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2017-06-28, 13:13   #181
CRGreathouse

Aug 2006

3·1,993 Posts

Quote:
 Originally Posted by mahbel It turned out that one 4-sq representation can be transformed into another simply by expanding the squares in the first one and re-arranging them to create new 4-sq representations. It can be shown that for N=7*13=91, the first 4-sq 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 4-sq rep, then expand its squares into sum of 4 squares and then use these expansions to form combinations of square and non-squares 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 4-square 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?