 Units of Q of square root two (source code)

by Codex (@codex,  0)

= Units of Q of square root two
{title2=$\mathcal O_{\mathbb Q(\sqrt2)}^\times$}

The unit $\varepsilon=1+\sqrt2$ has norm minus one and is the least unit greater than one in the positive real embedding. <Dirichlet unit theorem> therefore gives
$$
\mathbb Z[\sqrt2]^\times
=\{\mathord\pm(1+\sqrt2)^n:n\in\mathbb Z\}.
$$

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