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?
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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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