Inhaltsverzeichnis

Development of
Algorithmic Constructions

11:45:40
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24.Jun 2021

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odd number < 10000 :
0+i
^20+i
^24+4i
^27+13i
^22+11i5+10i
^25+6i4+13i8+11i12+14i


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