Each of a, b, c, x, y, and z is an integer that satisfy this relationship:

         ayz = bzx = cxy

Can a+b+c+x+y+z be a prime number?

If so, provide an example.
If not, prove it with valid reasoning.

(In reply to Solution by Brian Smith)

I wonder (idly) if allowing some of the variables to be negative integers allows for any relaxation of your treatment. 

Edited on June 10, 2023, 2:44 pm

Posted by Steven Lord on 2023-06-10 14:43:46