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

Home > Numbers
x^3 = y^2 15 (Posted on 2010-07-08) Difficulty: 3 of 5
Determine all possible pair(s) (x, y) of positive integers that satisfy the equation: x3 = y2 15

No Solution Yet Submitted by K Sengupta    
Rating: 2.5000 (2 votes)

Comments: ( Back to comment list | You must be logged in to post comments.)
Some Thoughts Catalan Conjecture | Comment 10 of 11 |

This problem reminded me of Catalan's Conjecture: prove 8 and 9 are the only consecutive powers.  This was proved true in 2002, but for our problem the difference is 15 and not 1. 

Catalan's Conjecture has an extension called Pillai's Conjecture which implies that given any difference d, there are a finite number of pairs of powers with a difference of d.  So by Pillai's Conjecture there is a finite number of solutions for any difference we choose to put in our problem.

http://en.wikipedia.org/wiki/Catalan's_conjecture


  Posted by Brian Smith on 2010-07-10 12:24:32
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 (1)
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