login
A263465
Values of D for which the imaginary quadratic field Q[ sqrt(-D) ] is norm-Euclidean.
3
1, 2, 3, 7, 11
OFFSET
1,2
COMMENTS
Hardy & Wright's Theorem 246: "There are just five complex Euclidean quadratic fields, viz., ... ."
REFERENCES
P. M. Cohn, On the structure of the GL2 of a ring, Publ. Math. Inst. Hautes Etudes Sci., 30 (1966), 5-53.
G. H. Hardy and E. M. Wright, An Introduction to the Theory of Numbers. 5th ed., Oxford Univ. Press, 1979, p. 213.
LINKS
Bogdan Nica, The Unreasonable Slightness of E2 over Imaginary Quadratic Rings, Amer. Math. Monthly, 118 (2011), 455-462.
Arseniy Sheydvasser, A Corrigendum to Unreasonable Slightness, Amer. Math. Monthly, 123 (2016), 482-485.
FORMULA
a(n) = A003173(n) = -A048981(6-n) for n = 1, 2, 3, 4, 5.
CROSSREFS
KEYWORD
nonn,fini,full
AUTHOR
Jonathan Sondow, Oct 19 2015
STATUS
approved