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On Simple Linear Recurrences

Chapter

Abstract

It is proved that every simple linear recurrence defined over a number field K, that has zeros modulo almost all prime ideals of K, takes the value 0 for a certain integer index. A similar theorem does not hold, in general, for simple linear recurrences of order n > 3. The case n = 3 is studied, but not decided.

AMS Classification 2010.

11B37 11D61 

References

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Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

  1. 1.Institute of MathematicsPolish Academy of SciencesWarsawPoland

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