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On Zeckendorf-Niven numbers and arithmetic progressions
[Submitted on 22 Jun 2026] · 2026-06-24 · via math updates on arXiv.org

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Abstract:A positive integer is Zeckendorf-Niven (respectively, Lucas-Niven) if it is divisible by the number of summands in its Zeckendorf decomposition (respectively, Lucas decomposition). We show that there exist infinitely many Zeckendorf-Niven numbers and Lucas-Niven numbers in every arithmetic progression. Furthermore, we provide bounds on the maximum number of consecutive Zeckendorf-Niven terms in certain arithmetic progressions.

Submission history

From: Wing Hong Tony Wong [view email]
[v1] Mon, 22 Jun 2026 23:25:17 UTC (10 KB)