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    On the number of residues of certain second-order linear recurrences by Accossato, Federico, Sanna, Carlo

    Published 2024-11-01
    “…As a corollary, we deduce that for all integers $a_1 \ge 1$ and $k \ge 2$ there exists $\xi \in \mathbb{R}$ such that the sequence of fractional parts $\bigl (\mathrm{frac}(\xi \alpha ^n)\big )_{n \ge 0}$, where $\alpha :=\big (a_1 + \sqrt{a_1^2 + 4}\,\big ) / 2$, has exactly $k$ limit points. …”
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