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Use of a computer scan to prove $ {\bf Q}(\sqrt{2+\sqrt 2})$ and $ {\bf Q}(\sqrt{3+\sqrt 2})$ are Euclidean

Authors: Harvey Cohn and Jesse Deutsch
Journal: Math. Comp. 46 (1986), 295-299
MSC: Primary 11R16; Secondary 11H50, 11Y40
MathSciNet review: 815850
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Abstract: The fields in the title are shown to be norm-Euclidean by a computer scan of the unit 4-cube representing coordinates of a field element translated by integers. The method is to subdivide this cube into sufficiently many small boxes so the norm is less than unity in each box, when referred to an appropriate "neighboring" integer.

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Keywords: Euclidean algorithm
Article copyright: © Copyright 1986 American Mathematical Society