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A048981
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Squarefree values of n for which the quadratic field Q[ sqrt(n) ] is norm-Euclidean.
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8
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-11, -7, -3, -2, -1, 2, 3, 5, 6, 7, 11, 13, 17, 19, 21, 29, 33, 37, 41, 57, 73
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OFFSET
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1,1
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COMMENTS
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These are norm-Euclidean fields, excluding for instance Q[sqrt(69)] which is Euclidean but not for norm. - Marc A. A. van Leeuwen, Feb 15 2011
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REFERENCES
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H. Cohn, A Second Course in Number Theory, Wiley, NY, 1962, pp. 107, 109.
G. H. Hardy and E. M. Wright, An Introduction to the Theory of Numbers. 3rd ed., Oxford Univ. Press, 1954, p. 213.
K. Inkeri, Über den Euklidischen Algorithmus in quadratischen Zahlkörpern. Ann. Acad. Sci. Fennicae Ser. A. 1. Math.-Phys., No. 41, 1-35, 1947. [Incorrectly gives 97 as a member of this sequence.]
W. J. LeVeque, Topics in Number Theory. Addison-Wesley, Reading, MA, 2 vols., 1956, Vol. 2, p. 57.
H. M. Stark, An Introduction to Number Theory. Markham, Chicago, 1970, p. 294.
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LINKS
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FORMULA
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MAPLE
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select(t -> traperror(numtheory:-factorEQ(-1, t)) <> lasterror, [$-11..77]); # Robert Israel, Jul 20 2016
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CROSSREFS
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KEYWORD
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fini,sign,full,nice
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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