A296818 Squarefree values of k for which the quadratic field Q[ sqrt(k) ] possesses a norm-Euclidean ideal class.

-15, -11, -7, -5, -3, -2, -1, 2, 3, 5, 6, 7, 10, 11, 13, 15, 17, 19, 21, 29, 33, 37, 41, 57, 73, 85

Offset: 1

Author

Robert C. Lyons, Dec 22 2017

Keywords

• fini
• sign
• full
• nice

Comments

This generalizes A048981, because the unit ideal of a norm-Euclidean number field is a norm-Euclidean ideal. In other words, this sequence is the union of {-15, -5, 10, 15, 85} and A048981.

Examples

			-5 is in the sequence because the ideal (2, 1+sqrt(-5)) is norm-Euclidean in the number field Q[ sqrt(-5) ].
		

Links

• Kelly Emmrich and Clark Lyons, Norm-Euclidean Ideals in Galois Cubic Fields, Slides, West Coast Number Theory, Dec 18 2017.
• H. W. Lenstra, Jr., Euclidean ideal classes, Soc. Math. France Astérisque, 1979, pp. 121-131.

Crossrefs

Cf. A003174, A048981.