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Dirichlet unit theorem

For $K=\mathbb Q(\sqrt5)$,
$$
\mathcal O_K=\mathbb Z\left[\frac{1+\sqrt5}{2}\right].
$$
Writing $\phi=(1+\sqrt5)/2$, the full unit group is
$$
\mathcal O_K^\times=\{\mathord\pm\phi^n:n\in\mathbb Z\}.
$$


Units of the quadratic field Q square root of five

Past exam of the mathematics course of the University of Cambridge / 2018 / ii / Paper 2 / 20G / c / Solution

Past exam of the mathematics course of the University of Cambridge / 2024 / ii / Paper 2 / 20F / Solution

Units of the fifth cyclotomic field are real up to roots of unity

Units of the quadratic field Q square root of five

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Units of the quadratic field Q square root of five

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