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

Home > Just Math
Floor Sum Formulation (Posted on 2014-10-05) Difficulty: 3 of 5
Determine all possible pairs (x, y) of positive integers satisfying:
floor(x2/y) + floor(y2/x) = floor(x/y + y/x)+ x*y.

Prove that there are no others.

No Solution Yet Submitted by K Sengupta    
No Rating

Comments: ( Back to comment list | You must be logged in to post comments.)
solution Comment 1 of 1
There are infinite number of solutions.
They are of the form (n, n^2 + 1)

(1,2), (2,5), (3,10), (4,17), (5,26), (6,37), (7,50), (8,65), (9,82), ....

  Posted by Benny on 2014-10-05 17:42:18
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 (6)
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