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

Home > Numbers
Special Natural Numbers (Posted on 2007-10-14) Difficulty: 3 of 5
Find all natural numbers which can be written in the form (a+b+c)2/(abc) where a,b,c are also natural numbers.

See The Solution Submitted by Praneeth    
No Rating

Comments: ( Back to comment list | You must be logged in to post comments.)
Some more thoughts | Comment 7 of 8 |

I noticed that the fraction is expressible as (a+b+c)/(a*b) + (a+b+c)/(a*c) + (a+b+c)/(b*c).  However, the fractions may or may not be integers for the sum to be an integer.

I also noticed that for the fraction to be an integer, then (a+b)^2 must be a multiple of c, similarily (a+c)^2 is a multiple of b and (b+c)^2 is a multiple of a.

Also, if any two of a,b,c have a common factor, that number is also a factor of the third.  Similarily, if any two of a,b,c are coprime, then they are also coprime to the third.

  Posted by Brian Smith on 2007-10-18 11:10:42
Please log in:
Remember me:
Sign up! | Forgot password

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

Copyright © 2002 - 2018 by Animus Pactum Consulting. All rights reserved. Privacy Information