Relations in the Set of Divisors of an Integer $n$

Patrick Letendre

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arXiv · 2404.17424

Relations in the Set of Divisors of an Integer $n$

Patrick Letendre

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Abstract

Let $\mathcal{D}_{n} \subset \mathbb{N}$ be the set of the $\tau(n)$ divisors of $n$. We generalize a method developed by Erd\H os, Tenenbaum and de la Bret\`eche for the study of the set $\mathcal{D}_{n}$. In particular, using these ideas, we establish that $$ |\{(d_{1},d_{2},d_{3}) \in \mathcal{D}_{n}^3 : d_{1}+d_{2}=d_{3}\}| \le \tau(n)^{2-\delta} $$ with $\delta=0.045072$.

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Patrick Letendre. 2024-04-26. Relations in the Set of Divisors of an Integer $n$. https://arxiv.org/abs/2404.17424

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