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arXiv · 2106.03509

On a family of cubic Thue Equations involving Fibonacci and Lucas numbers

Tobias Hilgart·Ingrid Vukusic·Volker Ziegler
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Abstract

Let $F_n$ denote the $n$-th Fibonacci number and $L_n$ the $n$-th Lucas number. We completely solve the family of cubic Thue equations $${(X-F_nY)(X-L_nY)X-Y^3=\pm1}$$ and show that there are no non-trivial solutions for $n\neq 1,3$.

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Tobias Hilgart, Ingrid Vukusic, Volker Ziegler. 2021-06-07. On a family of cubic Thue Equations involving Fibonacci and Lucas numbers. https://arxiv.org/abs/2106.03509

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