Quote:
Originally Posted by science_man_88
you can break down almost any partition that way though: partitions of 9:
all the red are partitions of another partition. some of these are also duplicates of earlier ones 3,4,2 and 4,3,2 and 2,3,4 for example ( there's actually 6 possible ways to rearrange these but that's also why you can cut the work back searching for the square sums because there are 16 with sign changes, each having 24 orderings.

It simply means that we only need to find the first 4sq rep, then expand its squares into sum of 4 squares and then use these expansions to form combinations of square and nonsquares as done before to find the factor.