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

Home > Just Math
Sum and Ratio Sum (Posted on 2011-01-16) Difficulty: 3 of 5
Determine all possible quadruplets (A, B, P, Q) of positive integers, with P ≤ Q, that satisfy this system of equations:

A + B = 21, and:

A/P2 + B/Q2 = 1

Prove that these are the only quadruplets that exist.

No Solution Yet Submitted by K Sengupta    
No Rating

Comments: ( Back to comment list | You must be logged in to post comments.)
Some Thoughts First Tiny Start (Spoiler) | Comment 1 of 4
Well, obviously, P can only be 2, 3, 4.

If P = 1, then A/Pis >= 1

And A/P2 + B/Q2 <= A/P2 + B/P= 21/P2

So, if P >= 5, then A/P2 + B/Q2 <= 21/25


Edited on January 16, 2011, 1:32 pm
  Posted by Steve Herman on 2011-01-16 13:27:58

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