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

Home > Just Math
Look for the pairs (Posted on 2010-10-15) Difficulty: 3 of 5
Find the number of positive integer pairs (x; y) satisfying:
1/x+1/y=1/2010

Try to generalize for 1/n.

No Solution Yet Submitted by Ady TZIDON    
Rating: 4.0000 (1 votes)

Comments: ( Back to comment list | You must be logged in to post comments.)
Solution No Subject | Comment 2 of 3 |
Well, xdog has done all the heavy lifting, except for a small typo.
2010 factors as 2*3*5*67.  Answer is still 81.

In general,
(x-n)(y-n) = n^2,
so the number of satisfying pairs is just the number of divisors of n^2.

Edited on October 15, 2010, 2:45 pm
  Posted by Steve Herman on 2010-10-15 14:41:30

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 (3)
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