Remote Access Mathematics of Computation
Green Open Access

Mathematics of Computation

ISSN 1088-6842(online) ISSN 0025-5718(print)



Cyclotomy with short periods

Authors: D. H. Lehmer and Emma Lehmer
Journal: Math. Comp. 41 (1983), 743-758
MSC: Primary 10G05; Secondary 10A40, 12C20
MathSciNet review: 717718
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: This paper develops cyclotomy for periods of lengths 2, 3 and 4 for moduli which are primes and products of two primes.

References [Enhancements On Off] (What's this?)

  • [1] William Adams & Daniel Shanks, "Strong primality tests that are not sufficient," Math. Comp., v. 39, 1982, pp. 255-300. MR 658231 (84c:10007)
  • [2] S. Gurak, "Minimal polynomials for Gauss circulants and cyclotomic units," Pacific J. Math., v. 102, 1982, pp. 347-353. MR 686555 (84c:10032)
  • [3] S. Gurak, "Minimal polynomials for circular numbers." (To appear). MR 743988 (85i:11107)
  • [4] E. E. Kummer, Theorie der idealen Primfactoren der complexen Zahlen, welche aus den Wurzeln der Gleichung $ {w^n} = 1$ gebildet sind, wenn n eine zusammengesetzte Zahl ist, Collected Papers, Vol. 1, Springer-Verlag, Berlin and New York, 1975, pp. 583-629.
  • [5] D. H. Lehmer, "An extended theory of Lucas functions," Ann. of Math., v. 52, 1930, pp. 293-304.
  • [6] D. H. Lehmer, "The Terry-Escott problem," Scripta Math., v. 13, 1947, pp. 37-41. MR 0021550 (9:78d)
  • [7] D. H. Lehmer & Emma Lehmer, Cyclotomy for Non-Square free Moduli, Lecture Notes in Math., Vol. 899, Springer-Verlag, Berlin and New York, 1981, pp. 276-300.
  • [8] D. H. Lehmer & Emma Lehmer, "Properties of polynomials having Fibonacci numbers for coefficients," Fibonacci Quart, v. 21, 1983, pp. 62-64. MR 696680 (84f:10018a)
  • [9] J. J. Sylvester, "On certain ternary cubic equations," Collected Papers, Vol. 3, Cambridge, 1909, pp. 325-339; Amer. J. Math., v. 2, 1879, pp. 357-381.

Similar Articles

Retrieve articles in Mathematics of Computation with MSC: 10G05, 10A40, 12C20

Retrieve articles in all journals with MSC: 10G05, 10A40, 12C20

Additional Information

Article copyright: © Copyright 1983 American Mathematical Society

American Mathematical Society