Hi,
How to check $x+4 \in <1+x+x^2+2x^3>$ in the ring $\mathbb{Z}_8[x]$, where
<1+x+x^2+2x^3> is the ideal generated by 1+x+x^2+2x^3?
If yes, how to find $g(x)$ so that $g(x) (1+x+x^2+2x^3)=x+4$?
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