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

Home > Numbers
169 (Posted on 2004-11-04) Difficulty: 4 of 5
Find all integers 1<=k<=169 for which 169 is not the sum of k nonzero squares.

The squares are not necessarily unique. For example k=5: 169=1+4+4+16+144.

This should be done without a brute force program.

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

Comments: ( Back to comment list | You must be logged in to post comments.)
re: No Subject | Comment 3 of 13 |
(In reply to No Subject by Nosher)

"k=166  165*1 + 1*4

k=163  161*1 + 2*4"

165 and 161 aren't square numbers (nor are many of the other first terms you use).  In the sums, you can only add up square numbers to reach 169.  If you could use other numbers, it would be very easy to add k terms to 169.

For example,

169

168 + 1

167 + 1 + 1

...

But you can't do these, because you can only use square numbers.


  Posted by Dustin on 2004-11-04 22:57:10
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