SOLUTION: If Ax + By = Cz, where A, B, C, x, y and z are positive integers and x, y and z are all greater than 2, then A, B and C must have a common prime factor. Can you write a rock-soli

Question 969733: If Ax + By = Cz, where A, B, C, x, y and z are positive integers and x, y and z
are all greater than 2, then A, B and C must have a common prime factor. Can you
write a rock-solid mathematical proof that it's always true?
Answer by Edwin McCravy(20055) (Show Source): You can put this solution on YOUR website!
If Ax + By = Cz, where A, B, C, x, y and z are positive integers and x, y and z
are all greater than 2, then A, B and C must have a common prime factor. Can you
write a rock-solid mathematical proof that it's always true?
--------------------------------------------------------------

No, but you can write a rock-solid proof that it is NOT true!
All you have to do is give just one counter-example.  
And here's one:

A=4, B=5, C=7,  x=8, y=9, z=11 

All those are positive integers greater than 2.

A*x + B*y = C*z  because

4*8 + 5*9 = 7*11
 32 +  45 = 77
       77 = 77

Yet A=4, B=5, C=7, have no common prime factor.

There are many other counter-examples.  They aren't hard to find.

Edwin

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