Inhaltsverzeichnis

Development of
Algorithmic Constructions

11:23:09
Deutsch
24.Jun 2021

<< 83 89 97 >>

odd number < 10000 :
0+i
^20+i
^20+i
^220+20i0+34i
^117+22i4+28i27+31i1+40i3+41i2+23i16+30i35+38i13+39i33+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