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My favorite numbers (Posted on 2005-07-22) Difficulty: 3 of 5
Find 4 different positive integers A,B,C,D for which: A+B = C*D and A*B = C+D How many sets of 4 numbers can you find? Prove that only those sets exist.

No Solution Yet Submitted by Jurgen    
Rating: 3.2000 (5 votes)

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re: No Subject | Comment 4 of 13 |
(In reply to No Subject by pcbouhid)

I believe your proof has an error somewhere, since as other comments have mentioned, there is a counterexample to your proof.  So I started to check over all the math.

The point where you lost me was when you started to include the variable x.  How is x defined?

Otherwise, the proof seems to make sense until the final conclusion.  It seems that if you solve for A as a function of C and D, you get two roots (since A and B can switch values).  These two roots are in fact equal to A and B.

I'm still not sure what x is for, but it seems that it must be C or D (remembering that C and D can switch values).  So how do you conclude from this that two of the variables are equal?

Edited on July 22, 2005, 4:14 am
  Posted by Tristan on 2005-07-22 04:02:59

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