Partialbruchzerlegung/Zmod5/1 durch (X^2)(X^3+X+1)/Aufgabe

a) Zeige, dass ${}X^{2}+2$ irreduzibel in ${}\mathbb {Z} /(5)[X]$ ist.

b) Zeige, dass ${}X^{3}+X+1$ irreduzibel in ${}\mathbb {Z} /(5)[X]$ ist.

{\frac {1}{{\left(X^{2}+2\right)}{\left(X^{3}+X+1\right)}}}

in

{}\mathbb {Z} /(5)(X)

.

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