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Is it possible, that $p^t$ (with a prime number $p \in \mathbb N$ and $t \in \mathbb N$) is a unit in an algebraic number field $K$ (e.g. a unit in the ring of integers $\mathcal O_K$) ? And if not, why it is not possible?

Thanks in advance,

David

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    What is the minimal polynomial of its inverse in $K$? Can it ever be monic? Equivalently, what is its norm? Can it ever be $\pm 1$?2011-06-28

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