 # Prove this conjecture and win \$100,000 smaia Posers and Puzzles 13 Feb '10 01:34
1. 13 Feb '10 01:34
(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
2. 06 Mar '10 04:551 edit
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
27^4+162^3=9^7

common prime is 1
3. 06 Mar '10 07:41
Originally posted by uzless
27^4+162^3=9^7

common prime is 1
Sadly, the common prime is 3 🙁
4. 06 Mar '10 08:16
Originally posted by uzless
27^4+162^3=9^7

common prime is 1
Is 1 really a prime?
5. 06 Mar '10 20:39
Originally posted by FabianFnas
Is 1 really a prime?
Nope.
6. 07 Mar '10 07:38
Originally posted by AThousandYoung
Nope.
So what does "common prime is 1" really mean?
7. 07 Mar '10 09:21
Originally posted by FabianFnas
So what does "common prime is 1" really mean?
Nothing. The statement should be

"common prime is <prime number>"

or

"there is no common prime"
8. 07 Mar '10 09:26
Originally posted by TheMaster37
Nothing. The statement should be

"common prime is <prime number>"

or

"there is no common prime"
Okay. Thanks.