Quote:
Originally Posted by mahbel
It turned out that one 4sq representation can be transformed into another simply by expanding the squares in the first one and rearranging them to create new 4sq representations. It can be shown that for N=7*13=91, the first 4sq rep (5,5,5,4) can be transformed into any other representation.

Quote:
Originally Posted by mahbel
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.

I'm concerned we're getting tricked by using small numbers again. Here's a random semiprime and the first 4square partition I found: 815181927142781578628738664212206467553690877685194559413249 = 902874258766292206129956425802^2 + 255400237710160^2 + 19610779^2 + 5938098^2. Could you expand its sum of four squares into a few others to show the process?