Problems & Puzzles: Conjectures Conjecture 31. The FermatCatalan & Beal's Conjectures Here we deal with the Diophantine equation x^p + y^q = z^r, for positive x, y, z, p, q & r values. As a matter of fact this equation generates two conjectures: The
FermatCatalan Conjecture
The last five
solutions were found by F. Beukers & D. Zagier (*)
BTW, solving this conjecture  or finding a counterxample  has a cash prize of $100,000 USD. A good starting
point to search
for the 11th solution and/or the counterexample
to Beal's conjecture, is
this web page by
Peter Norvig,
who is Chief of the Computational Sciences Division at the NASA
Ames Research Center. Questions:
1) Can you find an
eleventh
solution to
x^p + y^q = z^r
or demonstrate that there are no more solutions?
______________ Other
webreferences are:
Solution





