Thomas D. Dean on Sat, 25 Nov 2023 06:18:37 +0100


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N S.T. isfact returns 0


I was looking at foursquares-2.16.1.gp. In the function threesquares(n), isfact(n) is used to select the method of calculation. I think it always uses threesquares_fact(n,F).

I checked isfact(a^2+b^2+c^2) up to a==b==c==100 and found nothing.

Is there an N=a^2+b^2+c^2 S.T. isfact(N)==0?

? for(idx=20,50,print(idx," ",isfact(idx)))
20 [2, 2; 5, 1]
21 [3, 1; 7, 1]
22 [2, 1; 11, 1]
23 Mat([23, 1])   <-- should this be considered 0?
24 [2, 3; 3, 1]
25 Mat([5, 2])
26 [2, 1; 13, 1]
27 Mat([3, 3])
28 [2, 2; 7, 1]
29 Mat([29, 1])
...

Tom Dean