On the verification of Clark's example of a euclidean but not norm-euclidean number field

Niklasch, Gerhard

doi:10.1007/bf02567625

Cited by 2 publications

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“…The earliest known example of a quadratic Euclidean field that is not norm-Euclidean is Q( √ 69) ( [85,390]). Since Samuel asked the question, much has been done to find a function other than the norm which makes Z[ √ 14] Euclidean (see [290] In 1979, Lenstra [294] introduced the notion of a Euclidean ideal class which generalizes that of a Euclidean ring.…”

Section: Theorem 5 (Grh)mentioning

confidence: 99%

“…Harper's proof that Z[ √ 14] is Euclidean, but not norm-Euclidean, answered a question that had inspired a great deal of mathematical activity. The earliest known example of a quadratic Euclidean field that is not norm-Euclidean is Q( √ 69) ( [85,390]). Since Samuel asked the question, much has been done to find a function other than the norm which makes Z[ √ 14] Euclidean (see [290]).…”

Section: The Indicator Functionmentioning

confidence: 99%

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Artin's Primitive Root Conjecture – A Survey

Moree

2012

Integers

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Abstract. One of the first concepts one meets in elementary number theory is that of the multiplicative order. We give a survey of the literature on this topic emphasizing the Artin primitive root conjecture (1927). The first part of the survey is intended for a rather general audience and rather colloquial, whereas the second part is intended for number theorists and ends with several open problems. The contributions in the survey on 'elliptic Artin' are due to Alina Cojocaru. Wojciec Gajda wrote a section on 'Artin for K-theory of number fields', and Hester Graves (together with me) on 'Artin's conjecture and Euclidean domains'.

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Section: Theorem 5 (Grh)mentioning

confidence: 99%

Section: The Indicator Functionmentioning

confidence: 99%