Some integers cannot be written as a sum of distinct positive squares. Does there exist a largest such integer? If so, find it.

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