Let A⊆ N, and for each n∈ A choose some X_n⊆ Z/nZ. Let B = m∈ N : m ot∈ X_n pmodntextrm for all n∈ A textrm with m>n. Must B have a logarithmic density, i.e. is it true that lim_x→ ∞ frac1log x∑_substackm∈ B m<xfrac1m exists?

Erdős Problem #486 — Let $A\subseteq \mathbb{N}$ , and for each $n\in A$ choose some $X_n\subseteq \mathbb{Z}/n\mathbb{Z}$ .

About 65 years old · traced to 1961

Let $A\subseteq \mathbb{N}$ , and for each $n\in A$ choose some $X_n\subseteq \mathbb{Z}/n\mathbb{Z}$ . Let $B = \{ m\in \mathbb{N} : m ot\in X_n\pmod{n}\textrm{ for all }n\in A\textrm{ with }m>n\}.$ Must $B$ have a logarithmic density, i.e. is it true that $\lim_{x\to \infty} \frac{1}{\log x}\sum_{\substack{m\in B\\ m<x}}\frac{1}{m}$ exists?