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Incomplete Fibonacci and Lucas numbers

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Abstract

A particular use of well-known combinatorial expressions for Fibonacci and Lucas numbers gives rise to two interesting classes of integers (namely, the numbersF n(k) andL n(k)) governed by the integral parametersn andk. After establishing the main properties of these numbers and their interrelationship, we study some congruence properties ofL n(k), one of which leads to a supposedly new characterisation of prime numbers. A glimpse of possible generalisations and further avenues of research is also caught.

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  1. Fondazione Ugo Bordoni, Via B. Castiglione 59, I-00142, Rome, Italy

    Piero Filipponi

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  1. Piero Filipponi
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Filipponi, P. Incomplete Fibonacci and Lucas numbers. Rend. Circ. Mat. Palermo 45, 37–56 (1996). https://doi.org/10.1007/BF02845088

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  • DOI: https://doi.org/10.1007/BF02845088

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