beal'sconjecture
Beal's Conjecture
A^x+B^y = C^z => hcf (A,B,C) > 1
Proof:
Basically a corollary of the real Fermat’s Last Theorem (see attached 3 pages), with the following slight variation(s) in reasoning:
- Throughout, consider the equation:
- 1.A^x + B^(y-x).B^x = C^(z-x).C^x
- as opposed to the original Fermat equation:
- A^x + B^x = C^x
- Apply the same reasoning (see attached 3 pages) to deduce that there is no smallest C
- But hcf (A,B,C) = 1 => there is a smallest (A, B &) C
- (2) and (3) together => Beal’s Conjecture.