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Mathematics of Computation
Mathematics of Computation
ISSN 1088-6842(online) ISSN 0025-5718(print)

 

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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Additional Information

DOI: http://dx.doi.org/10.1090/S0025-5718-1986-0815850-8
PII: S 0025-5718(1986)0815850-8
Keywords: Euclidean algorithm
Article copyright: © Copyright 1986 American Mathematical Society