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# Norm-Euclidean domains

The following quadratic rings are norm-Euclidean: ${\displaystyle {\mathcal {O}}_{\mathbb {Q} ({\sqrt {-11}})}}$, ${\displaystyle {\mathcal {O}}_{\mathbb {Q} ({\sqrt {-7}})}}$, ${\displaystyle \mathbb {Z} [\omega ]}$, ${\displaystyle \mathbb {Z} [{\sqrt {-2}}]}$, ${\displaystyle \mathbb {Z} [i]}$, ${\displaystyle \mathbb {Z} [{\sqrt {2}}]}$, ${\displaystyle \mathbb {Z} [{\sqrt {3}}]}$, ${\displaystyle \mathbb {Z} [\phi ]}$, ${\displaystyle \mathbb {Z} [{\sqrt {6}}]}$, ${\displaystyle \mathbb {Z} [{\sqrt {7}}]}$, ${\displaystyle \mathbb {Z} [{\sqrt {11}}]}$, ${\displaystyle {\mathcal {O}}_{\mathbb {Q} ({\sqrt {13}})}}$, ${\displaystyle {\mathcal {O}}_{\mathbb {Q} ({\sqrt {17}})}}$, ${\displaystyle \mathbb {Z} [{\sqrt {19}}]}$, ${\displaystyle {\mathcal {O}}_{\mathbb {Q} ({\sqrt {21}})}}$, ${\displaystyle {\mathcal {O}}_{\mathbb {Q} ({\sqrt {29}})}}$, ${\displaystyle {\mathcal {O}}_{\mathbb {Q} ({\sqrt {33}})}}$, ${\displaystyle {\mathcal {O}}_{\mathbb {Q} ({\sqrt {37}})}}$, ${\displaystyle {\mathcal {O}}_{\mathbb {Q} ({\sqrt {41}})}}$, ${\displaystyle {\mathcal {O}}_{\mathbb {Q} ({\sqrt {57}})}}$, ${\displaystyle {\mathcal {O}}_{\mathbb {Q} ({\sqrt {73}})}}$ (see A048981).