Year: 2026
Type: preprint
Abstract: For any irrational number $ α>\frac{3+\sqrt{5}}{2}\approx2.618$ and given a positive $ n\in\mathbb{N} $, we use elementary number theory to introduce a necessary and sufficient condition for a natural number $ x $ to be in the $n$th iterate of the Beatty sequence of modulus $α$.
Source: arXiv (Cornell University)
Authors: Khani, Mohsen, Valizadeh, Ali N., Zarei, Afshin
Subfield: Algebra and Number Theory
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7168355268
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