Problem #432: Let $A,B\subseteq \mathbb{N}$ be two infinite sets

Let $A,B\subseteq \mathbb{N}$ be two infinite sets. How dense can $A+B$ be if all elements of $A+B$ are pairwise relatively prime?

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Problem Statement

Let $A,B\subseteq \mathbb{N}$ be two infinite sets. How dense can $A+B$ be if all elements of $A+B$ are pairwise relatively prime?

Categories: Number Theory

Asked by Straus, inspired by a problem of Ostmann (see [431]).

Source: erdosproblems.com/432 | Last verified: January 15, 2026