perplexus.info :: Numbers : Prime or Composite? (3)

Prime or Composite? (3) (Posted on 2023-06-10)

Each of a, b, c, x, y, and z is an integer that satisfy this relationship:

         ayz = bzx = cxy

Can a+b+c+x+y+z be a prime number?

If so, provide an example.
If not, prove it with valid reasoning.

See The Solution Submitted by K Sengupta

Rating: 5.0000 (1 votes)

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re(2): Solution

Comment 3 of 3 |

(In reply to re: Solution by Steven Lord)

With negative but non-zero integers allowed I can still find degenerate stuff.

Let b=-a, c=-a, y=-x, and z=-x. Then the compound equality becomes ax^2=ax^2=ax^2 and the sum a+b+c+x+y+z = -a-x.

Then it is trivial to find values a and x so that -a-x is prime.

Posted by Brian Smith on 2023-06-10 15:39:58

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