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    This article has been cited by the following publications. This list is generated based on data provided by CrossRef.
    van der Poorten, A. J. and Shparlinski, I. E. 1996. On linear recurrence sequences with polynomial coefficients. Glasgow Mathematical Journal, Vol. 38, Issue. 02, p. 147.
    Töpfer, Thomas 1993. Linear forms in Lucas numbers. Indagationes Mathematicae, Vol. 4, Issue. 3, p. 363.
    Pinch, R. G. E. 1988. Simultaneous Pellian equations. Mathematical Proceedings of the Cambridge Philosophical Society, Vol. 103, Issue. 01, p. 35.
    Shparlinskii, I. E. 1987. Number of different prime divisors of recurrence sequences. Mathematical Notes of the Academy of Sciences of the USSR, Vol. 42, Issue. 4, p. 773.
    Kiss, P. 1982. On common terms of linear recurrences. Acta Mathematica Academiae Scientiarum Hungaricae, Vol. 40, Issue. 1-2, p. 119.
    Biggs, Norman 1980. Girth, valency, and excess. Linear Algebra and its Applications, Vol. 31, Issue. , p. 55.
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On the growth of recurrence sequences

  • J. H. Loxton (a1) and A. J. van der Poorten (a1)
Extract

In this note, we discuss some questions on the arithmetic properties of recurrence sequences. Our primary purpose is to mention some methods which originated as lemmas in certain transcendence studies, but in order to give context to these ideas, we briefly review other techniques applicable to the problems considered. These problems concern the distribution of zeros in a recurrence, the rate of growth of its terms and the size of the greatest prime factor of the terms.

Copyright
COPYRIGHT: © Cambridge Philosophical Society 1977
References
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(1)Cassels, J. W. S.An embedding theorem for fields. Bull. Austral. Math. Soc. 14 (1976), 193–198.
Cassels, J. W. S.Addendum: Bull. Austral. Math. Soc. 14 (1976), 479–480.
(2)Kubota, K. K. On a conjecture of Morgan Ward: I, II. (To appear.)
(3)Laxton, R. R.Linear recurrences of order 2. J. Austral. Math. Soc. 7 (1967), 108–114.
(4)Lech, C.A note on recurring series. Ark. Mat. 2 (1953), 417–421.
(5)Lewis, D. J. Diophantine equations: p-adic methods. In ‘Studien in number theory’, ed. LeVeque, W. J.. Studies in Mathematics 6 (MAA, 1969), 25–75.
(6)Loxton, J. H. and Van Der Poorten, A. J.Arithmetic properties of certain functions in several variables. J. Number Theory (to appear).
(7)Mahler, K.Über das Verschwinden von Potenzreihen mehrerer Veränderlichen in speziellen Punktfolgen. Math. Ann. 103 (1930), 573–587.
(8)Mahler, K.Eine arithmetische Eigenschaft der rekurrierenden Reihe. Mathematica (Leiden) 3 (1934/1935), 153–156.
(9)Mahler, K.Eine arithmetische Eigenschaft der Taylor Koeffizienten rationaler Funktionen. Proc. Akad. Wet. Amsterdam 38 (1935), 51–60.
(10)Mahler, K.On the Taylor coefficients of rational functions. Proc. Cambridge Philos. Soc. 52 (1956), 39–48.
Mahler, K.Addendum: Proc. Cambridge Philos. Soc. 53 (1957), 544.
(11)Mahler, K.A remark on recursive sequences. J. Math. Sci. 1 (1966), 12–17.
(12)Mignotte, M. Suites récurrentes linéaires. Sém. Delange-Pisot-Poitou, 15e année (1973/1934), no. G 14.
(13)Mignotte, M.A note on linear recursive sequences. J. Austral. Math. Soc. (A) 20 (1975), 242–244.
(14)Poorten, A. J. Van Der. Generalisations of Turdn's main theorems on lower bounds for sums of powers. Bull. Austral. Math. Soc. 2 (1970), 15–37.
(15)Poorten, A. J. Van Der. Zeros of p-adic exponential polynomials. Nederl. Akad. Wetensch Indag. Math. 38 (1976), 46–49.
(16)Poorten, A. J. Van Der. Hermite interpolation and p-adic exponential polynomials. J. Austral. Math. Soc. 22 (1976), 12–26.
(17)Poorten, A. J. Van Der and Tijdeman, R.On common zeros of exponential polynomials. Enseignement Math. 21 (1975), 57–67.
(18)Ritt, J. F.A factorisation theory for functions. Trans. Amer. Math. Soc. 29 (1927), 584–596.
(19)Schinzel, A.On two theorems of Gelfond and some of their applications. Acta Arith. 13 (1967), 177–236.
Schinzel, A.Corrigendum: Acta Arith. 16 (1969/1970), 101.
(20)Skolem, T. Ein Verfahren zur Behandlung gewisser exponentialer Gleichungen und dio phantischer Gleichungen. Comptes rendus du 8e Congrès des Mathematicians scandinaves (Stockholm, 1934), pp. 163–188. (Lund, Häkan Ohlssons Boktryckeri, 1935.)
(21)Stewart, C. L. Divisor properties of arithmetical sequences. Ph.D. thesis, University of Cambridge (1976).
(22)Stewart, C. L. On the divisors of Fermat, Fibonacci, Lucas and Lehmer numbers. (To appear.)
(23)Strassman, R.Über den Wertevorrat von Potenzreihen im Gebiet der p-adischen Zahlen. J. Reine Angew. Math. 159 (1928), 13–28.
(24)Ward, M.Some diophantine problems connected with linear recurrences. Report of the Institute in the Theory of Numbers (University of Colorado, 1959), pp. 250–257.
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