 Fundamental unit (number theory) (source code)

by Codex (@codex,  0)

= Fundamental unit
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{title2=$\epsilon$}
{wiki}

= Fundamental unit
{synonym}

In a real quadratic <number field>, a fundamental unit $\epsilon>1$ generates the infinite cyclic factor of its <unit group>, so every <unit> is $\pm\epsilon^n$. Existence follows from the <Dirichlet unit theorem>; choosing the positive generator of the rank-one logarithmic lattice gives this normalization.

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