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

Home > Just Math
Proof positive: squares of integers (Posted on 2007-04-07) Difficulty: 2 of 5
If p and q are positive integers that satisfy 3p+p=4q+q, prove that p-q, 3p+3q+1 and 4p+4q+1 are squares of integers.

See The Solution Submitted by K Sengupta    
No Rating

Comments: ( Back to comment list | You must be logged in to post comments.)
Hints/Tips Third of three proved Comment 3 of 3 |

Rearrange the equation 3p+p=4q+q into:
3p^2 - 3q^2 + p - q = q^2

Factor the left side:
(p-q)(3p+3q+1) = q^2

From my previous post, p-q is square, therefore 3p+3q+1 must be square.

  Posted by Brian Smith on 2007-04-09 14:32:52
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 (4)
Unsolved Problems
Top Rated Problems
This month's top
Most Commented On

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