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

Home > Numbers
Sums of Squares (Posted on 2005-02-21) Difficulty: 4 of 5
Some integers cannot be written as a sum of distinct positive squares. Does there exist a largest such integer? If so, find it.

See The Solution Submitted by David Shin    
Rating: 3.2857 (7 votes)

Comments: ( Back to comment list | You must be logged in to post comments.)
Solution researched (spoiler) | Comment 2 of 8 |

A search (advanced look-up, for sum AND distinct squares) in the On-Line Encyclopedia of Integer Sequences, results in finding (among others), sequence number A001422, which has a link also to MathWorld, indicating exactly 31 numbers have this property: 2, 3, 6, 7, 8, 11, 12, 15, 18, 19, 22, 23, 24, 27, 28, 31, 32, 33, 43, 44, 47, 48, 60, 67, 72, 76, 92, 96, 108, 112, 128.  So 128 is the largest such integer.

I note for example, that 1 and 4 are not listed. So they are considered the "sum" of one square.  I don't know, if all perfect squares above 128 can be made to be the sum of more than one perfect square.  (... or perhaps they merely consider zero to be a perfect square, so 4 = 4 + 0).


  Posted by Charlie on 2005-02-22 14:04:09
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