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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

 

Thanks,

Anon

Guest Jun 22, 2015

Best Answer 

 #1
avatar+26322 
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Here's a counter-example:

 

A = 13   B = 17   C = 19  

x = 19   y = 38   z = 47

 

A*x + B*y = 13*19 + 17*38 = 893

C*z = 19*47 = 893

 

A, B and C are all different primes, so they have no common prime factor.

(x, y and C have common prime factors of course, so perhaps your question was intended to be phrased a little differently).

.

Alan  Jun 22, 2015
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1+0 Answers

 #1
avatar+26322 
+10
Best Answer

Here's a counter-example:

 

A = 13   B = 17   C = 19  

x = 19   y = 38   z = 47

 

A*x + B*y = 13*19 + 17*38 = 893

C*z = 19*47 = 893

 

A, B and C are all different primes, so they have no common prime factor.

(x, y and C have common prime factors of course, so perhaps your question was intended to be phrased a little differently).

.

Alan  Jun 22, 2015

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