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.

(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