Let $k$ be an algebraic number field.cShow that $O_k$ is a principal ideal domain if and only if it satisfies the following condition: for every $\alpha\in k$, but $\alpha\not\in O_k$,there are $\beta,\gamma\in O_{k}$ such that $0<|\alpha\beta-\gamma|<1$. I want to prove $h(k)=1$. But I don't know how to find $\beta$$\gamma$


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