Zeckendorf representations with at most two terms to x-coordinates of Pell equations

Carlos Alexis Gómez; Florian Luca

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arXiv · 1803.10732

Zeckendorf representations with at most two terms to x-coordinates of Pell equations

Carlos Alexis Gómez·Florian Luca

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Abstract

In this paper, we find all positive squarefree integers d such 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. This paper has been accepted for publication in SCIENCE CHINA Mathematics.

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BibTeX RIS

Carlos Alexis Gómez, Florian Luca. 2018-03-28. Zeckendorf representations with at most two terms to x-coordinates of Pell equations. https://arxiv.org/abs/1803.10732

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