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

Author:
Morgan Ward

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

MSC:
Primary 10.0X

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

MathSciNet review:
0068579

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References | Similar Articles | Additional Information

**[1]**E. Lucas,*Theorie des fonctions numeriques simplement periodiques*, Amer. J. Math. vol. 1 (1878) pp. 184-240. MR**1505161****[2]**P. R. D. Carmichael,*On sequences of integers defined by recurrence relations*, Quarterly Journal of Math. vol. 48 (1920) pp. 343-372.**[3]**M. Ward,*The characteristic number of a sequence of integers satisfying a linear recursion relation*. Trans. Amer. Math. Soc. vol. 33 (1931) pp. 153-165. MR**1501582****[4]**H. T. Engstrom,*On sequences defined by linear recurrence relations*, Trans. Amer. Math. Soc. vol. 33 (1931) pp. 210-218. MR**1501585****[5]**M. Hall,*An isomorphism between linear recurring sequences and algebraic rings*, Trans. Amer. Math. Soc. vol. 44 (1938) pp. 196-218. MR**1501967****[6]**M. Ward,*The arithmetical theory of linear recurring series*, Trans. Amer. Math. Soc. vol. 35 (1933) pp. 600-628. MR**1501705****[7]**-,*The null divisors of linear recurring series*, Duke Math. J. vol. 2 (1936) pp. 472-476. MR**1545940****[8]**-,*The maximal prime divisors of linear recurrences*, not yet published.**[9]**E. T. Bell,*Notes on recurring series of the third order*, Tôhoku Math. J. vol. 24 (1924) pp. 168-184.**[10]**M. Hall,*Divisibility sequences of the third order*, Amer. J. Math. vol. 58 (1936) pp. 577-584. MR**1507182****[11]**M. Ward,*Linear divisibility sequences*, Trans. Amer. Math. Soc. vol. 41 (1937) pp. 276-286. MR**1501902****[12]**-,*The prime divisors of second order recurring sequences*, not yet published.**[13]**Kurt Mahler,*Eine arithmetical Eigenschaft der Taylor-koeffizienten rationaler Funktionen*, Proc. Amsterdam Acad. vol. 38 (1935) pp. 50-60.

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

Article copyright:
© Copyright 1955
American Mathematical Society