Endliche Körper/Nicht Primkörper/Einige Operationstafeln

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Operationstafeln für {\mathbb F}_{4}

Wir nehmen die Darstellung

{\mathbb F}_4 \cong {\mathbb F}_2[X]/(X^2+X+1).

Dabei ist X2 + X + 1 irreduzibel in {\mathbb F}_2[X], da es keine Nullstelle in {\mathbb F}_2 besitzt. Es bezeichne x die Restklasse von X.


+ 0 1 x x + 1
0 0 1 x x + 1
1 1 0 x + 1 x
x x x + 1 0 1
x + 1 x + 1 x 1 0


\cdot 0 1 x x + 1
0 0 0 0 0
1 0 1 x x + 1
x 0 x x + 1 1
x + 1 0 x + 1 1 x

Operationstafeln für {\mathbb F}_{8}

Wir nehmen die Darstellung

{\mathbb F}_8 \cong {\mathbb F}_2[X]/(X^3+X+1).

Dabei ist X3 + X + 1 irreduzibel in {\mathbb F}_2[X], da es keine Nullstelle in {\mathbb F}_2 besitzt (03 + 0 + 1 = 1 und 13 + 1 + 1 = 1, also beide \neq 0). Es bezeichne x die Restklasse von X.


+ 0 1 x 1 + x x2 1 + x2 x + x2 1 + x + x2
0 0 1 x 1 + x x2 1 + x2 x + x2 1 + x + x2
1 1 0 1 + x x 1 + x2 x2 1 + x + x2 x + x2
x x 1 + x 0 1 x + x2 1 + x + x2 x2 1 + x2
1 + x 1 + x x 1 0 1 + x + x2 x + x2 1 + x2 x2
x2 x2 1 + x2 x + x2 1 + x + x2 0 1 x 1 + x
1 + x2 1 + x2 x2 1 + x + x2 x + x2 1 0 1 + x x
x + x2 x + x2 1 + x + x2 x2 1 + x2 x 1 + x 0 1
1 + x + x2 1 + x + x2 x + x2 1 + x2 x2 1 + x x 1 0


\cdot 0 1 x 1 + x x2 1 + x2 x + x2 1 + x + x2
0 0 0 0 0 0 0 0 0
1 0 1 x 1 + x x2 1 + x2 x + x2 1 + x + x2
x 0 x x2 x + x2 1 + x 1 1 + x + x2 1 + x2
1 + x 0 1 + x x + x2 1 + x2 1 + x + x2 x2 1 x
x2 0 x2 1 + x 1 + x + x2 x + x2 x 1 + x2 1
1 + x2 0 1 + x2 1 x2 x 1 + x + x2 1 + x x + x2
x + x2 0 x + x2 1 + x + x2 1 1 + x2 1 + x x x2
1 + x + x2 0 1 + x + x2 1 + x2 x 1 x + x2 x2 1 + x

Operationstafeln für {\mathbb F}_{9}

Wir nehmen die Darstellung

{\mathbb F}_9 \cong {\mathbb F}_3[X]/(X^2+1).

Dabei ist X2 + 1 irreduzibel in {\mathbb F}_3[X], da es keine Nullstelle in {\mathbb F}_3 besitzt (da − 1 kein Quadrat in {\mathbb F}_3[X] ist). Es bezeichne x die Restklasse von X.


+ 0 1 2 x x + 1 x + 2 2x 2x + 1 2x + 2
0 0 1 2 x x + 1 x + 2 2x 2x + 1 2x + 2
1 1 2 0 x + 1 x + 2 x 2x + 1 2x + 2 2x
2 2 0 1 x + 2 x x + 1 2x + 2 2x 2x + 1
x x x + 1 x + 2 2x 2x + 1 2x + 2 0 1 2
x + 1 x + 1 x + 2 x 2x + 1 2x + 2 2x 1 2 0
x + 2 x + 2 x x + 1 2x + 2 2x 2x + 1 2 0 1
2x 2x 2x + 1 2x + 2 0 1 2 x x + 1 x + 2
2x + 1 2x + 1 2x + 2 2x 1 2 0 x + 1 x + 2 x
2x + 2 2x + 2 2x 2x + 1 2 0 1 x + 2 x x + 1


\cdot 0 1 2 x x + 1 x + 2 2x 2x + 1 2x + 2
0 0 0 0 0 0 0 0 0 0
1 0 1 2 x x + 1 x + 2 2x 2x + 1 2x + 2
2 0 2 1 2x 2x + 2 2x + 1 x x + 2 x + 1
x 0 x 2x 2 x + 2 2x + 2 1 x + 1 2x + 1
x + 1 0 x + 1 2x + 2 x + 2 2x 1 2x + 1 2 x
x + 2 0 x + 2 2x + 1 2x + 2 1 x x + 1 2x 2
2x 0 2x x 1 2x + 1 x + 1 2 2x + 2 x + 2
2x + 1 0 2x + 1 x + 2 x + 1 2 2x 2x + 2 x 1
2x + 2 0 2x + 2 x + 1 2x + 1 x 2 x + 2 1 2x

Operationstafeln für {\mathbb F}_{16}

Wir nehmen die Darstellung

{\mathbb F}_{16} \cong {\mathbb F}_2[X]/(X^4+X+1).


Dabei ist X4 + X + 1 irreduzibel in {\mathbb F}_2[X], da es keine Nullstelle in {\mathbb F}_2 besitzt. Es bezeichne x die Restklasse von X.


+ 0 1 x x + 1 x2 x2 + 1 x2 + x x2 + x + 1 x3 x3 + 1 x3 + x x3 + x + 1 x3 + x2 x3 + x2 + 1 x3 + x2 + x x3 + x2 + x + 1
0 0 1 x x + 1 x2 x2 + 1 x2 + x x2 + x + 1 x3 x3 + 1 x3 + x x3 + x + 1 x3 + x2 x3 + x2 + 1 x3 + x2 + x x3 + x2 + x + 1
1 1 0 x + 1 x x2 + 1 x2 x2 + x + 1 x2 + x x3 + 1 x3 x3 + x + 1 x3 + x x3 + x2 + 1 x3 + x2 x3 + x2 + x + 1 x3 + x2 + x
x x x + 1 0 1 x2 + x x2 + x + 1 x2 x2 + 1 x3 + x x3 + x + 1 x3 x3 + 1 x3 + x2 + x x3 + x2 + x + 1 x3 + x2 x3 + x2 + 1
x + 1 x + 1 x 1 0 x2 + x + 1 x2 + x x2 + 1 x2 x3 + x + 1 x3 + x x3 + 1 x3 x3 + x2 + x + 1 x3 + x2 + x x3 + x2 + 1 x3 + x2
x2 x2 x2 + 1 x2 + x x2 + x + 1 0 1 x x + 1 x3 + x2 x3 + x2 + 1 x3 + x2 + x x3 + x2 + x + 1 x3 x3 + 1 x3 + x x3 + x + 1
x2 + 1 x2 + 1 x2 x2 + x + 1 x2 + x 1 0 x + 1 x x3 + x2 + 1 x3 + x2 x3 + x2 + x + 1 x3 + x2 + x x3 + 1 x3 x3 + x + 1 x3 + x
x2 + x x2 + x x2 + x + 1 x2 x2 + 1 x x + 1 0 1 x3 + x2 + x x3 + x2 + x + 1 x3 + x2 x3 + x2 + 1 x3 + x x3 + x + 1 x3 x3 + 1
x2 + x + 1 x2 + x + 1 x2 + x x2 + 1 x2 x + 1 x 1 0 x3 + x2 + x + 1 x3 + x2 + x x3 + x2 + 1 x3 + x2 x3 + x + 1 x3 + x x3 + 1 x3
x3 x3 x3 + 1 x3 + x x3 + x + 1 x3 + x2 x3 + x2 + 1 x3 + x2 + x x3 + x2 + x + 1 0 1 x x + 1 x2 x2 + 1 x2 + x x2 + x + 1
x3 + 1 x3 + 1 x3 x3 + x + 1 x3 + x x3 + x2 + 1 x3 + x2 x3 + x2 + x + 1 x3 + x2 + x 1 0 x + 1 x x2 + 1 x2 x2 + x + 1 x2 + x
x3 + x x3 + x x3 + x + 1 x3 x3 + 1 x3 + x2 + x x3 + x2 + x + 1 x3 + x2 x3 + x2 + 1 x x + 1 0 1 x2 + x x2 + x + 1 x2 x2 + 1
x3 + x + 1 x3 + x + 1 x3 + x x3 + 1 x3 x3 + x2 + x + 1 x3 + x2 + x x3 + x2 + 1 x3 + x2 x + 1 x 1 0 x2 + x + 1 x2 + x x2 + 1 x2
x3 + x2 x3 + x2 x3 + x2 + 1 x3 + x2 + x x3 + x2 + x + 1 x3 x3 + 1 x3 + x x3 + x + 1 x2 x2 + 1 x2 + x x2 + x + 1 0 1 x x + 1
x3 + x2 + 1 x3 + x2 + 1 x3 + x2 x3 + x2 + x + 1 x3 + x2 + x x3 + 1 x3 x3 + x + 1 x3 + x x2 + 1 x2 x2 + x + 1 x2 + x 1 0 x + 1 x
x3 + x2 + x x3 + x2 + x x3 + x2 + x + 1 x3 + x2 x3 + x2 + 1 x3 + x x3 + x + 1 x3 x3 + 1 x2 + x x2 + x + 1 x2 x2 + 1 x x + 1 0 1
x3 + x2 + x + 1 x3 + x2 + x + 1 x3 + x2 + x x3 + x2 + 1 x3 + x2 x3 + x + 1 x3 + x x3 + 1 x3 x2 + x + 1 x2 + x x2 + 1 x2 x + 1 x 1 0


\cdot 0 1 x x + 1 x2 x2 + 1 x2 + x x2 + x + 1 x3 x3 + 1 x3 + x x3 + x + 1 x3 + x2 x3 + x2 + 1 x3 + x2 + x x3 + x2 + x + 1
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
1 0 1 x x + 1 x2 x2 + 1 x2 + x x2 + x + 1 x3 x3 + 1 x3 + x x3 + x + 1 x3 + x2 x3 + x2 + 1 x3 + x2 + x x3 + x2 + x + 1
x 0 x x2 x2 + x x3 x3 + x x3 + x2 x3 + x2 + x x + 1 1 x2 + x + 1 x2 + 1 x3 + x + 1 x3 + 1 x3 + x2 + x + 1 x3 + x2 + 1
x + 1 0 x + 1 x2 + x x2 + 1 x3 + x2 x3 + x2 + x + 1 x3 + x x3 + 1 x3 + x + 1 x3 x3 + x2 + 1 x3 + x2 + x x2 + x + 1 x2 1 x
x2 0 x2 x3 x3 + x2 x + 1 x2 + x + 1 x3 + x + 1 x3 + x2 + x + 1 x2 + x x x3 + x2 + x x3 + x x2 + 1 1 x3 + x2 + 1 x3 + 1
x2 + 1 0 x2 + 1 x3 + x x3 + x2 + x + 1 x2 + x + 1 x x3 + x2 + 1 x3 x3 + x2 + x x3 + x + 1 x2 1 x3 + 1 x3 + x2 x + 1 x2 + x
x2 + x 0 x2 + x x3 + x2 x3 + x x3 + x + 1 x3 + x2 + 1 x2 + x + 1 1 x2 + 1 x + 1 x3 + 1 x3 + x2 + x + 1 x3 + x2 + x x3 x x2
x2 + x + 1 0 x2 + x + 1 x3 + x2 + x x3 + 1 x3 + x2 + x + 1 x3 1 x2 + x x3 + x2 + 1 x3 + x x + 1 x2 x x2 + 1 x3 + x2 x3 + x + 1
x3 0 x3 x + 1 x3 + x + 1 x2 + x x3 + x2 + x x2 + 1 x3 + x2 + 1 x3 + x2 x2 x3 + x2 + x + 1 x2 + x + 1 x3 + x x x3 + 1 1
x3 + 1 0 x3 + 1 1 x3 x x3 + x + 1 x + 1 x3 + x x2 x3 + x2 + 1 x2 + 1 x3 + x2 x2 + x x3 + x2 + x + 1 x2 + x + 1 x3 + x2 + x
x3 + x 0 x3 + x x2 + x + 1 x3 + x2 + 1 x3 + x2 + x x2 x3 + 1 x + 1 x3 + x2 + x + 1 x2 + 1 x3 x 1 x3 + x + 1 x2 + x x3 + x2
x3 + x + 1 0 x3 + x + 1 x2 + 1 x3 + x2 + x x3 + x 1 x3 + x2 + x + 1 x2 x2 + x + 1 x3 + x2 x x3 + 1 x3 + x2 + 1 x2 + x x3 x + 1
x3 + x2 0 x3 + x2 x3 + x + 1 x2 + x + 1 x2 + 1 x3 + 1 x3 + x2 + x x x3 + x x2 + x 1 x3 + x2 + 1 x3 + x2 + x + 1 x + 1 x2 x3
x3 + x2 + 1 0 x3 + x2 + 1 x3 + 1 x2 1 x3 + x2 x3 x2 + 1 x x3 + x2 + x + 1 x3 + x + 1 x2 + x x + 1 x3 + x2 + x x3 + x x2 + x + 1
x3 + x2 + x 0 x3 + x2 + x x3 + x2 + x + 1 1 x3 + x2 + 1 x + 1 x x3 + x2 x3 + 1 x2 + x + 1 x2 + x x3 x2 x3 + x x3 + x + 1 x2 + 1
x3 + x2 + x + 1 0 x3 + x2 + x + 1 x3 + x2 + 1 x x3 + 1 x2 + x x2 x3 + x + 1 1 x3 + x2 + x x3 + x2 x + 1 x3 x2 + x + 1 x2 + 1 x3 + x

Operationstafeln für {\mathbb F}_{25}

Wir nehmen die Darstellung

{\mathbb F}_{25} \cong {\mathbb F}_{5}[X]/(X^2+X+2).

Dabei ist X2 + X + 2 irreduzibel in {\mathbb F}_5[X], da es keine Nullstelle in {\mathbb F}_5 besitzt. Es bezeichne x die Restklasse von X.


+ 0 1 2 3 4 x x + 1 x + 2 x + 3 x + 4 2x 2x + 1 2x + 2 2x + 3 2x + 4 3x 3x + 1 3x + 2 3x + 3 3x + 4 4x 4x + 1 4x + 2 4x + 3 4x + 4
0 0 1 2 3 4 x x + 1 x + 2 x + 3 x + 4 2x 2x + 1 2x + 2 2x + 3 2x + 4 3x 3x + 1 3x + 2 3x + 3 3x + 4 4x 4x + 1 4x + 2 4x + 3 4x + 4
1 1 2 3 4 0 x + 1 x + 2 x + 3 x + 4 x 2x + 1 2x + 2 2x + 3 2x + 4 2x 3x + 1 3x + 2 3x + 3 3x + 4 3x 4x + 1 4x + 2 4x + 3 4x + 4 4x
2 2 3 4 0 1 x + 2 x + 3 x + 4 x x + 1 2x + 2 2x + 3 2x + 4 2x 2x + 1 3x + 2 3x + 3 3x + 4 3x 3x + 1 4x + 2 4x + 3 4x + 4 4x 4x + 1
3 3 4 0 1 2 x + 3 x + 4 x x + 1 x + 2 2x + 3 2x + 4 2x 2x + 1 2x + 2 3x + 3 3x + 4 3x 3x + 1 3x + 2 4x + 3 4x + 4 4x 4x + 1 4x + 2
4 4 0 1 2 3 x + 4 x x + 1 x + 2 x + 3 2x + 4 2x 2x + 1 2x + 2 2x + 3 3x + 4 3x 3x + 1 3x + 2 3x + 3 4x + 4 4x 4x + 1 4x + 2 4x + 3
x x x + 1 x + 2 x + 3 x + 4 2x 2x + 1 2x + 2 2x + 3 2x + 4 3x 3x + 1 3x + 2 3x + 3 3x + 4 4x 4x + 1 4x + 2 4x + 3 4x + 4 0 1 2 3 4
x + 1 x + 1 x + 2 x + 3 x + 4 x 2x + 1 2x + 2 2x + 3 2x + 4 2x 3x + 1 3x + 2 3x + 3 3x + 4 3x 4x + 1 4x + 2 4x + 3 4x + 4 4x 1 2 3 4 0
x + 2 x + 2 x + 3 x + 4 x x + 1 2x + 2 2x + 3 2x + 4 2x 2x + 1 3x + 2 3x + 3 3x + 4 3x 3x + 1 4x + 2 4x + 3 4x + 4 4x 4x + 1 2 3 4 0 1
x + 3 x + 3 x + 4 x x + 1 x + 2 2x + 3 2x + 4 2x 2x + 1 2x + 2 3x + 3 3x + 4 3x 3x + 1 3x + 2 4x + 3 4x + 4 4x 4x + 1 4x + 2 3 4 0 1 2
x + 4 x + 4 x x + 1 x + 2 x + 3 2x + 4 2x 2x + 1 2x + 2 2x + 3 3x + 4 3x 3x + 1 3x + 2 3x + 3 4x + 4 4x 4x + 1 4x + 2 4x + 3 4 0 1 2 3
2x 2x 2x + 1 2x + 2 2x + 3 2x + 4 3x 3x + 1 3x + 2 3x + 3 3x + 4 4x 4x + 1 4x + 2 4x + 3 4x + 4 0 1 2 3 4 x x + 1 x + 2 x + 3 x + 4
2x + 1 2x + 1 2x + 2 2x + 3 2x + 4 2x 3x + 1 3x + 2 3x + 3 3x + 4 3x 4x + 1 4x + 2 4x + 3 4x + 4 4x 1 2 3 4 0 x + 1 x + 2 x + 3 x + 4 x
2x + 2 2x + 2 2x + 3 2x + 4 2x 2x + 1 3x + 2 3x + 3 3x + 4 3x 3x + 1 4x + 2 4x + 3 4x + 4 4x 4x + 1 2 3 4 0 1 x + 2 x + 3 x + 4 x x + 1
2x + 3 2x + 3 2x + 4 2x 2x + 1 2x + 2 3x + 3 3x + 4 3x 3x + 1 3x + 2 4x + 3 4x + 4 4x 4x + 1 4x + 2 3 4 0 1 2 x + 3 x + 4 x x + 1 x + 2
2x + 4 2x + 4 2x 2x + 1 2x + 2 2x + 3 3x + 4 3x 3x + 1 3x + 2 3x + 3 4x + 4 4x 4x + 1 4x + 2 4x + 3 4 0 1 2 3 x + 4 x x + 1 x + 2 x + 3
3x 3x 3x + 1 3x + 2 3x + 3 3x + 4 4x 4x + 1 4x + 2 4x + 3 4x + 4 0 1 2 3 4 x x + 1 x + 2 x + 3 x + 4 2x 2x + 1 2x + 2 2x + 3 2x + 4
3x + 1 3x + 1 3x + 2 3x + 3 3x + 4 3x 4x + 1 4x + 2 4x + 3 4x + 4 4x 1 2 3 4 0 x + 1 x + 2 x + 3 x + 4 x 2x + 1 2x + 2 2x + 3 2x + 4 2x
3x + 2 3x + 2 3x + 3 3x + 4 3x 3x + 1 4x + 2 4x + 3 4x + 4 4x 4x + 1 2 3 4 0 1 x + 2 x + 3 x + 4 x x + 1 2x + 2 2x + 3 2x + 4 2x 2x + 1
3x + 3 3x + 3 3x + 4 3x 3x + 1 3x + 2 4x + 3 4x + 4 4x 4x + 1 4x + 2 3 4 0 1 2 x + 3 x + 4 x x + 1 x + 2 2x + 3 2x + 4 2x 2x + 1 2x + 2
3x + 4 3x + 4 3x 3x + 1 3x + 2 3x + 3 4x + 4 4x 4x + 1 4x + 2 4x + 3 4 0 1 2 3 x + 4 x x + 1 x + 2 x + 3 2x + 4 2x 2x + 1 2x + 2 2x + 3
4x 4x 4x + 1 4x + 2 4x + 3 4x + 4 0 1 2 3 4 x x + 1 x + 2 x + 3 x + 4 2x 2x + 1 2x + 2 2x + 3 2x + 4 3x 3x + 1 3x + 2 3x + 3 3x + 4
4x + 1 4x + 1 4x + 2 4x + 3 4x + 4 4x 1 2 3 4 0 x + 1 x + 2 x + 3 x + 4 x 2x + 1 2x + 2 2x + 3 2x + 4 2x 3x + 1 3x + 2 3x + 3 3x + 4 3x
4x + 2 4x + 2 4x + 3 4x + 4 4x 4x + 1 2 3 4 0 1 x + 2 x + 3 x + 4 x x + 1 2x + 2 2x + 3 2x + 4 2x 2x + 1 3x + 2 3x + 3 3x + 4 3x 3x + 1
4x + 3 4x + 3 4x + 4 4x 4x + 1 4x + 2 3 4 0 1 2 x + 3 x + 4 x x + 1 x + 2 2x + 3 2x + 4 2x 2x + 1 2x + 2 3x + 3 3x + 4 3x 3x + 1 3x + 2
4x + 4 4x + 4 4x 4x + 1 4x + 2 4x + 3 4 0 1 2 3 x + 4 x x + 1 x + 2 x + 3 2x + 4 2x 2x + 1 2x + 2 2x + 3 3x + 4 3x 3x + 1 3x + 2 3x + 3


\cdot 0 1 2 3 4 x x + 1 x + 2 x + 3 x + 4 2x 2x + 1 2x + 2 2x + 3 2x + 4 3x 3x + 1 3x + 2 3x + 3 3x + 4 4x 4x + 1 4x + 2 4x + 3 4x + 4
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
1 0 1 2 3 4 x x + 1 x + 2 x + 3 x + 4 2x 2x + 1 2x + 2 2x + 3 2x + 4 3x 3x + 1 3x + 2 3x + 3 3x + 4 4x 4x + 1 4x + 2 4x + 3 4x + 4
2 0 2 4 1 3 2x 2x + 2 2x + 4 2x + 1 2x + 3 4x 4x + 2 4x + 4 4x + 1 4x + 3 x x + 2 x + 4 x + 1 x + 3 3x 3x + 2 3x + 4 3x + 1 3x + 3
3 0 3 1 4 2 3x 3x + 3 3x + 1 3x + 4 3x + 2 x x + 3 x + 1 x + 4 x + 2 4x 4x + 3 4x + 1 4x + 4 4x + 2 2x 2x + 3 2x + 1 2x + 4 2x + 2
4 0 4 3 2 1 4x 4x + 4 4x + 3 4x + 2 4x + 1 3x 3x + 4 3x + 3 3x + 2 3x + 1 2x 2x + 4 2x + 3 2x + 2 2x + 1 x x + 4 x + 3 x + 2 x + 1
x 0 x 2x 3x 4x 4x + 3 3 x + 3 2x + 3 3x + 3 3x + 1 4x + 1 1 x + 1 2x + 1 2x + 4 3x + 4 4x + 4 4 x + 4 x + 2 2x + 2 3x + 2 4x + 2 2
x + 1 0 x + 1 2x + 2 3x + 3 4x + 4 3 x + 4 2x 3x + 1 4x + 2 1 x + 2 2x + 3 3x + 4 4x 4 x 2x + 1 3x + 2 4x + 3 2 x + 3 2x + 4 3x 4x + 1
x + 2 0 x + 2 2x + 4 3x + 1 4x + 3 x + 3 2x 3x + 2 4x + 4 1 2x + 1 3x + 3 4x 2 x + 4 3x + 4 4x + 1 3 x 2x + 2 4x + 2 4 x + 1 2x + 3 3x
x + 3 0 x + 3 2x + 1 3x + 4 4x + 2 2x + 3 3x + 1 4x + 4 2 x 4x + 1 4 x + 2 2x 3x + 3 x + 4 2x + 2 3x 4x + 3 1 3x + 2 4x 3 x + 1 2x + 4
x + 4 0 x + 4 2x + 3 3x + 2 4x + 1 3x + 3 4x + 2 1 x 2x + 4 x + 1 2x 3x + 4 4x + 3 2 4x + 4 3 x + 2 2x + 1 3x 2x + 2 3x + 1 4x 4 x + 3
2x 0 2x 4x x 3x 3x + 1 1 2x + 1 4x + 1 x + 1 x + 2 3x + 2 2 2x + 2 4x + 2 4x + 3 x + 3 3x + 3 3 2x + 3 2x + 4 4x + 4 x + 4 3x + 4 4
2x + 1 0 2x + 1 4x + 2 x + 3 3x + 4 4x + 1 x + 2 3x + 3 4 2x 3x + 2 3 2x + 4 4x x + 1 2x + 3 4x + 4 x 3x + 1 2 x + 4 3x 1 2x + 2 4x + 3
2x + 2 0 2x + 2 4x + 4 x + 1 3x + 3 1 2x + 3 4x x + 2 3x + 4 2 2x + 4 4x + 1 x + 3 3x 3 2x 4x + 2 x + 4 3x + 1 4 2x + 1 4x + 3 x 3x + 2
2x + 3 0 2x + 3 4x + 1 x + 4 3x + 2 x + 1 3x + 4 2 2x 4x + 3 2x + 2 4x x + 3 3x + 1 4 3x + 3 1 2x + 4 4x + 2 x 4x + 4 x + 2 3x 3 2x + 1
2x + 4 0 2x + 4 4x + 3 x + 2 3x + 1 2x + 1 4x x + 4 3x + 3 2 4x + 2 x + 1 3x 4 2x + 3 x + 3 3x + 2 1 2x 4x + 4 3x + 4 3 2x + 2 4x + 1 x
3x 0 3x x 4x 2x 2x + 4 4 3x + 4 x + 4 4x + 4 4x + 3 2x + 3 3 3x + 3 x + 3 x + 2 4x + 2 2x + 2 2 3x + 2 3x + 1 x + 1 4x + 1 2x + 1 1
3x + 1 0 3x + 1 x + 2 4x + 3 2x + 4 3x + 4 x 4x + 1 2x + 2 3 x + 3 4x + 4 2x 1 3x + 2 4x + 2 2x + 3 4 3x x + 1 2x + 1 2 3x + 3 x + 4 4x
3x + 2 0 3x + 2 x + 4 4x + 1 2x + 3 4x + 4 2x + 1 3 3x x + 2 3x + 3 x 4x + 2 2x + 4 1 2x + 2 4 3x + 1 x + 3 4x x + 1 4x + 3 2x 2 3x + 4
3x + 3 0 3x + 3 x + 1 4x + 4 2x + 2 4 3x + 2 x 4x + 3 2x + 1 3 3x + 1 x + 4 4x + 2 2x 2 3x x + 3 4x + 1 2x + 4 1 3x + 4 x + 2 4x 2x + 3
3x + 4 0 3x + 4 x + 3 4x + 2 2x + 1 x + 4 4x + 3 2x + 2 1 3x 2x + 3 2 3x + 1 x 4x + 4 3x + 2 x + 1 4x 2x + 4 3 4x + 1 2x 4 3x + 3 x + 2
4x 0 4x 3x 2x x x + 2 2 4x + 2 3x + 2 2x + 2 2x + 4 x + 4 4 4x + 4 3x + 4 3x + 1 2x + 1 x + 1 1 4x + 1 4x + 3 3x + 3 2x + 3 x + 3 3
4x + 1 0 4x + 1 3x + 2 2x + 3 x + 4 2x + 2 x + 3 4 4x 3x + 1 4x + 4 3x 2x + 1 x + 2 3 x + 1 2 4x + 3 3x + 4 2x 3x + 3 2x + 4 x 1 4x + 2
4x + 2 0 4x + 2 3x + 4 2x + 1 x + 3 3x + 2 2x + 4 x + 1 3 4x x + 4 1 4x + 3 3x 2x + 2 4x + 1 3x + 3 2x x + 2 4 2x + 3 x 2 4x + 4 3x + 1
4x + 3 0 4x + 3 3x + 1 2x + 4 x + 2 4x + 2 3x 2x + 3 x + 1 4 3x + 4 2x + 2 x 3 4x + 1 2x + 1 x + 4 2 4x 3x + 3 x + 3 1 4x + 4 3x + 2 2x
4x + 4 0 4x + 4 3x + 3 2x + 2 x + 1 2 4x + 1 3x 2x + 4 x + 3 4 4x + 3 3x + 2 2x + 1 x 1 4x 3x + 4 2x + 3 x + 2 3 4x + 2 3x + 1 2x x + 4

Operationstafeln für {\mathbb F}_{27}

Endlicher Körper/27/Operationstafeln

Operationstafeln für {\mathbb F}_{32}

Endlicher Körper/32/Operationstafeln

Operationstafeln für {\mathbb F}_{64}

Endlicher Körper/64/Operationstafeln

Operationstafeln für {\mathbb F}_{81}

Endlicher Körper/81/Operationstafeln

Operationstafeln für {\mathbb F}_{121}

Endlicher Körper/121/Operationstafeln

Operationstafeln für {\mathbb F}_{125}

Endlicher Körper/125/Operationstafeln

Operationstafeln für {\mathbb F}_{128}

Endlicher Körper/128/Operationstafeln

Von „http://de.wikiversity.org/wiki/Endliche_K%C3%B6rper/Nicht_Primk%C3%B6rper/Einige_Operationstafeln“
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