consider $f(x)=x^4+5x^3+1$. Let $\alpha$ be a root of this polynomial and consider $K=\mathbb{Q}(\alpha)$. Which are the absolute values on $K$ extending the usual absolute values on $\mathbb{Q}$? Are these finitely many? In general, if $K$ is a number field how to find them? Thanks
2026-03-28 04:53:24.1774673604
Find valuations of $f(x)=x^4+5x^3+1$
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