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

Home > Numbers
Cubes can do all (Posted on 2019-05-31) Difficulty: 4 of 5
Prove or disprove that every integer can be expressed as either the sum of 3 cubes, or the sum of 3 cubes + 4.

No Solution Yet Submitted by Danish Ahmed Khan    
No Rating

Comments: ( Back to comment list | You must be logged in to post comments.)
comments, links | Comment 2 of 3 |
N=33 was cracked earlier this year.  

If you add the cubes of each of 8866128975287528, -8778405442862239 and -2736111468807040 you'll get 33.

N=42 is the only uncracked number < 100.

Here's a general article.
https://www.quantamagazine.org/sum-of-three-cubes-problem-solved-for-stubborn-number-33-20190326/

The solver's paper is mostly accessible.
https://people.maths.bris.ac.uk/~maarb/papers/cubesv1.pdf

  Posted by xdog on 2019-06-01 13:02:57
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 (8)
Unsolved Problems
Top Rated Problems
This month's top
Most Commented On

Chatterbox:
Copyright © 2002 - 2024 by Animus Pactum Consulting. All rights reserved. Privacy Information