+0  
 
0
456
1
avatar

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+27052 
+10

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
 #1
avatar+27052 
+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

15 Online Users

avatar

New Privacy Policy

We use cookies to personalise content and advertisements and to analyse access to our website. Furthermore, our partners for online advertising receive information about your use of our website.
For more information: our cookie policy and privacy policy.