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

Home > Just Math
Dark Divisibility (Posted on 2013-04-27) Difficulty: 3 of 5
The natural numbers a,b,c,d are such that their least common multiple equals a+b+c+d. Prove that abcd is divisible by 3 or by 5.

No Solution Yet Submitted by Danish Ahmed Khan    
Rating: 5.0000 (2 votes)

Comments: ( Back to comment list | You must be logged in to post comments.)
Some Thoughts re(3): Infinite examples, no proof yet. | Comment 13 of 18 |
(In reply to re(2): Infinite examples, no proof yet. by Jer)

Maybe I don't understand your question, Jer, but it is easy to prove that abcd must be a multiple of 2.  


Assume that the LCM is odd.  
Then a, b, c and d are all odd.  
Then a + b + c + d is even.  But a + b + c + d is the LCM, so this is a contradiction.   
Therefore, the initial assumption is wrong, and the LCM must be even.

  Posted by Steve Herman on 2013-04-29 17:03:36
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 (4)
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