On the Euclidean nature of four cyclic cubic fields

On the Euclidean nature of four cyclic cubic fields
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by H. J. Godwin and J. R. Smith PDF

Math. Comp. 60 (1993), 421-423 Request permission

It is shown that the cyclic cubic fields with discriminants ${103^2},{109^2},{127^2}$, and ${157^2}$ are Euclidean

References

E. S. Barnes and H. P. F. Swinnerton-Dyer, The inhomogeneous minima of binary quadratic forms. I, Acta Math. 87 (1952), 259–323. MR 53162, DOI 10.1007/BF02392288
H. Heilbronn, On Euclid’s algorithm in cubic self-conjugate fields, Proc. Cambridge Philos. Soc. 46 (1950), 377–382. MR 35313, DOI 10.1017/s0305004100025883
P. A. Samet, The product of non-homogeneous linear forms. I, Proc. Cambridge Philos. Soc. 50 (1954), 372–379. MR 64820, DOI 10.1017/s0305004100029479
P. A. Samet, The product of non-homogeneous linear forms. II. The minimum of a class of non-homogeneous linear forms, Proc. Cambridge Philos. Soc. 50 (1954), 380–390. MR 64821, DOI 10.1017/s0305004100029480
J. R. Smith, On Euclid’s algorithm in some cyclic cubic fields, J. London Math. Soc. 44 (1969), 577–582. MR 240075, DOI 10.1112/jlms/s1-44.1.577