Endlicher Körper/25/Operationstafeln

Wir nehmen die Darstellung

${𝔽}_{25}\cong {𝔽}_5[X]/(X^2+X+2)$.

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

$+$

$0$

$1$

$2$

$3$

$4$

$x$

$x+1$

$x+2$

$x+3$

$x+4$

$2x$

$2x+1$

$2x+2$

$2x+3$

$2x+4$

$3x$

$3x+1$

$3x+2$

$3x+3$

$3x+4$

$4x$

$4x+1$

$4x+2$

$4x+3$

$4x+4$

$0$

$0$

$1$

$2$

$3$

$4$

$x$

$x+1$

$x+2$

$x+3$

$x+4$

$2x$

$2x+1$

$2x+2$

$2x+3$

$2x+4$

$3x$

$3x+1$

$3x+2$

$3x+3$

$3x+4$

$4x$

$4x+1$

$4x+2$

$4x+3$

$4x+4$

$1$

$1$

$2$

$3$

$4$

$0$

$x+1$

$x+2$

$x+3$

$x+4$

$x$

$2x+1$

$2x+2$

$2x+3$

$2x+4$

$2x$

$3x+1$

$3x+2$

$3x+3$

$3x+4$

$3x$

$4x+1$

$4x+2$

$4x+3$

$4x+4$

$4x$

$2$

$2$

$3$

$4$

$0$

$1$

$x+2$

$x+3$

$x+4$

$x$

$x+1$

$2x+2$

$2x+3$

$2x+4$

$2x$

$2x+1$

$3x+2$

$3x+3$

$3x+4$

$3x$

$3x+1$

$4x+2$

$4x+3$

$4x+4$

$4x$

$4x+1$

$3$

$3$

$4$

$0$

$1$

$2$

$x+3$

$x+4$

$x$

$x+1$

$x+2$

$2x+3$

$2x+4$

$2x$

$2x+1$

$2x+2$

$3x+3$

$3x+4$

$3x$

$3x+1$

$3x+2$

$4x+3$

$4x+4$

$4x$

$4x+1$

$4x+2$

$4$

$4$

$0$

$1$

$2$

$3$

$x+4$

$x$

$x+1$

$x+2$

$x+3$

$2x+4$

$2x$

$2x+1$

$2x+2$

$2x+3$

$3x+4$

$3x$

$3x+1$

$3x+2$

$3x+3$

$4x+4$

$4x$

$4x+1$

$4x+2$

$4x+3$

$x$

$x$

$x+1$

$x+2$

$x+3$

$x+4$

$2x$

$2x+1$

$2x+2$

$2x+3$

$2x+4$

$3x$

$3x+1$

$3x+2$

$3x+3$

$3x+4$

$4x$

$4x+1$

$4x+2$

$4x+3$

$4x+4$

$0$

$1$

$2$

$3$

$4$

$x+1$

$x+1$

$x+2$

$x+3$

$x+4$

$x$

$2x+1$

$2x+2$

$2x+3$

$2x+4$

$2x$

$3x+1$

$3x+2$

$3x+3$

$3x+4$

$3x$

$4x+1$

$4x+2$

$4x+3$

$4x+4$

$4x$

$1$

$2$

$3$

$4$

$0$

$x+2$

$x+2$

$x+3$

$x+4$

$x$

$x+1$

$2x+2$

$2x+3$

$2x+4$

$2x$

$2x+1$

$3x+2$

$3x+3$

$3x+4$

$3x$

$3x+1$

$4x+2$

$4x+3$

$4x+4$

$4x$

$4x+1$

$2$

$3$

$4$

$0$

$1$

$x+3$

$x+3$

$x+4$

$x$

$x+1$

$x+2$

$2x+3$

$2x+4$

$2x$

$2x+1$

$2x+2$

$3x+3$

$3x+4$

$3x$

$3x+1$

$3x+2$

$4x+3$

$4x+4$

$4x$

$4x+1$

$4x+2$

$3$

$4$

$0$

$1$

$2$

$x+4$

$x+4$

$x$

$x+1$

$x+2$

$x+3$

$2x+4$

$2x$

$2x+1$

$2x+2$

$2x+3$

$3x+4$

$3x$

$3x+1$

$3x+2$

$3x+3$

$4x+4$

$4x$

$4x+1$

$4x+2$

$4x+3$

$4$

$0$

$1$

$2$

$3$

$2x$

$2x$

$2x+1$

$2x+2$

$2x+3$

$2x+4$

$3x$

$3x+1$

$3x+2$

$3x+3$

$3x+4$

$4x$

$4x+1$

$4x+2$

$4x+3$

$4x+4$

$0$

$1$

$2$

$3$

$4$

$x$

$x+1$

$x+2$

$x+3$

$x+4$

$2x+1$

$2x+1$

$2x+2$

$2x+3$

$2x+4$

$2x$

$3x+1$

$3x+2$

$3x+3$

$3x+4$

$3x$

$4x+1$

$4x+2$

$4x+3$

$4x+4$

$4x$

$1$

$2$

$3$

$4$

$0$

$x+1$

$x+2$

$x+3$

$x+4$

$x$

$2x+2$

$2x+2$

$2x+3$

$2x+4$

$2x$

$2x+1$

$3x+2$

$3x+3$

$3x+4$

$3x$

$3x+1$

$4x+2$

$4x+3$

$4x+4$

$4x$

$4x+1$

$2$

$3$

$4$

$0$

$1$

$x+2$

$x+3$

$x+4$

$x$

$x+1$

$2x+3$

$2x+3$

$2x+4$

$2x$

$2x+1$

$2x+2$

$3x+3$

$3x+4$

$3x$

$3x+1$

$3x+2$

$4x+3$

$4x+4$

$4x$

$4x+1$

$4x+2$

$3$

$4$

$0$

$1$

$2$

$x+3$

$x+4$

$x$

$x+1$

$x+2$

$2x+4$

$2x+4$

$2x$

$2x+1$

$2x+2$

$2x+3$

$3x+4$

$3x$

$3x+1$

$3x+2$

$3x+3$

$4x+4$

$4x$

$4x+1$

$4x+2$

$4x+3$

$4$

$0$

$1$

$2$

$3$

$x+4$

$x$

$x+1$

$x+2$

$x+3$

$3x$

$3x$

$3x+1$

$3x+2$

$3x+3$

$3x+4$

$4x$

$4x+1$

$4x+2$

$4x+3$

$4x+4$

$0$

$1$

$2$

$3$

$4$

$x$

$x+1$

$x+2$

$x+3$

$x+4$

$2x$

$2x+1$

$2x+2$

$2x+3$

$2x+4$

$3x+1$

$3x+1$

$3x+2$

$3x+3$

$3x+4$

$3x$

$4x+1$

$4x+2$

$4x+3$

$4x+4$

$4x$

$1$

$2$

$3$

$4$

$0$

$x+1$

$x+2$

$x+3$

$x+4$

$x$

$2x+1$

$2x+2$

$2x+3$

$2x+4$

$2x$

$3x+2$

$3x+2$

$3x+3$

$3x+4$

$3x$

$3x+1$

$4x+2$

$4x+3$

$4x+4$

$4x$

$4x+1$

$2$

$3$

$4$

$0$

$1$

$x+2$

$x+3$

$x+4$

$x$

$x+1$

$2x+2$

$2x+3$

$2x+4$

$2x$

$2x+1$

$3x+3$

$3x+3$

$3x+4$

$3x$

$3x+1$

$3x+2$

$4x+3$

$4x+4$

$4x$

$4x+1$

$4x+2$

$3$

$4$

$0$

$1$

$2$

$x+3$

$x+4$

$x$

$x+1$

$x+2$

$2x+3$

$2x+4$

$2x$

$2x+1$

$2x+2$

$3x+4$

$3x+4$

$3x$

$3x+1$

$3x+2$

$3x+3$

$4x+4$

$4x$

$4x+1$

$4x+2$

$4x+3$

$4$

$0$

$1$

$2$

$3$

$x+4$

$x$

$x+1$

$x+2$

$x+3$

$2x+4$

$2x$

$2x+1$

$2x+2$

$2x+3$

$4x$

$4x$

$4x+1$

$4x+2$

$4x+3$

$4x+4$

$0$

$1$

$2$

$3$

$4$

$x$

$x+1$

$x+2$

$x+3$

$x+4$

$2x$

$2x+1$

$2x+2$

$2x+3$

$2x+4$

$3x$

$3x+1$

$3x+2$

$3x+3$

$3x+4$

$4x+1$

$4x+1$

$4x+2$

$4x+3$

$4x+4$

$4x$

$1$

$2$

$3$

$4$

$0$

$x+1$

$x+2$

$x+3$

$x+4$

$x$

$2x+1$

$2x+2$

$2x+3$

$2x+4$

$2x$

$3x+1$

$3x+2$

$3x+3$

$3x+4$

$3x$

$4x+2$

$4x+2$

$4x+3$

$4x+4$

$4x$

$4x+1$

$2$

$3$

$4$

$0$

$1$

$x+2$

$x+3$

$x+4$

$x$

$x+1$

$2x+2$

$2x+3$

$2x+4$

$2x$

$2x+1$

$3x+2$

$3x+3$

$3x+4$

$3x$

$3x+1$

$4x+3$

$4x+3$

$4x+4$

$4x$

$4x+1$

$4x+2$

$3$

$4$

$0$

$1$

$2$

$x+3$

$x+4$

$x$

$x+1$

$x+2$

$2x+3$

$2x+4$

$2x$

$2x+1$

$2x+2$

$3x+3$

$3x+4$

$3x$

$3x+1$

$3x+2$

$4x+4$

$4x+4$

$4x$

$4x+1$

$4x+2$

$4x+3$

$4$

$0$

$1$

$2$

$3$

$x+4$

$x$

$x+1$

$x+2$

$x+3$

$2x+4$

$2x$

$2x+1$

$2x+2$

$2x+3$

$3x+4$

$3x$

$3x+1$

$3x+2$

$3x+3$

$\cdot$

$0$

$1$

$2$

$3$

$4$

$x$

$x+1$

$x+2$

$x+3$

$x+4$

$2x$

$2x+1$

$2x+2$

$2x+3$

$2x+4$

$3x$

$3x+1$

$3x+2$

$3x+3$

$3x+4$

$4x$

$4x+1$

$4x+2$

$4x+3$

$4x+4$

$0$

$0$

$0$

$0$

$0$

$0$

$0$

$0$

$0$

$0$

$0$

$0$

$0$

$0$

$0$

$0$

$0$

$0$

$0$

$0$

$0$

$0$

$0$

$0$

$0$

$0$

$1$

$0$

$1$

$2$

$3$

$4$

$x$

$x+1$

$x+2$

$x+3$

$x+4$

$2x$

$2x+1$

$2x+2$

$2x+3$

$2x+4$

$3x$

$3x+1$

$3x+2$

$3x+3$

$3x+4$

$4x$

$4x+1$

$4x+2$

$4x+3$

$4x+4$

$2$

$0$

$2$

$4$

$1$

$3$

$2x$

$2x+2$

$2x+4$

$2x+1$

$2x+3$

$4x$

$4x+2$

$4x+4$

$4x+1$

$4x+3$

$x$

$x+2$

$x+4$

$x+1$

$x+3$

$3x$

$3x+2$

$3x+4$

$3x+1$

$3x+3$

$3$

$0$

$3$

$1$

$4$

$2$

$3x$

$3x+3$

$3x+1$

$3x+4$

$3x+2$

$x$

$x+3$

$x+1$

$x+4$

$x+2$

$4x$

$4x+3$

$4x+1$

$4x+4$

$4x+2$

$2x$

$2x+3$

$2x+1$

$2x+4$

$2x+2$

$4$

$0$

$4$

$3$

$2$

$1$

$4x$

$4x+4$

$4x+3$

$4x+2$

$4x+1$

$3x$

$3x+4$

$3x+3$

$3x+2$

$3x+1$

$2x$

$2x+4$

$2x+3$

$2x+2$

$2x+1$

$x$

$x+4$

$x+3$

$x+2$

$x+1$

$x$

$0$

$x$

$2x$

$3x$

$4x$

$4x+3$

$3$

$x+3$

$2x+3$

$3x+3$

$3x+1$

$4x+1$

$1$

$x+1$

$2x+1$

$2x+4$

$3x+4$

$4x+4$

$4$

$x+4$

$x+2$

$2x+2$

$3x+2$

$4x+2$

$2$

$x+1$

$0$

$x+1$

$2x+2$

$3x+3$

$4x+4$

$3$

$x+4$

$2x$

$3x+1$

$4x+2$

$1$

$x+2$

$2x+3$

$3x+4$

$4x$

$4$

$x$

$2x+1$

$3x+2$

$4x+3$

$2$

$x+3$

$2x+4$

$3x$

$4x+1$

$x+2$

$0$

$x+2$

$2x+4$

$3x+1$

$4x+3$

$x+3$

$2x$

$3x+2$

$4x+4$

$1$

$2x+1$

$3x+3$

$4x$

$2$

$x+4$

$3x+4$

$4x+1$

$3$

$x$

$2x+2$

$4x+2$

$4$

$x+1$

$2x+3$

$3x$

$x+3$

$0$

$x+3$

$2x+1$

$3x+4$

$4x+2$

$2x+3$

$3x+1$

$4x+4$

$2$

$x$

$4x+1$

$4$

$x+2$

$2x$

$3x+3$

$x+4$

$2x+2$

$3x$

$4x+3$

$1$

$3x+2$

$4x$

$3$

$x+1$

$2x+4$

$x+4$

$0$

$x+4$

$2x+3$

$3x+2$

$4x+1$

$3x+3$

$4x+2$

$1$

$x$

$2x+4$

$x+1$

$2x$

$3x+4$

$4x+3$

$2$

$4x+4$

$3$

$x+2$

$2x+1$

$3x$

$2x+2$

$3x+1$

$4x$

$4$

$x+3$

$2x$

$0$

$2x$

$4x$

$x$

$3x$

$3x+1$

$1$

$2x+1$

$4x+1$

$x+1$

$x+2$

$3x+2$

$2$

$2x+2$

$4x+2$

$4x+3$

$x+3$

$3x+3$

$3$

$2x+3$

$2x+4$

$4x+4$

$x+4$

$3x+4$

$4$

$2x+1$

$0$

$2x+1$

$4x+2$

$x+3$

$3x+4$

$4x+1$

$x+2$

$3x+3$

$4$

$2x$

$3x+2$

$3$

$2x+4$

$4x$

$x+1$

$2x+3$

$4x+4$

$x$

$3x+1$

$2$

$x+4$

$3x$

$1$

$2x+2$

$4x+3$

$2x+2$

$0$

$2x+2$

$4x+4$

$x+1$

$3x+3$

$1$

$2x+3$

$4x$

$x+2$

$3x+4$

$2$

$2x+4$

$4x+1$

$x+3$

$3x$

$3$

$2x$

$4x+2$

$x+4$

$3x+1$

$4$

$2x+1$

$4x+3$

$x$

$3x+2$

$2x+3$

$0$

$2x+3$

$4x+1$

$x+4$

$3x+2$

$x+1$

$3x+4$

$2$

$2x$

$4x+3$

$2x+2$

$4x$

$x+3$

$3x+1$

$4$

$3x+3$

$1$

$2x+4$

$4x+2$

$x$

$4x+4$

$x+2$

$3x$

$3$

$2x+1$

$2x+4$

$0$

$2x+4$

$4x+3$

$x+2$

$3x+1$

$2x+1$

$4x$

$x+4$

$3x+3$

$2$

$4x+2$

$x+1$

$3x$

$4$

$2x+3$

$x+3$

$3x+2$

$1$

$2x$

$4x+4$

$3x+4$

$3$

$2x+2$

$4x+1$

$x$

$3x$

$0$

$3x$

$x$

$4x$

$2x$

$2x+4$

$4$

$3x+4$

$x+4$

$4x+4$

$4x+3$

$2x+3$

$3$

$3x+3$

$x+3$

$x+2$

$4x+2$

$2x+2$

$2$

$3x+2$

$3x+1$

$x+1$

$4x+1$

$2x+1$

$1$

$3x+1$

$0$

$3x+1$

$x+2$

$4x+3$

$2x+4$

$3x+4$

$x$

$4x+1$

$2x+2$

$3$

$x+3$

$4x+4$

$2x$

$1$

$3x+2$

$4x+2$

$2x+3$

$4$

$3x$

$x+1$

$2x+1$

$2$

$3x+3$

$x+4$

$4x$

$3x+2$

$0$

$3x+2$

$x+4$

$4x+1$

$2x+3$

$4x+4$

$2x+1$

$3$

$3x$

$x+2$

$3x+3$

$x$

$4x+2$

$2x+4$

$1$

$2x+2$

$4$

$3x+1$

$x+3$

$4x$

$x+1$

$4x+3$

$2x$

$2$

$3x+4$

$3x+3$

$0$

$3x+3$

$x+1$

$4x+4$

$2x+2$

$4$

$3x+2$

$x$

$4x+3$

$2x+1$

$3$

$3x+1$

$x+4$

$4x+2$

$2x$

$2$

$3x$

$x+3$

$4x+1$

$2x+4$

$1$

$3x+4$

$x+2$

$4x$

$2x+3$

$3x+4$

$0$

$3x+4$

$x+3$

$4x+2$

$2x+1$

$x+4$

$4x+3$

$2x+2$

$1$

$3x$

$2x+3$

$2$

$3x+1$

$x$

$4x+4$

$3x+2$

$x+1$

$4x$

$2x+4$

$3$

$4x+1$

$2x$

$4$

$3x+3$

$x+2$

$4x$

$0$

$4x$

$3x$

$2x$

$x$

$x+2$

$2$

$4x+2$

$3x+2$

$2x+2$

$2x+4$

$x+4$

$4$

$4x+4$

$3x+4$

$3x+1$

$2x+1$

$x+1$

$1$

$4x+1$

$4x+3$

$3x+3$

$2x+3$

$x+3$

$3$

$4x+1$

$0$

$4x+1$

$3x+2$

$2x+3$

$x+4$

$2x+2$

$x+3$

$4$

$4x$

$3x+1$

$4x+4$

$3x$

$2x+1$

$x+2$

$3$

$x+1$

$2$

$4x+3$

$3x+4$

$2x$

$3x+3$

$2x+4$

$x$

$1$

$4x+2$

$4x+2$

$0$

$4x+2$

$3x+4$

$2x+1$

$x+3$

$3x+2$

$2x+4$

$x+1$

$3$

$4x$

$x+4$

$1$

$4x+3$

$3x$

$2x+2$

$4x+1$

$3x+3$

$2x$

$x+2$

$4$

$2x+3$

$x$

$2$

$4x+4$

$3x+1$

$4x+3$

$0$

$4x+3$

$3x+1$

$2x+4$

$x+2$

$4x+2$

$3x$

$2x+3$

$x+1$

$4$

$3x+4$

$2x+2$

$x$

$3$

$4x+1$

$2x+1$

$x+4$

$2$

$4x$

$3x+3$

$x+3$

$1$

$4x+4$

$3x+2$

$2x$

$4x+4$

$0$

$4x+4$

$3x+3$

$2x+2$

$x+1$

$2$

$4x+1$

$3x$

$2x+4$

$x+3$

$4$

$4x+3$

$3x+2$

$2x+1$

$x$

$1$

$4x$

$3x+4$

$2x+3$

$x+2$

$3$

$4x+2$

$3x+1$

$2x$

$x+4$