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

Home > Just Math
More than 3 cubes (Posted on 2017-11-04) Difficulty: 3 of 5
Prove the following statement:

There is an infinite number of integer pairs (n,n+1) such that each of the integers cannot be represented by a sum of 3 integer cubes.

No Solution Yet Submitted by Ady TZIDON    
No Rating

Comments: ( Back to comment list | You must be logged in to post comments.)
Solution No Subject Comment 1 of 1
This is fairly easy to solve.  Cubes mod 9 are congruent to 0, 1, or 8.  There is no way to choose with repeats three of those congruences to add up to a number congruent to 4 or 5 mod 9.  So all integer pairs (9x+4,9x+5) require at least four cubes.

It turns out we had this before with 3 cubes? - not always.
  Posted by Brian Smith on 2017-11-04 09:26:04
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