Cyclotomy with short periods

Authors:
D. H. Lehmer and Emma Lehmer

Journal:
Math. Comp. **41** (1983), 743-758

MSC:
Primary 10G05; Secondary 10A40, 12C20

DOI:
https://doi.org/10.1090/S0025-5718-1983-0717718-1

MathSciNet review:
717718

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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.

**[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**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.

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DOI:
https://doi.org/10.1090/S0025-5718-1983-0717718-1

Article copyright:
© Copyright 1983
American Mathematical Society