All about flooble | fun stuff | Get a free chatterbox | Free JavaScript | Avatars    
perplexus dot info

Home > Numbers
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)

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

Please log in:
Login:
Password:
Remember me:
Sign up! | Forgot password


Search:
Search body:
Forums (0)
Newest Problems
Random Problem
FAQ | About This Site
Site Statistics
New Comments (2)
Unsolved Problems
Top Rated Problems
This month's top
Most Commented On

Chatterbox:
Copyright © 2002 - 2017 by Animus Pactum Consulting. All rights reserved. Privacy Information