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.)
answer | Comment 12 of 13 |

(A, B, C, D) = (1, 5, 2, 3); (1, 5, 3, 2); (5, 1, 2, 3);(5, 1, 3, 2); (2, 3, 1, 5); (2, 3, 5, 1); (3, 2, 1, 5); (3, 2, 5, 1).

Note: When the restriction of all the numbers being distinct is ignored, then we arrive at an additional quadruplet (A ,B, C, , D) = (2,2,2,2) as solution.

Edited on May 19, 2007, 3:58 am
  Posted by K Sengupta on 2007-05-07 12:20:03

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