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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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3
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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
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,1
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COMMENTS
| 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
| 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.
Inkeri, K. "Uber den Euklidischen Algorithmus in quadratischen Zahlk"orpern." 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
| A. Bogomolny, Strange Integers
P. Samuel, Unique factorization, Amer. Math. Monthly 75 (1968), 945-952.
Eric Weisstein's World of Mathematics, Quadratic Field
Index entries for sequences related to quadratic fields
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CROSSREFS
| Cf. A003174.
Sequence in context: A010185 A005603 A109828 * A132361 A155914 A087896
Adjacent sequences: A048978 A048979 A048980 * A048982 A048983 A048984
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KEYWORD
| fini,sign,full
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com), Jud McCranie (JudMcCranie(AT)ugaalum.uga.edu)
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EXTENSIONS
| Name corrected by Marc A. A. van Leeuwen (Marc.van-Leeuwen(AT)math.univ-poitiers.fr), Feb 15 2011
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