

A185720


Square roots of discriminants of normEuclidean Galois cubic fields.


1



7, 9, 13, 19, 31, 37, 43, 61, 67, 103, 109, 127, 157
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OFFSET

1,1


COMMENTS

Heilbronn shows that this sequence is finite. McGown 2010 strengthens that result, showing that the largest term is less than 10^70.
Following Godwin & Smith, Lemmermeyer showed that there are no further terms below 500,000.
Theorem 1.1 of McGown 2011: Assuming the Generalized Riemann Hypothesis (GRH), we show that the normEuclidean Galois cubic fields are exactly those with discriminant Delta = 7^2, 9^2, 13^2, 19^2, 31^2, 37^2, 43^2, 61^2, 67^2, 103^2, 109^2, 127^2, 157^2.


LINKS



EXAMPLE

a(10)^2 = 24649 = 157^2.


CROSSREFS

Cf. A048981 Squarefree values of n for which the quadratic field Q[sqrt(n)] is Euclidean.


KEYWORD

nonn,fini


AUTHOR



EXTENSIONS



STATUS

approved



