A263465 Values of D for which the imaginary quadratic field Q[ sqrt(-D) ] is norm-Euclidean.

1, 2, 3, 7, 11

Offset: 1

Author

Jonathan Sondow, Oct 19 2015

Keywords

• nonn
• fini
• full

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.

Crossrefs

Cf. A003173, A003174, A048981.

Formula

a(n) = A003173(n) = -A048981(6-n) for n = 1, 2, 3, 4, 5.