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arXiv · 2504.09545

Note on a problem of S\'ark\"ozy on multiplicative representation functions

Yuchen Ding
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Abstract

Motivated by a 2001 problem of S\'ark\"ozy, we classify all situations of the integers $b,c,e$ and $f$ satisfying \begin{align*} \limsup_{n\rightarrow\infty}|d(\mathcal{A},bn+c)-d(\mathcal{A},en+f)|=\infty \end{align*} for any infinite $\mathcal{A}\subset \mathbb{N}$, where $ d(\mathcal{A},m)=\#\{a\in \mathcal{A}:a|m\}. $

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Yuchen Ding. 2025-04-13. Note on a problem of S\'ark\"ozy on multiplicative representation functions. https://arxiv.org/abs/2504.09545

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