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20170629, 13:31  #188  
"mahfoud belhadj"
Feb 2017
Kitchener, Ontario
2^{2}·3·5 Posts 
Quote:
1that one 4sq rep can be transformed into another 4sq rep. And my previous comment was not about this. 2that the expansion of elements of a 4sq rep (a,b,c,d) can themselves be expanded into sums of 4sq then those expansions can be used to make combinations that lead to factors. The example I provided (5,5,5,4) clearly showed that the expansion helps greatly because it allowed us to find factors more often than in just considering the original (5,5,5,4) to find factors. We don't really need a sum of square that produce Pythagorean triplets. Yes, they may appear in any expansion but more often than not, they don't. Last fiddled with by mahbel on 20170629 at 13:32 

20170629, 15:18  #189 
Aug 2006
3×1,993 Posts 
I still think this is an artifact of working with small numbers. It's not clear to me that you could produce a lot of 4square representations for a moderatesize number given one such representation.

20170629, 15:36  #190  
Feb 2017
Nowhere
3×1,669 Posts 
Quote:
Just to review, in the very first post to this thread here you said: Quote:
Quote:
And, when challenged with a number of any size to test your new "method" on, you again refuse the challenge, whining that Quote:
Let's see here. You've gone from 4 squares to, now, 16 squares. And, of course, the overhead of computing four additional 4square representations, for each representation of the original number. If your original method was slow, this is slow to the fifth power! Let's see. How did you describe your method originally? Straightforward? Efficient? 

20170629, 18:11  #191 
"mahfoud belhadj"
Feb 2017
Kitchener, Ontario
2^{2}×3×5 Posts 
You may be right. It could be just an artifact. But as long as we don't have a proof, we can't rule it out.

20170629, 19:16  #192 
Aug 2006
3·1,993 Posts 

20170630, 13:44  #193  
Feb 2017
Nowhere
3×1,669 Posts 
Quote:
Quote:
Last fiddled with by Dr Sardonicus on 20170630 at 13:50 

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