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

#1**+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**+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