Deep wrote: > >Consider (1) below for the given conditions > >z^p - x^p = 2y^2 (1) > >Conditions: z, x, y are co prime integers taken two at a time, >2|y, prime p > 3, z > x > y > 0. > >Conjecture: (1) can not be satisfied for the given conditions. > >Any helpful comment upon the correctness of the Conjecture >will be appreciated.
It's probably correct, but so what?
Here's a more general conjecture ...
Let p be an odd prime and let
f(x,y) = x^p - y^p
If f is restricted to
If y,z are coprime positive integers with y < z then the function
f(y,z) = y
> >Relevant references about the properties of (1) will be very helpful.