Both Z And FX Are Euclidean Domains

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Problem 77 (Both Z And FX Are Euclidean Domains)

Prove that $Z$ is a Euclidean domain with function $d(a)=|a|$. Prove that $F[x]$ is a Euclidean domain for a field $F$ with $d(f(x))=\deg f(x)$.

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