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

Home > Just Math
Near Pythagoras (Posted on 2013-07-31) Difficulty: 3 of 5
Determine all possible pairs (x,y) of half-integers, with x ≤ y, that satisfy this equation:

[x2] + [y2] = 2016

Prove that there are no others.

*** [x] denotes the greatest integer ≤ x.

No Solution Yet Submitted by K Sengupta    
No Rating

Comments: ( Back to comment list | You must be logged in to post comments.)
re(2): computer solution Comment 4 of 4 |
(In reply to re: computer solution by broll)

Of the 16 WolframAlpha solutions, only half have x <= y. The only two that my list failed to include were two cases where both x and y were negative:

x=-85/2, y=-29/2

x=-71/2, y=-55/2

So there are actually 8 solutions.

  Posted by Charlie on 2013-08-01 09:41:59
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 (1)
Unsolved Problems
Top Rated Problems
This month's top
Most Commented On

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