Let $F$ be a field of order 4. Divide $x^2+1$ by $x+1$ in $F[x]$.
I have that $x^2+1=x(x+1)+(-x+1)$. I'm not sure how I can represent $-1$ without knowing the field? Is there a general method for polynomial division in general fields?
Polynomial Division in an arbitrary field
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field-theory
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0The field of order $4 = 2^2$ has characteristic $2$. So $1 = -1$. – 2017-02-17
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The field of order $4$ has characteristic $2$, so $-1 = 1$.