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On Prime Factors of Terms of Linear Recurrence Sequences

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Number Theory and Related Fields

Part of the book series: Springer Proceedings in Mathematics & Statistics ((PROMS,volume 43))

Abstract

Let k be a positive integer, \(r_{1},\ldots,r_{k}\) and \(u_{0},\ldots,u_{k-1}\) be integers and put

$$\displaystyle{u_{n} = r_{1}u_{n-1} + \cdots + r_{k}u_{n-k},}$$

for n = k, \(k + 1,\ldots \,\). Suppose that r k is non-zero and that \(u_{0},\ldots,u_{k-1}\) are not all zero. The sequence \((u_{n})_{n=0}^{\infty }\) is a recurrence sequence of order k.

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Acknowledgements

Research supported in part by the Canada Research Chairs Program and by Grant A3528 from the Natural Sciences and Engineering Research Council of Canada.

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Authors and Affiliations

  1. Department of Pure Mathematics, University of Waterloo, Waterloo, Ontario, Canada, N2L 3G1

    C. L. Stewart

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  1. C. L. Stewart
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Correspondence to C. L. Stewart .

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Editors and Affiliations

  1. , School of Math. & Physical Sciences, University of Newcastle, Callaghan, 2308, Australia

    Jonathan M. Borwein

  2. , Department of Computing, Macquarie University, Herring Road, North Ryde, 2109, New South Wales, Australia

    Igor Shparlinski

  3. , School of Math. & Physical Sciences, University of Newcastle, Callaghan, 2308, Australia

    Wadim Zudilin

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In memory of Alf van der Poorten

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Stewart, C.L. (2013). On Prime Factors of Terms of Linear Recurrence Sequences. In: Borwein, J., Shparlinski, I., Zudilin, W. (eds) Number Theory and Related Fields. Springer Proceedings in Mathematics & Statistics, vol 43. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-6642-0_18

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