The laws of apparition and repetition of primes in a cubic recurrence

The laws of apparition and repetition of primes in a cubic recurrence
HTML articles powered by AMS MathViewer

by Morgan Ward

Trans. Amer. Math. Soc. 79 (1955), 72-90

DOI: https://doi.org/10.1090/S0002-9947-1955-0068579-7

PDF | Request permission

References

Edouard Lucas, Theorie des Fonctions Numeriques Simplement Periodiques, Amer. J. Math. 1 (1878), no. 2, 184–196 (French). MR 1505161, DOI 10.2307/2369308

On sequences of integers defined by recurrence relations

Morgan Ward, The characteristic number of a sequence of integers satisfying a linear recursion relation, Trans. Amer. Math. Soc. 33 (1931), no. 1, 153–165. MR 1501582, DOI 10.1090/S0002-9947-1931-1501582-X
H. T. Engstrom, On sequences defined by linear recurrence relations, Trans. Amer. Math. Soc. 33 (1931), no. 1, 210–218. MR 1501585, DOI 10.1090/S0002-9947-1931-1501585-5
Marshall Hall, An isomorphism between linear recurring sequences and algebraic rings, Trans. Amer. Math. Soc. 44 (1938), no. 2, 196–218. MR 1501967, DOI 10.1090/S0002-9947-1938-1501967-8
Morgan Ward, The arithmetical theory of linear recurring series, Trans. Amer. Math. Soc. 35 (1933), no. 3, 600–628. MR 1501705, DOI 10.1090/S0002-9947-1933-1501705-4
Morgan Ward, The null divisors of linear recurring series, Duke Math. J. 2 (1936), no. 3, 472–476. MR 1545940, DOI 10.1215/S0012-7094-36-00240-5

The maximal prime divisors of linear recurrences

Notes on recurring series of the third order

Marshall Hall, Divisibility Sequences of Third Order, Amer. J. Math. 58 (1936), no. 3, 577–584. MR 1507182, DOI 10.2307/2370976
Morgan Ward, Linear divisibility sequences, Trans. Amer. Math. Soc. 41 (1937), no. 2, 276–286. MR 1501902, DOI 10.1090/S0002-9947-1937-1501902-1

The prime divisors of second order recurring sequences

Eine arithmetical Eigenschaft der Taylor-koeffizienten rationaler Funktionen