Abstract
In this paper, we find all positive squarefree integers d satisfying that the Pell equation X2–dY2 = ±1 has at least two positive integer solutions (X, Y) and (X′, Y′) such that both X and X′ have Zeckendorf representations with at most two terms.
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Acknowledgements
The first author was supported by the Project from Universidad del Valle (Grant No. 71079). The second author was supported by NRF of South Africa (Grant No. CPRR160325161141), an A-Rated Scientist Award from the NRF of South Africa and by Czech Granting Agency (Grant No. 17-02804S).
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Gómez, C.A., Luca, F. Zeckendorf representations with at most two terms to x-coordinates of Pell equations. Sci. China Math. 63, 627–642 (2020). https://doi.org/10.1007/s11425-017-9283-6
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DOI: https://doi.org/10.1007/s11425-017-9283-6