona conjecture is that it is
virtually unknown outside of this newsgroup since I've only posted it
here and in the research math group. I came up with it while
attempting to prove FLT using elementary techniques ( ok, once we are
done laughing the question remains - who hasn't? I mean even JSH keeps
on trying.)
In some respects it should be easier to prove FLT using the Barcelona
conjecture as the latter places less restrictions on the value of c -
maybe even Fermat was working on this approach as it only requires
elementary methods, though I really doubt it as it isn't documented in
Ribenboim's book on FLT.
If anyone can lend me a hand I'm trying to get a grip on how FLT was
tied to elliptic curves, my goal being to see how feasible it is to
apply the same methods to the Barcelona conjecture - for the moment it
is way too difficult for me.
Regards, mantroh
