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

Home > Just Math
Mixed Muddle (Posted on 2011-07-05) Difficulty: 3 of 5
Each of x and y is a positive mixed fraction with the respective fractional parts of x and y equal to 1/3 and 2/3 and, z is a positive integer such that:

[x2] + [y2] = z2, and:

x + y is a perfect square

(I) Determine the pairs (x, y) that generate the first five smallest values of z.

(II) Determine the smallest common value of z, such that there are precisely two pairs (x, y) that satisfy all the given conditions. What are the next two smallest values of z with this property?

Note: [N] denotes the greatest integer ≤ N

No Solution Yet Submitted by K Sengupta    
No Rating

Comments: ( You must be logged in to post comments.)
  Subject Author Date
There are no comments yet.
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