Tobias Hilgart

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20212026

most citedOn a family of cubic Thue Equations involving Fibonacci and Lucas numbers

2 citations · 2 across the 8 of their papers we have counts for

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math.NT2021

On families of cubic split Thue equations parametrised by linear recurrence sequences

Tobias Hilgart

Let $(A_{n})_{n \in N}, (B_{n})_{n \in N} \in Z^{N}$ be two linear-recurrent sequences that meet a dominant root condition and a few more technical re…

math.NT2021★ 2 cited

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

Tobias Hilgart, Ingrid Vukusic, Volker Ziegler

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 $(X - F_{n} Y) (X - L_{n} Y) X - Y^{3} = \pm 1$ and show tha…