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Hello Guys, i have the following problem.

I got the Ring $R = \mathbb{Z} /(x^7 -1)$ and the polynom f(x) = $x^6 - x^4 +x^3 + x^2 -1 \in R$ and want to compute the inverse of f(x), $f(x)^{-1}$. How do I do that?

Hello Guys, i have the following problem.

I got the Ring $R = \mathbb{Z} /(x^7 -1)$ and the polynom f(x) = $x^6 - x^4 +x^3 + x^2 -1 \in R$ and want to compute the inverse of f(x), $f(x)^{-1}$. How do I do that?