References
F. Cajori, Pierre Laurent Wantzel,Bull. Amer. Math. Soc. 24(1918), 339–347
A. Cauchy,Oeuvres complètes, sér. 1, tome X, GauthierVillars, Paris 1897.
Comptes Rendus de ľAcadémie des Sciences 24 (1847)
L. E. Dickson,History of the theory of numbers, vol. II, Ch. XXVI, Chelsea, New York 1952 (reprint)
L. E. Dickson et al.,Algebraic numbers, Chelsea, Bronx, n. d. (reprint)
G. Lejeune Dirichlet,Werke, Chelsea, Bronx 1969 (reprint)
H. M. Edwards, The background of Kummer’s proof of Fermat’s last theorem for regular primes,Arch. History Exact Sci. 14 (1975), 219–236; Postscript, ibid. 17 (1977), 381–394
G. Eisenstein,Mathematische Werke, Chelsea, New York 1975
C. F. Gauss,Werke, Zweiter Band, Göttingen 1876
C. G. J. Jacobi,Gesammelte Werke, Sechster Band, Chelsea, New York 1969 (reprint)
E. E. Kummer,Collected Papers, Springer, Berlin 1975
R. B. Lakein, Eucliďs algorithm in complex quartic fields,Acta Arith. 20 (1972), 393–400
H. W. Lenstra{jrjr.}, Eucliďs algorithm in cyclotomic fields,J. London Math. Soc. (2) 10 (1975), 457–465
H. W. Lenstra, {jrJr.}, Quelques exemples ďanneaux euclidiens,C. R. Acad. Se. Paris, Sér. A, 286 (1978), 683–685
J. M. Masley, On Euclidean rings of integers in cyclotomic fields.J. Reine Angew. Math. 272 (1975), 45–48
J. M. Masley, H. L. Montgomery, Cyclotomic fields with unique factorization,J. Reine Angew. Math. 286/287 (1976), 248–256
T. Ojala, Eucliďs algorithm in the cyclotomic field Q(ζ 16),Math. Comp. 31 (1977), 268–273
J. Ouspensky, Note sur les nombres entiers dépendant ďune racine cinquième de ľunité,Math. Ann. 66 (1909), 109–112. Cf.Jbuch Fortschr. Math. 37 (1906) 241
H. J. S. Smith,Report on the theory of numbers, Chelsea, Bronx 1965 (reprint)
S. S. Wagstaff, {jrJr.}, The irregular primes to 125,000,Math. Comp. 32(1978), 583–591
A. Weil, La cyclotomie jadis et naguère,Sém. Bourbaki (1973/74), exp. 452,Lecture Notes Math. 431. Springer, Berlin 1975
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Lenstra, H.W., van der Poorten, A.J. Euclidean number fields 1. The Mathematical Intelligencer 2, 6–15 (1979). https://doi.org/10.1007/BF03024378
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DOI: https://doi.org/10.1007/BF03024378