Zeckendorf representations with at most two terms to x-coordinates of Pell equations
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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.
KeywordsPell equation Fibonacci numbers lower bounds for linear forms in logarithms reduction method
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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).