Development of
Algorithmic Constructions

20:14:30

18.Apr 2024

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	0+i
^2	0+i
^2	0+i
^2	7+7i						0+i
^2	2+26i						0+i		7+7i
^2	35+36i			7+12i			0+22i	40+40i	10+44i
^3	7+12i	15+29i	8+41i	1+17i	35+36i	37+45i	11+13i	14+26i	21+25i	28+31i	10+44i

The complex number are calculated by exponentation from the botton to the top modulo the input number.

I have sorted the complex numbers: b>a, otherwise I have replaced (a,b) by (b,a)

The listed green complex numbers have norm (a,b)=a²+b²=1 mod p
The listed red complex numbers have norm (a,b)=a²+b²=-1 mod p

The factorisation depends of the number modulo 4:
Let p be an odd prime, then
for p = 1 mod 4 the factorisation depends on p-1
for p = 3 mod 4 the factorisation depends on p+1

The green elements a+bi are quadratic residues and have jacobi (a²+b², f)=1
The red elements a+bi are non quadratic residues and have jacobi (a²+b², f)=-1

Development ofAlgorithmic Constructions

Development of
Algorithmic Constructions