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

Home > Numbers
Cubic AND Quartic Challenge (Posted on 2004-02-06) Difficulty: 4 of 5
What is the smallest positive integer that is the sum of two different pairs of (non-zero, positive) cubes?
_____________________________

What is the smallest positive integer that is the sum of two different pairs of integers raised to the 4th power? and how did you find it?

In other words what is the smallest x such that:
x = a^4 + b^4 = c^4 + d^4
(where x, a, b, c, and d are all different, non-zero, positive integers)?
_____________________________

Are you able to determine the answer without looking it up on the internet?

See The Solution Submitted by SilverKnight    
Rating: 2.5000 (2 votes)

Comments: ( Back to comment list | You must be logged in to post comments.)
re: LOL | Comment 4 of 15 |
(In reply to LOL by nikki)

And yet... someone answered without giving an explanation as to how he found the answer. :-( (At least he could/should have have indicated that he didn't have a way to prove or brute force it.)

BTW, *MY* solution would have been to write a program (similar to Charlie's) to brute force the answer. But I would very much like to see a less 'brute force' approach if someone finds a good way to 'cull' the solution domain--which I think is possible. And *could* be done manually (if one doesn't mind doing a few dozen/hundred long-multiplications, 4th power).
  Posted by SilverKnight on 2004-02-06 10:42:59

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 (2)
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