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On Fibonacci numbers which are elliptic Carmichael

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Abstract

Here, we show that if E is a CM elliptic curve with CM field different from \({\mathbb {Q}}\left( {\sqrt{-1}}\right) \), then the set of n for which the nth Fibonacci number \(F_n\) is elliptic Carmichael for E is of asymptotic density zero.

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Acknowledgments

This paper was written during a visit of P. S. to the School of Mathematics of the University of the Witwatersrand in 2014. This author thanks the institution for hospitality.

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Authors and Affiliations

  1. School of Mathematics, University of the Witwatersrand, Private Bag X3, Wits 2050, Johannesburg, South Africa

    Florian Luca

  2. Applied Mathematics Department, Naval Postgraduate School, Monterey, CA, 93943, USA

    Pantelimon Stănică

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  1. Florian Luca
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  2. Pantelimon Stănică
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Correspondence to Pantelimon Stănică.

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Luca, F., Stănică, P. On Fibonacci numbers which are elliptic Carmichael. Period Math Hung 72, 171–179 (2016). https://doi.org/10.1007/s10998-016-0117-4

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  • DOI: https://doi.org/10.1007/s10998-016-0117-4

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