Prove this conjecture and win $100,000

(or give a counterexample)

If A^x + B^y = C^z where A,B,C,x,y,z are positive integers and x, y, z are all greater than 2, then A, B, and C must have a common prime factor.
This is the Beal conjecture.

http://www.math.unt.edu/~mauldin/beal.html

Originally posted by smaia
(or give a counterexample)

If A^x + B^y = C^z where A,B,C,x,y,z are positive integers and x, y, z are all greater than 2, then A, B, and C must have a common prime factor.
This is the Beal conjecture.

http://www.math.unt.edu/~mauldin/beal.html

Originally posted by uzless
27^4+162^3=9^7

common prime is 1

Originally posted by uzless
27^4+162^3=9^7

common prime is 1

Originally posted by FabianFnas
Is 1 really a prime?

Originally posted by AThousandYoung
Nope.

Originally posted by FabianFnas
So what does "common prime is 1" really mean?

Originally posted by TheMaster37
Nothing. The statement should be

"common prime is <prime number>"

or

"there is no common prime"