Inhaltsverzeichnis

Development of
Algorithmic Constructions

11:25:10
Deutsch
24.Jun 2021

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odd number < 10000 :
0+i
^20+i
^20+i
^27+7i0+i
^22+26i0+i7+7i
^235+36i7+12i0+22i40+40i10+44i
^37+12i15+29i8+41i1+17i35+36i37+45i11+13i14+26i21+25i28+31i10+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