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Prime or Composite? (3) (Posted on 2023-06-10) Difficulty: 3 of 5
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)

Comments: ( Back to comment list | You must be logged in to post comments.)
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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